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[Illustration: THE MOST IMPORTANT "TOOL" IN THE BUILDING OF MODEL
AEROPLANES.

[_Illustration by permission from_ MESSRS. A. GALLENKAMP & CO'S.
CHEMICAL CATALOGUE.]]




    THE THEORY AND PRACTICE
    OF
    MODEL AEROPLANING

    BY
    V.E. JOHNSON, M.A.

    AUTHOR OF
    'THE BEST SHAPE FOR AN AIRSHIP,' 'SOARING FLIGHT,'
    'HOW TO ADVANCE THE SCIENCE OF AERONAUTICS,'
    'HOW TO BUILD A MODEL AEROPLANE,' ETC.

    "Model Aeroplaning is an Art in itself"

    [Illustration]

    London
    E. & F.N. SPON, LTD., 57 HAYMARKET

    New York
    SPON & CHAMBERLAIN, 123 LIBERTY STREET

    1910




PREFACE


The object of this little book is not to describe how to construct
some particular kind of aeroplane; this has been done elsewhere: but
to narrate in plain language the general practice and principles of
model aeroplaning.

There is a _science_ of model aeroplaning--just as there is a science
of model yachting and model steam and electric traction, and an
endeavour is made in the following pages to do in some measure for
model aeroplanes what has already been done for model yachts and
locomotives. To achieve the best results, theory and practice must go
hand in hand.

From a series of carefully conducted experiments empirical formulæ can
be obtained which, combined later with mathematical induction and
deduction, may lead, not only to a more accurate and generalized law
than that contained in the empirical formula, but to valuable
deductions of a totally new type, embodying some general law hitherto
quite unknown by experimentalists, which in its turn may serve as a
foundation or stepping stone for suggesting other experiments and
empirical formulæ which may be of especial importance, to be treated
in _their_ turn like their predecessor. By "especial importance," I
mean not only to "model," but "Aeroplaning" generally.

As to the value of experiments on or with models with respect to
full-sized machines, fifteen years ago I held the opinion that they
were a very doubtful factor. I have since considerably modified that
view, and now consider that experiments with models--if properly
carried out, and given due, not _undue_, weight--both can and will be
of as much use to the science of Aeronautics as they have already
proved themselves to be in that of marine engineering.

The subject of model propellers and motors has been somewhat fully
dealt with, as but little has been published (in book form, at any
rate) on these all-important departments. On similar grounds the
reasons why and how a model aeroplane flies have been practically
omitted, because these have been dealt with more or less in every book
on heavier-than-air machines.

Great care has been exercised in the selection of matter, and in the
various facts stated herein; in most cases I have personally verified
them; great pains have also been exercised to exclude not only
misleading, but also doubtful matter. I have no personal axe to grind
whatever, nor am I connected either directly or indirectly with any
firm of aeroplane builders, model or otherwise.

The statements contained in these pages are absolutely free from bias
of any kind, and for them I am prepared to accept full responsibility.

I have to thank Messrs. A.W. GAMAGE (Holborn) for the use of various
model parts for testing purposes, and also for the use of various
electros from their modern Aviation Catalogue; also Messrs. T.W.K.
CLARKE & CO., of Kingston-on-Thames. For the further use of electros,
and for permission to reproduce illustrations which have previously
appeared in their papers, I must express my acknowledgment and thanks
to the publishers of the "Model Engineer," "Flight," and the "Aero."
Corrections and suggestions of any kind will be gratefully received,
and duly acknowledged.

    V.E. JOHNSON.




CONTENTS


    INTRODUCTION.
                                                                   PAGE

    §§ 1-5. The two classes of models--First requisite of a model
    aeroplane. § 6. An art in itself. § 7. The leading principle      1


    CHAPTER I.

    THE QUESTION OF WEIGHT.

    §§ 1-2. Its primary importance both in rubber and
    power-driven models--Professor Langley's experiences. § 3.
    Theoretical aspect of the question. § 4. Means whereby more
    weight can be carried--How to obtain maximum strength with
    minimum weight. § 5. Heavy models versus light ones               4


    CHAPTER II.

    THE QUESTION OF RESISTANCE.

    § 1. The chief function of a model in the medium in which it
    travels. § 2. Resistance considered as load percentage. § 3.
    How made up. § 4. The shape of minimum resistance. § 5. The
    case of rubber-driven models. § 6. The aerofoil
    surface--Shape and material as affecting this question. § 7.
    Skin friction--Its coefficient. § 8. Experimental proofs of
    its existence and importance                                      7


    CHAPTER III.

    THE QUESTION OF BALANCE.

    § 1. automatic stability essential in a flying model. § 2.
    theoretical researches on this question. §§ 3-6. a brief
    summary of the chief conclusions arrived at--remarks on and
    deductions from the same--conditions for automatic stability.
    § 7. theory and practice--stringfellow--pénaud--tatin--the
    question of fins--clarke's models--some further
    considerations. § 8. longitudinal stability. § 9. transverse
    stability. § 10. the dihedral angle. § 11. different forms of
    the latter. § 12. the "upturned" tip. § 13. the most
    efficient section                                                13


    CHAPTER IV.

    THE MOTIVE POWER.

    SECTION I.--RUBBER MOTORS.

    § 1. Some experiments with rubber cord. § 2. Its extension
    under various weights. § 3. The laws of elongation
    (stretching)--Permanent set. § 4. Effects of elongation on
    its volume. § 5. "Stretched-twisted" rubber cord--Torque
    experiments with rubber strands of varying length and number.
    § 6. Results plotted as graphs--Deductions--Various
    relations--How to obtain the most efficient
    results--Relations between the torque and the number of
    strands, and between the length of the strands and their
    number. § 7. Analogy between rubber and "spring"
    motors--Where it fails to hold. § 8. Some further practical
    deductions. § 9. The number of revolutions that can be given
    to rubber motors. § 10. The maximum number of turns. § 11.
    "Lubricants" for rubber. § 12. Action of copper upon rubber.
    § 12A. Action of water, etc. § 12B. How to preserve rubber.
    § 13. To test rubber. § 14. The shape of the section. § 15.
    Size of section. § 16. Geared rubber motors. § 17. The only
    system worth consideration--Its practical difficulties. § 18.
    Its advantages                                                   24

    SECTION II.--OTHER FORMS OF MOTORS.

    § 18A. _Spring motors_; their inferiority to rubber. § 18B.
    The most efficient form of spring motor. § 18C. _Compressed
    air motors_--A fascinating form of motor, "on paper." § 18D.
    The pneumatic drill--Application to a model aeroplane--Length
    of possible flight. § 18E. The pressure in motor-car tyres.
    § 19. Hargraves' compressed air models--The best results
    compared with rubber motors. § 20. The effect of heating the
    air in its passage from the reservoir to the motor--The great
    gain in efficiency thereby attained--Liquid air--Practical
    drawbacks to the compressed-air motor. § 21. Reducing
    valves--Lowest working pressure. § 22. The inferiority of
    this motor compared with the steam engine. § 22A. Tatin's
    air-compressed motor. § 23. _Steam engine_--Steam engine
    model--Professor Langley's models--His experiment with
    various forms of motive power--Conclusions arrived at. § 24.
    His steam engine models--Difficulties and failures--and final
    success--The "boiler" the great difficulty--His model
    described. § 25. The use of spirit or some very volatile
    hydrocarbon in the place of water. § 26. Steam turbines.
    § 27. Relation between "difficulty in construction" and the
    "size of the model." § 28. Experiments in France. § 29.
    _Petrol motors._--But few successful models. § 30. Limit to
    size. § 31. Stanger's successful model described and
    illustrated. § 32. One-cylinder petrol motors. § 33.
    _Electric motors_                                                39


    CHAPTER V.

    PROPELLERS OR SCREWS.

    § 1. The position of the propeller. § 2. The number of
    blades. § 3. Fan _versus_ propeller. § 4. The function of a
    propeller. § 5. The pitch. § 6. Slip. § 7. Thrust. § 8. Pitch
    coefficient (or ratio). § 9. Diameter. § 10. Theoretical
    pitch. § 11. Uniform pitch. § 12. How to ascertain the pitch
    of a propeller. § 13. Hollow-faced blades. § 14. Blade area.
    § 15. Rate of rotation. § 16. Shrouding. § 17. General
    design. § 18. The shape of the blades. § 19. Their general
    contour--Propeller design--How to design a propeller. § 20.
    Experiments with propellers--Havilland's design for
    experiments--The author experiments on dynamic thrust and
    model propellers generally. § 21. Fabric-covered screws.
    § 22. Experiments with twin propellers. § 23. The Fleming
    Williams propeller. § 24. Built-up _v._ twisted wooden
    propellers                                                       52


    CHAPTER VI.

    THE QUESTION OF SUSTENTATION.
    THE CENTRE OF PRESSURE.

    § 1. The centre of pressure--Automatic stability. § 2.
    Oscillations. § 3. Arched surfaces and movements of the
    centre of pressure--Reversal. § 4. The centre of gravity and
    the centre of pressure. § 5. Camber. § 6. Dipping front
    edge--Camber--The angle of incidence and camber--Attitude of
    the Wright machine. § 7. The most efficient form of camber.
    § 8. The instability of a deeply cambered surface. § 9.
    Aspect ratio. § 10. Constant or varying camber. § 11. Centre
    of pressure on arched surfaces                                   78


    CHAPTER VII.

    MATERIALS FOR AEROPLANE
    CONSTRUCTION.

    § 1. The choice strictly limited. § 2. Bamboo. § 3.
    Ash--spruce-- whitewood--poplar. § 4. Steel. § 5. Umbrella
    section steel. § 6. Steel wire. § 7. Silk. § 8. Aluminium and
    magnalium. § 9. Alloys. § 10. Sheet ebonite--Vulcanized
    fibre--Sheet celluloid--Mica                                     86


    CHAPTER VIII.

    HINTS ON THE BUILDING OF MODEL
    AEROPLANES.

    § 1. The chief difficulty to overcome. § 2. General
    design--The principle of continuity. § 3. Simple monoplane.
    § 4. Importance of soldering. § 5. Things to avoid. § 6.
    Aerofoil of metal--wood--or fabric. § 7. Shape of aerofoil.
    § 8. How to camber an aerocurve without ribs. § 9. Flexible
    joints. § 10. Single surfaces. § 11. The rod or tube carrying
    the rubber motor. § 12. Position of the rubber. § 13. The
    position of the centre of pressure. § 14. Elevators and
    tails. § 15. Skids _versus_ wheels--Materials for skids.
    § 16. Shock absorbers, how to attach--Relation between the
    "gap" and the "chord"                                            93


    CHAPTER IX.

    THE STEERING OF THE MODEL.

    § 1. A problem of great difficulty--Effects of propeller
    torque. § 2. How obviated. § 3. The two-propeller
    solution--The reason why it is only a partial success. § 4.
    The _speed_ solution. § 5. Vertical fins. § 6. Balancing tips
    or ailerons. § 7. Weighting. § 8. By means of transversely
    canting the elevator. § 9. The necessity for some form of
    "keel"                                                          105


    CHAPTER X.

    THE LAUNCHING OF THE MODEL.

    § 1. The direction in which to launch them. § 2. The
    velocity--wooden aerofoils and fabric-covered
    aerofoils--Poynter's launching apparatus. § 3. The launching
    of very light models. § 4. Large size and power-driven
    models. § 5. Models designed to rise from the
    ground--Paulhan's prize model. § 6. The setting of the
    elevator. § 7. The most suitable propeller for this form of
    model. § 8. Professor Kress' method of launching. § 9. How to
    launch a twin screw model. § 10. A prior revolution of the
    propellers. § 11. The best angle at which to launch a model     109


    CHAPTER XI.

    HELICOPTER MODELS.

    § 1. Models quite easy to make. § 2. Sir George Cayley's
    helicopter model. § 3. Phillips' successful power-driven
    model. § 4. Toy helicopters. § 5. Incorrect and correct way
    of arranging the propellers. § 6. Fabric covered screws. § 7.
    A design to obviate weight. § 8. The question of a fin or
    keel.                                                           113


    CHAPTER XII.

    EXPERIMENTAL RECORDS                                            116


    CHAPTER XIII.

    MODEL FLYING COMPETITIONS.

    § 1. A few general details concerning such. § 2. Aero Models
    Association's classification, etc. § 3. Various points to be
    kept in mind when competing                                     119


    CHAPTER XIV.

    USEFUL NOTES, TABLES, FORMULÆ, ETC.

    § 1. Comparative velocities. § 2. Conversions. § 3. Areas of
    various shaped surfaces. § 4. French and English measures.
    § 5. Useful data. § 6. Table of equivalent inclinations. § 7.
    Table of skin friction. § 8. Table I. (metals). § 9. Table
    II. (wind pressures). § 10. Wind pressure on various shaped
    bodies. § 11. Table III. (lift and drift) on a cambered
    surface. § 12. Table IV. (lift and drift)--On a plane
    aerofoil--Deductions. § 13. Table V. (timber). § 14. Formula
    connecting weight lifted and velocity. § 15. Formula
    connecting models of similar design but different weights.
    § 16. Formula connecting power and speed. § 17. Propeller
    thrust. § 18. To determine experimentally the static thrust
    of a propeller. § 19. Horse-power and the number of
    revolutions. § 20. To compare one model with another. § 21.
    Work done by a clockwork spring motor. § 22. To ascertain the
    horse-power of a rubber motor. § 23. Foot-pounds of energy in
    a given weight of rubber--Experimental determination of.
    § 24. Theoretical length of flight. § 25. To test different
    motors. § 26. Efficiency of a model. § 27. Efficiency of
    design. § 28. Naphtha engines. § 29. Horse-power and weight
    of model petrol motors. § 30. Formula for rating the same.
    § 30A. Relation between static thrust of propeller and total
    weight of model. § 31. How to find the height of an
    inaccessible object (kite, balloon, etc.). § 32. Formula for
    I.H.P. of model steam engines                                   125

    APPENDIX A. Some models which have won medals at open
    competitions                                                    143




GLOSSARY OF TERMS USED IN MODEL AEROPLANING.


_Aeroplane._ A motor-driven flying machine which relies upon surfaces
for its support in the air.

_Monoplane_ (single). An aeroplane with one pair of outstretched
wings.

_Aerofoil._ These outstretched wings are often called aerofoil
surfaces. One pair of wings forming one aerofoil surface.

_Monoplane_ (double). An aeroplane with two aerofoils, one behind the
other or two main planes, tandem-wise.

_Biplane._ An aeroplane with two aerofoils, one below the other, or
having two main planes superposed.

_Triplane._ An aeroplane having three such aerofoils or three such
main planes.

_Multiplane._ Any such machine having more than three of the above.

_Glider._ A motorless aeroplane.

_Helicopter._ A flying machine in which propellers are employed to
raise the machine in the air by their own unaided efforts.

_Dihedral Angle._ A dihedral angle is an angle made by two surfaces
that do not lie in the same plane, i.e. when the aerofoils are
arranged V-shaped. It is better, however, to somewhat extend this
definition, and not to consider it as necessary that the two surfaces
_do_ actually meet, but would do so if produced thus in figure. BA and
CD are still dihedrals, sometimes termed "upturned tips."

[Illustration: Dihedrals.]

_Span_ is the distance from tip to tip of the main supporting surface
measured transversely (across) the line of flight.

_Camber_ (a slight arching or convexity upwards). This term denotes
that the aerofoil has such a curved transverse section.

_Chord_ is the distance between the entering (or leading) edge of the
main supporting surface (aerofoil) and the trailing edge of the same;
also defined as the fore and aft dimension of the main planes measured
in a straight line between the leading and trailing edges.

                       span
    _Aspect Ratio_ is -----
                      chord

_Gap_ is the vertical distance between one aerofoil and the one which
is immediately above it.

(The gap is usually made equal to the chord).

_Angle of Incidence._ The angle of incidence is the angle made by the
chord with the line of flight.

[Illustration:

  AB = chord.            AB = cambered surface.
  SP = line of flight.  ASP = {alpha} = L of incidence.]

_Width._ The width of an aerofoil is the distance from the front to
the rear edge, allowing for camber.

_Length._ This term is usually applied to the machine as a whole, from
the front leading edge of elevator (or supports) to tip of tail.

_Arched._ This term is usually applied to aerofoil surfaces which dip
downwards like the wings of a bird. The curve in this case being at
right angles to "camber." A surface can, of course, be both cambered
and arched.

_Propeller._ A device for propelling or pushing an aeroplane forward
or for raising it vertically (lifting screw).

_Tractor Screw._ A device for pulling the machine (used when the
propeller is placed in the front of the machine).

_Keel._ A vertical plane or planes (usually termed "fins") arranged
longitudinally for the purposes of stability and steering.

_Tail._ The plane, or group of planes, at the rear end of an
aeroplane for the purpose chiefly of giving longitudinal stability. In
such cases the tail is normally (approx.) horizontal, but not
unfrequently vertical tail-pieces are fitted as well for steering
(transversely) to the right or left, or the entire tail may be twisted
for the purpose of transverse stability (vide _Elevator_). Such
appendages are being used less and less with the idea of giving actual
support.

_Rudder_ is the term used for the vertical plane, or planes, which are
used to steer the aeroplane sideways.

_Warping._ The flexing or bending of an aerofoil out of its normal
shape. The rear edges near the tips of the aerofoil being dipped or
tilted respectively, in order to create a temporary difference in
their inclinations to the line of flight. Performed in conjunction
with rudder movements, to counteract the excessive action of the
latter.

_Ailerons_ (also called "righting-tips," "balancing-planes," etc.).
Small aeroplanes in the vicinity of the tips of the main aerofoil for
the purpose of assisting in the maintenance of equilibrium or for
steering purposes either with or without the assistance of the rudder.

_Elevator._ The plane, or planes, in front of the main aerofoil used
for the purpose of keeping the aeroplane on an even keel, or which
cause (by being tilted or dipped) the aeroplane to rise or fall (vide
_Tail_).




MODEL AEROPLANING




INTRODUCTION.


§ 1. Model Aeroplanes are primarily divided into two classes: first,
models intended before all else to be ones that shall _fly_; secondly,
_models_, using the word in its proper sense of full-sized machines.
Herein model aeroplanes differ from model yachts and model
locomotives. An extremely small model locomotive _built to scale_ will
still _work_, just as a very small yacht built to scale will _sail_;
but when you try to build a scale model of an "Antoinette" monoplane,
_including engine_, it cannot be made to fly unless the scale be a
very large one. If, for instance, you endeavoured to make a 1/10 scale
model, your model petrol motor would be compelled to have eight
cylinders, each 0·52 bore, and your magneto of such size as easily to
pass through a ring half an inch in diameter. Such a model could not
possibly work.[1]

    _Note._--Readers will find in the "Model Engineer" of June 16,
    1910, some really very fine working drawings of a prize-winning
    Antoinette monoplane model.

§ 2. Again, although the motor constitutes the _chief_, it is by no
means the sole difficulty in _scale_ model aeroplane building. To
reproduce to scale at _scale weight_, or indeed anything approaching it,
_all_ the _necessary_--in the case of a full-sized machine--framework is
not possible in a less than 1/5 scale.

§ 3. Special difficulties occur in the case of any prototype taken.
For instance, in the case of model Blériots it is extremely difficult
to get the centre of gravity sufficiently forward.

§ 4. Scale models of actual flying machines _that will fly_ mean
models _at least_ 10 or 12 feet across, and every other dimension in
like proportion; and it must always be carefully borne in mind that
the smaller the scale the greater the difficulties, but not in the
same proportion--it would not be _twice_ as difficult to build a
¼-in. scale model as a ½-in., but _four_, _five_ or _six_ times as
difficult.

§ 5. Now, the _first_ requirement of a model aeroplane, or flying
machine, is that it shall FLY.

As will be seen later on--unless the machine be of large size, 10 feet
and more spread--the only motor at our disposal is the motor of
twisted rubber strands, and this to be efficient requires to be long,
and is of practically uniform weight throughout; this alone alters the
entire _distribution of weight_ on the machine and makes:

§ 6. "=Model Aeroplaning an Art in itself=," and as such we propose to
consider it in the following pages.

We have said that the first requisite of a model aeroplane is that it
shall fly, but there is no necessity, nor is it indeed always to be
desired, that this should be its only one, unless it be built with the
express purpose of obtaining a record length of flight. For ordinary
flights and scientific study what is required is a machine in which
minute detail is of secondary importance, but which does along its
main lines "_approximate_ to the real thing."

§ 7. Simplicity should be the first thing aimed at--simplicity means
efficiency, it means it in full-sized machines, still more does it
mean it in models--and this very question of simplicity brings us to
that most important question of all, namely, the question of _weight_.

FOOTNOTE:

[1] The smallest working steam engine that the writer has ever heard
of has a net weight of 4 grains. One hundred such engines would be
required to weigh one ounce. The bore being 0·03 in., and stroke 1/32
of an inch, r.p.m. 6000 per min., h.p. developed 1/489000 ("Model
Engineer," July 7, 1910). When working it hums like a bee.




CHAPTER I.

THE QUESTION OF WEIGHT.


§ 1. The following is an extract from a letter that appeared in the
correspondence columns of "The Aero."[2]

"To give you some idea how slight a thing will make a model behave
badly, I fitted a skid to protect the propeller underneath the
aeroplane, and the result in retarding flight could be seen very
quickly, although the weight of the skid was almost nil.[3] To all
model makers who wish to make a success I would say, strip all that
useless and heavy chassis off, cut down the 'good, honest stick' that
you have for a backbone to half its thickness, stay it with wire if it
bends under the strain of the rubber, put light silk on the planes,
and use an aluminium[4] propeller. The result will surpass all
expectations."

§ 2. The above refers, of course, to a rubber-motor driven model. Let
us turn to a steam-driven prototype. I take the best known example of
all, Professor Langley's famous model. Here is what the professor has
to say on the question[5]:--

"Every bit of the machinery had to be constructed with scientific
accuracy. It had to be tested again and again. The difficulty of
getting the machine light enough was such that every part of it had to
be remade several times. It would be in full working order when
something would give way, and this part would have to be strengthened.
This caused additional weight, and necessitated cutting off so much
weight from some other part of the machinery. At times the difficulty
seemed almost heartbreaking; but I went on, piece by piece and atom by
atom, until I at last succeeded in getting all the parts of the right
strength and proportion."

How to obtain the maximum strength with the minimum of weight is one
of the, if not the most, difficult problems which the student has to
solve.

§ 3. The theoretical reason why _weight_ is such an all-important item
in model aeroplaning, much more so than in the case of full-size
machines, is that, generally speaking, such models do not fly fast
enough to possess a high weight carrying capacity. If you increase the
area of the supporting surface you increase also the resistance, and
thereby diminish the speed, and are no better off than before. The
only way to increase the weight carrying capacity of a model is to
increase its speed. This point will be recurred to later on. One of
Mr. T.W.K. Clarke's well-known models, surface area 1¼ sq. ft.,
weight 1¼ lb., is stated to have made a flight of 300 yards
carrying 6 oz. of lead. This works out approximately at 21 oz. per sq.
ft.

The velocity (speed) is not stated, but some earlier models by the
same designer, weight 1½ lb., supporting area 1½ sq. ft., i.e.,
at rate of 16 oz. per sq. ft., travelled at a rate of 37 ft. per
second, or 25 miles an hour.

The velocity of the former, therefore, would certainly not be less
than 30 miles an hour.

§ 4. Generally speaking, however, models do not travel at anything
like this velocity, or carry anything like this weight per sq. ft.

An average assumption of 13 to 15 miles an hour does nor err on the
minimum side. Some very light fabric covered models have a speed of
less than even 10 miles an hour. Such, of course, cannot be termed
efficient models, and carry only about 3 oz. per sq. ft. Between these
two types--these two extremes--somewhere lies the "Ideal Model."

The maximum of strength with the minimum of weight can be obtained
only:--

1. By a knowledge of materials.

2. Of how to combine those materials in a most efficient and skilful
manner.

3. By a constant use of the balance or a pair of scales, and noting
(in writing) the weight and result of every trial and every experiment
in the alteration and change of material used. WEIGH EVERYTHING.

§ 5. The reader must not be misled by what has been said, and think
that a model must not weigh anything if it is to fly well. A heavy
model will fly much better against the wind than a light one, provided
that the former _will_ fly. To do this it must fly _fast_. To do this
again it must be well powered, and offer the minimum of resistance to
the medium through which it moves. This means its aerofoil
(supporting) surfaces must be of polished wood or metal. This point
brings us to the question of Resistance, which we will now consider.

FOOTNOTES:

[2] "Aero," May 3, 1910.

[3] Part of this retardation was, of course, "increased resistance."

[4] Personally I do not recommend aluminium.--V.E.J.

[5] "Aeronautical Journal," January 1897, p. 7.




CHAPTER II.

THE QUESTION OF RESISTANCE.


§ 1. It is, or should be, the function of an aeroplane--model or
otherwise--to pass through the medium in which it travels in such a
manner as to leave that medium in as motionless a state as possible,
since all motion of the surrounding air represents so much power
wasted.

Every part of the machine should be so constructed as to move through
the air with the minimum of disturbance and resistance.

§ 2. The resistance, considered as a percentage of the load itself,
that has to be overcome in moving a load from one place to another,
is, according to Mr. F.W. Lanchester, 12½ per cent. in the case of
a flying machine, and 0·1 per cent. in the case of a cargo boat, and
of a solid tyre motor car 3 per cent., a locomotive 1 per cent. Four
times at least the resistance in the case of aerial locomotion has to
be overcome to that obtained from ordinary locomotion on land. The
above refer, of course, to full-sized machines; for a model the
resistance is probably nearer 14 or 15 per cent.

§ 3. This resistance is made up of--

    1. Aerodynamic resistance.
    2. Head resistance.
    3. Skin-friction (surface resistance).

The first results from the necessity of air supporting the model
during flight.

The second is the resistance offered by the framework, wires, edges of
aerofoils, etc.

The third, skin-friction or surface resistance, is very small at low
velocities, but increases as the square of the velocity. To reduce the
resistance which it sets up, all surfaces used should be as smooth as
possible. To reduce the second, contours of ichthyoid, or fish-like,
form should be used, so that the resultant stream-line flow of the
medium shall keep in touch with the surface of the body.

§ 4. As long ago as 1894 a series of experiments were made by the
writer[6] to solve the following problem: given a certain length and
breadth, to find the shape which will offer the least resistance. The
experiments were made with a whirling table 40 ft. in diameter, which
could be rotated so that the extremity of the arm rotated up to a
speed of 45 miles an hour. The method of experimenting was as follows:
The bodies (diam. 4 in.) were balanced against one another at the
extremity of the arm, being so balanced that their motions forward and
backward were parallel. Provision was made for accurately balancing
the parallel scales on which the bodies were suspended without
altering the resistance offered by the apparatus to the air. Two
experiments at least (to avoid error) were made in each case, the
bodies being reversed in the second experiment, the top one being put
at the bottom, and _vice versa_. The conclusions arrived at were:--

For minimum (head) resistance a body should have--

1. Its greatest diameter two-fifths of its entire length from its
head.

2. Its breadth and its depth in the proportion of four to three.

3. Its length at least from five to nine times its greatest breadth
(nine being better than five).

4. A very tapering form of stern, the actual stern only being of just
sufficient size to allow of the propeller shaft passing through. In
the case of twin propellers some slight modification of the stern
would be necessary.

5. Every portion of the body in contact with the fluid to be made as
smooth as possible.

6. A body of such shape gives at most only _one-twentieth_ the
resistance offered by a flat disk of similar maximum sectional area.

_Results since fully confirmed._

[Illustration: FIG. 1.--SHAPE OF LEAST RESISTANCE.]

The design in Fig. 2 is interesting, not only because of its probable
origin, but because of the shape of the body and arrangement of the
propellers; no rudder is shown, and the long steel vertical mast
extending both upwards and downwards through the centre would render
it suitable only for landing on water.

§ 5. In the case of a rubber-driven model, there is no containing body
part, so to speak, a long thin stick, or tubular construction if
preferred, being all that is necessary.

The long skein of elastic, vibrating as well as untwisting as it
travels with the machine through the air, offers some appreciable
resistance, and several experimenters have _enclosed_ it in a light
tube made of _very thin_ veneer wood rolled and glued, or paper even
may be used; such tubes can be made very light, and possess
considerable rigidity, especially longitudinally. If the model be a
biplane, then all the upright struts between the two aerofoils should
be given a shape, a vertical section of which is shown in Fig. 3.

§ 6. In considering this question of resistance, the substance of
which the aerofoil surface is made plays a very important part, as
well as whether that surface be plane or curved. For some reason not
altogether easy to determine, fabric-covered planes offer
_considerably_ more resistance than wooden or metal ones. That they
should offer _more_ resistance is what common sense would lead one to
expect, but hardly to the extent met with in actual practice.

[Illustration: FIG. 2.--DESIGN FOR AN AEROPLANE MODEL (POWER DRIVEN).

This design is attributed to Professor Langley.]

_Built up fabric-covered aeroplanes[7] gain in lightness, but lose in
resistance._ In the case of curved surfaces this difference is
considerably more; one reason, undoubtedly, is that in a built up
model surface there is nearly always a tendency to make this curvature
excessive, and much more than it should be. Having called attention to
this under the head of resistance, we will leave it now to recur to it
later when considering the aerofoil proper.

[Illustration: FIG. 3.--HORIZONTAL SECTION OF VERTICAL STRUT
(ENLARGED.)]

§ 7. Allusion has been made in this chapter to skin friction, but no
value given for its coefficient.[8] Lanchester's value for planes from
½ to 1½ sq. ft. in area, moving about 20 to 30 ft. per second, is

    0·009 to 0·015.

Professor Zahm (Washington) gives 0·0026 lb. per sq. ft. at 25 ft. per
second, and at 37 ft. per second, 0·005, and the formula

    _f_ = 0·00000778_l_^{·93}_v_^{1·85}

_f_ being the average friction in lb. per sq. in., _l_ the length in
feet, and _v_ the velocity in ft. per second. He also experimented
with various kinds of surfaces, some rough, some smooth, etc.

His conclusion is:--"All even surfaces have approximately the same
coefficient of skin friction. Uneven surfaces have a greater
coefficient." All formulæ on skin friction must at present be accepted
with reserve.

§ 8. The following three experiments, however, clearly prove its
_existence_, and _that it has considerable effect_:--

1. A light, hollow celluloid ball, supported on a stream of air
projected upwards from a jet, rotates in one direction or the other as
the jet is inclined to the left or to the right. (F.W. Lanchester.)

2. When a golf ball (which is rough) is hit so as to have considerable
underspin, its range is increased from 135 to 180 yards, due entirely
to the greater frictional resistance to the air on that side on which
the whirl and the progressive motion combine. (Prof. Tait.)

3. By means of a (weak) bow a golf ball can be made to move point
blank to a mark 30 yards off, provided the string be so adjusted as to
give a good underspin; adjust the string to the centre of the ball,
instead of catching it below, and the drop will be about 8 ft. (Prof.
Tait.)

FOOTNOTES:

[6] _Vide_ "Invention," Feb. 15, 22, and 29, 1896.

[7] Really aerofoils, since we are considering only the supporting
surface.

[8] I.e., to express it as a decimal fraction of the resistance,
encountered by the same plane when moving "face" instead of "edge" on.




CHAPTER III.

THE QUESTION OF BALANCE.


§ 1. It is perfectly obvious for successful flight that any model
flying machine (in the absence of a pilot) must possess a high degree
of automatic stability. The model must be so constructed as to be
naturally stable, _in the medium through which it is proposed to drive
it_. The last remark is of the greatest importance, as we shall see.

§ 2. In connexion with this same question of automatic stability, the
question must be considered from the theoretical as well as from the
practical side, and the labours and researches of such men as
Professors Brian and Chatley, F.W. Lanchester, Captain Ferber,
Mouillard and others must receive due weight. Their work cannot yet be
fully assessed, but already results have been arrived at far more
important than are generally supposed.

The following are a few of the results arrived at from theoretical
considerations; they cannot be too widely known.

(A) Surfaces concave on the under side are not stable unless some form
of balancing device (such as a tail, etc.) is used.

(B) If an aeroplane is in equilibrium and moving uniformly, it is
necessary for stability that it shall tend towards a condition of
equilibrium.

(C) In the case of "oscillations" it is absolutely necessary for
stability that these oscillations shall decrease in amplitude, in
other words, be damped out.

(D) In aeroplanes in which the dihedral angle is excessive or the
centre of gravity very low down, a dangerous pitching motion is quite
likely to be set up. [Analogy in shipbuilding--an increase in the
metacentre height while increasing the stability in a statical sense
causes the ship to do the same.]

(E) The propeller shaft should pass through the centre of gravity of
the machine.

(F) The front planes should be at a greater angle of inclination than
the rear ones.

(G) The longitudinal stability of an aeroplane grows much less when
the aeroplane commences to rise, a monoplane becoming unstable when
the angle of ascent is greater than the inclination of the main
aerofoil to the horizon.

(H) Head resistance increases stability.

(I) Three planes are more stable than two. [Elevator--main
aerofoil--horizontal rudder behind.]

(J) When an aeroplane is gliding (downwards) stability is greater than
in horizontal flight.

(K) A large moment of inertia is inimical (opposed) to stability.

(M) Aeroplanes (naturally) stable up to a certain velocity (speed) may
become unstable when moving beyond that speed. [Possible explanation.
The motion of the air over the edges of the aerofoil becomes
turbulent, and the form of the stream lines suddenly changes.
Aeroplane also probably becomes deformed.]

(N) In a balanced glider for stability a separate surface at a
negative angle to the line of flight is essential. [Compare F.]

(O) A keel surface should be situated well above and behind the centre
of gravity.

(P) An aeroplane is a conservative system, and stability is greatest
when the kinetic energy is a maximum. [Illustration, the pendulum.]

§ 3. Referring to A. Models with a plane or flat surface are not
unstable, and will fly well without a tail; such a machine is called a
simple monoplane.

[Illustration: FIG. 4.--ONE OF MR. BURGE WEBB'S SIMPLE MONOPLANES.

Showing balance weight A (movable), and also his winding-up gear--a
very handy device.]


§ 4. Referring to D. Many model builders make this mistake, i.e., the
mistake of getting as low a centre of gravity as possible under the
quite erroneous idea that they are thereby increasing the stability of
the machine. Theoretically the _centre of gravity should be the centre
of head resistance, as also the centre of pressure_.

In practice some prefer to put the centre of gravity in models
_slightly_ above the centre of head resistance, the reason being that,
generally speaking, wind gusts have a "lifting" action on the machine.
It must be carefully borne in mind, however, that if the centre of
wind pressure on the aerofoil surface and the centre of gravity do not
coincide, no matter at what point propulsive action be applied, it can
be proved by quite elementary mechanics that such an arrangement,
known as "acentric," produces a couple tending to upset the machine.

This action is the probable cause of many failures.

[Illustration: FIG. 5.--THE STRINGFELLOW MODEL MONOPLANE OF 1848.]

§ 5. Referring to E. If the propulsive action does not pass through
the centre of gravity the system again becomes "acentric." Even
supposing condition D fulfilled, and we arrive at the following most
important result, viz., that for stability:--

THE CENTRES OF GRAVITY, OF PRESSURE, OF HEAD RESISTANCE, SHOULD BE
COINCIDENT, AND THE PROPULSIVE ACTION OF THE PROPELLER PASS THROUGH
THIS SAME POINT.

[Illustration: FIG. 6.--THE STRINGFELLOW MODEL TRIPLANE OF 1868.]

§ 6. Referring to F and N--the problem of longitudinal stability.
There is one absolutely essential feature not mentioned in F or N, and
that is for automatic longitudinal stability _the two surfaces, the
aerofoil proper and the balancer_ (elevator or tail, or both), _must
be separated by some considerable distance, a distance not less than
four times the width of the main aerofoil_.[9] More is better.

[Illustration: FIG. 7. _PÉNAUD 1871_]

§ 7. With one exception (Pénaud) early experimenters with model
aeroplanes had not grasped this all-important fact, and their models
would not fly, only make a series of jumps, because they failed to
balance longitudinally. In Stringfellow's and Tatin's models the main
aerofoil and balancer (tail) are practically contiguous.

Pénaud in his rubber-motored models appears to have fully realised
this (_vide_ Fig. 7), and also the necessity for using long strands of
rubber. Some of his models flew 150 ft., and showed considerable
stability.

[Illustration: FIG. 8.--TATIN'S AEROPLANE (1879).

Surface 0·7 sq. metres, total weight 1·75 kilogrammes, velocity of
sustentation 8 metres a second. Motor, compressed air (for description
see § 23, ch. iv). Revolved round and round a track tethered to a post
at the centre. In one of its jumps it cleared the head of a
spectator.]

With three surfaces one would set the elevator at a slight plus angle,
main aerofoil horizontal (neither positive nor negative), and the tail
at a corresponding negative angle to the positive one of the elevator.

Referring to O.[10] One would naturally be inclined to put a keel
surface--or, in other words, vertical fins--beneath the centre of
gravity, but D shows us this may have the opposite effect to what we
might expect.

In full-sized machines, those in which the distance between the main
aerofoil and balancers is considerable (like the Farman) show
considerable automatic longitudinal stability, and those in which it
is short (like the Wright) are purposely made so with the idea of
doing away with it, and rendering the machine quicker and more
sensitive to personal control. In the case of the Stringfellow and
Tatin models we have the extreme case--practically the bird entirely
volitional and personal--which is the opposite in every way to what we
desire on a model under no personal or volitional control at all.

[Illustration: FIG. 9.--CLARK'S MODEL FLYER.

Main aerofoil set at a slight negative angle. Dihedral angles on both
aerofoils.]

The theoretical conditions stated in F and N are fully borne out in
practice.

And since a curved aerofoil even when set at a _slight_ negative
angle has still considerable powers of sustentation, it is possible to
give the main aerofoil a slight negative angle and the elevator a
slight positive one. This fact is of the greatest importance, since it
enables us to counteract the effect of the travel of the "centre of
pressure."[11]

[Illustration: FIG. 10.--LARGE MODEL MONOPLANE.

Designed and constructed by the author, with vertical fin (no dihedral
angle). With a larger and more efficient propeller than the one here
shown some excellent flights were obtained. Constructed of bamboo and
nainsook. Stayed with steel wire.]

§ 8. Referring to I. This, again, is of primary importance in
longitudinal stability. The Farman machine has three such
planes--elevator, main aerofoil, tail the Wright originally had _not_,
but is now being fitted with a tail, and experiments on the
Short-Wright biplane have quite proved its stabilising efficiency.

The three plane (triple monoplane) in the case of models has been
tried, but possesses no advantage so far over the double monoplane
type. The writer has made many experiments with vertical fins, and has
found the machine very stable, even when the fin or vertical keel is
placed some distance above the centre of gravity.

§ 9. The question of transverse (side to side) stability at once
brings us to the question of the dihedral angle, practically similar
in its action to a flat plane with vertical fins.

[Illustration: FIG. 11.--SIR GEORGE CAYLEY'S FLYING MACHINE.

Eight feathers, two corks, a thin rod, a piece of whalebone, and a
piece of thread.]

§ 10. The setting up of the front surface at an angle to the rear, or
the setting of these at corresponding compensatory angles already
dealt with, is nothing more nor less than the principle of the
dihedral angle for longitudinal stability.

[Illustration: FIG. 12.--VARIOUS FORMS OF DIHEDRALS.]

As early as the commencement of last century Sir George Cayley (a
man more than a hundred years ahead of his times) was the first to
point out that two planes at a dihedral angle constitute a basis of
stability. For, on the machine heeling over, the side which is
required to rise gains resistance by its new position, and that which
is required to sink loses it.

§ 11. The dihedral angle principle may take many forms.

As in Fig. 12 _a_ is a monoplane, the rest biplanes. The angles and
curves are somewhat exaggerated. It is quite a mistake to make the
angle excessive, the "lift" being thereby diminished. A few degrees
should suffice.

Whilst it is evident enough that transverse stability is promoted by
making the sustaining surface trough-shaped, it is not so evident what
form of cross section is the most efficient for sustentation and
equilibrium combined.

[Illustration: FIG. 13.]

It is evident that the righting moment of a unit of surface of an
aeroplane is greater at the outer edge than elsewhere, owing to the
greater lever arm.

§ 12. The "upturned tip" dihedral certainly appears to have the
advantage.

_The outer edges of the aerofoil then should be turned upward for the
purpose of transverse stability, while the inner surface should remain
flat or concave for greater support._

§ 13. The exact most favourable outline of transverse section for
stability, steadiness and buoyancy has not yet been found; but the
writer has found the section given in Fig. 13, a very efficient one.

FOOTNOTES:

[9] If the width be not uniform the mean width should be taken.

[10] This refers, of course, to transverse stability.

[11] See ch. vi.




CHAPTER IV.

THE MOTIVE POWER.


SECTION I.--RUBBER MOTORS.

§ 1. Some forty years have elapsed since Pénaud first used elastic
(rubber) for model aeroplanes, and during that time no better
substitute (in spite of innumerable experiments) has been found. Nor
for the smaller and lighter class of models is there any likelihood of
rubber being displaced. Such being the case, a brief account of some
experiments on this substance as a motive power for the same may not
be without interest. The word _elastic_ (in science) denotes: _the
tendency which a body has when distorted to return to its original
shape_. Glass and ivory (within certain limits) are two of the most
elastic bodies known. But the limits within which most bodies can be
distorted (twisted or stretched, or both) without either fracture or a
LARGE _permanent_ alteration of shape is very small. Not so rubber--it
far surpasses in this respect even steel springs.

§ 2. Let us take a piece of elastic (rubber) cord, and stretch it with
known weights and observe carefully what happens. We shall find that,
first of all: _the extension is proportional to the weight
suspended_--but soon we have an _increasing_ increase of extension. In
one experiment made by the writer, when the weights were removed the
rubber cord remained 1/8 of an inch longer, and at the end of an hour
recovered itself to the extent of 1/16, remaining finally permanently
1/16 of an inch longer. Length of elastic cord used in this experiment
8-1/8 inches, 3/16 of an inch thick. Suspended weights, 1 oz. up to 64
oz. Extension from ¼ inch up to 24-5/8 inches. Graph drawn in Fig.
14, No. B abscissæ extension in eighths of an inch, ordinates weights
in ounces. So long as the graph is a straight line it shows the
extension is proportional to the suspended weight; afterwards in
excess.

[Illustration: FIG. 14.--WEIGHT AND EXTENSION.

B, rubber 3/16 in. thick; C, 2/16 in. thick; D, 1/16 in. thick. A,
theoretical line if extension were proportional to weight.]

In this experiment we have been able to stretch (distort) a piece of
rubber to more than three times its original length, and afterwards it
finally returns to almost its original length: not only so, a piece of
rubber cord can be stretched to eight or nine times its original
length without fracture. Herein lies its supreme advantage over steel
or other springs. Weight for weight more energy can be got or more
work be done by stretched (or twisted, or, to speak more correctly, by
stretched-twisted) rubber cord than from any form of steel spring.[12]
It is true it is stretched--twisted--far beyond what is called the
"elastic limit," and its efficiency falls off, but with care not
nearly so quickly as is commonly supposed, but in spite of this and
other drawbacks its advantages far more than counterbalance these.

§ 3. Experimenting with cords of varying thickness we find that: _the
extension is inversely proportional to the thickness_. If we leave a
weight hanging on a piece of rubber cord (stretched, of course, beyond
its "elastic limit") we find that: _the cord continues to elongate as
long as the weight is left on_. For example: a 1 lb. weight hung on a
piece of rubber cord, 8-1/8 inches long and 1/8 of an inch thick,
stretched it--at first--6¼ inches; after two minutes this had
increased to 6-5/8 (3/8 of an inch more). One hour later 1/8 of an
inch more, and sixteen hours later 1/8 of an inch more, i.e. a sixteen
hours' hang produced an additional extension of ¾ of an inch. On a
thinner cord (half the thickness) same weight produced _an additional
extension_ (_after_ 14 _hours_) _of _10-3/8 _in_.

N.B.--An elastic cord or spring balance should never have a weight
left permanently on it--or be subjected to a distorting force for a
longer time than necessary, or it will take a "permanent set," and not
return to even approximately its original length or form.

In a rubber cord the extension is _directly proportional to the
length_ as well as _inversely proportional to the thickness and to the
weight suspended_--true only within the limits of elasticity.

[Illustration: FIG. 15.--EXTENSION AND INCREASE IN VOLUME.]

§ 4. =When a Rubber Cord is stretched there is an Increase of
Volume.=--On stretching a piece of rubber cord to _twice_ its
original (natural) length, we should perhaps expect to find that the
string would only be _half_ as thick, as would be the case if the
volume remained the same. Performing the experiment, and measuring the
cord as accurately as possible with a micrometer, measuring to the
one-thousandth of an inch, we at once perceive that this is not the
case, being about _two-thirds_ of its former volume.

§ 5. In the case of rubber cord used for a motive power on model
aeroplanes, the rubber is _both_ twisted and stretched, but chiefly
the latter.

Thirty-six strands of rubber, weight about 56 grammes, at 150 turns
give a torque of 4 oz. on a 5-in. arm, but an end thrust, or end pull,
of about 3½ lb. (Ball bearings, or some such device, can be used to
obviate this end thrust when desirable.) A series of experiments
undertaken by the writer on the torque produced by twisted rubber
strands, varying in number, length, etc., and afterwards carefully
plotted out in graph form, have led to some very interesting and
instructive results. Ball bearings were used, and the torque, measured
in eighths of an ounce, was taken (in each case) from an arm 5 in. in
length.

The following are the principal results arrived at. For graphs, see
Fig. 16.

§ 6. A. Increasing the number of (rubber) strands by _one-half_
(length and thickness of rubber remaining constant) increases the
torque (unwinding tendency) _twofold_, i.e., doubles the motive power.

B. _Doubling_ the number of strands increases the torque _more than
three times_--about 3-1/3 times, 3 times up to 100 turns, 3½ times
from 100 to 250 turns.

C. _Trebling_ the number of strands increases the torque at least
_seven times_.

The increased _size_ of the coils, and thereby _increased_ extension,
explains this result. As we increase the number of strands, the
_number_ of twists or turns that can be given it becomes less.

D. _Doubling_ the number of strands (length, etc., remaining
constant) _diminishes_ the number of turns by _one-third to
one-half_. (In few strands one-third, in 30 and over one-half.)

[Illustration: FIG. 16.--TORQUE GRAPHS OF RUBBER MOTORS.

    Abscissæ = Turns. Ordinates = Torque measured in 1/16 of an oz.
    Length of arm, 5 in.

    A.  38 strands of new rubber, 2 ft. 6 in. long; 58 grammes weight.
    B.  36 strands, 2 ft. 6 in. long; end thrust at 150 turns, 3½ lb.
    C.  32 strands, 2 ft. 6 in. long.
    D.  24    "        "        "
    E.  18    "        "        "     weight 28 grammes.
    F.  12    "     1 ft. 3 in. long
    G.  12    "     2 ft. 6 in. long.]

E. If we halve the length of the rubber strands, keeping the _number_
of strands the same, the torque is but slightly increased for the
first 100 turns; at 240 turns it is double. But the greater number of
turns--in ratio of about 2:1--that can be given the longer strand much
more than compensates for this.

F. No arrangement of the strands, _per se_, gets more energy (more
motive power) out of them than any other, but there are special
reasons for making the strands--

G. As long and as few in number as possible.

1. More turns can be given it.

2. It gives a far more even torque. Twelve strands 2 ft. 6 in. long
give practically a line of small constant angle. Thirty-six strands
same length a much steeper angle, with considerable variations.

A very good result, which the writer has verified in practice, paying
due regard to _both_ propeller and motor, is to make--

H. _The length of the rubber strands twice[13] in feet the number of
the strands in inches_,[14] e.g., if the number of strands is 12 their
length should be 2 ft., if 18, 3 ft., and so on.

§ 7. Experiments with 32 to 38 strands 2 ft. 6 in. long give a torque
curve almost precisely similar to that obtained from experiments made
with flat spiral steel springs, similar to those used in watches and
clocks; and, as we know, the torque given by such springs is very
uneven, and has to be equalised by use of a fusee, or some such
device. In the case of such springs it must not be forgotten that the
turning moment (unwinding tendency) is NOT proportional to the amount
of winding up, this being true only in the "balance" springs of
watches, etc., where _both_ ends of the spring are rigidly fastened.

In the case of SPRING MOTORS.[15]

I. The turning moment (unwinding tendency) is proportional to the
difference between the angle of winding and yielding, proportional to
the moment of inertia of its section, i.e., to the breadth and the
cube of its thickness, also proportional to the modulus of elasticity
of the substance used, and inversely proportional to the length of the
strip.

§ 8. Referring back to A, B, C, there are one or two practical
deductions which should be carefully noted.

Supposing we have a model with one propeller and 36 strands of
elastic. If we decide to fit it with twin screws, then, other reasons
apart, we shall require two sets of strands of more than 18 in number
each to have the same motive power (27 if the same torque be
required).[16] This is an important point, and one not to be lost
sight of when thinking of using two propellers.

Experiments on--

§9. =The Number of Revolutions= (turns) =that can be given to Rubber
Motors= led to interesting results, e.g., the number of turns to
produce a double knot in the cord from end to end were, in the case of
rubber, one yard long:--

    No. of Strands.   No. of Turns.  No. of Strands. No. of Turns.
            4             440              16            200
            8             310              28            170
           12             250

It will be at once noticed that the greater the number of rubber
strands used in a given length, the fewer turns will it stand in
proportion. For instance, 8 strands double knot at 310, and 4 at 440
(and not at 620), 16 at 200, and 8 at 310 (and not 400), and so on.
The reason, of course, is the more the strands the greater the
distance they have to travel round themselves.

§ 10. =The Maximum Number of Turns.=--As to the maximum number of
permissible turns, rubber has rupture stress of 330 lb. per sq. in.,
_but a very high permissible stress_, as much as 80 per cent. The
resilience (power of recovery after distortion) in tension of rubber
is in considerable excess of any other substance, silk being the only
other substance which at all approaches it in this respect, the ratio
being about 11 : 9. The resilience of steel spiral spring is very
slight in comparison.

A rubber motor in which the double knot is not exceeded by more than
100 turns (rubber one yard in length) should last a good time. When
trying for a record flight, using new elastic, as many as even 500 or
600 or even more turns have been given in the case of 32-36 strands a
yard in length; but such a severe strain soon spoils the rubber.

§ 11. =On the Use of "Lubricants."=--One of the drawbacks to rubber is
that if it be excessively strained it soon begins to break up. One of
the chief causes of this is that the strands stick together--they
should always be carefully separated, if necessary, after a
flight--and an undue strain is thereby cast on certain parts. Apart
also from this the various strands are not subject to the same
tension. It has been suggested that if some means could be devised to
prevent this, and allow the strands to slip over one another, a
considerable increase of power might result. It must, however, be
carefully borne in mind that anything of an oily or greasy nature has
an injurious effect on the rubber, and must be avoided at all costs.
Benzol, petroleum, ether, volatile oils, turpentine, chloroform,
naphtha, vaseline, soap, and all kinds of oil must be carefully
avoided, as they soften the rubber, and reduce it more or less to the
consistence of a sticky mass. The only oil which is said to have no
action on rubber, or practically none, is castor oil; all the same, I
do not advise its use as a lubricant.

There are three only which we need consider:--

    1. Soda and water.
    2. French chalk.
    3. Pure redistilled glycerine.

The first is perfectly satisfactory when freshly applied, but soon
dries up and evaporates.

The second falls off; and unless the chalk be of the softest kind,
free from all grit and hard particles, it will soon do more harm than
good.

The third, glycerine, is for ordinary purposes by far the best, and
has a beneficial rather than a deleterious effect on the rubber; but
it must be _pure_. The redistilled kind, free from all traces of
arsenic, grease, etc., is the only kind permissible. It does not
evaporate, and a few drops, comparatively speaking, will lubricate
fifty or sixty yards of rubber.

Being of a sticky or tacky nature it naturally gathers up dust and
particles of dirt in course of time. To prevent these grinding into
the rubber, wash it from time to time in warm soda, and warm and apply
fresh glycerine when required.

Glycerine, unlike vaseline (a product of petroleum), is not a grease;
it is formed from fats by a process known as _saponification_, or
treatment of the oil with caustic alkali, which decomposes the
compound, forming an alkaline stearate (soap), and liberating the
glycerine which remains in solution when the soap is separated by
throwing in common salt. In order to obtain pure glycerine, the fat
can be decomposed by lead oxide, the glycerine remaining in solution,
and the lead soap or plaster being precipitated.

By using glycerine as a lubricant the number of turns that can be
given a rubber motor is greatly increased, and the coils slip over one
another freely and easily, and prevent the throwing of undue strain on
some particular portion, and absolutely prevent the strands from
sticking together.

§ 12. =The Action of Copper upon Rubber.=--Copper, whether in the form
of the metal, the oxides, or the soluble salts, has a marked injurious
action upon rubber.

In the case of metallic copper this action has been attributed to
oxidation induced by the dissolved oxygen in the copper. In working
drawings for model aeroplanes I have noticed designs in which the
hooks on which the rubber strands were to be stretched were made of
_copper_. In no case should the strands be placed upon bare metal. I
always cover mine with a piece of valve tubing, which can easily be
renewed from time to time.

§ 12A. =The Action of Water, etc., on Rubber.=--Rubber is quite
insoluble in water; but it must not be forgotten that it will absorb
about 25 per cent. into its pores after soaking for some time.

Ether, chloroform, carbon-tetrachloride, turpentine, carbon
bi-sulphide, petroleum spirit, benzene and its homologues found in
coal-tar naphtha, dissolve rubber readily. Alcohol is absorbed by
rubber, but is not a solvent of it.

§ 12B. =How to Preserve Rubber.=--In the first place, in order that it
shall be _possible_ to preserve and keep rubber in the best condition
of efficiency, it is absolutely essential that the rubber shall be,
when obtained, fresh and of the best kind. Only the best Para rubber
should be bought; to obtain it fresh it should be got in as large
quantities as possible direct from a manufacturer or reliable rubber
shop. The composition of the best Para rubber is as follows:--Carbon,
87·46 per cent.; hydrogen, 12·00 per cent.; oxygen and ash, 0·54 per
cent.

In order to increase its elasticity the pure rubber has to be
vulcanised before being made into the sheet some sixty or eighty yards
in length, from which the rubber threads are cut; after vulcanization
the substance consists of rubber plus about 3 per cent. of sulphur.
Now, unfortunately, the presence of the sulphur makes the rubber more
prone to atmospheric oxidation. Vulcanized rubber, compared to pure
rubber, has then but a limited life. It is to this process of
oxidation that the more or less rapid deterioration of rubber is due.

To preserve rubber it should be kept from the sun's rays, or, indeed,
any actinic rays, in a cool, airy place, and subjected to as even a
temperature as possible. Great extremes of temperature have a very
injurious effect on rubber, and it should be washed from time to time
in warm soda water. It should be subjected to no tension or
compression.

Deteriorated rubber is absolutely useless for model aeroplanes.

§ 13. =To Test Rubber.=--Good elastic thread composed of pure Para
rubber and sulphur should, if properly made, stretch to seven times
its length, and then return to its original length. It should also
possess a stretching limit at least ten times its original length.

As already stated, the threads or strands are cut from sheets; these
threads can now be cut fifty to the inch. For rubber motors a very
great deal so far as length of life depends on the accuracy and skill
with which the strands are cut. When examined under a microscope (not
too powerful) the strands having the least ragged edge, i.e., the best
cut, are to be preferred.

§ 14. =The Section--Strip or Ribbon versus Square.=--In section the
square and not the ribbon or strip should be used. The edge of the
strip I have always found more ragged under the microscope than the
square. I have also found it less efficient. Theoretically no doubt a
round section would be best, but none such (in small sizes) is on the
market. Models have been fitted with a tubular section, but such
should on no account be used.

§ 15. =Size of the Section.=--One-sixteenth or one-twelfth is the best
size for ordinary models; personally, I prefer the thinner. If more
than a certain number of strands are required to provide the necessary
power, a larger size should be used. It is not easy to say _what_ this
number is, but fifty may probably be taken as an outside limit.
Remember the size increases by area section; twice the _sectional_
height and breadth means four times the rubber.

§ 16. =Geared Rubber Motors.=--It is quite a mistake to suppose that
any advantage can be obtained by using a four to one gearing, say; all
that you do obtain is one-fourth of the power minus the increased
friction, minus the added weight. This presumes, of course, you make
no alteration in your rubber strands.

Gearing such as this means _short_ rubber strands, and such are not to
be desired; in any case, there is the difficulty of increased friction
and added weight to overcome. It is true by splitting up your rubber
motor into two sets of strands instead of one you can obtain more
turns, but, as we have seen, you must increase the number of strands
to get the same thrust, and you have this to counteract any advantage
you gain as well as added weight and friction.

§ 17. The writer has tried endless experiments with all kinds of
geared rubber motors, and the only one worth a moment's consideration
is the following, viz., one in which two gear wheels--same size,
weight, and number of teeth--are made use of, the propeller being
attached to the axle of one of them, and the same number of strands
are used on each axle. The success or non-success of this motor
depends entirely on the method used in its construction. At first
sight it may appear that no great skill is required in the
construction of such a simple piece of apparatus. No greater mistake
could be made. It is absolutely necessary that _the friction and
weight be reduced to a minimum_, and the strength be a maximum. The
torque of the rubber strands on so short an arm is very great.

Ordinary light brass cogwheels will not stand the strain.

A. The cogwheels should be of steel[17] and accurately cut of diameter
sufficient to separate the two strands the requisite distance, _but no
more_.

B. The weight must be a minimum. This is best attained by using solid
wheels, and lightening by drilling and turning.

C. The friction must be a minimum. Use the lightest ball bearings
obtainable (these weigh only 0·3 gramme), adjust the wheels so that
they run with the greatest freedom, but see that the teeth overlap
sufficiently to stand the strain and slight variations in direction
without fear of slipping. Shallow teeth are useless.

D. Use vaseline on the cogs to make them run as easily as possible.

[Illustration: FIG. 17.--GEARED RUBBER MOTOR.

Designed and constructed by the writer. For description of the model,
etc., see Appendix.]

E. The material of the containing framework must be of maximum
strength and minimum lightness. Construct it of minimum size, box
shaped, use the thinnest tin (really tinned sheet-iron) procurable,
and lighten by drilling holes, not too large, all over it. Do not use
aluminium or magnalium. Steel, could it be procured thin enough, would
be better still.

F. Use steel pianoforte wire for the spindles, and hooks for the
rubber strands, using as thin wire as will stand the strain.

Unless these directions are carefully carried out no advantage will be
gained--the writer speaks from experience. The requisite number of
rubber strands to give the best result must be determined by
experiment.

§ 18. One advantage in using such a motor as this is that the two
equal strands untwisting in opposite directions have a decided
steadying effect on the model, similar almost to the case in which two
propellers are used.

The "best" model flights that the writer has achieved have been
obtained with a motor of this description.[18]

In the case of twin screws two such gearings can be used, and the
rubber split up into four strands. The containing framework in this
case can be simply light pieces of tubing let into the wooden
framework, or very light iron pieces fastened thereto.

Do not attempt to split up the rubber into more than two strands to
each propeller.


SECTION II.--OTHER FORMS OF MOTORS.

§ 18A. =Spring Motors.=--This question has already been dealt with
more or less whilst dealing with rubber motors, and the superiority of
the latter over the former pointed out. Rubber has a much greater
superiority over steel or other springs, because in stretch-twisted
rubber far more energy can be stored up weight for weight. One pound
weight of elastic can be made to store up some 320 ft.-lb. of energy,
and steel only some 65 lb. And in addition to this there is the
question of gearing, involving extra weight and friction; that is, if
flat steel springs similar to those used in clockwork mechanism be
made use of, as is generally the case. The only instance in which such
springs are of use is for the purpose of studying the effects of
different distributions of weight on the model, and its effect on the
balance of the machine; but effects such as this can be brought about
without a change of motor.

§ 18B. A more efficient form of spring motor, doing away with gearing
troubles, is to use a long spiral spring (as long as the rubber
strands) made of medium-sized piano wire, similar in principle to
those used in some roller-blinds, but longer and of thinner steel.

The writer has experimented with such, as well as scores of other
forms of spring motors, but none can compare with rubber.

The long spiral form of steel spring is, however, much the best.

§ 18C. =Compressed Air Motors.=--This is a very fascinating form of
motor, on paper, and appears at first sight the ideal form. It is so
easy to write: "Its weight is negligible, and it can be provided free
of cost; all that is necessary is to work a bicycle pump for as many
minutes as the motor is desired to run. This stored-up energy can be
contained in a mere tube, of aluminium or magnalium, forming the
central rib of the machine, and the engine mechanism necessary for
conveying this stored-up energy to the revolving propeller need weigh
only a few ounces." Another writer recommends "a pressure of 300 lb."

§ 18D. A pneumatic drill generally works at about 80 lb. pressure,
and when developing 1 horse-power, uses about 55 cubic ft. of free air
per minute. Now if we apply this to a model aeroplane of average size,
taking a reservoir 3 ft. long by 1½ in. internal diameter, made of
magnalium, say--steel would, of course, be much better--the weight of
which would certainly not be less than 4 oz., we find that at 80 lb.
pressure such a motor would use

    55/Horse Power (H.P.)

cub. ft. per minute.

Now 80 lb. is about 5½ atmospheres, and the cubical contents of the
above motor some 63 cub. in. The time during which such a model would
fly depends on the H.P. necessary for flight; but a fair allowance
gives a flight of from 10 to 30 sec. I take 80 lb. pressure as a fair
practical limit.

§ 18E. The pressure in a motor-car tyre runs from 40 to 80 lb.,
usually about 70 lb. Now 260 strokes are required with an ordinary
inflator to obtain so low a pressure as 70 lb., and it is no easy job,
as those who have done it know.

§ 19. Prior to 1893 Mr. Hargraves (of cellular kite fame) studied the
question of compressed-air motors for model flying machines. His motor
was described as a marvel of simplicity and lightness, its cylinder
was made like a common tin can, the cylinder covers cut from sheet tin
and pressed to shape, the piston and junk rings of ebonite.

One of his receivers was 23-3/8 in. long, and 5·5 in. diameter, of
aluminium plate 0·2 in. thick, 3/8 in. by 1/8 in. riveting strips were
insufficient to make tight joints; it weighed 26 oz., and at 80 lb.
water pressure one of the ends blew out, the fracture occurring at the
bend of the flange, and not along the line of rivets. The receiver
which was successful being apparently a tin-iron one; steel tubing was
not to be had at that date in Sydney. With a receiver of this
character, and the engine referred to above, a flight of 343 ft. was
obtained, this flight being the best. (The models constructed by him
were not on the aeroplane, but ornithoptere, or wing-flapping
principle.) The time of flight was 23 _seconds_, with 54½ double
vibrations of the engines. The efficiency of this motor was estimated
to be 29 per cent.

§ 20. By using compressed air, and heating it in its passage to the
cylinder, far greater efficiency can be obtained. Steel cylinders can
be obtained containing air under the enormous pressure of 120
atmospheres.[19] This is practically liquid air. A 20-ft. cylinder
weighs empty 23 lb. The smaller the cylinder the less the
proportionate pressure that it will stand; and supposing a small steel
cylinder, produced of suitable form and weight, and capable of
withstanding with safety a pressure of from 300 to 600 lb. per sq.
in., or from 20 to 40 atmospheres. The most economical way of working
would be to admit the air from the reservoir directly to the motor
cylinders; but this would mean a very great range in the initial
working pressure, entailing not-to-be-thought-of weight in the form of
multi-cylinder compound engines, variable expansion gear, etc.

§ 21. This means relinquishing the advantages of the high initial
pressure, and the passing of the air through a reducing valve, whereby
a constant pressure, say, of 90 to 150, according to circumstances,
could be maintained. By a variation in the ratio of expansion the air
could be worked down to, say, 30 lb.

The initial loss entailed by the use of a reducing valve may be in a
great measure restored by heating the air before using it in the motor
cylinders; by heating it to a temperature of only 320°F., by means of
a suitable burner, the volume of air is increased by one half, the
consumption being reduced in the same proportion; the consumption of
air used in this way being 24 lb. per indicated horse-power per hour.
But this means extra weight in the form of fuel and burners, and what
we gain in one way we lose in another. It is, of course, desirable
that the motor should work at as low a pressure as possible, since as
the store of air is used up the pressure in the reservoir falls, until
it reaches a limit below which it cannot usefully be employed. The air
then remaining is dead and useless, adding only to the weight of the
aeroplane.

§ 22. From calculations made by the writer the _entire_ weight of a
compressed-air model motor plant would be at least _one-third_ the
weight of the aeroplane, and on a small scale probably one-half, and
cannot therefore hold comparison with the _steam engine_ discussed in
the next paragraph. In concluding these remarks on compressed-air
motors, I do not wish to dissuade anyone from trying this form of
motor; but they must not embark on experiments with the idea that
anything useful or anything superior to results obtained with
infinitely less expense by means of rubber can be brought to pass with
a bicycle pump, a bit of magnalium tube, and 60 lb. pressure.

§ 22A. In Tatin's air-compressed motor the reservoir weighed 700
grammes, and had a capacity of 8 litres. It was tested to withstand a
pressure of 20 atmospheres, but was worked only up to seven. The
little engine attached thereto weighed 300 grammes, and developed a
motive power of 2 kilogram-metres per second (_see_ ch. iii.).

§ 23. =Steam-Driven Motors.=--Several successful steam-engined model
aeroplanes have been constructed, the most famous being those of
Professor Langley.

Having constructed over 30 modifications of rubber-driven models, and
experimented with compressed air, carbonic-acid gas, electricity, and
other methods of obtaining energy, he finally settled upon the steam
engine (the petrol motor was not available at that time, 1893). After
many months' work it was found that the weight could not be reduced
below 40 lb., whilst the engine would only develop ½ H.P., and
finally the model was condemned. A second apparatus to be worked by
compressed air was tried, but the power proved insufficient. Then came
another with a carbonic-acid gas engine. Then others with various
applications of electricity and gas, etc., but the steam engine was
found most suitable; yet it seemed to become more and more doubtful
whether it could ever be made sufficiently light, and whether the
desired end could be attained at all. The chief obstacle proved not to
be with the engines, which were made surprisingly light after
sufficient experiment. _The great difficulty was to make a boiler of
almost no weight which would give steam enough._

§ 24. At last a satisfactory boiler and engine were produced.

The engine was of 1 to 1½ H.P., total weight (including moving
parts) 26 oz. The cylinders, two in number, had each a diameter of
1¼ in., and piston stroke 2 in.

The boiler, with its firegrate, weighed a little over 5 lb. It
consisted of a continuous helix of copper tubing, 3/8 in. external
diameter, the diameter of the coil being 3 in. altogether. Through the
centre of this was driven the blast from an "Ælopile," a modification
of the naphtha blow-torch used by plumbers, the flame of which is
about 2000° F.[20] The pressure of steam issuing into the engines
varied from 100 to 150 lb. per sq. in.; 4 lb. weight of water and
about 10 oz. of naphtha could be carried. The boiler evaporated 1 lb.
of water per minute.

The twin propellers, 39 in. in diam., pitch 1¼, revolved from 800
to 1000 a minute. The entire aeroplane was 15 ft. in length, the
aerofoils from tip to tip about 14 ft., and the total weight slightly
less than 30 lb., of which _one-fourth was contained in the
machinery_. Its flight was a little over half a mile in length, and of
1½ minutes' duration. Another model flew for about three-quarters
of a mile, at a rate of about 30 miles an hour.

It will be noted that engine, generator, etc., work out at about 7 lb.
per H.P. Considerable advance has been made in the construction of
light and powerful model steam engines since Langley's time, chiefly
in connexion with model hydroplanes, and a pressure of from 500 to 600
lb. per sq. in. has been employed; the steam turbine has been brought
to a high state of perfection, and it is now possible to make a model
De Laval turbine of considerable power weighing almost next to
nothing,[21] the real trouble, in fact the only one, being the steam
generator. An economization of weight means a waste of steam, of which
models can easily spend their only weight in five minutes.

§ 25. One way to economize without increased weight in the shape of a
condenser is to use spirit (methylated spirit, for instance) for both
fuel and boiler, and cause the exhaust from the engines to be ejected
on to the burning spirit, where it itself serves as fuel. By using
spirit, or some very volatile hydrocarbon, instead of water, we have a
further advantage from the fact that such vaporize at a much lower
temperature than water.

§ 26. When experimenting with an engine of the turbine type we must
use a propeller of small diameter and pitch, owing to the very high
velocity at which such engines run.

Anyone, however, who is not an expert on such matters would do well to
leave such motors alone, as the very highest technical skill, combined
with many preliminary disappointments and trials, are sure to be
encountered before success is attained.

§ 27. And the smaller the model the more difficult the problem--halve
your aeroplane, and your difficulties increase anything from fourfold
to tenfold.

The boiler would in any case be of the flash type of either copper or
steel tubing (the former for safety), with a magnalium container for
the spirit, and a working pressure of from 150 to 200 lb. per sq. in.
Anything less than this would not be worth consideration.

§ 28. Some ten months after Professor Langley's successful model
flights (1896), experiments were made in France at Carquenez, near
Toulon. The total weight of the model aeroplane in this case was 70
lb.; the engine power a little more than 1 H.P. Twin screws were
used--_one in front and one behind_. The maximum velocity obtained was
40 miles per hour; but the length of run only 154 yards, and duration
of flight only a few seconds. This result compares very poorly with
Langley's distance (of best flight), nearly one mile, duration 1 min.
45 sec. The maximum velocity was greater--30 to 40 miles per hour. The
total breadth of this large model was rather more than 6 metres, and
the surface a little more than 8 sq. metres.

§ 29. =Petrol Motors.=--Here it would appear at first thought is the
true solution of the problem of the model aeroplane motor. Such a
motor has solved the problem of aerial locomotion, as the steam engine
solved that of terrestrial and marine travel, both full sized and
model; and if in the case of full sized machines, then why not models.

[Illustration: FIG. 18.--MR. STANGER'S MODEL IN FULL FLIGHT.]

[Illustration: FIG. 19.--MR. STANGER'S PETROL-DRIVEN MODEL AEROPLANE.

(_Illustrations by permission from electros supplied by the "Aero."_)]

§ 30. The exact size of the smallest _working_ model steam engine that
has been made I do not know,[22] but it is or could be surprisingly
small; not so the petrol motor--not one, that is, that would _work_.
The number of petrol motor-driven model aeroplanes that have actually
flown is very small. Personally I only know of one, viz., Mr. D.
Stanger's, exhibited at the aero exhibition at the Agricultural Hall
in 1908.

[Illustration: FIG. 20.--MR. STANGER'S MODEL PETROL ENGINE.]

[Illustration: FIG. 21.--MR. STANGER'S MODEL PETROL ENGINE.]

    In Fig. 21 the motor is in position on the aeroplane. Note
    small carburettor. In Fig. 20 an idea of the size of engine may
    be gathered by comparing it with the ordinary sparking-plug
    seen by the side, whilst to the left of this is one of the
    special plugs used on this motor. (_Illustrations by permission
    from electros supplied by the "Aero."_)

§ 31. The following are the chief particulars of this interesting
machine:--The engine is a four-cylinder one, and weighs (complete with
double carburetter and petrol tank) 5½ lb., and develops 1¼ H.P.
at 1300 revolutions per minute.

[Illustration: FIG. 22.--ONE-CYLINDER PETROL MOTOR.

(_Electro from Messrs. A.W. Gamage's Aviation Catalogue._)]

The propeller, 29 in. in diam. and 36 in. in pitch, gives a static
thrust of about 7 lb. The machine has a spread of 8 ft. 2 in., and is
6 ft. 10 in. in length. Total weight 21 lb. Rises from the ground when
a speed of about 16 miles an hour is attained. A clockwork
arrangement automatically stops the engine. The engine air-cooled. The
cylinder of steel, cast-iron heads, aluminium crank-case, double float
feed carburetter, ignition by single coil and distributor. The
aeroplane being 7 ft. 6 in. long, and having a span 8 ft.

§ 32. =One-cylinder Petrol Motors.=--So far as the writer is aware no
success has as yet attended the use of a single-cylinder petrol motor
on a model aeroplane. Undoubtedly the vibration is excessive; but this
should not be an insuperable difficulty. It is true it is heavier in
proportion than a two-cylinder one, and not so efficient; and so far
has not proved successful. The question of vibration on a model
aeroplane is one of considerable importance. A badly balanced
propeller even will seriously interfere with and often greatly curtail
the length of flight.

§ 33. =Electric Motors.=--No attempt should on any account be made to
use electric motors for model aeroplanes. They are altogether too
heavy, apart even from the accumulator or source of electric energy,
for the power derivable from them. To take an extreme case, and
supposing we use a 2-oz. electric motor capable of driving a propeller
giving a static thrust of 3 oz.,[23] on weighing one of the smallest
size accumulators without case, etc., I find its weight is 4½ oz.
One would, of course, be of no use; at least three would be required,
and they would require practically short circuiting to give sufficient
amperage (running them down, that is, in some 10 to 15 seconds). Total
weight, 1 lb. nearly. Now from a _pound_ weight of rubber one could
obtain a thrust of _pounds_, not ounces. For scale models not intended
for actual flight, of course, electric motors have their uses.

FOOTNOTES:

[12] Also there is no necessity for gearing.

[13] In his latest models the writer uses strands even three times and
not twice as long, viz. fourteen strands 43 in. long.

[14] This refers to 1/16 in. square sectioned rubber.

[15] Of uniform breadth and thickness.

[16] In practice I find not quite so high a proportion as this is
always necessary.

[17] Steel pinion wire is very suitable.

[18] See Appendix.

[19] As high a pressure as 250 atmospheres has been used.

[20] There was a special pump keeping the water circulating rapidly
through the boiler, the intense heat converting some of it into steam
as it flowed. The making of this boiler alone consumed months of work;
the entire machine taking a year to construct, with the best
mechanical help available.

[21] Model Steam Turbines. "Model Engineer" Series, No. 13, price
6_d._

[22] See Introduction, note to § 1.

[23] The voltage, etc., is not stated.




CHAPTER V.

PROPELLERS OR SCREWS.


§ 1. The design and construction of propellers, more especially the
former, is without doubt one of the most difficult parts of model
aeroplaning.

With elastic or spring driven models the problem is more complicated
than for models driven by petrol or some vaporized form of liquid
fuel; and less reliable information is to hand. The problem of
_weight_, unfortunately, is of primary importance.

We will deal with these points in due course; to begin with let us
take:--


THE POSITION OF THE PROPELLER.

In model aeroplanes the propeller is usually situated either in front
or in the rear of the model; in the former case it is called a TRACTOR
SCREW, i.e., it pulls instead of pushes.

As to the merits of the two systems with respect to the tractor, there
is, we know, in the case of models moving through water a distinct
advantage in placing the propeller behind, and using a pushing or
propulsive action, on account of the frictional "wake" created behind
the boat, and which causes the water to flow after the vessel, but at
a lesser velocity.

In placing the propeller behind, we place it in such a position as to
act upon and make use of this phenomenon, the effect of the propeller
being to bring this following wake to rest. Theoretically a boat,
model or otherwise, can be propelled with less horse-power than it can
be towed. But with respect to aeroplanes, apart altogether from the
difference of medium, there is _at present_ a very considerable
difference of _form_, an aeroplane, model or otherwise, bearing at
present but little resemblance to the hull of a boat.

Undoubtedly there is a frictional wake in the case of aeroplanes,
possibly quite as much in proportion as in the case of a boat,
allowing for difference of medium. Admitting, then, that this wake
does exist, it follows that a propulsive screw is better than a
tractor. In a matter of this kind constructional considerations, or
"ease of launching," and "ability to land without damage," must be
given due weight.

In the case of model aeroplanes constructional details incline the
balance neither one way nor the other; but "ease in launching" and
"ability to land without damage" weigh the balance down most decidedly
in favour of a driving or propulsive screw.

In the case of full-sized monoplanes constructional details had most
to do with the use of tractors; but monoplanes are now being built
with propulsive screws.[24]

In the case of models, not models of full-sized machines, but actual
model flyers, the writer considers propulsive screws much the
best.[25]

In no case should the propeller be placed in the centre of the model,
or in such a position as to _shorten the strands of the elastic
motor_, if good flights are desired.

In the case of petrol or similar driven models the position of the
propeller can be safely copied from actual well-recognised and
successful full-sized machines.

§ 2. =The Number of Blades.=--Theoretically the number of blades does
not enter into consideration. The mass of air dealt with by the
propeller is represented by a cylinder of indefinite length, whose
diameter is the same as that of the screw, and the rate at which this
cylinder is projected to the rear depends theoretically upon the pitch
and revolutions (per minute, say) of the propeller and not the number
of blades. Theoretically one blade (helix incomplete) would be
sufficient, but such a screw would not "balance," and balance is of
primary importance; the minimum number of blades which can be used is
therefore _two_.

In marine models three blades are considered best, as giving a better
balance.

In the case of their aerial prototypes the question of _weight_ has
again to be considered, and two blades is practically the invariable
custom.[26] Here, again, constructional considerations again come to
the fore, and in the case of wooden propellers one of two blades is of
far more easy construction than one of three.

By increasing the number of blades the "thrust" is, of course, more
evenly distributed over a larger area, but the weight is considerably
increased, and in models a greater advantage is gained by keeping down
the weight than might follow from the use of more blades.

§ 3. =Fan versus Propeller.=--It must always be most carefully borne
in mind that a fan (ventilating) and a propeller are not the same
thing. Because many blades are found in practice to be efficient in
the case of the former, it is quite wrong to assume that the same
conclusion holds in the case of the latter.

By increasing the number of blades the skin friction due to the
resistance that has to be overcome in rotating the propeller through
the air is added to.

Moreover a fan is stationary, whilst a propeller is constantly
_advancing_ as well as _rotating_ through the air.

The action of a fan blower is to move a small quantity of air at a
high velocity; whereas the action of a propeller is, or should be, to
move _a large quantity of air at a small velocity_, for the function
of a screw is to create thrust. Operating on a yielding fluid medium
this thrust will evidently be in proportion to the mass of fluid
moved, and also to the velocity at which it is put in motion.

But the power consumed in putting this mass of fluid in motion is
proportional to the mass and to the _square_ of the velocity at which
it moves. From this it follows, as stated above, that in order to
obtain a given thrust with the least loss of power, the mass of fluid
acted on should be as large as possible, and the velocity imparted to
it as little as possible.

A fan requires to be so designed as to create a thrust when stationary
(static thrust), and a propeller whilst moving through the air
(dynamic thrust).

§ 4. =The Function of a Propeller= is to produce dynamic thrust; and
the great advantage of the use of a propeller as a thrusting or
propulsive agent is that its surface is always active. It has no
_dead_ points, and its motion is continuous and not reciprocating, and
it requires no special machinery or moving parts in its construction
and operation.

§ 5. =The Pitch= of a propeller or screw is the linear distance a
screw moves, backwards or forwards, in one complete revolution. This
distance is purely a theoretical one. When, for instance, a screw is
said to have a pitch of 1 ft., or 12 in., it means that the model
would advance 1 ft. through the air for each revolution of the screw,
provided that the propeller blade were mounted in _solid_ guides, like
a nut on a bolt with one thread per foot. In a yielding fluid such as
water or air it does not practically advance this distance, and hence
occurs what is known as--

§ 6. =Slip=, which may be defined as the distance which ought to be
traversed, but which is lost through imperfections in the propelling
mechanism; or it may be considered as power which should have been
used in driving the model forward. In the case of a locomotive running
on dry rails nothing is lost in slip, there being none. In the case of
a steamer moored and her engines set going, or of an aeroplane held
back prior to starting, all the power is used in slip, i.e. in putting
the fluid in motion, and none is used in propulsion.

Supposing the propeller on our model has a pitch of 1 ft., and we give
the elastic motor 100 turns, theoretically the model should travel 100
ft. in calm air before the propeller is run down; no propeller yet
designed will do this. Supposing the actual length 77 ft., 23 per
cent. has been lost in "slip." For this to be actually correct the
propeller must stop at the precise instant when the machine comes to
ground.

Taking "slip" into account, then--

_The speed of the model in feet per minute = pitch (in feet) ×
revolutions per minute -- slip (feet per minute)._

This slip wants to be made small--just how small is not yet known.

If made too small then the propeller will not be so efficient, or, at
any rate, such is the conclusion come to in marine propulsion, where
it is found for the most economical results to be obtained that the
slip should be from 10 to 20 per cent.

In the case of aerial propellers a slip of 25 per cent. is quite good,
40 per cent. bad; and there are certain reasons for assuming that
possibly about 15 per cent. may be the best.

§ 7. It is true that slip represents energy lost; but some slip is
essential, because without slip there could be no "thrust," this same
thrust being derived from the reaction of the volume of air driven
backwards.

The thrust is equal to--

_Weight of mass of air acted on per second × slip velocity in feet per
second._

In the case of an aeroplane advancing through the air it might be
thought that the thrust would be less. Sir Hiram Maxim found, however,
as the result of his experiments that the thrust with a propeller
travelling through the air at a velocity of 40 miles an hour was the
same as when stationary, the r.p.m. remaining constant throughout. The
explanation is that when travelling the propeller is continually
advancing on to "undisturbed" air, the "slip" velocity is reduced, but
the undisturbed air is equivalent to acting upon a greater mass of
air.

§ 8. =Pitch Coefficient or Pitch Ratio.=--If we divide the pitch of a
screw by its diameter we obtain what is known as pitch coefficient or
ratio.

The mean value of eighteen pitch coefficients of well-known full-sized
machines works out at 0·62, which, as it so happens, is exactly the
same as the case of the Farman machine propeller considered alone,
this ratio varying from 0·4 to 1·2; in the case of the Wright's
machine it is (probably) 1. The efficiency of their propeller is
admitted on all hands. Their propeller is, of course, a slow-speed
propeller, 450 r.p.m. The one on the Blériot monoplane (Blériot XI.)
pitch ratio 0·4, r.p.m. 1350.

In marine propulsion the pitch ratio is generally 1·3 for a slow-speed
propeller, decreasing to 0·9 for a high-speed one. In the case of
rubber-driven model aeroplanes the pitch ratio is often carried much
higher, even to over 3.

Mr. T.W.K. Clarke recommends a pitch angle of 45°, or less, at the
tips, and a pitch ratio of 3-1/7 (with an angle of 45°). Within limits
the higher the pitch ratio the better the efficiency. The higher the
pitch ratio the slower may be the rate of revolution. Now in a rubber
motor we do not want the rubber to untwist (run out) too quickly; with
too fine a pitch the propeller "races," or does something remarkably
like it. It certainly revolves with an abnormally high percentage of
slip. And for efficiency it is certainly desirable to push this ratio
to its limit; but there is also the question of the

§ 9. =Diameter.=--"The diameter (says Mr. T.W.K. Clarke) should be
equal to one-quarter the span of the machine."

If we increase the diameter we shall decrease the pitch ratio. From
experiments which the writer has made he prefers a lower pitch ratio
and increased diameter, viz. a pitch ratio of 1·5, and a diameter of
one-third to even one-half the span, or even more.[27] Certainly not
less than one-third. Some model makers indulge in a large pitch ratio,
angle, diameter, and blade area as well, but such a course is not to
be recommended.

§ 10. =Theoretical Pitch.=--Theoretically the pitch (from boss to
tip) should at all points be the same; the boss or centre of the blade
at right angles to the plane of rotation, and the angle decreasing as
one approaches the tips. This is obvious when one considers that the
whole blade has to move forward the same amount. In the diagrams Figs.
23 and 24 the tip A of the propeller travels a distance = 2 {pi} R every
revolution. At a point D on the blade, distant _r_ from the centre,
the distance is 2 {pi} _r_. In both instances the two points must advance
a distance equal to the pitch, i.e. the distance represented by P O.

[Illustration: FIG. 23.]

[Illustration: FIG. 24.

A O = 2 {pi} R; D O = 2 {pi} _r_.]

A will move along A P, B along B P, and so on. The angles at the
points A, B, C ... (Fig. 24), showing the angles at which the
corresponding parts of the blade at A, B, C ... in Fig. 23 must be set
in order that a uniform pitch may be obtained.

§ 11. If the pitch be not uniform then there will be some portions of
the blade which will drag through the air instead of affording useful
thrust, and others which will be doing more than they ought, putting
air in motion which had better be left quiet. This uniform total pitch
for all parts of the propeller is (as already stated) a decreasing
rate of pitch from the centre to the edge. With a total pitch of 5
ft., and a radius of 4 ft., and an angle at the circumference of 6°,
then the angle of pitch at a point midway between centre and
circumference should be 12°, in order that the total pitch may be the
same at all parts.

§ 12. =To Ascertain the Pitch of a Propeller.=--Take any point on one
of the blades, and carefully measure the inclination of the blade at
that point to the plane of rotation.

If the angle so formed be about 19° (19·45),[28] i.e., 1 in 3, and the
point 5 in. from the centre, then every revolution this point will
travel a distance

    2 {pi} _r_ = 2 × 22/7 × 5 = 31·34.

Now since the inclination is 1 in 3,[29] the propeller will travel
forward theoretically one-third of this distance, or

    31·43/3 = 10·48 = 10½ in. approx.

Similarly any other case may be dealt with. If the propeller have a
uniform _constant angle_ instead of a uniform pitch, then the pitch
may be calculated at a point about one-third the length of the blade
from the tip.

§ 13. =Hollow-Faced Blades.=[30]--It must always be carefully borne
in mind that a propeller is nothing more nor less than a particular
form of aeroplane specially designed to travel a helical path. It
should, therefore, be hollow faced and partake of the "stream line"
form, a condition not fulfilled if the face of the blade be flat--such
a surface cutting into the air with considerable shock, and by no
means creating as little undesirable motion in the surrounding medium
as possible.

It must not be forgotten that a curved face blade has of necessity an
increasing pitch from the cutting to the trailing edge (considering,
of course, any particular section). In such a case the pitch is the
_mean effective pitch_.

§ 14. =Blade Area.=--We have already referred to the fact that the
function of a propeller is to produce dynamic thrust--to drive the
aeroplane forward by driving the air backwards. At the same time it is
most desirable for efficiency that the air should be set in motion as
little as possible, this being so much power wasted; to obtain the
greatest reaction or thrust the greatest possible volume of air should
be accelerated to the smallest velocity.

In marine engineering in slow-speed propellers (where cavitation[31]
does not come in) narrow blades are usually used. In high-speed marine
propellers (where cavitation is liable to occur) the projected area of
the blades is sometimes as much as 0·6 of the total disk area. In the
case of aerial propellers, where cavitation does not occur, or not
unless the velocity be a very high one (1500 or more a minute), narrow
blades are the best. Experiments in marine propulsion also show that
the thrust depends more on the disk area than on the width of the
blades. All the facts tend to show that for efficiency the blades of
the propeller should be narrow, in order that the air may not be acted
on for too long a time, and so put too much in motion, and the blades
be so separated that one blade does not disturb the molecules of air
upon which the next following one must act. Both in the case of marine
and aerial propellers multiplicity of blades (i.e. increased blade
area) tends to inefficiency of action, apart altogether from the
question of weight and constructional difficulties. The question of
increasing pitch in the case of hollow-faced blades, considered in the
last paragraph, has a very important bearing on the point we are
considering. To make a wide blade under such circumstances would be to
soon obtain an excessive angle.

In the case of a flat blade the same result holds, because the air has
by the contact of its molecules with the "initial minimum width" been
already accelerated up to its final velocity, and further area is not
only wasted, but inimical to good flights, being our old bugbear
"weight in excess."

Requisite strength and stiffness, of course, set a limit on the final
narrowness of the blades, apart from other considerations.

§ 15. The velocity with which the propeller is rotated has also an
important bearing on this point; but a higher speed than 900 r.p.m.
does not appear desirable, and even 700 or less is generally
preferable.[32] In case of twin-screw propellers, with an angle at the
tips of 40° to 45°, as low a velocity of 500 or even less would be
still better.[33]

§ 16. =Shrouding.=--No improvement whatever is obtained by the use of
any kind of shrouding or ring round the propeller tips, or by
corrugating the surface of the propeller, or by using cylindrical or
cone-shaped propeller chamber or any kind of air guide either before
or after the propeller; allow it to revolve in as free an air-feed as
possible, the air does not fly off under centrifugal force, but is
powerfully sucked inwards in a well-designed propeller.

[Illustration: FIG. 25.

A TUBE OF AIR.]

[Illustration: FIG. 26.

A CYLINDER OF AIR.]

§ 17. =General Design.=--The propeller should be so constructed as to
act upon a tube and not a "cylinder" of air. Many flying toys
(especially the French ones) are constructed with propellers of the
cylinder type. Ease of manufacture and the contention that those
portions of the blades adjacent to the boss do little work, and a
slight saving in weight, are arguments that can be urged in their
favour. But all the central cut away part offers resistance in the
line of travel, instead of exerting its proportionate propulsive
power, and their efficiency is affected by such a practice.

§ 18. A good =Shape= for the blades[34] is rectangular with rounded
corners; the radius of the circle for rounding off the corners may be
taken as about one-quarter of the width of the blade. The shape is not
_truly rectangular, for the width of this rectangular at (near) the
boss should be one-half the width at the tip_.

The thickness should diminish uniformly from the boss to the tip. (In
models the thickness should be as little as is consistent with
strength to keep down the weight). _The pitch uniform and large._

[Illustration: FIG. 27.--O T = 1/3 O P.]

§ 19. =The Blades, two in number=, and hollow faced--the maximum
concavity being one-third the distance from the entering to the
trailing edge; the ratio of A T to O P (the width) being 0·048 or 1 :
21, these latter considerations being founded on the analogy between a
propeller and the aerofoil surface. (If the thickness be varied from
the entering to the trailing edge the greatest thickness should be
towards the former.) The convex surface of the propeller must be taken
into account, in fact, it is no less important than the concave, and
the entire surface must be given a true "stream line" form.

[Illustration: FIG. 28.]

[Illustration: FIG. 29.]

If the entering and trailing edge be not both straight, but one be
curved as in Fig. 28, then the straight edge must be made the
_trailing_ edge. And if both be curved as in Fig. 29, then the
_concave_ edge must be the trailing edge.

§ 19. =Propeller Design.=--To design a propeller, proceed as follows.
Suppose the diameter 14 in. and the pitch three times the diameter,
i.e. 52 in. (See Fig. 30.)

Take one-quarter scale, say. Draw a centre line A B of convenient
length, set of half the pitch 52 in. -- ¼ scale = 5¼ in. = C - D.
Draw lines through C and D at right angles to C D.

With a radius equal to half the diameter (i.e. in this case 1¾ in.)
of the propeller, describe a semicircle E B F and complete the
parallelogram F H G E. Divide the semicircle into a number of equal
parts; twelve is a convenient number to take, then each division
subtends an angle of 15° at the centre D.

Divide one of the sides E G into the same number of equal parts
(twelve) as shown. Through these points draw lines parallel to F E or
H G.

And through the twelve points of division on the semicircle draw lines
parallel to F H or E G as shown. The line drawn through the successive
intersections of these lines is the path of the tip of the blade
through half a revolution, viz. the line H S O T E.

S O T X gives the angle at the tip of the blades = 44°.

Let the shape of the blade be rectangular with rounded corners, and
let the breadth at the tip be twice that at the boss.

Then the area (neglecting the rounded off corners) is 10½ sq. in.

[Illustration: FIG. 30.--PROPELLER DESIGN.

One quarter scale. Diameter 14 in. Pitch 52 in. Angle at tip 44°.]

The area being that of a rectangle 7 in. × 1 in. = 7 sq. in. plus area
of two triangles, base ½ in., height 7 in. Now area of triangle =
half base × height. Therefore area of both triangles = ½ in. × 7
in. = 3½ sq. in. Now the area of the disc swept out by the
propeller is

    {pi}/4 × (diam.)²  ({pi} = 22/7)

[Illustration: FIG. 31.--PROPELLER DESIGN.

Scale one-eighth for A B and B C; but sections of blade are
full-sized.]

And if _d_ A _r_ = the "disc area ratio" we have

    (_d_ A _r_) × {pi}/4 × (14)² = area of blade = 10½,

whence _d_ A _r_ = 0·07 about.

[Illustration: FIG. 32.]

[Illustration: FIG. 33.]

In Fig. 31 set off A B equal to the pitch of the propeller (42 in.),
one-eighth scale. Set off B C at right angles to A B and equal to

    {pi} × diameter = 22/7 × 14 = 44 in. to scale 5½ in.

Divide B C into a convenient number of equal parts in the figure; five
only are taken, D, E, F, G, H; join A D, A E, A F, A G, A H and
produce them; mark off distances P O, S R, Y T ... equal to the width
of the blade at these points (H P = H O; G S = G R ...) and sketch in
the sections of blade as desired. In the figure the greatest concavity
of the blade is supposed to be one-third the distances P O, S R ...
from PS.... The concavity is somewhat exaggerated. The angles A H B, A
G B, A F B ... represent the pitch angle at the points H, G, F ... of
the blade.

Similarly any other design may be dealt with; in a propeller of 14 in.
diameter the diameter of the "boss" should not be more than 10/16 in.

§ 20. =Experiments with Propellers.=--The propeller design shown in
Figs. 32 and 33, due to Mr. G. de Havilland,[35] is one very suitable
for experimental purposes. A single tube passing through a T-shaped
boss forms the arms. On the back of the metal blade are riveted four
metallic clips; these clips being tightened round the arm by
countersunk screws in the face of the blade.

The tube and clips, etc., are all contained with the back covering of
the blade, as shown in Fig. 35, if desired, the blade then practically
resembling a wooden propeller. The construction, it will be noticed,
allows of the blade being set at any angle, constant or otherwise;
also the pitch can be constant or variable as desired, and any "shape"
of propeller can be fitted.

The advantage of being able to _twist_ the blade (within limits) on
the axis is one not to be underestimated in experimental work.

[Illustration: FIG. 34.--THE AUTHOR'S PROPELLER TESTING APPARATUS.]

With a view to ascertain some practical and reliable data with respect
to the _dynamic_, or actual thrust given when moving through free air
at the velocity of actual travel, the author experimented with the
apparatus illustrated in Figs. 34 and 35, which is so simple and
obvious as to require scarcely any explanation.

The wires were of steel, length not quite 150 ft., fitted with wire
strainers for equalising tension, and absolutely free from "kinks."
As shown most plainly in Fig. 35, there were two parallel wires
sufficiently far apart for the action of one propeller not to affect
the other. Calling these two wires A and B, and two propellers _x_ and
_y_, then _x_ is first tried on A and _y_ on B. Results carefully
noted.

[Illustration: FIG. 35.--PROPELLER TESTING.

Showing distance separating the two wires.]

Then _x_ is tried on B and _y_ on A, and the results again carefully
noted. If the results confirm one another, the power used in both
cases being the same, well and good; if not, adjustments, etc., are
made in the apparatus until satisfactory results are obtained. This
was done when the propellers "raced" one against the other. At other
times one wire only was made use of, and the time and distance
traversed was noted in each case. Propellers were driven through
smoke, and with silk threads tied to a light framework slightly larger
than their disc area circumference. Results of great interest were
arrived at. These results have been assumed in much that has been said
in the foregoing paragraphs.

[Illustration: FIG. 36.--ONE GROUP OF PROPELLERS TESTED BY THE AUTHOR.]

Briefly put, these results showed:--

1. The inefficiency of a propeller of the fan blower or of the static
thrust type.

2. The advantage of using propellers having hollow-faced blades and
large diameter.

3. That diameter was more useful than blade area, i.e. given a certain
quantity (weight) of wood, make a long thin blade and not a shorter
one of more blade area--blade area, i.e., as proportionate to its
corresponding disc area.

4. That the propeller surface should be of true stream-line form.

5. That it should act on a cylinder and not tubes of air.

6. That a correctly designed and proportioned propeller was just as
efficacious in a small size of 9 in. to 28 in. as a full-sized
propeller on a full-sized machine.

[Illustration: FIG. 37.--AN EFFICIENT PROPELLER, BUT RATHER HEAVY.

Ball bearings, old and new. Note difference in sizes and weights.
Propeller, 14 in. diam.; weight 36 grammes.]

A propeller of the static-thrust type was, of course, "first off,"
sometimes 10 ft. or 12 ft. ahead, or even more; but the correctly
designed propeller gradually gathered up speed and acceleration, just
as the other fell off and lost it, and finally the "dynamic" finished
along its corresponding wire far ahead of the "static," sometimes
twice as far, sometimes six times. "Freak" propellers were simply not
in it.

[Illustration: FIG. 38.--"VENNA" PROPELLER.

A 20 per cent. more efficient propeller than that shown in Fig. 41; 14
per cent. lighter; 6 per cent. better in dynamic thrust--14 in. diam.;
weight 31 grammes.]

Metal propellers of constant angle, as well as wooden ones of uniform
(constant) pitch, were tested; the former gave good results, but not
so good as the latter.

The best angle of pitch (at the tip) was found to be from 20° to 30°.

In all cases when the slip was as low as 25 per cent., or even
somewhat less, nearly 20 per cent., a distinct "back current" of air
was given out by the screw. This "slip stream," as it is caused, is
absolutely necessary for efficiency.

§ 21. =Fabric-covered= screws did not give very efficient results; the
only point in their use on model aeroplanes is their extreme
lightness. Two such propellers of 6 in. diameter can be made to weigh
less than 1/5 oz. the pair; but wooden propellers (built-up principle)
have been made 5 in. diameter and 1/12 oz. in weight.

§ 22. Further experiments were made with twin screws mounted on model
aeroplanes. In one case two propellers, both turning in the _same_
direction, were mounted (without any compensatory adjustment for
torque) on a model, total weight 1½ lb. Diameter of each propeller
14 in.; angle of blade at tip 25°. The result was several good
flights--the model (_see_ Fig. 49c) was slightly unsteady across the
wind, that was all.

In another experiment two propellers of same diameter, pitch, etc.,
but of shape similar to those shown in Figs. 28 and 29, were tried as
twin propellers on the same machine. The rubber motors were of equal
weight and strength.

The model described circled to the right or left according to the
position of the curved-shaped propeller, whether on the left or right
hand, thereby showing its superiority in dynamic thrust. Various
alterations were made, but always with the same result. These
experiments have since been confirmed, and there seems no doubt that
the double-curved shaped blade _is_ superior. (See Fig. 39.)

§ 23. =The Fleming-Williams Propeller.=--A chapter on propellers would
scarcely be complete without a reference to the propeller used on a
machine claiming a record of over a quarter of a mile. This form of
propeller, shown in the group in Fig. 36 (top right hand), was found
by the writer to be extremely deficient in dynamic thrust, giving the
worst result of any shown there.

[Illustration: FIG. 39.--CURVED DOUBLE PROPELLER.

The most efficient type yet tested by the writer, when the blade is
made hollow-faced. When given to the writer to test it was flat-faced
on one side.]

[Illustration: FIG. 40.--THE FLEMING-WILLIAMS MODEL.]

It possesses large blade area, large pitch angle--more than 45° at the
tip--and large diameter. These do not combine to propeller efficiency
or to efficient dynamic thrust; but they do, of course, combine to
give the propeller a very slow rotational velocity. Provided they give
_sufficient_ thrust to cause the model to move through the air at a
velocity capable of sustaining it, a long flight may result, not
really owing to true efficiency on the part of the propellers,[36] but
owing to the check placed on their revolutions per minute by their
abnormal pitch angle, etc. The amount of rubber used is very great for
a 10 oz. model, namely, 34 strands of 1/16 in. square rubber to each
propeller, i.e. 68 strands in all.

[Illustration: FIG. 41.--THE SAME IN FLIGHT.

(_Reproduced by permission from "The Aero."_)]

On the score of efficiency, when it is desired to make a limited
number of turns give the longest flight (which is the problem one
always has to face when using a rubber motor) it is better to make use
of an abnormal diameter, say, more than half the span, and using a tip
pitch angle of 25°, than to make use of an abnormal tip pitch 45° and
more, and large blade area. In a large pitch angle so much energy is
wasted, not in dynamic thrust, but in transverse upsetting torque. On
no propeller out of dozens and dozens that I have tested have I ever
found a tip-pitch of more than 35° give a good dynamic thrust; and for
length of flight velocity due to dynamic thrust must be given due
weight, as well as the duration of running down of the rubber motor.

§ 24. Of built up or carved out and twisted wooden propellers, the
former give the better result; the latter have an advantage, however,
in sometimes weighing less.

FOOTNOTES:

[24] _Note._--Since the above was written some really remarkable
flights have been obtained with a 1 oz. model having two screws, one
in front and the other behind. Equally good flights have also been
obtained with the two propellers behind, one revolving in the
immediate rear of the other. Flying, of course, with the wind,
_weight_ is of paramount importance in these little models, and in
both these cases the "single stick" can be made use of. _See also_ ch.
iv., § 28.

[25] _See also_ ch. viii., § 5.

[26] Save in case of some models with fabric-covered propellers. Some
dirigibles are now being fitted with four-bladed wooden screws.

[27] Vide Appendix.

[28] Vide Equivalent Inclinations--Table of.

[29] One in 3 or 0·333 is the _sine_ of the angle; similarly if the
angle were 30° the sine would be 0·5 or ½, and the theoretical
distance travelled one-half.

[30] _Flat-Faced Blades._--If the blade be not hollow-faced--and we
consider the screw as an inclined plane and apply the Duchemin formula
to it--the velocity remaining the same, the angle of maximum thrust is
35¼°. Experiments made with such screws confirm this.

[31] Cavitation is when the high speed of the screw causes it to carry
round a certain amount of the medium with it, so that the blades
strike no undisturbed, or "solid," air at all, with a proportionate
decrease in thrust.

[32] In the Wright machine r.p.m. = 450; in Blériot XI. r.p.m. = 1350.

[33] Such propellers, however, require a considerable amount of
rubber.

[34] But _see also_ § 22.

[35] "Flight," March 10, 1910. (Illustration reproduced by
permission.)

[36] According to the author's views on the subject.




CHAPTER VI.

THE QUESTION OF SUSTENTATION THE CENTRE OF PRESSURE.


§ 1. Passing on now to the study of an aeroplane actually in the air,
there are two forces acting on it, the upward lift due to the air
(i.e. to the movement of the aeroplane supposed to be continually
advancing on to fresh, undisturbed _virgin_ air), and the force due to
the weight acting vertically downwards. We can consider the resultant
of all the upward sustaining forces as acting at a single point--that
point is called the "Centre of Pressure."

Suppose A B a vertical section of a flat aerofoil, inclined at a small
angle _a_ to the horizon C, the point of application of the resultant
upward 'lift,' D the point through which the weight acts vertically
downwards. Omitting for the moment the action of propulsion, if these
two forces balance there will be equilibrium; but to do this they must
pass through the same point, but as the angle of inclination varies,
so does the centre of pressure, and some means must be employed
whereby if C and D coincide at a certain angle the aeroplane will come
back to the correct angle of balance if the latter be altered.

In a model the means must be automatic. Automatic stability depends
for its action upon the movement of the centre of pressure when the
angle of incidence varies. When the angle of incidence increases the
centre of pressure moves backwards towards the rear of the aerofoil,
and vice versa.

Let us take the case when steady flight is in progress and C and D are
coincident, suppose the velocity of the wind suddenly to
increase--increased lifting effect is at once the result, and the fore
part of the machine rises, i.e. the angle of incidence increases and
the centre of pressure moves back to some point in the rear of C D.
The weight is now clearly trying to pull the nose of the aeroplane
down, and the "lift" tending to raise the tail. The result being an
alteration of the angle of incidence, or angle of attack as it is
called, until it resumes its original position of equilibrium. A drop
in the wind causes exactly an opposite effect.

[Illustration: FIG. 42.]

§ 2. The danger lies in "oscillations" being set up in the line of
flight due to changes in the position of the centre of pressure. Hence
the device of an elevator or horizontal tail for the purpose of
damping out such oscillations.

§ 3. But the aerofoil surface is not flat, owing to the increased
"lift" given by arched surfaces, and a much more complicated set of
phenomena then takes place, the centre of pressure moving forward
until a certain critical angle of incidence is reached, and after
this a reversal takes place, the centre of pressure then actually
moving backwards.

The problem then consists in ascertaining the most efficient aerocurve
to give the greatest "lift" with the least "drift," and, having found
it, to investigate again experimentally the movements of the centre of
pressure at varying angles, and especially to determine at what angle
(about) this "reversal" takes place.

[Illustration: FIG. 43.]

§ 4. Natural automatic stability (the only one possible so far as
models are concerned) necessitates permanent or a permanently
recurring coincidence (to coin a phrase) of the centre of gravity and
the centre of pressure: the former is, of course, totally unaffected
by the vagaries of the latter, any shifting of which produces a couple
tending to destroy equilibrium.

§ 5. As to the best form of camber (for full sized machine) possibly
more is known on this point than on any other in the whole of
aeronautics.

In Figs. 44 and 45 are given two very efficient forms of cambered
surfaces for models.

[Illustration: FIG. 44.--AN EFFICIENT FORM OF CAMBER.

  B D Maximum Altitude.        A C Chord.
  Ratio of B D: A C :: 1:17.   A D 1/3 of A C.]

[Illustration: FIG. 45.--ANOTHER EFFICIENT FORM.

Ratio of B D to A C 1 to 17. AD rather more than ¼ of A C.]

The next question, after having decided the question of aerocurve, or
curvature of the planes, is at what angle to set the cambered surface
to the line of flight. This brings us to the question of the--

§ 6. =Dipping Front Edge.=--The leading or front edge is not
tangential to the line of flight, but to a relative upward wind. It is
what is known as the "cyclic up-current," which exists in the
neighbourhood of the entering edge. Now, as we have stated before, it
is of paramount importance that the aerofoil should receive the air
with as little shock as possible, and since this up-current does
really exist to do this, it must travel through the air with a dipping
front edge. The "relative wind" (the only one with which we are
concerned) _is_ thereby met tangentially, and as it moves onward
through the air the cambered surface (or aerocurve) gradually
transforms this upward trend into a downward wake, and since by
Newton's law, "Action and reaction are equal and opposite," we have
an equal and opposite upward reaction.

We now know that the top (or convex side) of the cambered surface is
practically almost as important as the underneath or concave side in
bringing this result about.

The exact amount of "dipping edge," and the exact angle at which the
chord of the aerocurve, or cambered surface, should be set to the line
of flight--whether at a positive angle, at no angle, or at a negative
angle--is one best determined by experiment on the model in question.

[Illustration: FIG. 46.]

But _if at any angle, that angle either way should be a very small
one_. If you wish to be very scientific you can give the underside of
the front edge a negative angle of 5° to 7° for about one-eighth of
the total length of the section, after that a positive angle,
gradually increasing until you finally finish up at the trailing edge
with one of 4°. Also, the form of cambered surface should be a
paraboloid--not arc or arc of circles. The writer does not recommend
such an angle, but prefers an attitude similar to that adopted in the
Wright machine, as in Fig. 47.

§ 7. Apart from the attitude of the aerocurve: _the greatest depth of
the camber should be at one-third of the length of the section from
the front edge, and the total depth measured from the top surface to
the chord at this point should not be more than one-seventeenth of the
length of section_.

§ 8. It is the greatest mistake in model aeroplanes to make the camber
otherwise than very slight (in the case of surfaced aerofoils the
resistance is much increased), and aerofoils with anything but a _very
slight_ arch are liable to be very unstable, for the aerocurve has
always a decided tendency to "follow its own curve."

[Illustration: FIG. 47.--ATTITUDE OF WRIGHT MACHINE.]

The nature of the aerocurve, its area, the angle of inclination of its
chord to the line of flight, its altitude, etc., are not the only
important matters one must consider in the case of the aerofoil, we
must also consider--

§ 9. Its =Aspect Ratio=, i.e. the ratio of the span (length) of the
aerofoil to the chord--usually expressed by span/chord. In the Farman
machine this ratio is 5·4; Blériot, 4·3; Short, 6 to 7·5; Roe
triplane, 7·5; a Clark flyer, 9·6.

Now the higher the aspect ratio the greater should be the efficiency.
Air escaping by the sides represents loss, and the length of the sides
should be kept short. A broader aerofoil means a steeper angle of
inclination, less stability, unnecessary waste of power, and is
totally unsuited for a model--to say nothing of a full-sized machine.

In models this aspect ratio may with advantage be given a higher value
than in full-sized machines, where it is well known a practical safe
constructional limit is reached long before theory suggests the
limit. The difficulty consists in constructing models having a very
high aspect ratio, and yet possessing sufficient strength and
lightness for successful flight. It is in such a case as this where
the skill and ingenuity of the designer and builder come in.

It is this very question of aspect ratio which has given us the
monoplane, the biplane, and the triplane. A biplane has a higher
aspect ratio than a monoplane, and a triplane (see above) a higher
ratio still.

It will be noticed the Clark model given has a considerably higher
aspect ratio, viz. 9·6. And even this can be exceeded.

_An aspect ratio of_ 10:1 _or even_ 12:1 _should be used if
possible._[37]

§ 10. =Constant or Varying Camber.=--Some model makers vary the camber
of their aerofoils, making them almost flat in some parts, with
considerable camber in others; the tendency in some cases being to
flatten the central portions of the aerofoil, and with increasing
camber towards the tips. In others the opposite is done. The writer
has made a number of experiments on this subject, but cannot say he
has arrived at any very decisive results, save that the camber should
in all cases be (as stated before) very slight, and so far as his
experiments do show anything, they incline towards the further
flattening of the camber in the end portions of the aerofoil. It must
not be forgotten that a flat-surfaced aerofoil, constructed as it is
of more or less elastic materials, assumes a natural camber, more or
less, when driven horizontally through the air. Reference has been
made to a reversal of the--

§ 11. =Centre of Pressure on Arched Surfaces.=--Wilbur Wright in his
explanation of this reversal says: "This phenomenon is due to the fact
that at small angles the wind strikes the forward part of the aerofoil
surface on the upper side instead of the lower, and thus this part
altogether ceases to lift, instead of being the most effective part of
all." The whole question hangs on the value of the critical angle at
which this reversal takes place; some experiments made by Mr. M.B.
Sellers in 1906 (published in "Flight," May 14, 1910) place this angle
between 16° and 20°. This angle is much above that used in model
aeroplanes, as well as in actual full-sized machines. But the
equilibrium of the model might be upset, not by a change of attitude
on its part, but on that of the wind, or both combined. By giving (as
already advised) the aerofoil a high aspect ratio we limit the travel
of the centre of pressure, for a high aspect ratio means, as we have
seen, a short chord; and this is an additional reason for making the
aspect ratio as high as practically possible. The question is, is the
critical angle really as high as Mr. Seller's experiments would show.
Further experiments are much needed.

FOOTNOTES:

[37] Nevertheless some models with a very low aspect ratio make good
flyers, owing to their extreme lightness.




CHAPTER VII.

MATERIALS FOR AEROPLANE CONSTRUCTION.


§ 1. The choice of materials for model aeroplane construction is more
or less limited, if the best results are to be obtained. The lightness
absolutely essential to success necessitates--in addition to skilful
building and best disposition of the materials--materials of no undue
weight relative to their strength, of great elasticity, and especially
of great resilience (capacity to absorb shock without injury).

§ 2. =Bamboo.=--Bamboo has per pound weight a greater resilience than
any other suitable substance (silk and rubber are obviously useless as
parts of the _framework_ of an aeroplane). On full-sized machines the
difficulty of making sufficiently strong connections and a liability
to split, in the larger sizes, are sufficient reasons for its not
being made more use of; but it makes an almost ideal material for
model construction. The best part to use (split out from the
centrepiece) is the strip of tough wood immediately below the hard
glazed surface. For struts, spars, and ribs it can be used in this
manner, and for the long strut supporting the rubber motor an entire
tube piece should be used of the requisite strength required; for an
ordinary rubber motor (one yard long), 30 to 50 strands, this should
be a piece 3/8 in. in diameter, and weight about 5/8 oz. per ft.
_Bamboo may be bent_ by either the "dry" heat from a spirit lamp or
stove, or it may be steamed, the latter for preference, as there is
no danger of "scorching" the fibres on the inside of the bend. When
bent (as in the case of other woods) it should be bound on to a
"former" having a somewhat greater curvature than the curve required,
because when cool and dry it will be sure to "go back" slightly. It
must be left on the former till quite dry. When bending the "tube"
entire, and not split portions thereof, it should be immersed in very
hot, or even boiling, water for some time before steaming. The really
successful bending of the tube _en bloc_ requires considerable
patience and care.

Bamboo is inclined to split at the ends, and some care is required in
making "joints." The ribs can be attached to the spars by lashing them
to thin T strips of light metal, such as aluminium. Thin thread, or
silk, is preferable to very thin wire for lashing purpose, as the
latter "gives" too much, and cuts into the fibres of the wood as well.

§ 3. =Ash=, =Spruce=, =Whitewood= are woods that are also much used by
model makers. Many prefer the last named owing to its uniform freedom
from knots and ease with which it can be worked. It is stated 15 per
cent. additional strength can be imparted by using hot size and
allowing it to soak into the wood at an increase only of 3·7 per cent.
of weight. It is less than half the weight of bamboo, but has a
transverse rupture of only 7,900 lb. per sq. in. compared to 22,500 in
the case of bamboo tubing (thickness one-eighth diameter) and a
resilience per lb. weight of slightly more than one half. Some model
makers advocate the use of =poplar= owing to its extreme lightness
(about the same as whitewood), but its strength is less in the ratio
of about 4:3; its resilience is very slightly more. It must be
remembered that wood of the same kind can differ much as to its
strength, etc., owing to what part of the tree it may have been cut
from, the manner in which it may have been seasoned, etc. For model
aeroplanes all wood used should have been at least a year in
seasoning, and should be so treated when in the structure that it
cannot absorb moisture.

If we take the resilience of ash as 1, then (according to Haswell)
relative resilience of beech is 0·86, and spruce 0·64.

The strongest of woods has a weight when well seasoned of about 40 lb.
per cub. ft. and a tenacity of about 10,000 lb. per sq. in.

[Illustration: FIG. 47A.--"AEROPLANE ALMA."

A very effective French Toy Monoplane.]

§ 4. =Steel.=--Ash has a transverse rupture of 14,300 lb. per sq. in.,
steel tubing (thickness = 1/30 its diameter) 100,000 lb. per sq. in.
Ash weighs per cub. ft. 47 lb., steel 490. Steel being more than ten
times as heavy as ash--but a transverse rupture stress seven times as
high.

Bamboo in tube form, thickness one-third of diameter, has a
transverse rupture of 22,500 lb. per sq. in., and a weight of 55 lb.
per cub. ft.

Steel then is nine times as heavy as bamboo--and has a transverse
rupture stress 4·4 times as great. In comparing these three substances
it must be carefully borne in mind that lightness and strength are not
the only things that have to be provided for in model aeroplane
building; there is the question of _resistance_--we must offer as
small a cross-section to moving through the air as possible.

Now while ash or bamboo and certain other timbers may carry a higher
load per unit of weight than steel, they will present about three to
three and a half times the cross-section, and this produces a serious
obstacle, while otherwise meeting certain requirements that are most
desirable. Steel tubing of sufficiently small bore is not, so far as
the writer knows, yet on the market in England. In France very thin
steel tubes are made of round, oval, hexagon, etc., shape, and of
accurate thickness throughout, the price being about 18s. a lb.

Although suitable steel tubing is not yet procurable under ordinary
circumstances, umbrella steel is.

§ 5. =Umbrella Section Steel= is a section 5/32 in. by 1/8 in. deep, 6
ft. long weighing 2·1 oz., and a section 3/32 in. across the base by
1/8 in. deep, 6 ft. long weighing 1·95 oz.

It is often stated that umbrella ribs are too heavy--but this entirely
depends on the length you make use of, in lengths of 25 in. for small
aerofoils made from such lengths it is so; but in lengths of 48 in.
(two such lengths joined together) the writer has used it with great
success; often making use of it now in his larger models; the
particular size used by him weighs 13½ grammes, to a length of 25
in. He has never had one of these aerofoils break or become
kinked--thin piano wire is used to stay them and also for spars when
employed--the front and ends of the aerofoil are of umbrella steel,
the trailing edge of steel wire, comparatively thin, kept taut by
steel wire stays.

§ 6. =Steel Wire.=--Tensile strength about 300,000 lb. per sq. in. For
the aerofoil framework of small models and for all purposes of
staying, or where a very strong and light tension is required, this
substance is invaluable. Also for framework of light fabric covered
propellers as well as for skids and shock absorber--also for hooks to
hold the rubber motor strands, etc. No model is complete without it in
some form or another.

§ 7. =Silk.=--This again is a _sine qua non_. Silk is the strongest of
all organic substances for certain parts of aeroplane construction. It
has, in its best form, a specific gravity of 1·3, and is three times
as strong as linen, and twice as strong in the thread as hemp. Its
finest fibres have a section of from 0·0010 to 0·0015 in diameter. It
will sustain about 35,000 lb. per sq. in. of its cross section; and
its suspended fibre should carry about 150,000 ft. of its own
material. This is six times the same figure for aluminium, and equals
about 75,000 lb. steel tenacity, and 50 more than is obtained with
steel in the form of watch springs or wire. For aerofoil surface no
substance can compare with it. But it must be used in the form of an
"oiled" or specially treated silk. Several such are on the market.
Hart's "fabric" and "radium" silk are perhaps the best known. Silk
weighs 62 lb. per cub. ft., steel has, we have seen, 490 lb., thus
paying due regard to this and to its very high tensile strength it is
superior to even steel wire stays.

§ 8. =Aluminium and Magnalium.=--Two substances about which a great
deal has been heard in connection with model aeroplaning; but the
writer does not recommend their use save in the case of fittings for
scale models, not actual flyers, unless especially light ones meant
to fly with the wind. Neither can compare with steel. Steel, it is
true, is three times as heavy as aluminium, but it has four or five
times its strength; and whereas aluminium and magnalium may with
safety be given a permissible breaking strength of 60 per cent. and 80
per cent. respectively, steel can easily be given 80 per cent. Being
also less in section, resistance to air travel is again less as in the
case of wood. In fact, steel scores all round. Weight of magnalium :
weight of aluminium :: 8:9.

§ 9. =Alloys.=--During recent years scores, hundreds, possibly
thousands of different alloys have been tried and experimented on, but
steel still easily holds its own. It is no use a substance being
lighter than another volume for volume, it must be _lighter and
stronger weight for weight_, to be superior for aeronautical purpose,
and if the difference be but slight, question of _bulk_ may decide it
as offering _less resistance_.

§ 10. =Sheet Ebonite.=--This substance is sometimes useful for
experiments with small propellers, for it can be bent and moulded in
hot water, and when cold sets and keeps its shape. _Vulcanized fibre_
can be used for same purpose. _Sheet celluloid_ can be used in the
same way, but in time it becomes brittle and shrinks. _Mica_ should be
avoided. _Jointless cane_ in various sizes is a very useful
material--the main aerofoil can be built of it, and it is useful for
skids, and might be made more use of than it is.[38] _Three ply wood_,
from 1/50 in. in thickness, is now on the market. Four or five ply
wood can also be obtained. To those desiring to build models having
wooden aerofoils such woods offer the advantage of great strength and
extreme lightness.

Referring to Table V. (Timber) at the end of the book, apparently the
most suitable wood is Lombardy poplar; but its light weight means
increased bulk, i.e. additional air resistance. Honduras mahogany is
really a better all-round wood, and beech is not far behind.

Resilience is an important factor. Ash heads the list; but mahogany's
factor is also good, and in other respects superior.

Lombardy poplar ought to be a very good wood for propellers, owing to
its lightness and the ease with which it can be worked.

_Hollow reeds_, and even _porcupine quills_, have been pressed into
the service of the model maker, and owing to their great strength and
extreme lightness, more especially the latter, are not without their
uses.

FOOTNOTES:

[38] The chief advantage of cane--its want of stiffness, or facility
in bending--is for some parts of the machine its chief disadvantage,
where stiffness with resilience is most required.




CHAPTER VIII.

HINTS ON THE BUILDING OF MODEL AEROPLANES.


§ 1. The chief difficulty in the designing and building of model
aeroplanes is to successfully combat the conflicting interests
contained therein. Weight gives stability, but requires extra
supporting surface or a higher speed, i.e. more power, i.e. more
weight. Inefficiency in one part has a terrible manner of repeating
itself; for instance, suppose the aerofoil surface inefficient--badly
designed--this means more resistance; more resistance means more
power, i.e. weight, i.e. more surface, and so on _ad infinitum_.

It is because of circumstances like the above that it is so difficult
to _design_ really good and efficient flying models; the actual
building of them is not so difficult, but few tools are required, none
that are expensive or difficult to use.

In the making of any particular model there are special points that
require special attention; but there are certain general rules and
features which if not adhered to and carefully carried out, or as
carefully avoided, will cause endless trouble and failure.

§ 2. In constructing a model aeroplane, or, indeed, any piece of
aerial apparatus, it is very important not to interrupt the continuity
of any rib, tube, spar, etc., by drilling holes or making too thinned
down holding places; if such be done, additional strength by binding
(with thread, not wire), or by slipping a small piece of slightly
larger tube over the other, must be imparted to the apparatus.

§ 3. Begin by making a simple monoplane, and afterwards as you gain
skill and experience proceed to construct more elaborate and
scientific models.

§ 4. Learn to solder--if you do not know how to--it is absolutely
essential.

§ 5. Do not construct models (intended for actual flight) with a
tractor screw-main plane in front and tail (behind). Avoid them as you
would the plague. Allusion has already been made in the Introduction
to the difficulty of getting the centre of gravity sufficiently
forward in the case of Blériot models; again with the main aerofoil in
front, it is this aerofoil and not the balancing elevator, or tail,
that _first_ encounters the upsetting gust, and the effect of such a
gust acting first on the larger surface is often more than the
balancer can rectify in time to avert disaster. The proper place for
the propeller is behind, in the wake of the machine. If the screw be
in front the backwash from it strikes the machine and has a decidedly
retarding action. It is often contended that it drives the air at an
increased velocity under (and over) the main aerofoil, and so gives a
greater lifting effect. But for proper lifting effect which it can
turn without effort into air columns of proper stream line form what
the aerofoil requires is undisturbed air--not propeller backwash.

The rear of the model is the proper place for the propeller, in the
centre of greatest air disturbance; in such a position it will recover
a portion of the energy lost in imparting a forward movement to the
air, caused by the resistance, the model generally running in such
air--the slip of the screw is reduced to a corresponding degree--may
even vanish altogether, and what is known as negative slip occur.

§ 6. Wooden or metal aerofoils are more efficient than fabric covered
ones. But they are only satisfactory in the smaller sizes, owing, for
one thing, to the smash with which they come to the ground. This being
due to the high speed necessary to sustain their weight. For
larger-sized models fabric covered aerofoils should be used.

§ 7. As to the shape of such, only three need be considered--the (_a_)
rectangular, (_b_) the elongated ellipse, (_c_) the chamfered rear
edge.

[Illustration: FIG. 48.--(_a_), (_b_), (_c_).]

§ 8. The stretching of the fabric on the aerofoil framework requires
considerable care, especially when using silk. It is quite possible,
even in models of 3 ft. to 4 ft. spread, to do without "ribs," and
still obtain a fairly correct aerocurve, if the material be stretched
on in a certain way. It consists in getting a correct longitudinal and
transverse tension. We will illustrate it by a simple case. Take a
piece of thickish steel pianoforte wire, say, 18 in. long, bend it
round into a circle, allowing ½ in. to 1 in. to overlap, tin and
solder, bind this with soft very thin iron wire, and again solder
(always use as little solder as possible). Now stitch on to this a
piece of nainsook or silk, deforming the circle as you do so until it
has the accompanying elliptical shape. The result is one of double
curvature; the transverse curve (dihedral angle) can be regulated by
cross threads or wires going from A to B and C to D.

[Illustration: FIG. 49.]

[Illustration: FIG. 49A.--MR. T.W.K. CLARKE'S 1 OZ. MODEL.]

The longitudinal curve on the camber can be regulated by the original
tension given to it, and by the manner of its fixing to the main
framework. Suitable wire projections or loops should be bound to it by
wire, and these fastened to the main framework by binding with _thin_
rubber cord, a very useful method of fastening, since it acts as an
excellent shock absorber, and "gives" when required, and yet
possesses quite sufficient practical rigidity.

§ 9. Flexible joints are an advantage in a biplane; these can be made
by fixing wire hooks and eyes to the ends of the "struts," and holding
them in position by binding with silk or thread. Rigidity is obtained
by use of steel wire stays or thin silk cord.

[Illustration: FIG. 49B.--MR. T.W.K. CLARKE'S 1 OZ. MODEL.

Showing the position of C. of G., or point of support.]

§ 10. Owing to the extra weight and difficulties of construction on so
small a scale it is not desirable to use "double surface" aerofoils
except on large size power-driven models.

§ 11. It is a good plan not to have the rod or tube carrying the
rubber motor connected with the outrigger carrying the elevator,
because the torque of the rubber tends to twist the carrying
framework, and interferes with the proper and correct action of the
elevator. If it be so connected the rod must be stayed with piano
wire, both longitudinally (to overcome the pull which we know is very
great), and also laterally, to overcome the torque.

[Illustration: FIG. 49C.--A LARGE MODEL AEROPLANE.

Shown without rubber or propellers. Designed and constructed by the
writer. As a test it was fitted with two 14 in. propellers revolving
in the _same_ direction, and made some excellent flights under these
conditions, rolling slightly across the wind, but otherwise keeping
quite steady. Total weight, 1½ lb.; length, 6 ft.; span of main
aerofoil, 5 ft. Constructed of bamboo, cane, and steel wire. Front
skids steel wire. Back skids cane. Aerofoil covering nainsook.]


§ 12. Some builders place the rubber motor above the rod, or bow frame
carrying the aerofoils, etc., the idea being that the pull of the
rubber distorts the frame in such a manner as to "lift" the elevator,
and so cause the machine to rise rapidly in the air. This it does; but
the model naturally drops badly at the finish and spoils the effect.
It is not a principle that should be copied.

[Illustration: FIG. 49D.--A VERY LIGHT WEIGHT MODEL.

Constructed by the author. Provided with twin propellers of a modified
Fleming-Williams type. This machine flew well when provided with an
abnormal amount of rubber, owing to the poor dynamic thrust given by
the propellers.]

§ 13. In the Clarke models with the small front plane, the centre of
pressure is slightly in front of the main plane.

The balancing point of most models is generally slightly in front, or
just within the front edge of the main aerofoil. The best plan is to
adjust the rod carrying the rubber motor and propeller until the best
balance is obtained, then hang up the machine to ascertain the centre
of gravity, and you will have (approximately) the centre of pressure.

[Illustration: FIG. 49E.--USEFUL FITTINGS FOR MODELS.

1. Rubber tyred wheels. 2. Ball-bearing steel axle shafts. 3. Brass wire
strainers with steel screws; breaking strain 200 lb. 4. Magnalium
tubing. 5. Steel eyebolt. 6. Aluminium "T" joint. 7. Aluminium "L"
piece. 8. Brass brazed fittings. 9. Ball-bearing thrust. 10. Flat
aluminium "L" piece. (_The above illustrations taken (by permission)
from Messrs. Gamage's catalogue on Model Aviation._)]

§ 14. The elevator (or tail) should be of the non-lifting type--in
other words, the entire weight should be carried by the main aerofoil
or aerofoils; the elevator being used simply as a balancer.[39] If the
machine be so constructed that part of the weight be carried by the
elevator, then either it must be large (in proportion) or set up at a
large angle to carry it. Both mean considerably more resistance--which
is to be avoided. In practice this means the propeller being some
little distance in rear of the main supporting surface.

[Illustration: FIG. 49F.--USEFUL FITTINGS FOR MODELS.

11. Aluminium ball thrust and racket. 12. Ball-bearing propeller,
thrust, and stay.

(_The above illustrations taken (by permission) from Messrs. Gamage's
catalogue on Model Aviation._)]

§ 15. In actual flying models "skids" should be used and not "wheels";
the latter to be of any real use must be of large diameter, and the
weight is prohibitive. Skids can be constructed of cane, imitation
whalebone, steel watch or clock-spring, steel pianoforte wire. Steel
mainsprings are better than imitation whalebone, but steel pianoforte
wire best of all. For larger sized models bamboo is also suitable, as
also ash or strong cane.

§ 16. Apart from or in conjunction with skids we have what are termed
"shock absorbers" to lessen the shock on landing--the same substances
can be used--steel wire in the form of a loop is very effectual;
whalebone and steel springs have a knack of snapping. These shock
absorbers should be so attached as to "give all ways" for a part side
and part front landing as well as a direct front landing. For this
purpose they should be lashed to the main frame by thin indiarubber
cord.

§ 17. In the case of a biplane model the "gap" must not be less than
the "chord"--preferably greater.

In a double monoplane (of the Langley type) there is considerable
"interference," i.e. the rear plane is moving in air already acted on
by the front one, and therefore moving in a downward direction. This
means decreased efficiency. It can be overcome, more or less, by
varying the dihedral angle at which the two planes are set; but cannot
be got rid of altogether, or by placing them far apart. In biplanes
not possessing a dihedral angle--the propeller can be placed
_slightly_ to one side--in order to neutralise the torque of the
propeller--the best portion should be found by experiment--unless the
pitch be very large; with a well designed propeller this is not by any
means essential. If the propeller revolve clockwise, place it towards
the right hand of the machine, and vice versa.

§ 18. In designing a model to fly the longest possible distance the
monoplane type should be chosen, and when desiring to build one that
shall remain the longest time in the air the biplane or triplane type
should be adopted.[40] For the longest possible flight twin propellers
revolving in opposite directions[41] are essential. To take a concrete
case--one of the writer's models weighed complete with a single
propeller 8½ oz. It was then altered and fitted with two propellers
(same diameter and weight); this complete with double rubber weighed
10¼ oz. The advantage double the power. Weight increased only 20
per cent., resistance about 10 per cent., total 30 per cent. Gain 70
per cent. Or if the method of gearing advocated (see Geared Motors) be
adopted then we shall have four bunches of rubber instead of two, and
can thereby obtain so many more turns.[42] The length of the strands
should be such as to render possible at least a thousand turns.

The propellers should be of large diameter and pitch (not less than
35° at the tips), of curved shape, as advocated in § 22 ch. v.; the
aerofoil surface of as high an aspect ratio as possible, and but
slight camber if any; this is a very difficult question, the question
of camber, and the writer feels bound to admit he has obtained as long
flights with surfaces practically flat, but which do, of course,
camber slightly in a suitable wind, as with stiffer cambered surfaces.

Wind cambered surfaces are, however, totally unsuitable in gusty
weather, when the wind has frequently a downward trend, which has the
effect of cambering the surface the wrong way about, and placing the
machine flat on the ground. Oiled or specially prepared silk of the
lightest kind should be used for surfacing the aerofoils. Some form of
keel, or fin, is essential to assist in keeping the machine in a
straight course, combined with a rudder and universally jointed
elevator.

The manner of winding up the propellers has already been referred to
(_see_ chap. iii., § 9). A winder is essential.

Another form of aerofoil is one of wood (as in Clarke's flyers) or
metal, such a machine relying more on the swiftness of its flight than
on its duration. In this the gearing would possibly not be so
advantageous--but experiment alone could decide.

The weight of the machine would require to be an absolute minimum, and
everything not absolutely essential omitted.

It is quite possible to build a twin-screw model on one central stick
alone; but the isosceles triangular form of framework, with two
propellers at the base corners, and the rubber motors running along
the two sides and terminating at the vertex, is preferred by most
model makers. It entails, of course, extra weight. A light form of
skid, made of steel pianoforte wire, should be used. As to the weight
and size of the model, the now famous "one-ouncers" have made some
long flights of over 300 yards[43]; but the machine claiming the
record, half a mile,[44] weighs about 10 oz. And apart from this
latter consideration altogether the writer is inclined to think that
from 5 oz. to 10 oz. is likely to prove the most suitable. It is not
too large to experiment with without difficulty, nor is it so small as
to require the skill of a jeweller almost to build the necessary
mechanism. The propeller speed has already been discussed (_see_ ch.
v., § 15). The model will, of course, be flown with the wind. The
_total_ length of the model should be at least twice the span of the
main aerofoil.

FOOTNOTES:

[39] This is a good plan--not a rule. Good flying models can, of
course, be made in which this does not hold.

[40] This is in theory only: in practice the monoplane holds both
records.

[41] The best position for the propellers appears to be one in front
and one behind, when extreme lightness is the chief thing desired.

[42] Because the number of strands of rubber in each bunch will be
much less.

[43] Mr. Burge Webb claims a record of 500 yards for one of his.

[44] Flying, of course, with the wind. _Note._--In the "Model
Engineer" of July 7, 1910, will be found an interesting account (with
illustrations) of Mr. W.G. Aston's 1 oz. model, which has remained in
the air for over a minute.




CHAPTER IX.

THE STEERING OF THE MODEL.


§ 1. Of all the various sections of model aeroplaning that which is
the least satisfactory is the above.

The torque of the propeller naturally exerts a twisting or tilting
effect upon the model as a whole, the effect of which is to cause it
to fly in (roughly speaking) a circular course, the direction
depending on whether the pitch of the screw be a right or left handed
one. There are various devices by which the torque may be
(approximately) got rid of.

§ 2. In the case of a monoplane, by not placing the rod carrying the
rubber motor in the exact centre of the main aerofoil, but slightly to
one side, the exact position to be determined by experiment.

In a biplane the same result is obtained by keeping the rod in the
centre, but placing the bracket carrying the bearing in which the
propeller shaft runs at right angles horizontally to the rod to obtain
the same effect.

§ 3. The most obvious solution of the problem is to use _two_ equal
propellers (as in the Wright biplane) of equal and opposite pitch,
driven by two rubber motors of equal strength.

Theoretically this idea is perfect. In practice it is not so. It is
quite possible, of course, to use two rubber motors of an equal number
of strands (equality should be first tested by _weighing_). It should
be possible to obtain two propellers of equal and opposite pitch,
etc., and it is also possible to give the rubber motors the same
number of turns. In practice one is always wound up before the other.
This is the first mistake. They should be wound up _at the same time_,
using a double winder made for the purpose.

The fact that this is _not_ done is quite sufficient to give an
unequal torsion. The friction in both cases must also be exactly
equal. Both propellers must be released at exactly the same instant.

Supposing _all_ these conditions fulfilled (in practice they never
are), supposing also the propellers connected by gearing (prohibitive
on account of the weight), and the air quite calm (which it never is),
then the machine should and undoubtedly would _fly straight_.

For steering purposes by winding up one propeller _many more times_
than the other, the aeroplane can generally speaking be steered to the
right or left; but from what I have both seen and tried twin-screw
model aeroplanes are _not_ the success they are often made out to be,
and they are much more troublesome to deal with, in spite of what some
say to the contrary.

The solution of the problem of steering by the use of two propellers
is only partially satisfactory and reliable, in fact, it is no
solution at all.[45] The torque of the propeller and consequent
tilting of the aeroplane is not the only cause at work diverting the
machine from its course.

§ 4. As it progresses through the air it is constantly meeting air
currents of varying velocity and direction, all tending to make the
model deviate more or less from its course; the best way, in fact, the
only way, to successfully overcome such is by means of _speed_, by
giving the aeroplane a high velocity, not of ten or twelve to fifteen
miles an hour, as is usual in built up fabric-covered aerofoils, but a
velocity of twenty to thirty miles an hour, attainable only in models
(petrol or steam driven) or by means of wooden or metal aerofoils.

§ 5. Amongst devices used for horizontal steering are vertical "FINS."
These should be placed in the rear above the centre of gravity. They
should not be large, and can be made of fabric tightly stretched over
a wire frame, or of a piece of sheet magnalium or aluminium, turning
on a pivot at the front edge, adjustment being made by simply twisting
the fin round to the desired angle. As to the size, think of rudder
and the size of a boat, but allow for the difference of medium. The
frame carrying the pivot and fin should be made to slide along the rod
or backbone of the model in order to find the most efficient position.

§ 6. Steering may also be attempted by means of little balancing tips,
or ailerons, fixed to or near the main aerofoil, and pivoted (either
centrally or otherwise) in such a manner that they can be rotated one
in one direction (tilted) and the other in the other (dipped), so as
to raise one side and depress the other.

§ 7. The model can also be steered by giving it a cant to one side by
weighting the tip of the aerofoil on that side on which it is desired
it should turn, but this method is both clumsy and "weighty."

§ 8. Another way is by means of the elevator; and this method, since
it entails no additional surfaces entailing extra resistance and
weight, is perhaps the most satisfactory of all.

It is necessary that the elevator be mounted on some kind of universal
joint, in order that it may not only be "tipped" or "dipped," but also
canted sideways for horizontal steering.

§ 9. A vertical fin in the rear, or something in the nature of a
"keel," i.e. a vertical fin running down the backbone of the machine,
greatly assists this movement.

If the model be of the tractor screw and tail (Blériot) type, then the
above remarks _re_ elevator apply _mutatis mutandis_ to the tail.

§ 10. It is of the most vital importance that the propeller torque
should be, as far as possible, correctly balanced. This can be tested
by balancing the model transversely on a knife edge, winding up the
propeller, and allowing it to run down, and adjusting matters until
the torque and compensatory apparatus balance. As the torque varies
the mean should be used.

In the case of twin propellers, suspend the model by its centre of
gravity, wind up the propellers, and when running down if the model is
drawn forward without rotation the thrust is equal; if not adjustment
must be made till it does. The easiest way to do this _may_ be by
placing one propeller, the one giving the greater thrust, slightly
nearer the centre.

In the case of two propellers rotating in opposite directions (by
suitable gearing) on the common centre of two axes, one of the axes
being, of course, hollow, and turning on the other--the rear propeller
working in air already driven back by the other will require a coarser
pitch or larger diameter to be equally efficient.

FOOTNOTE:

[45] These remarks apply to rubber driven motors. In the case of
two-power driven propellers in which the power was automatically
adjusted, say, by a gyroscope as in the case of a torpedo--and the
_speed_ of each propeller varied accordingly--the machine could, of
course, be easily steered by such means; but the model to carry such
power and appliances would certainly weigh from 40 lb. to 60 lb.




CHAPTER X.

THE LAUNCHING OF THE MODEL.


§ 1. Generally speaking, the model should be launched into the air
_against the wind_.

§ 2. It should (theoretically) be launched into the air with a
velocity equal to that with which it flies. If it launch with a
velocity in excess of that it becomes at once unstable and has to
"settle down" before assuming its normal line of flight. If the
velocity be insufficient, it may be unable to "pick up" its requisite
velocity in time to prevent its falling to the ground. Models with
wooden aerofoils and a high aspect ratio designed for swift flying,
such as the well-known Clarke flyers, require to be practically
"hurled" into the air.

Other fabric-covered models capable of sustentation at a velocity of 8
to 10 miles an hour, may just be "released."

§ 3. Light "featherweight" models designed for long flights when
travelling with the wind should be launched with it. They will not
advance into it--if there be anything of a breeze--but, if well
designed, just "hover," finally sinking to earth on an even keel. Many
ingenious pieces of apparatus have been designed to mechanically
launch the model into the air. Fig. 50 is an illustration of a very
simple but effective one.

§ 4. For large size power-driven models, unless provided with a
chassis and wheels to enable them to run along and rise from the
ground under their own power, the launching is a problem of
considerable difficulty.

§ 5. In the case of rubber-driven models desired to run along and rise
from the ground under their own power, this rising must be
accomplished quickly and in a short space. A model requiring a 50 ft.
run is useless, as the motor would be practically run out by that
time. Ten or twelve feet is the limit; now, in order to rise quickly
the machine must be light and carry considerable surface, or, in other
words, its velocity of sustentation must be a low one.

[Illustration: FIG. 50.--MR. POYNTER'S LAUNCHING APPARATUS.

(_Reproduced by permission from the "Model Engineer."_)]

§ 6. It will not do to tip up the elevator to a large angle to make it
rise quickly, because when once off the ground the angle of the
elevator is wrong for actual flight and the model will probably turn a
somersault and land on its back. I have often seen this happen. If the
elevator be set at an increased angle to get it to rise quickly, then
what is required is a little mechanical device which sets the elevator
at its proper flight angle when it leaves the ground. Such a device
does not present any great mechanical difficulties; and I leave it to
the mechanical ingenuity of my readers to devise a simple little
device which shall maintain the elevator at a comparatively large
angle while the model is on the ground, but allowing of this angle
being reduced when free flight is commenced.

§ 7. The propeller most suitable to "get the machine off the ground"
is one giving considerable statical thrust. A small propeller of fine
pitch quickly starts a machine, but is not, of course, so efficient
when the model is in actual flight. A rubber motor is not at all well
adapted for the purpose just discussed.

§ 8. Professor Kress uses a polished plank (down which the models slip
on cane skids) to launch his models.

§ 9. When launching a twin-screw model the model should be held by
each propeller, or to speak more correctly, the two brackets holding
the bearings in which the propeller shafts run should be held one in
each hand in such a way, of course, as to prevent the propellers from
revolving. Hold the machine vertically downwards, or, if too large for
this, allow the nose to rest slightly on the ground; raise (or swing)
the machine up into the air until a little more than horizontal
position is attained, and boldly push the machine into the air (moving
forward if necessary) and release both brackets and screws
simultaneously.[46]

§ 10. In launching a model some prefer to allow the propellers to
revolve for a few moments (a second, say) _before_ actually launching,
contending that this gives a steadier initial flight. This is
undoubtedly the case, see note on page 111.

§ 11. In any case, unless trying for a height prize, do not point the
nose of the machine right up into the air with the idea that you will
thereby obtain a better flight.

Launch it horizontally, or at a very small angle of inclination. When
requiring a model to run along a field or a lawn and rise therefrom
this is much facilitated by using a little strip of smooth oilcloth on
which it can run. Remember that swift flying wooden and metal models
require a high initial velocity, particularly if of large size and
weight. If thrown steadily and at the proper angle they can scarcely
be overthrown.

FOOTNOTE:

[46] Another and better way--supposing the model constructed with a
central rod, or some suitable holdfast (this should be situated at the
centre of gravity of the machine) by which it can be held in one
hand--is to hold the machine with both hands above the head, the right
hand grasping it ready to launch it, and the left holding the two
propellers. Release the propellers and allow them a brief interval
(about half a second) to start. Then launch boldly into the air. The
writer has easily launched 1½ lb. models by this means, even in a
high wind. Never launch a model by one hand only.




CHAPTER XI.

HELICOPTER MODELS.


§ 1. There is no difficulty whatever about making successful model
helicopters, whatever there may be about full-sized machines.

§ 2. The earliest flying models were helicopters. As early as 1796 Sir
George Cayley constructed a perfectly successful helicopter model (see
ch. iii.); it should be noticed the screws were superimposed and
rotated in opposite directions.

§ 3. In 1842 a Mr. Phillips constructed a successful power-driven
model helicopter. The model was made entirely of metal, and when
complete and charged weighed 2 lb. It consisted of a boiler or steam
generator and four fans supported between eight arms. The fans had an
inclination to the horizon of 20°, and through the arms the steam
rushed on the principle of Hero's engines (Barker's Mill Principle
probably). By the escape of steam from the arms the fans were caused
to revolve with immense energy, so much so that the model rose to an
immense altitude and flew across two fields before it alighted. The
motive power employed was obtained from the combustion of charcoal,
nitre and gypsum, as used in the original fire annihilator; the
products of combustion mixing with water in the boiler and forming
gas-charged steam, which was delivered at high pressure from the
extremities of the eight arms.[47] This model and its flight (fully
authenticated) is full of interest and should not be lost sight of, as
in all probability being the first model actuated by steam which
actually flew.

The helicopter is but a particular phase of the aeroplane.

§ 4. The simplest form of helicopter is that in which the torque of
the propeller is resisted by a vertical loose fabric plane, so
designed as itself to form a propeller, rotating in the opposite
direction. These little toys can be bought at any good toy shop from
about 6_d._ to 1_s._ Supposing we desire to construct a helicopter of
a more ambitious and scientific character, possessing a vertically
rotating propeller or propellers for horizontal propulsion, as well as
horizontally rotating propellers for lifting purposes.

[Illustration: FIG. 51.--INCORRECT WAY OF ARRANGING SCREWS.]

§ 5. There is one essential point that must be carefully attended to,
and that is, _that the horizontal propulsive thrust must be in the
same plane as the vertical lift_, or the only effect will be to cause
our model to turn somersaults. I speak from experience.

When the horizontally revolving propellers are driven in a horizontal
direction their "lifting" powers will be materially increased, as they
will (like an ordinary aeroplane) be advancing on to fresh undisturbed
air.

§ 6. I have not for ordinary purposes advocated very light weight wire
framework fabric-covered screws, but in a case like this where the
thrust from the propeller has to be more than the total weight of the
machine, these might possibly be used with advantage.

§ 7. Instead of using two long vertical rods as well as one long
horizontal one for the rubber strands, we might dispense with the two
vertical ones altogether and use light gearing to turn the torque
action through a right angle for the lifting screws, and use three
separate horizontal rubber strands for the three propellers on a
suitable light horizontal framework. Such should result in a
considerable saving of weight.

[Illustration: FIG. 52.--CORRECT MANNER. A, B, C = Screws.]

§ 8. The model would require something in the nature of a vertical fin
or keel to give the sense of direction. Four propellers, two for
"lift" and two for "drift," would undoubtedly be a better
arrangement.

FOOTNOTE:

[47] Report on First Exhibition of Aeronautical Society of Great
Britain, held at Crystal Palace, June 1868.




CHAPTER XII.

EXPERIMENTAL RECORDS.


A model flying machine being a scientific invention and not a toy,
every devotee to the science should make it his or her business to
keep, as far as they are able, accurate and scientific records. For by
such means as this, and the making known of the same, can a _science_
of model aeroplaning be finally evolved. The following experimental
entry forms, left purposely blank to be filled in by the reader, are
intended as suggestions only, and can, of course, be varied at the
reader's discretion. When you _have_ obtained carefully established
data, do not keep them to yourself, send them along to one of the
aeronautical journals. Do not think them valueless; if carefully
arranged they cannot be that, and may be very valuable.


EXPERIMENTAL DATA.

  FORM I.

  Column Headings:

  A:  Model
  B:  Weight
  C:  Area of Supporting Surface
  D:  Aspect Ratio
  E:  Average Length of Flight in Feet
  F:  Maximum Flight
  G:  Time of Flight, A. average
  H:  M. maximum
  I:  Kind and Direction of Wind
  J:  Camber
  K:  Angle of Inclination of Main Aerofoil to Line of Flight

  -----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----
    A  |  B  |  C  |  D  |  E  |  F  |  G  |  H  |  I  |  J  |  K
  -----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----
       |     |     |     |     |     |  A  |  M  |     |     |
    1  |     |     |     |     |     |     |     |     |     |
    2  |     |     |     |     |     |     |     |     |     |
    3  |     |     |     |     |     |     |     |     |     |
    4  |     |     |     |     |     |     |     |     |     |
    5  |     |     |     |     |     |     |     |     |     |
    6  |     |     |     |     |     |     |     |     |     |
    7  |     |     |     |     |     |     |     |     |     |
    8  |     |     |     |     |     |     |     |     |     |
    9  |     |     |     |     |     |     |     |     |     |
   10  |     |     |     |     |     |     |     |     |     |
   11  |     |     |     |     |     |     |     |     |     |
   12  |     |     |     |     |     |     |     |     |     |
       |     |     |     |     |     |     |     |     |     |
  -----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----

  FORM I.--_continued_.

  Column Headings:

  A: Model
  B: Weight of (Rubber) Motor
  C: Kind of Rubber, Flat, Square or Round
  D: Lenght in Inches and Number of Strands
  E: Number of Turns
  F: Condition at End of Flight
  G: Number of Propellers (No.) and Diameter (Diam.)
  H: Number of Blades
  I: Disc Area (DiscA.) and Pitch (Pitch)
  J: Percentage of Slip
  K: Thrust
  L: Torque in Inche-Ounces

  ----+----+----+-----+----+----+-----+----+-----+----+----+----+
    A |  B |  C |  D  |  E |  F |  G  |  H |  I  |  J |  K |  L |
  ----+----+----+-----+----+----+-----+----+-----+----+----+----+
      |    |    |  |  |    |    |  |  |    |  |  |    |    |    |
    1 |    |    |  |  |    |    |  |  |    |  |  |    |    |    |
    2 |    |    |  |  |    |    |  |  |    |  |  |    |    |    |
    3 |    |    |  |  |    |    |  |  |    |  |  |    |    |    |
    4 |    |    |  |  |    |    |  |  |    |  |  |    |    |    |
    5 |    |    |  |  |    |    |  |  |    |  |  |    |    |    |
    6 |    |    |  |  |    |    |  |  |    |  |  |    |    |    |
    7 |    |    |  |  |    |    |  |  |    |  |  |    |    |    |
    8 |    |    |  |  |    |    |  |  |    |  |  |    |    |    |
    9 |    |    |  |  |    |    |  |  |    |  |  |    |    |    |
   10 |    |    |  |  |    |    |  |  |    |  |  |    |    |    |
   11 |    |    |  |  |    |    |  |  |    |  |  |    |    |    |
   12 |    |    |  |  |    |    |  |  |    |  |  |    |    |    |
      |    |    |  |  |    |    |  |  |    |  |  |    |    |    |
  ----+----+----+-----+----+----+-----+----+-----+----+----+----+




CHAPTER XIII.

MODEL FLYING COMPETITIONS.


§ 1. From time to time flying competitions are arranged for model
aeroplanes. Sometimes these competitions are entirely open, but more
generally they are arranged by local clubs with both closed and open
events.

No two programmes are probably exactly alike, but the following may be
taken as fairly representative:--

1. Longest flight measured in a straight line (sometimes both with and
against the wind).[48]

2. Stability (both longitudinal and transverse).

3. Longest glide when launched from a given height without power, but
with motor and propeller attached.

4. Steering.

5. Greatest height.

6. The best all-round model, including, in addition to the above,
excellence in building.

Generally so many "points" or marks are given for each test, and the
model whose aggregate of points makes the largest total wins the
prize; or more than one prize may be offered--

One for the longest flight.

One for the swiftest flight over a measured distance.

One for the greatest height.

One for stability and steering.

And one for the best all-round model.

The models are divided into classes:--

§ 2. _Aero Models Association's Classification, etc._

    A.   Models of 1 sq. ft. surface and under.
    B.     "       2 sq. ft.     "       "
    C.     "       4 sq. ft.     "       "
    D.     "       8 sq. ft.     "       "
    E.     "       over 8 sq. ft.

All surfaces, whether vertical, horizontal, or otherwise, to be
calculated together for the above classification.

All round efficiency--marks or points as percentages:--

    Distance              40 per cent.
    Stability             35    "
    Directional control   15    "
    Gliding angle         10    "[49]

Two prizes:--

One for length of flight.

One for all-round efficiency (marked as above).

Every competitor to be allowed three trials in each competition, the
best only to count.

All flights to be measured in a straight line from the starting to the
landing point.

Repairs may be made during the competition at the direction of the
judges.[50]

There are one or two other points where flights are _not_ made with
and against the wind. The competitors are usually requested to start
their models from within a given circle of (say) six feet diameter,
and fly them _in any direction_ they please.

"Gliding angle" means that the model is allowed to fall from a height
(say) of 20 ft.

[Illustration: FIG. 53.--MODEL DESIGNED AND CONSTRUCTED BY THE AUTHOR
FOR "GREATEST HEIGHT."

A very lightly built model with a very low aspect ratio, and screw
giving a very powerful dynamic thrust, and carrying rather a large
amount of rubber. Climbs in left-handed spirals.]

"Directional control," that the model is launched in some specified
direction, and must pass as near as possible over some indicated
point.

The models are practically always launched by hand.

§ 3. Those who desire to win prizes at such competitions would do well
to keep the following points well in mind.

1. The distance is always measured in a straight line. It is
absolutely essential that your model should be capable of flying
(approximately) straight. To see, as I have done, model after model
fly quite 150 to 200 yards and finish within 50 yards of the
starting-point (credited flight 50 yards) is useless, and a severe
strain on one's temper and patience.

[Illustration: FIG. 54.--THE GAMAGE CHALLENGE CUP.

Open Competition for longest flight. Crystal Palace, July 27. Won by
Mr. E.W. Twining.]

[Illustration: FIG. 55.--MEDAL WON BY THE AUTHOR IN THE SAME
COMPETITION.]

2. Always enter more than one model, there nearly always is an
entrance fee; never mind the extra shilling or so. Go in to win.

3. It is not necessary that these models should be replicas of one
another. On some days a light fabric-covered model might stand the
best chance; on another day, a swift flying wooden or metal aerofoil.

Against the wind the latter have an immense advantage; also if the day
be a "gusty" one.[51]

4. Always make it a point of arriving early on the ground, so that you
can make some trial flights beforehand. Every ground has its local
peculiarities of air currents, etc.

5. Always be ready in time, or you may be disqualified. If you are
flying a twin-screw model use a special winder, so that both
propellers are wound up at the same time, and take a competent friend
with you as assistant.

6. For all-round efficiency nothing but a good all-round model, which
can be absolutely relied on to make a dozen (approximately) equivalent
flights, is any good.

7. In an open distance competition, unless you have a model which you
can rely on to make a _minimum_ flight of 200 yards, do not enter
unless you know for certain that none of the "crack" flyers will be
present.

8. Do not neglect the smallest detail likely to lead to success; be
prepared with spare parts, extra rubber, one or two handy tools, wire,
thread, etc. Before a lecture, that prince of experimentalists,
Faraday, was always careful to see that the stoppers of all the
bottles were loose, so that there should be no delay or mishap.

9. If the rating of the model be by "weight" (1 oz., 2 oz., 4 oz.,
etc.) and not area, use a model weighing from 10 oz. to a pound.

10. If there is a greatest height prize, a helicopter model should win
it.[52] (The writer has attained an altitude of between three and four
hundred feet with such.) The altitude was arrived at by observation,
not guesswork.

11. It is most important that your model should be able to "land"
without damage, and, as far as possible, on an even keel; do not omit
some form of "skid" or "shock-absorber" with the idea of saving
weight, more especially if your model be a biplane, or the number of
flights may be restricted to the number "one."

12. Since the best "gliding" angle and "flying" angle are not the
same, being, say, 7° in the former case and 1°-3°, say, in the latter,
an adjustable angle might in some cases be advantageous.

13. Never turn up at a competition with a model only just finished and
practically untested which you have flown only on the morning of the
competition, using old rubber and winding to 500 turns; result, a
flight of 250 yards, say. Arrived on the competition ground you put on
new rubber and wind to 750 turns, and expect a flight of a quarter of
a mile at least; result 70 yards, _measured in a straight line_ from
the starting-point.

14. Directional control is the most difficult problem to overcome with
any degree of success under all adverse conditions, and 15 per cent.,
in the writer's opinion, is far too low a percentage; by directional I
include flying in a straight line; personally I would mark for
all-round efficiency: (A) distance and stability, 50 per cent.; (B)
directional control, 30 per cent.; (C) duration of flight, 20 per
cent. In A the competitor would launch his model _in any direction_;
in B as directed by the judges. No separate flights required for C.

FOOTNOTES:

[48] The better way, undoubtedly, is to allow the competitor to choose
his direction, the starting "circle" only to be fixed.

[49] Or 10 per cent. for duration of flight.

[50] In another competition, held under the rules and regulations of
the Kite and Model Aeroplane Association for the best all-round model,
open to the world, for machines not under 2 sq. ft. of surface, the
tests (50 marks for each) were:--A. Longest flight in a straight line.
B. Circular flight to the right. C. Circular flight to the left. D.
Stability and landing after a flight. E. Excellence in building of the
model.

[51] On the assumption that the model will fly straight.

[52] If permitted to enter; if not see Fig. 53.




CHAPTER XIV.

USEFUL NOTES, TABLES, FORMULÆ, ETC.


§ 1. COMPARATIVE VELOCITIES.

    Miles per hr.    Feet per sec.     Metres per sec.
         10       =     14·7        =      4·470
         15       =     22          =      6·705
         20       =     29·4        =      8·940
         25       =     36·7        =     11·176
         30       =     44          =     13·411
         35       =     51·3        =     15·646

§ 2. A metre = 39·37079 inches.

    _In order to convert_:--
               Metres into inches multiply by 39·37
                     "     feet        "       3·28
                     "     yards       "       1·09
                     "     miles       "       0·0006214
    Miles per hour into ft. per min. multiply by 88·0
         "    min.      "       sec.      "      88·0
         "    hr. into kilometres per hr. "       1·6093
         "       "     metres per sec.    "       0·44702
         Pounds into grammes multiply by 453·593
             "       kilogrammes   "       0·4536

§ 8. Total surface of a cylinder = circumference of base × height + 2
area of base.

Area of a circle = square of diameter × 0·7854.

Area of a circle = square of rad. × 3·14159.

Area of an ellipse = product of axes × 0·7854.

Circumference of a circle = diameter × 3·14159.

Solidity of a cylinder = height × area of base.

Area of a circular ring = sum of diameters × difference of diameters ×
0·7854.

For the area of a sector of a circle the rule is:--As 360 : number of
degrees in the angle of the sector :: area of the sector : area of
circle.

To find the area of a segment less than a semicircle:--Find the area
of the sector which has the same arc, and subtract the area of the
triangle formed by the radii and the chord.

The areas of corresponding figures are as the squares of corresponding
lengths.

  § 4.  1 mile     =   1·609 kilometres.
        1 kilometre   =   1093 yards.
        1 oz.         =   28·35 grammes.
        1 lb.         =   453·59   "
        1 lb.         =   0·453 kilogrammes.
        28 lb.        =   12·7       "
        112 lb.       =   50·8       "
        2240 lb.      =   1016       "
        1 kilogram    =   2·2046 lb.
        1 gram        =   0·0022 lb.
        1 sq. in.     =   645 sq. millimetres.
        1 sq. ft.     =   0·0929 sq. metres.
        1 sq. yard    =   0·836      "
        1 sq. metre   =   10·764 sq. ft.

§ 5. One atmosphere = 14·7 lb. per sq. in. = 2116 lb. per sq. ft. =
760 millimetres of mercury.

A column of water 2·3 ft. high corresponds to a pressure of 1 lb. per
sq. in.

1 H.P. = 33,000 ft.-lb. per min. = 746 watts.

Volts × amperes = watts.

{pi} = 3·1416. _g_ = 32·182 ft. per sec. at London.

§ 6. TABLE OF EQUIVALENT INCLINATIONS.

     Rise.            Angle in Degs.
    1 in 30               1·91
    1 "  25               2·29
    1 "  20               2·87
    1 "  18               3·18
    1 "  16               3·58
    1 "  14               4·09
    1 "  12               4·78
    1 "  10               5·73
    1 "   9               6·38
    1 "   8               7·18
    1 "   7               8·22
    1 "   6               9·6
    1 "   5              11·53
    1 "   4              14·48
    1 "   3              19·45
    1 "   2              30·00
    1 " {square root}2   45·00

§ 7. TABLE OF SKIN FRICTION.

Per sq. ft. for various speeds and surface lengths.

  -----------------+-------------+-------------+-------------+------------
  Velocity of Wind | 1 ft. Plane | 2 ft. Plane | 4 ft. Plane | 8 ft. Plane
  -----------------+-------------+-------------+-------------+------------
         10        |   ·00112    |   ·00105    |   ·00101    |   ·000967
         15        |   ·00237    |   ·00226    |   ·00215    |   ·00205
         20        |   ·00402    |   ·00384    |   ·00365    |   ·00349
         25        |   ·00606    |   ·00579    |   ·00551    |   ·00527
         30        |   ·00850    |   ·00810    |   ·00772    |   ·00736
         35        |   ·01130    |   ·0108     |   ·0103     |   ·0098
  -----------------+-------------+-------------+-------------+------------

This table is based on Dr. Zahm's experiments and the equation

    _f_ = 0·00000778_l_^{-0·07}_v_^{1·85}

Where _f_ = skin friction per sq. ft.; _l_ = length of surface; _v_ =
velocity in feet per second.

In a biplane model the head resistance is probably from twelve to
fourteen times the skin friction; in a racing monoplane from six to
eight times.

§ 8. TABLE I.--(METALS).

  --------------+------------+-----------------+-------------
     Material   |  Specific  | Elasticity E[A] |  Tenacity
                |  Gravity   |                 | per sq. in.
  --------------+------------+-----------------+-------------
  Magnesium     |    1·74    |                 |   {22,000-
                |            |                 |   {32,000
  Magnalium[B]  |  2·4-2·57  |      10·2       |
  Aluminium- }  |            |                 |
    Copper[C]}  |    2·82    |                 |    54,773
  Aluminium     |    2·6     |      11·1       |    26,535
  Iron          | 7·7 (about)|       29        |    54,000
  Steel         | 7·8 (about)|       32        |   100,000
  Brass         |  7·8-8·4   |       15        |    17,500
  Copper        |    8·8     |       36        |    33,000
  Mild Steel    |    7·8     |       30        |    60,000
                |            |                 |
  --------------+------------+-----------------+-------------
  [A] E in millions of lb. per sq. in.
  [B] Magnalium is an alloy of magnesium and aluminium.
  [C] Aluminium 94 per cent., copper 6 per cent. (the best
      percentage), a 6 per cent. alloy thereby doubles the
      tenacity of pure aluminium with but 5 per cent.
      increase of density.
  --------------+------------+-----------------+-------------

§ 9. TABLE II.--WIND PRESSURES.

    _p_ = _kv²_.

_k_ coefficient (mean value taken) ·003 (miles per hour) = 0·0016 ft.
per second. _p_ = pressure in lb. per sq. ft. _v_ = velocity of wind.

    Miles per hr.   Ft. per sec.   Lb. per sq. ft.
         10             14·7          0·300
         12             17·6          0·432
         14             20·5          0·588
         16             23·5          0·768
         18             26·4          0·972
         20             29·35         1·200
         25             36·7          1·875
         30             43·9          2·700
         35             51·3          3·675

§ 10. Representing normal pressure on a plane surface by 1; pressure
on a rod (round section) is 0·6; on a symmetrical elliptic cross
section (axes 2:1) is 0·2 (approx.). Similar shape, but axes 6:1, and
edges sharpened (_see_ ch. ii., § 5), is only 0·05, or 1/20, and for
the body of minimum resistance (_see_ ch. ii., § 4) about 1/24.

§ 11. TABLE III.--LIFT AND DRIFT.

On a well shaped aerocurve or correctly designed cambered surface.
Aspect ratio 4·5.

    Inclination.   Ratio Lift to Drift.
           0°            19:1
        2·87°            15:1
        3·58°            16:1
        4·09°            14:1
        4·78°            12:1
        5·73°           9·6:1
        7·18°           7·9:1

Wind velocity 40 miles per hour. (The above deduced from some
experiments of Sir Hiram Maxim.)

At a velocity of 30 miles an hour a good aerocurve should lift 21 oz.
to 24 oz. per sq. ft.


§ 12. TABLE IV.--LIFT AND DRIFT.

On a plane aerofoil.

    N = P(2 sin {alpha}/1 + sin² {alpha})

    Inclination.   Ratio Lift to Drift.
         1°              58·3:1
         2°              29·2:1
         3°              19·3:1
         4°              14·3:1
         5°              11·4:1
         6°               9·5:1
         7°               8·0:1
         8°               7·0:1
         9°               6·3:1
        10°               5·7:1

    P = 2_kd_ AV² sin {alpha}.

A useful formula for a single plane surface. P = pressure supporting
the plane in pounds per square foot, _k_ a constant = 0·003 in miles
per hour, _d_ = the density of the air.

A = the area of the plane, V relative velocity of translation through
the air, and {alpha} the angle of flight.

Transposing we have

    AV² = P/(2_kd_ sin {alpha})

If P and {alpha} are constants; then AV² = a constant or area is
inversely as velocity squared. Increase of velocity meaning diminished
supporting surface (_and so far as supporting surface goes_), diminished
resistance and skin friction. It must be remembered, however, that while
the work of sustentation diminishes with the speed, the work of
penetration varies as the cube of the speed.


§ 13. TABLE V.--TIMBER.

  Column Headings:

  A. Material
  B. Specific Gravity
  C. Weight per Cub. Ft. in Lb.
  D. Strength per Sq. In. in Lb.
  E. Ultimate Breaking Load (Lb.) span 1' x 1" x 1"
  F. Relative Resilience in Bending
  G. Modulus of Elasticity in millions of Lb. per Sq. In. for Bending
  H. Relative Value. Bending Strength compared with Weight

  ---------------+-----+-------+-------------+-------+-----+-----+----
    A            |B    | C     |  D          |E      |F    |G    | H
  ---------------+-----+-------+-------------+-------+-----+-----+----
  Ash            | ·79 | 43-52 |14,000-17,000| 622   |4·69 |1·55 |13·0
  Bamboo         |     |  25[A]|    6300[53] |       |3·07 |3·20 |
  Beech          | ·69 |  43   |10,000-12,000| 850   |     |1·65 |19·8
  Birch          | ·71 |  45   |   15,000    | 550   |     |3·28 |12·2
  Box            |1·28 |  80   |20,000-23,000| 815   |     |     |10·2
  Cork           | ·24 |  15   |             |       |     |     |
  Fir (Norway    |     |       |             |       |     |     |
    Spruce)      | ·51 |  32   | 9,000-11,000| 450   |3·01 |1·70 |14·0
  American       |     |       |             |       |     |     |
    Hickory      |     |  49   |   11,000    | 800   |3·47 |2·40 |16·3
  Honduras       |     |       |             |       |     |     |
    Mahogany     | ·56 |  35   |   20,000    | 750   |3·40 |1·60 |21·4
  Maple          | ·68 |  44   |   10,600    | 750   |     |     |17·0
  American White |     |       |             |       |     |     |
    Pine         | ·42 |  25   |   11,800    | 450   |2·37 |1·39 |18·0
  Lombardy Poplar|     |  24   |    7,000    | 550   |2·89 | 0·77|22·9
  American Yellow|     |       |             |       |     |     |
    Poplar       |     |  44   |   10,000    |       |3·63 |1·40 |
  Satinwood      | ·96 |  60   |             |1,033  |     |     |17·2
  Spruce         | ·50 |  31   |   12,400    | 450   |     |     |14·5
  Tubular Ash,   |     |       |             |       |     |     |
   _t_ = 1/8 _d_ |     |  47   |             |       |3·50 |1·55 |
  ---------------+-----+-------+-------------+-------+-----+-----+----

                         _t_ = thickness: _d_ = diameter.

  [A] Given elsewhere as 55 and 22,500 (_t_ = 1/3_d_), evidently
  regarded as solid.

§ 14.--=Formula connecting the Weight Lifted in Pounds per Square Foot
and the Velocity.=--The empirical formula

    W = (V²C)/_g_

    Where W   = weight lifted in lb. per sq. ft.
          V   = velocity in ft. per sec.
          C   = a constant = 0·025.
          _g_ = 32·2, or 32 approx.

may be used for a thoroughly efficient model. This gives
(approximately)

      1 lb. per sq. ft. lift at 25 miles an hour.
     21 oz.     "        "      30       "
      6 oz.     "        "      15       "
      4 oz.     "        "      12       "
    2·7 oz.     "        "      10       "

Remember the results work out in feet per second. To convert
(approximately) into miles per hour multiply by 2/3.

§ 15. =Formula connecting Models of Similar Design, but Different
Weights.=

    D {proportional to} {square root}W.

or in models of _similar design_ the distances flown are proportional
to the square roots of the weights. (Derived from data obtained from
Clarke's flyers.)

For models from 1 oz. to 24-30 oz. the formula appears to hold very
well. For heavier models it appears to give the heavier model rather
too great a distance.

Since this was deduced a 1 oz. Clarke model of somewhat similar design
but longer rubber motor has flown 750 ft. at least; it is true the
design is not, strictly speaking, similar, but not too much reliance
must be placed on the above. The record for a 1 oz. model to date is
over 300 yards (with the wind, of course), say 750 ft. in calm air.

§ 16. =Power and Speed.=--The following formula, given by Mr. L. Blin
Desbleds, between these is--

    W/W{0} = (3_v{0}_)/(4_v_) + ¼(_v_/_v{0}_)³.

    Where   _v{0}_ = speed of minimum power
              W{0} = work done at speed _v{0}_.
                 W = work done at speed _v_.

Making _v_ = 2_v{0}_, i.e. doubling the speed of minimum power, and
substituting, we have finally

    W = (2-3/8)W{0}

i.e. the speed of an aeroplane can be doubled by using a power 2-3/8
times as great as the original one. The "speed of minimum power" being
the speed at which the aeroplane must travel for the minimum
expenditure of power.

§ 17. The thrust of the propeller has evidently to balance the

    Aerodynamic resistance                        = R
    The head resistance (including skin friction) = S

Now according to Renard's theorem, the power absorbed by R + S is a
minimum when

    S = R/3.

Having built a model, then, in which the total resistance

    = (4/3)R.

This is the thrust which the propeller should be designed to give. Now
supposing the propeller's efficiency to be 80 per cent., then P--the
minimum propulsion power

    = (4/3)R × 100/80 × 100/75 × _v_.

Where 25 per cent. is the slip of the screw, _v_ the velocity of the
aeroplane.

§ 18. =To determine experimentally the Static Thrust of a
Propeller.=--Useful for models intended to raise themselves from the
ground under their own power, and for helicopters.

The easiest way to do this is as follows: Mount the propeller on the
shaft of an electric motor, of sufficient power to give the propeller
1000 to 1500 revolutions per minute; a suitable accumulator or other
source of electric energy will be required, a speedometer or speed
counter, also a voltmeter and ammeter.

Place the motor in a pair of scales or on a suitable spring balance
(the former is preferable), the axis of the motor vertical, with the
propeller attached. Rotate the propeller so that the air current is
driven _upwards_. When the correct speed (as indicated by the speed
counter) has been attained, notice the difference in the readings if a
spring balance be used, or, if a pair of scales, place weights in the
scale pan until the downward thrust of the propeller is exactly
balanced. This gives you the thrust in ounces or pounds.

Note carefully the voltage and amperage, supposing it is 8 volts and
10 amperes = 80 watts.

Remove the propeller and note the volts and amperes consumed to run
the motor alone, i.e. to excite itself, and overcome friction and air
resistance; suppose this to be 8 volts and 2 amperes = 16; the
increased load when the propeller is on is therefore

    80 - 16 = 64 watts.

All this increased power is not, however, expended on the propeller.

The lost power in the motor increases as C²R.

R = resistance of armature and C = current. If we deduct 10 per cent.
for this then the propeller is actually driven by 56 watts.

Now 746 watts = 1 h.p.

    {therefore} 56/746 = 1/13 h.p. approx.

at the observed number of revolutions per minute.

§ 19. N.B.--The h.p. required to drive a propeller varies as the cube
of the revolutions.

_Proof._--Double the speed of the screw, then it strikes the air twice
as hard; it also strikes twice as much air, and the motor has to go
twice as fast to do it.

§ 20. To compare one model with another the formula

    Weight × velocity (in ft. per sec.)/horse-power

is sometimes useful.

§ 21. =A Horse-power= is 33,000 lb. raised one foot in one minute, or
550 lb. one foot in one second.

A clockwork spring raised 1 lb. through 4½ ft. in 3 seconds. What
is its h.p.?

         1 lb. through 4½ ft. in 3 seconds
    is   1 lb.    "    90 ft.  " 1 minute.

          {therefore} Work done is 90 ft.-lb.
           = 90/33000 = 0·002727 h.p.

The weight of the spring was 6¾ oz. (this is taken from an actual
experiment), i.e. this motor develops power at the rate of 0·002727
h.p. for 3½ seconds only.

§ 22. =To Ascertain the H.P. of a Rubber Motor.= Supposing a propeller
wound up to 250 turns to run down in 15 seconds, i.e. at a mean speed
of 1200 revolutions per minute or 20 per second. Suppose the mean
thrust to be 2 oz., and let the pitch of the propeller be 1 foot. Then
the number of foot-pounds of energy developed

    = (2 oz. × 1200 revols. × 1 ft. (pitch)) / 16 oz.

= 150 ft.-lb. per minute.

But the rubber motor runs down in 15 seconds.

    {therefore} Energy really developed is

          = (150 × 15) / 60 = 37·5 ft.-lb.

The motor develops power at rate of 150/33000 = 0·004545 h.p., but for
15 seconds only.

§ 23. =Foot-pounds of Energy in a Given Weight of Rubber=
(experimental determination of).

         Length of rubber    36 yds.
         Weight     "        2-7/16 oz.
         Number of turns     = 200.

    12 oz. were raised 19 ft. in 5 seconds.
    i.e. ¾ lb. was raised 19 × 12 ft. in 1 minute.
    i.e. 1 lb. was raised 19 × 3 × 3 ft. in 1 minute.
                               = 171 ft. in 1 minute.

i.e. 171 ft.-lb. of energy per minute. But actual time was 5 seconds.

{therefore} Actual energy developed by 2-7/16 oz. of rubber of 36
yards, i.e. 36 strands 1 yard each at 200 turns is

    = 171/12 ft.-lb.

    = 14¼ ft.-lb.

This allows nothing for friction or turning the axle on which the cord
was wound. Ball bearings were used; but the rubber was not new and
twenty turns were still unwound at the end of the experiment. Now
allowing for friction, etc. being the same as on an actual model, we
can take ¾ of a ft.-lb. for the unwound amount and estimate the
total energy as 15 ft.-lb. as a minimum. The energy actually developed
being at the rate of 0·0055 h.p., or 1/200 of a h.p. if supposed
uniform.

§ 24. The actual energy derivable from 1 lb. weight of rubber is
stated to be 300 ft.-lb. On this basis 2-7/16 oz. should be capable of
giving 45·7 ft.-lb. of energy, i.e. three times the amount given
above. Now the motor-rubber not lubricated was only given 200
turns--lubricated 400 could have been given it, 600 probably before
rupture--and the energy then derivable would certainly have been
approximating to 45 ft.-lb., i.e. 36·25. Now on the basis of 300
ft.-lb. per lb. a weight of ½ oz. (the amount of rubber carried in
"one-ouncers") gives 9 ft.-lb. of energy. Now assuming the gliding
angle (including weight of propellers) to be 1 in 8; a perfectly
efficient model should be capable of flying eight times as great a
distance in a horizontal direction as the energy in the rubber motor
would lift it vertically. Now 9 ft.-lb. of energy will lift 1 oz. 154
ft. Therefore theoretically it will drive it a distance (in yards) of

    (8 × 154)/3 = 410·6 yards.

Now the greatest distance that a 1 oz. model has flown in perfectly
calm air (which never exists) is not known. Flying with the wind 500
yards is claimed. Admitting this what allowance shall we make for the
wind; supposing we deduct half this, viz. 250 yards. Then, on this
assumption, the efficiency of this "one ouncer" works out (in
perfectly still air) at 61 per cent.

The gliding angle assumption of 1 in 8 is rather a high one, possibly
too high; all the writer desires to show is the method of working out.

Mr. T.W.K. Clarke informs me that in his one-ouncers the gliding
angle is about 1 in 5.

§ 25. =To Test Different Motors or Different Powers of the Same Kind
of Motor.=--Test them on the same machine, and do not use different
motors or different powers on different machines.

§ 26. =Efficiency of a Model.=--The efficiency of a model depends on
the weight carried per h.p.

§ 27. =Efficiency of Design.=--The efficiency of some particular
design depends on the amount of supporting surface necessary at a
given speed.

§ 28. =Naphtha Engines=, that is, engines made on the principle of the
steam engine, but which use a light spirit of petrol or similar agent
in their generator instead of water with the same amount of heat, will
develop twice as much energy as in the case of the ordinary steam
engine.

§ 29.=Petrol Motors.=

    Horse-power.     No. of Cylinders.   Weight.
        ¼                Single          4½ lb.
        ½ to ¾             "             6½  "
        1½               Double          9   "

§ 30. =The Horse-power of Model Petrol Motors.=--Formula for rating of
the above.

    (R.P.M. = revolutions per minute.)

    H.P. = ((Bore)² × stroke × no. of cylinders × R.P.M.)/12,000

If the right-hand side of the equation gives a less h.p. than that
stated for some particular motor, then it follows that the h.p. of the
motor has been over-estimated.

[Illustration: FIG. 56.]

§ 30A. =Relation between Static Thrust of Propeller and Total Weight
of Model.=--The thrust should be approx. = ¼ of the weight.

§ 31. =How to find the Height of an Inaccessible Object by Means of
Three Observations taken on the Ground (supposed flat) in the same
Straight Line.=--Let A, C, B be the angular elevations of the object
D, as seen from these points, taken in the same straight line. Let the
distances B C, C A and A B be _a_, _b_, _c_ respectively. And let
required height P D = _h_; then by trigonometry we have (see Fig. 56)

    _h²_ = _abc_/(_a_ cot²A - _c_ cot²C + _b_ cot²B).

§ 32. =Formula= for calculating the I.H.P. (indicated horse-power) of
a single-cylinder double-acting steam-engine.

Indicated h.p. means the h.p. actually exerted by the steam in the
cylinder without taking into account engine friction. Brake h.p. or
effective h.p. is the actual h.p. delivered by the crank shaft of the
engine.

    I.H.P. = (2 × S × R × A × P)/33,000.

    Where    S = stroke in feet.
             R = revolutions per minute.
             A = area of piston in inches.
             P = mean pressure in lb. exerted per sq. in. on the piston.

The only difficulty is the mean effective pressure; this can be found
approximately by the following rule and accompanying table.


TABLE VI.

    ---------+----------+---------+----------+---------+---------
     Cut-off | Constant | Cut-off | Constant | Cut-off | Constant
    ---------+----------+---------+----------+---------+---------
       1/6   |   ·566   |   3/8   |   ·771   |   2/3   |  ·917
       1/5   |   ·603   |    ·4   |   ·789   |    ·7   |  ·926
       1/4   |   ·659   |   1/2   |   ·847   |   3/4   |  ·937
        ·3   |   ·708   |    ·6   |   ·895   |    ·8   |  ·944
       1/3   |   ·743   |   5/8   |   ·904   |   7/8   |  ·951
    ---------+----------+---------+----------+---------+---------

Rule.--"Add 14·7 to gauge pressure of boiler, this giving 'absolute
steam pressure,' multiply this sum by the number opposite the fraction
representing the point of cut-off in the cylinder in accompanying
table. Subtract 17 from the product and multiply the remainder by 0·9.
The result will be very nearly the M.E.P." (R.M. de Vignier.)


FOOTNOTE:

[53] Given elsewhere as 55 and 22,500 (_t_ = 1/3 _d_), evidently
regarded as solid.




APPENDIX A.

SOME MODELS WHICH HAVE WON MEDALS AT OPEN COMPETITIONS.


[Illustration: FIG. 57.--THE G.P.B. SMITH MODEL.]

The model shown in Fig. 57 has won more competition medals than any
other. It is a thoroughly well designed[54] and well constructed
model. Originally a very slow flyer, the design has been simplified,
and although by no means a fast flyer, its speed has been much
accelerated. Originally a one-propeller machine, it has latterly been
fitted with twin propellers, with the idea of obtaining more
directional control; but in the writer's opinion, speaking from
personal observation, with but little, if any, success. The steering
of the model is effected by canting the elevator. Originally the
machine had ailerons for the purpose, but these were removed owing, I
understand, to their retarding the speed of the machine.

In every competition in which this machine has been entered it has
always gained very high marks for stability.

[Illustration: FIG. 58.--THE GORDON-JONES DIHEDRAL BIPLANE.]

Up to the time of writing it has not been provided with anything in
the nature of fins or rudder.

Fig. 58 is a biplane very much after the type of the model just
alluded to, but the one straight and one curved aerofoil surfaces are
here replaced by two parallel aerofoils set on a dihedral angle. The
large size of the propeller should be noted; with this the writer is
in complete agreement. He has not unfortunately seen this model in
actual flight.

The scientifically designed and beautifully made models illustrated in
Fig. 59 are so well known that any remarks on them appear
superfluous. Their efficiency, so far as their supporting area goes,
is of the highest, as much as 21 oz. per square foot having been
carried.

[Illustration: FIG. 59.--MESSRS. T.W.K. CLARKE AND CO.'S MODEL
FLYERS.]

For illustrations, etc., of the Fleming-Williams model, _see_ ch. v.,
§ 23.

(Fig. 60.) This is another well-constructed and efficient model, the
shape and character of the aerofoil surfaces much resembling those of
the French toy monoplane AL-MA (see § 4, ch. vii.), but they are
supported and held in position by quite a different method, a neat
little device enabling the front plane to become partly detached on
collision with any obstacle. The model is provided with a keel (below
the centre of gravity), and rudder for steering; in fact, this machine
especially claims certainty of directional control. The writer has
seen a number of flights by this model, but it experiences, like other
models, the greatest difficulty in keeping straight if the conditions
be adverse.

The model which will do this is, in his opinion, yet to be evolved.
The small size of the propellers is, of course, in total disagreement
with the author's ideas. All the same, the model is in many respects
an excellent one, and has flown over 300 yards at the time of writing.

[Illustration: FIG. 60.--THE DING SAYERS MONOPLANE.]

More than a year ago the author made a number of models with
triangular-shaped aerofoils, using umbrella ribs for the leading edge
and steel piano wire for the trailing, but has latterly used aerofoils
of the elongated ellipse shape.

Fig. 61 is an illustration of one of the author's latest models which
won a Bronze Medal at the Long Distance Open Competition, held at the
Crystal Palace on July 27, 1910, the largest and most keenly contested
competition held up to that date.

The best and straightest flight against the wind was made by this
model.

On the morning of the competition a flight of about 320 yards
(measured in a straight line) was made on Mitcham Common, the model
being launched against the wind so as to gain altitude, and then
flying away with the breeze behind the writer. Duration of flight 50
seconds. The following are the chief particulars of the
model:--Weight, 7½ oz. Area of supporting surface, 1-1/3 sq. ft.
Total length, 4 ft. Span of main aerofoil, 25 in. Aspect ratio, 4 : 1.
Diameter of propeller, 14 in. Two strand geared rubber motor, carrying
altogether 28 strands of 1/16 square rubber cord 43 in. long. The
propeller was originally a Venna, but with the weight reduced by
one-third, and considerable alteration made in its central contours.
The front skid of steel pianoforte wire, the rear of jointless cane
wire tipped; the rear skid was a necessity in order to protect the
delicate gearing mechanism, the weight of which was reduced to a
minimum.

[Illustration: FIG. 61.--THE AUTHOR'S "GRASSHOPPER" MODEL.]

The very large diameter of the propeller should be noted, being 56
per cent. of the span. The fin, high above the centre of gravity, was
so placed for transverse stability and direction. At the rear of the
fin was a rudder. The small amount of rubber carried (for a long
distance machine) should also be noted, especially when allowing for
friction in gearing, etc.

The central rod was a penny bamboo cane, the large aerofoil of
jointless cane and Hart's fabric, and the front aerofoil of steel wire
surfaced with the same material.


LONDON: PRINTED BY WILLIAM CLOWES AND SONS, LIMITED, GREAT WINDMILL
STREET, W., AND DUKE STREET, STAMFORD STREET, S.E.

FOOTNOTE:

[54] The design is patented.




    _October, 1910_

A SHORT LIST OF

SCIENTIFIC BOOKS

PUBLISHED AND SOLD BY

E. & F.N. SPON, Limited,

57 Haymarket, London, S.W.

SOLE ENGLISH AGENTS for the Books of--

    MYRON C. CLARK, NEW YORK
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                                 PAGE
    AERONAUTICS                    2
    AGRICULTURE                    2
    ARCHITECTURE                   3
    ARTILLERY                      5
    BRIDGES AND ROOFS              5
    BUILDING                       3
    CEMENT AND CONCRETE            7
    CIVIL ENGINEERING              8
    DICTIONARIES                  11
    DOMESTIC ECONOMY              12
    DRAWING                       13
    ELECTRICAL ENGINEERING        14
    FOREIGN EXCHANGE              19
    GAS AND OIL ENGINES           20
    GAS LIGHTING                  20
    HISTORICAL; BIOGRAPHICAL      21
    HOROLOGY                      22
    HYDRAULICS                    22
    INDUSTRIAL CHEMISTRY          24
    IRRIGATION                    27
    LOGARITHM TABLES              28
    MANUFACTURES                  24
    MARINE ENGINEERING            28
    MATERIALS                     30
    MATHEMATICS                   31
    MECHANICAL ENGINEERING        33
    METALLURGY                    36
    METRIC TABLES                 38
    MINERALOGY AND MINING         38
    MUNICIPAL ENGINEERING         45
    NAVAL ARCHITECTURE            28
    ORGANISATION                  40
    PHYSICS                       41
    PRICE BOOKS                   42
    RAILWAY ENGINEERING           43
    SANITATION                    45
    STRUCTURAL DESIGN             45
    TELEGRAPH CODES               47
    WARMING; VENTILATION          47
    WATER SUPPLY                  48
    WORKSHOP PRACTICE             49
    USEFUL TABLES                 52
    MISCELLANEOUS                 53


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         In preparation.

         Vol. IV. SPANISH-FRENCH-ENGLISH-GERMAN.
         750 pp. (_1910_)

    _net_     10  6

    =English-French and French-English Dictionary of the Motor-Car, Cycle
    and Boat.= By F. LUCAS. 171 pp. crown 8vo. (_1905_)

    _net_      5  0

    =Spanish-English Dictionary of Mining Terms.= By F. LUCAS. 78 pp. 8vo.
    (_1905_)

    _net_      5  0

    =English-Russian and Russian-English Engineering Dictionary.= By L.
    MEYCLIAR. 100 pp. 16mo. (_1909_)

    _net_      2  6

    =Reed's Polyglot Guide to the Marine Engine,= in English, French,
    German and Norsk. Second edition, oblong 8vo. (_1900_).

    _net_      6  0


    DOMESTIC ECONOMY.

    =Food Adulteration and its Detection.= By J.P. BATTERSHALL. 12 plates,
    328 pp. demy 8vo. (_New York, 1887_)

              15  0

    =How to Check Electricity Bills.= By S.W. BORDEN. 41 illus. 54 pp.
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    =Practical Hints on Taking a House.= By H.P. BOULNOIS. 71 pp. 18mo.
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               1  6

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               0  6

    =The Kitchen Boiler and Water Pipes.= By H. GRIMSHAW. 8vo, sewed.
    (_1887_)

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    =Cookery and Domestic Management,= including economic and middle class
    Practical Cookery. By K. MELLISH. 56 coloured plates and 441 illus.
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    =Spons' Household Manual.= 250 illus. 1043 pp. demy 8vo. (_1902_)

               7  6

        Ditto ditto half-bound French morocco

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    =Handbook of Sanitary Information= for Householders. By R.S. TRACY. 33
    illus. 114 pp. 18mo. (_New York, 1900_)

               2  6


    DRAWING.

    =The Ornamental Penman's,= Engraver's and Sign Writer's Pocket Book of
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               0  6

    =The Draughtsman's Handbook= of Plan and Map Drawing. By G.G. ANDRE.
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               9  0

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    =A System of Easy Lettering.= By J.H. CROMWELL. With Supplement by G.
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    =Plane Geometrical Drawing.= BY R.C. FAWDRY. Illustrated, 185 pp.
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    =Twelve Plates on Projection Drawing.= By O. GUETH. Oblong 4to. (_New
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    =Hints on Architectural Draughtsmanship.= By G.W.T. HALLATT. Fourth
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    =A First Course of Mechanical Drawing= (Tracing). By G. HALLIDAY.
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               2  0

    =Drawings for Medium-sized Repetition Work.= By R.D. SPINNEY. With 47
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    =Mathematical Drawing Instruments.= By W.F. STANLEY. Seventh edition,
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               5  0


    ELECTRICAL ENGINEERING.

    =Practical Electric Bell Fitting.= By F.C. ALLSOP. Tenth edition, 186
    illus. including 8 folding plates, 185 pp. crown 8vo. (_1903_)

               3  6

    =Telephones:= their Construction and Fitting. By F.C. ALLSOP. Eighth
    edition, 184 illus. 222 pp. crown 8vo. (_1909_)

               3  6

    =Thermo-electric Reactions= and Currents between Metals in Fused
    Salts. By T. ANDREWS. 8vo, sewed. (_1896_)

               1  0

    =Auto-Transformer Design.= By A.H. AVERY. 25 illus. 60 pp. 8vo.
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    =Principles of Electric Power= (Continuous Current) for Mechanical
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    _net_      4  6

    =Practical Construction of Electric Tramways.= By WILLIAM R. BOWKER.
    93 illus. 119 pp. 8vo. (_1903_)

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    =Design and Construction of Induction Coils.= By A.F. COLLINS. 155
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    =Switchboard Measuring Instruments= for Continuous and Polyphase
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    _net_      5  0

    =Electric Cables, their Construction and Cost.= By D. COYLE and F.J.
    O. HOWE. With many diagrams and 216 tables, 467 pp. crown 8vo,
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    =Management of Electrical Machinery.= By F.B. CROCKER and S.S.
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    =Electric Lighting:= A Practical Exposition of the Art. By F.B.
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          Vol. I. =The Generating Plant.= Sixth edition, 213 illus. 470
          pp. (_1904_)

    _net_     12  6

          Vol. II. =Distributing Systems and Lamps.= Second edition, 391
          illus. 505 pp. (_1905_)

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    12 illus. 74 pp. crown 8vo, limp. (S. & C. SERIES, NO. 19.) (_1910_)

    _net_      1  6

    =Elementary Telegraphy and Telephony.= By ARTHUR CROTCH. 238 illus.
    223 pp. 8vo. (_1903._) (FINSBURY TECHNICAL MANUAL)

    _net_      4  6

    =Electricity and Magnetism in Telephone Maintenance.= By G.W.
    CUMMINGS. 45 illus. 137 pp. 8vo. (_New York, 1908_) . ..

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    =Grouping of Electric Cells.= By W.F. DUNTON. 4 illus. 50 pp. fcap.
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    MAGNETS AND ELECTRIC CURRENTS. By Prof. J.A. FLEMING. Second edition,
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    =Notes on Design of Small Dynamo.= By GEORGE HALLIDAY. Second edition,
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    Transmission.= By N. HARRISON. 172 illus. 375 pp.
    crown 8vo. (_New York, 1906_)

              10  6

    =Making Wireless Outfits.= By N. HARRISON. 27 illus. 61 pp. crown 8vo,
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    _net_      1  6

    =Wireless Telephone Construction.= By N. HARRISON. 43 illus. 73 pp.
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    _net_      1  6

    =The Phoenix Fire Office Rules= for Electric Light and Electrical
    Power Installations. By M. HEAPHY. Thirty-seventh edition, 8vo, sewed.
    (_1908_)

               0  6

    =Testing Telegraph Cables.= By Colonel V. HOSKIOER. Third edition,
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               4  6

    =Long Distance Electric Power Transmission.= By R.W. HUTCHINSON. 136
    illus. 345 pp. crown 8vo. (_New York, 1907_)

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    =Theory and Practice of Electric Wiring.= By W.S. IBBETSON. 119 illus.
    366 pp. crown 8vo. (_1909_)

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    =Practical Electrical Engineering for Elementary Students.= By W.S.
    IBBETSON. With 61 illus. 155 pp. crown 8vo. (_1910_)

    _net_      3  0

    =General Rules recommended for Wiring= for the Supply of Electrical
    Energy. Issued by THE INSTITUTION OF ELECTRICAL ENGINEERS. 8vo, sewed.
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    =Form of Model General Conditions= recommended by THE INSTITUTION OF
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    =A Handbook of Electrical Testing.= By H.R. KEMPE. Seventh edition,
    285 illus. 706 pp. demy 8vo. (_1908_)

    _net_     18  0

    =Application of Electricity to Railway Working.= By W.E. LANGDON.
    142 illus. and 5 plates, 347 pp. 8vo. (_1897_)

              10  6

    =How to Become a Competent Motorman.= By V.B. LIVERMORE and J.
    WILLIAMS. 45 illus. 252 pp. 12mo. (_New York, 1903_)

    _net_      4  6

    =Electromagnets,= their design and construction. By A.N. MANSFIELD. 36
    illus. 155 pp. 18mo, boards. (_New York, 1901_)

    _net_      2  0

    =Telephone Construction, Methods and Cost.= By C. MAYER. With
    Appendices on the cost of materials and labour by J.C. SLIPPY. 103
    illus. 284 pp. crown 8vo. (_New York, 1908_)

    _net_     12  6

    =Induction Coils.= By N.H. SCHNEIDER. Second edition, 79 illus. 285
    pp. crown 8vo. (_New York, 1901_)

    _net_      4  6

    =Electric Gas Lighting.= By N.H. SCHNEIDER. 57 illus. 101 pp. 12mo.
    (S. & C. SERIES, NO. 8.) (_New York, 1901_)

    _net_      2  0

    =How to Install Electric Bells, Annunciators and Alarms.= By N.H.
    SCHNEIDER. 59 illus. 63 pp. crown 8vo, limp. (S. & C. SERIES, NO. 2.)
    (_New York, 1905_)

    _net_      1  6

    =Modern Primary Batteries,= their construction, use and maintenance.
    By N.H. SCHNEIDER. 54 illus. 94 pp. crown 8vo, limp. (S. & C. SERIES,
    NO. 1.) (_New York, 1905_)

    _net_      1  6

    =Practical Engineers' Handbook on the Care and Management of Electric
    Power Plants.= By N.H. SCHNEIDER. 203 illus. 274 pp. crown 8vo. (_New
    York, 1906_)

    _net_      5  0

    =Electrical Circuits and Diagrams,= illustrated and explained. By N.H.
    SCHNEIDER. 8vo, limp. (S. & C. SERIES, NOS. 3 AND 4.) (_New York_)

          Part 1. 217 illus. 72 pp. (_1905_)

    _net_      1  6

          Part 2. 73 pp. (_1909_)

    _net_      1  6

    =Electrical Instruments and Testing.= By N.H. SCHNEIDER. Third
    edition. 133 illus. 239 pp. crown 8vo. (_New York, 1907_)

    _net_      4  6

    =Experimenting with Induction Coils.= By N.H. SCHNEIDER. 26 illus. 73
    pp. crown 8vo, limp. (S. & C. SERIES, NO. 5.) (_New York, 1906_)

    _net_      1  6

    =Study of Electricity for Beginners.= By N.H. SCHNEIDER. 54 illus. 88
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    _net_      1  6

    =Practical Electrics:= a Universal Handybook on Every Day Electrical
    Matters. Seventh edition, 126 illus. 135 pp. 8vo. (S. & C. SERIES, NO.
    13.) (_New York, 1902_)

    _net_      1  6

    =The Voltaic Accumulator:= an elementary treatise. By E. REYNIER.
    Translated from the French by J.A. BERLY. 62 illus. 202 pp. 8vo

               9  0

    =Dry Batteries:= how to Make and Use them. By a DRY BATTERY EXPERT.
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    sewed. (S. & C. SERIES, NO. 7.) (_New York, 1905_)

    _net_      1  6

    =The Diseases of Electrical Machinery.= By E. SCHULZ. Edited, with a
    Preface, by Prof. S.P. THOMPSON. 42 illus. 84 pp. crown 8vo

    _net_      2  0

    =Electric Toy-Making.= By T.O. SLOANE. Fifteenth edition, 70 illus.
    183 pp. crown 8vo. (_New York, 1903_)

    _net_      4  6

    =Electricity Simplified.= By T.O. SLOANE. Tenth edition, 29 illus. 158
    pp. crown 8vo. (_New York, 1901_)

    _net_      4  6

    =How to become a Successful Electrician.= By T.O. SLOANE. Third
    edition, illustrated, crown 8vo. (_New York, 1899_)

    _net_      4  6

    =Electricity:= its Theory, Sources and Applications. By J.T. SPRAGUE.
    Third edition, 109 illus. 658 pp. crown 8vo. (_1892_)

    _net_      7  6

    =Telegraphic Connections.= By C. THOM and W.H. JONES. 20 plates, 59
    pp. oblong 8vo. (_New York, 1892_)

    _net_      3  6

    =Röntgen Rays= and Phenomena of the Anode and Cathode. By E.P.
    THOMPSON and W.A. ANTHONY. 105 illus. 204 pp. 8vo. (_New York, 1896_)

    _net_      4  6

    =Dynamo Electric Machinery.= By Prof. S.P. THOMPSON. Seventh edition,
    demy 8vo. (FINSBURY TECHNICAL MANUAL.)

          Vol. I. =Continuous-Current Machinery.= With 4 coloured and 30
          folding plates, 573 illus. 984 pp. (_1904_)

    _net_   1 10  0

          Vol. II. =Alternating Current Machinery.= 15 coloured and 24
          folding plates, 546 illus. 900 pp. (_1905_)

    _net_   1 10  0

    =Design of Dynamos= (Continuous Currents). By Prof. S.P. THOMPSON. 4
    coloured and 8 folding plates, 243 pp. demy 8vo. (_1903_)

    _net_     12  0

    =Schedule for Dynamo Design,= issued with the above. 6_d_. each, 4_s_.
    per doz., or 18_s_. per 100 _net_

    =Curves of Magnetic Data for Various Materials.= A reprint on
    transparent paper for office use of Plate L from Dynamo Electric
    Machinery, and measuring 25 in. by 16 in.

    _net_      0  7

    =The Electromagnet.= By C.R. UNDERHILL. 67 illus. 159 pp. crown 8vo.
    (_New York, 1903_)

    _net_      6  6

    =Practical Guide to the Testing of Insulated Wires and Cables.= By
    H.L. WEBB. Fifth edition, 38 illus. 118 pp. crown 8vo. (_New York,
    1902_)

    _net_      4  6


    FOREIGN EXCHANGE.

    =English Prices with Russian Equivalents= (at Fourteen Rates of
    Exchange). English prices per lb., with equivalents in roubles and
    kopecks per pood. By A. ADIASSEWICH. 182 pp. fcap. 32mo, roan.
    (_1908_)

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    =English Prices with German Equivalents= (at Seven Rates of Exchange).
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    _net_      1  0

    =English Prices with Spanish Equivalents.= At Seven Rates of Exchange.
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    =English Prices with French Equivalents= (at Seven Rates of Exchange).
    English prices per lb. to francs per kilogramme. By H.P. MCCARTNEY. 97
    pp. 32mo, roan. (_1907_)

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    =Principles of Foreign Exchange.= By E. MATHESON. Fourth edition, 54
    pp. 8vo, sewed. (_1905_)

    _net_      0  3


    GAS AND OIL ENGINES.

    =The Theory of the Gas Engine.= By D. CLERK. Edited by F.E. IDELL.
    Third edition, 19 illus. 180 pp. 18mo, boards. (_New York, 1903_)

    _net_      2  0

    =The Design and Construction of Oil Engines.= By A.H. GOLDINGHAM.
    Third edition, 112 illus. 260 pp. crown 8vo. (_New York, 1910_)

    _net_     10  6

    =Gas Engine in Principle and Practice.= By A.H. GOLDINGHAM. 107 illus.
    195 pp. 8vo, cloth. (_New York, 1907_)

    _net_      6  6

    =Practical Hand-Book on the Care and Management of Gas Engines.= By
    G. LIECKFELD. Third edition, square 16mo. (_New York, 1896_)

               3  6

    =Elements of Gas Engine Design.= By S.A. MOSS. 197 pp. 18mo, boards.
    (_New York, 1907_)

    _net_      2  0

    =Gas and Petroleum Engines.= A Manual for Students and Engineers.
    (FINSBURY TECHNICAL MANUAL.) By Prof. W. ROBINSON. _Third edition in
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    GAS LIGHTING.

    =Gas Analyst's Manual= (incorporating Hartley's "Gas Analyst's Manual"
    and "Gas Measurement"). By J. ABADY. 102 illustrations, 576 pp. demy
    8vo. (_1902_)

    _net_     18  0

    =Gas Works:= their Arrangement, Construction, Plant and Machinery. By
    F. COLYER. 31 folding plates, 134 pp. 8vo. (_1884_)

    _net_      8  6

    =Transactions of the Institution of Gas Engineers.= Edited by WALTER
    T. DUNN, _Secretary_. Published annually. 8vo

    _net_     10  6

    =Lighting by Acetylene.= By F. DYE. 75 illus. 200 pp. crown 8vo.
    (_1902_)

    _net_      6  0

    =A Comparison of the English and French Methods of Ascertaining the
    Illuminating Power of Coal Gas.= By A.J. VAN EIJNDHOVEN. Illustrated,
    crown 8vo. (_1897_)

               4  0

    =Gas Lighting and Gas Fitting.= By W.P. GERHARD. Second edition, 190
    pp. 18mo, boards. (_New York, 1894_)

    _net_      2  0

    =A Treatise on the Comparative Commercial Values of Gas Coals and
    Cannels.= By D.A. GRAHAM. 3 plates, 100 pp. 8vo. (_1882_)

               4  6

    =The Gas Engineer's Laboratory Handbook.= By J. HORNBY. Third edition,
    revised, 70 illus. 330 pp. crown 8vo. (_1910_)

    _net_      6  0


    HISTORICAL AND BIOGRAPHICAL.

    =Extracts from the Private Letters of the late Sir William Fothergill
    Cooke,= 1836-9, relating to the Invention and Development of the
    Electric Telegraph; also a Memoir by LATIMER CLARK. Edited by F.H.
    WEBB. Sec. Inst.E.E. 8vo. (_1895_)

               3  0

    =A Chronology of Inland Navigation= in Great Britain. By H.R. DE
    SALIS. Crown 8vo. (1897)

               4  6

    =A History of Electric Telegraphy= to the year 1837. By J.J. FAHIE. 35
    illus. 542 pp. crown 8vo. (_1889_)

               2  0

    =History and Development of Steam Locomotion on Common Roads.= By W.
    FLETCHER. 109 illus. 288 pp. 8vo

               5  0

    =Life as an Engineer:= its Lights, Shades, and Prospects. By J.W.C.
    HALDANE. 23 plates, 338 pp. crown 8vo. (_1905_)

    _net_      5  0

    =Philipp Reis,= Inventor of the Telephone: a Biographical Sketch. By
    Prof. S.P. THOMPSON. 8vo, cloth. (_1883_)

               7  6

    =The Development of the Mercurial Air Pump.= By Prof. S.P. THOMPSON.
    Illustrated, royal 8vo, sewed. (_1888_)

               1  6


    HOROLOGY.

    =Watch and Clock Maker's Handbook,= Dictionary and Guide. By F.J.
    BRITTEN. Tenth edition, 450 illus. 492 pp. crown 8vo. (_1902_)

    _net_      5  0

    =The Springing and Adjusting of Watches.= By F.J. BRITTEN. 75 illus.
    152 pp. crown 8vo. (_1898_)

    _net_      3  0

    =Prize Essay on the Balance Spring= and its Isochronal Adjustments. By
    M. IMMISCH. 7 illus. 50 pp. crown 8vo. (_1872_)

               2  6


    HYDRAULICS AND HYDRAULIC MACHINERY.

    (_See also_ WATER SUPPLY.)

    =Pumps:= Historically, Theoretically and Practically Considered. By
    P.R. BJÖRLING. Second edition, 156 illus. 234 pp. crown 8vo. (_1895_)

               7  6

    =Pump Details.= By P.R. BJÖRLING. 278 illus. 211 pp. crown 8vo.
    (_1892_)

               7  6

    =Pumps and Pump Motors:= A Manual for the use of Hydraulic Engineers.
    By P.R. BJÖRLING. Two vols. 261 plates, 369 pp. royal 4to. (_1895_).

    _net_   1 10  0

    =Practical Handbook on Pump Construction.= By P.R. BJÖRLING. Second
    edition, 9 plates, 90 pp. crown 8vo. (_1904_)

               5  0

    =Water or Hydraulic Motors.= By P.R. BJÖRLING. 206 illus. 287 pp.
    crown 8vo. (_1903_)

               9  0

    =Hydraulic Machinery,= with an Introduction to Hydraulics. By R.G.
    BLAINE. Second edition with 307 illus. 468 pp. 8vo. (FINSBURY
    TECHNICAL MANUAL). (_1905_)

    _net_     14  0

    =Practical Hydraulics.= By T. BOX. Fifteenth edition, 8 plates, 88 pp.
    crown 8vo. (_1909_)

    _net_      5  0

    =Hydraulic, Steam, and Hand Power Lifting and Pressing Machinery.= By
    F. COLYER. Second edition, 88 plates, 211 pp. imperial 8vo. (_1892_)

    _net_     10  6

    =Pumps and Pumping Machinery.= By F. COLYER.

          Vol. I. Second edition, 53 plates, 212 pp. 8vo (_1892_)

    _net_     10  6

          Vol. II. Second edition, 48 plates, 169 pp. 8vo. (_1900_)

    _net_     10  6

    =Construction of Horizontal and Vertical Water-wheels.= By W. CULLEN.
    Second edition, small 4to. (_1871_)

               5  0

    =Donaldson's Poncelet Turbine= and Water Pressure Engine and Pump.
    By W. DONALDSON. 4to. (_1883_)

               5  0

    =Principles of Construction and Efficiency of Water-wheels.= By W.
    DONALDSON. 13 illus. 94 pp. 8vo. (_1876_)

               5  0

    =Practical Hydrostatics and Hydrostatic Formulæ.= By E.S. GOULD. 27
    illus. 114 pp. 18mo, boards. (_New York, 1903_)

    _net_      2  0

    =Hydraulic and other Tables= for purposes of Sewerage and Water
    Supply. By T. HENNELL. Third edition, 70 pp. crown 8vo. (_1908_)

    _net_      4  6

    =Hydraulic Tables= for finding the Mean Velocity and Discharge in Open
    Channels. By T. HIGHAM. Second edition, 90 pp. super-royal 8vo.
    (_1898_)

               7  6

    =Tables for Calculating the Discharge of Water= in Pipes for Water and
    Power Supplies. Indexed at side for ready reference. By A.E. SILK. 63
    pp. crown 8vo. (_1899_)

               5  0

    =Simple Hydraulic Formulæ.= By T.W. STONE. 9 plates, 98 pp. crown 8vo.
    (_1881_)

               4  0


    INDUSTRIAL CHEMISTRY AND MANUFACTURES.

    =Perfumes and their Preparation.= By G.W. ASKINSON. Translated from
    the Third German Edition by I. FUEST. Third edition, 32 illus. 312 pp.
    8vo. (_New York, 1907_)

    _net_     12  6

    =Brewing Calculations,= Gauging and Tabulation. By C.H. BATER. 340 pp.
    64mo, roan, gilt edges. (_1897_)

    _net_      1  6

    =A Pocket Book for Chemists,= Chemical Manufacturers, Metallurgists,
    Dyers, Distillers, etc. By T. BAYLEY. Seventh edition, 550 pp. royal
    32mo, roan, gilt edges. (_1905_)

    _net_      5  0

    =Practical Receipts= for the Manufacturer, the Mechanic, and for
    Home use. By Dr. H.R. BERKELEY and W.M. WALKER. 250 pp. demy 8vo.
    (_1902_)

    _net_      7  6

    =A Treatise on the Manufacture of Soap and Candles,= Lubricants and
    Glycerine. By W.L. CARPENTER and H. LEASK. Second edition, 104 illus.
    456 pp. crown 8vo. (_1895_)

              12  6

    =A Text Book of Paper Making.= By C.F. CROSS and E.J. BEVAN. Third
    edition, 97 illus. 411 pp. crown 8vo. (_1907_)

    _net_     12  6

    =C.B.S. Standard Units and Standard Paper Tests.= By C.F. CROSS, E.J.
    BEVAN, C. BEADLE and R.W. SINDALL. 25 pp. crown 4to. (_1903_)

    _net_     2  6

    =Soda Fountain Requisites.= A Practical Receipt Book for Druggists,
    Chemists, etc. By G.H. DUBELLE. Third edition, 157 pp. crown 8vo.
    (_New York, 1905_)

    _net_      4  6

    =The Chemistry of Fire= and Fire Prevention. By H. and H. INGLE. 45
    illus. 290 pp. crown 8vo. (_1900_)

               9  0

    =Ice-Making Machines.= By M. Ledoux and others. Sixth edition. 190 pp.
    18mo, boards. (_New York, 1906_)

    _net_      2  0

    =Brewing with Raw Grain.= By T.W. Lovibond. 75 pp. crown 8vo. (1883)

               5  0

    =Sugar, a Handbook for Planters and Refiners.= By the late J.A.R.
    NEWLANDS and B.E.R. NEWLANDS. 236 illus. 876 pp. demy 8vo. (_London,
    1909_)

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    =Principles of Leather Manufacture.= By Prof. H.R. PROCTER. 101 illus.
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    =Reform in Chemical and Physical Calculations.= By C.J.T. HANSSEN.
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    =Galvanic Circuit investigated Mathematically.= By G.S. OHM.
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    =Elementary Practical Mathematics.= By M.T. ORMSBY. 420 pp. demy 8vo.
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    =Elements of Graphic Statics.= By K. VON OTT. Translated by G.S.
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    MECHANICAL ENGINEERING.

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    =Handbook for Mechanical Engineers.= By HY. ADAMS. Fourth edition, 426
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    =The Repair and Maintenance of Machinery.= By T.W. BARBER. 417 illus.
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    =Practical Treatise on Mill Gearing.= By T. BOX. Fifth edition, 11
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               7  6

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    =Machine Design.= By Prof. W.L. CATHCART. Part I. FASTENINGS. 123
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    =Furnace Draft:= its Production by Mechanical Methods. By W.W.
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    =Working and Management of Steam Boilers and Engines.= By F. COLYER.
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    =Treatise on the use of Belting for the Transmission of Power.= By
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    =The Steam Engine considered as a Thermodynamic Machine.= By J.H.
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    =Fireman's Guide=, a Handbook on the Care of Boilers. By K.P.
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    =Heat for Engineers.= By C.R. DARLING. 110 illus. 430 pp. 8vo.
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    =Diseases of a Gasolene Automobile=, and How to Cure Them. By A.L.
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    _net_      6  6

    =Belt Driving.= By G. HALLIDAY. 3 folding plates, 100 pp. 8vo.
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               3  6

    =Worm and Spiral Gearing.= By F.A. HALSEY. 13 plates, 85 pp. 18mo,
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    =Commercial Efficiency of Steam Boilers.= By A. HANSSEN. Large 8vo,
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    =Liquid Fuel= for Mechanical and Industrial Purposes. By E.A.
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               5  0

    =Elementary Text-Book on Steam Engines and Boilers.= By J.H.
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    =Centrifugal Fans.= By J.H. KINEALY. 33 illus. 206 pp. fcap.
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    =Mechanical Draft.= By J.H. KINEALY. 27 original tables and 13
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    =The A.B.C. of the Steam Engine=, with a description of the
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    =Valve Setting Record Book.= By P.A. LOW. 8vo, boards.

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    =Steam Boilers=, their Management and Working. By J. PEATTIE.
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    =Treatise on the Richards Steam Engine Indicator.= By C.T.
    PORTER. Sixth edition, 3 plates and 73 diagrams, 285 pp. 8vo.
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               9  0

    =Practical Treatise on the Steam Engine.= By A. RIGG. Second
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    =Power and its Transmission.= A Practical Handbook for the
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    =Drawings for Medium Sized Repetition Work.= By R.D. SPINNEY.
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    =Slide Valve Simply Explained.= By W.J. TENNANT. Revised by
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    =Shaft Governors.= By W. TRINKS and C. HOOSUM. 27 illus. 97 pp.
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    =Slide and Piston Valve Geared Steam Engines.= By W.H. UHLAND.
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    =How to run Engines and Boilers.= By E.P. WATSON. Fifth
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               3  6

    =Position Diagram of Cylinder with Meyer Cut-off.= By W.H.
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    =Practical Method of Designing Slide Valve Gearing.= By E.J.
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    =Elements of Mechanics.= By T.W. WRIGHT. Eighth edition,
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    METALLURGY.

    IRON AND STEEL MANUFACTURE.

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               1  0

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    =Microscopic Internal Flaws, Inducing Fracture in Steel.= By T.
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    =Brassfounders' Alloys.= By J.F. BUCHANAN. Illustrated, 129 pp.
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    =American Standard Specifications for Steel.= By A.L. COLBY.
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    =Galvanised Iron=: its Manufacture and Uses. By J. DAVIES. 139
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    =Management of Steel.= By G. EDE. Seventh edition, 216 pp.
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    =Galvanising and Tinning=, with a special Chapter on Tinning
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    =Practical Notes on Pipe Founding.= By J.W. MACFARLANE. 15
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    =French Measure and English Equivalents.= By J. BROOK. Second
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    =A Dictionary of Metric and other useful Measures.= By L.
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    =Rock Blasting.= By G.G. ANDRE. 12 plates and 56 illus. in
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    =Practical Treatise on Hydraulic Mining in California.= By A.J.
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    =Manual of Assaying Gold, Silver, Copper and Lead Ores.= By
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    =Fire Assaying.= By E.W. BUSKETT. 69 illus. 105 pp. crown 8vo.
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    =Tin=: Describing the Chief Methods of Mining, Dressing, etc.
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              12  6

    =Gold Mining and Milling= in Western Australia, with Notes upon
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    =Miners' Geology and Prospectors' Guide.= By G.A. CORDER. 29
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    =Blasting of Rock in Mines, Quarries, Tunnels, etc.= By A.W.
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    =Conversations on Mines.= By W. HOPTON. Ninth edition, 33
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               4  6

    =Our Coal Resources= at the End of the Nineteenth Century. By
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               6  0

    =Hydraulic Gold Miners' Manual.= By T.S.G. KIRKPATRICK. Second
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    =Economic Mining.= By C.G.W. LOCK. 175 illus. 680 pp. 8vo.
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               7  6

    =Theory and Practice of Centrifugal Ventilating Machines.= By
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    ORGANISATION.

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    =Commercial Organisation of Engineering Factories.= By H.
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    =Reform in Chemical and Physical Calculations.= By C.J.T.
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    =Simple and Automatic Vacuum Brakes.= By C. BRIGGS, G.N.R. 11
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    =Permanent-Way Diagrams.= By F.H. FRERE. Mounted on linen in
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    =Formulæ for Railway Crossings and Switches.= By J. GLOVER. 9
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    =Setting out of Tube Railways.= By G.M. HALDEN. 9 plates, 46
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    =Railway Engineering, Mechanical and Electrical.= By J.W.C.
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    =The Construction of the Modern Locomotive.= By G. HUGHES. 300
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               9  0

    =Practical Hints for Light Railways= at Home and Abroad. By
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               2  6

    =Handbook on Railway Stores Management.= By W.O. KEMPTHORNE.
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    =Railway Stores Price Book.= By W.O. KEMPTHORNE. 487 pp. demy
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    =Railroad Location Surveys and Estimates.= By F. LAVIS. 68
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    =Tables for Computing the Contents of Earthwork= in the
    Cuttings and Embankments of Railways. By W. MACGREGOR. Royal
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               6  0

    =Bridge and Tunnel Centres.= By J.B. MCMASTERS. Illustrated,
    106 pp. 18mo, boards. (_New York, 1893_)

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    =Pioneering.= By F. SHELFORD. Illustrated, 88 pp. crown 8vo.
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    =Handbook on Railway Surveying= for Students and Junior
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    _net_      2  6

    =Spiral Tables.= By J.G. SULLIVAN. 47 pp. 12mo, leather. (_New
    York, 1908_)

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    =Modern British Locomotives.= By A.T. TAYLOR. 100 diagrams of
    principal dimensions, 118 pp. oblong 8vo. (_1907_)

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    =Locomotive Slide Valve Setting.= By C.E. TULLY. Illustrated,
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    =The Walschaert Locomotive Valve Gear.= By W.W. WOOD. 4 plates
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    =The Westinghouse E.T. Air-Brake Instruction Pocket Book.= By
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    _net_      8  6


    SANITATION, PUBLIC HEALTH AND MUNICIPAL ENGINEERING.

    =Sewers and Drains for Populous Districts.= By J.W. ADAMS.
    Ninth edition, 81 illus. 236 pp. 8vo. (_New York, 1902_)

    _net_     10  6

    =Public Abattoirs=, their Planning, Design and Equipment. By
    R.S. AYLING. 33 plates, 100 pp. demy 4to. (_1908_)

    _net_      8  6

    =Sewage Purification.= By E. BAILEY-DENTON. 8 plates, 44 pp.
    8vo. (_1896_)

               5  0

    =Water Supply and Sewerage of Country Mansions= and Estates. By
    E. BAILEY-DENTON. 76 pp. crown 8vo. (_1901_)

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    =Sewerage and Sewage Purification.= By M.N. BAKER. Second
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    _net_      2  0

    =Sewage Irrigation by Farmers.= By R.W.P. BIRCH. 8vo, sewed.
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               2  6

    =Sanitary House Drainage=, its Principles and Practice. By T.E.
    COLEMAN. 98 illus. 206 pp. crown 8vo. (_1896_)

               6  0

    =Stable Sanitation and Construction.= By T.E. COLEMAN. 183
    illus. 226 pp. crown 8vo. (_1897_)

               6  0

    =Public Institutions=, their Engineering, Sanitary and other
    Appliances. By F. COLYER. 231 pp. 8vo. (_1889_)

    _net_      2  0

    =Discharge of Pipes and Culverts.= By P.M. CROSTHWAITE. Large
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    and 21 folding plates, 830 pp. 4to, cloth. (_1899_)

    _net_   1 10  0

    =Standard Practical Plumbing.= By P.J. DAVIES.

        Vol. I. Fourth edition, 768 illus. 355 pp. royal 8vo. (_1905_)

    _net_      7  6

        Vol. II. Second edition, 953 illus. 805 pp. (_1905_)

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        Vol. III. 313 illus. 204 pp. (_1905_)

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    =Conservancy, or Dry Sanitation versus Water Carriage.= By J.
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    =Sewage Disposal Works=, their Design and Construction. By W.C.
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    _net_     10  6

    =House Drainage and Sanitary Plumbing.= By W.P. GERHARD. Tenth
    edition, 6 illus. 231 pp. 18mo, boards. (_New York, 1902_)

    _net_      2  0

    =Engineering Work in Towns and Cities.= By E. MCCULLOCH. 44
    illus. 502 pp. crown 8vo. (_New York, 1908_)

    _net_     12  6

    =The Treatment of Septic Sewage.= By G.W. RAFTER. 137 pp. 18mo,
    boards. (_New York, 1904_)

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    =Reports and Investigations on Sewer Air= and Sewer
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    =The Law and Practice of Paving= Private Street Works. By W.
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    _net_     12  6


    STRUCTURAL DESIGN.

    (_See_ BRIDGES AND ROOFS.)


    TELEGRAPH CODES.

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    1909_)

    _net_   1 10  0

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    _net_      6  6


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    =Hot Water Supply.= By F. DYE. Fifth edition, 48 illus. 86 pp.
    crown 8vo. (_1902_)

    _net_      3  0

    =A Practical Treatise upon Steam Heating.= By F. DYE. 129
    illus. 246 pp. demy 8vo. (_1901_)

    _net_     10  0

    =Practical Treatise on Warming Buildings by Hot Water.= By F.
    DYE. 192 illus. 319 pp. 8vo. cloth. (_1905_)

    _net_      8  6

    =Charts for Low Pressure Steam Heating.= By J.H. KINEALY. Small
    folio. (_New York_)

               4  6

    =Formulæ and Tables for Heating.= By J.H. KINEALY. 18 illus. 53
    pp. 8vo. (_New York, 1899_)

               3  6

    =Mechanics of Ventilation.= By G.W. RAFTER. Second edition,
    18mo, boards. (_New York, 1896_)

    _net_      2  0

    =Principles of Heating.= By W.G. SNOW. 62 illus. 161 pp. 8vo.
    (_New York, 1907_)

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    =Furnace Heating.= By W.G. SNOW. Fourth edition, 52 illus. 216
    pp. 8vo. (_New York, 1909_)

    _net_      6  6

    =Ventilation of Buildings.= By W.G. SNOW and T. NOLAN. 83 pp.
    18mo, boards. (_New York, 1906_)

    _net_      2  0

    =Heating Engineers' Quantities.= By W.L. WHITE and G.M. WHITE.
    4 plates, 33 pp. folio. (_1910_)

    _net_     10  6


    WATER SUPPLY.

    (_See also_ HYDRAULICS.)

    =Potable Water and Methods of Testing Impurities.= By M.N.
    BAKER. 97 pp. 18mo, boards. (_New York, 1905_)

    _net_      2  0

    =Manual of Hydrology.= By N. BEARDMORE. New impression, 18
    plates, 384 pp. 8vo. (_1906_)

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    =Boiler Waters=, Scale, Corrosion and Fouling. By W.W.
    CHRISTIE. 77 illus. 235 pp. 8vo, cloth. (_New York, 1907_)

    _net_     12  6

    =Water Softening and Purification.= By H. COLLET. Second
    edition, 6 illus. 170 pp. crown 8vo. (_1908_)

    _net_      5  0

    =Treatise on Water Supply=, Drainage and Sanitary Appliances of
    Residences. By F. COLYER. 100 pp. crown 8vo. (_1899_)

    _net_      1  6

    =Report on the Investigations into the Purification of the Ohio
    River Water= at Louisville, Kentucky. By G.W. FULLER. 8 plates,
    4to, cloth. (_New York, 1898_)

    _net_   2  2  0

    =Purification of Public Water Supplies.= By J.W. HILL. 314 pp.
    8vo. (_New York, 1898_)

              10  6

    =Well Boring for Water, Brine and Oil.= By C. ISLER. _New
    edition in the Press._

    =Method of Measuring Liquids Flowing through Pipes by means of
    Meters of Small Calibre.= By Prof. G. LANGE. 1 plate, 16 pp.
    8vo, sewed

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    =On Artificial Underground Water.= By G. RICHERT. 16 illus. 33
    pp. 8vo, sewed. (_1900_)

    _net_      1  6

    =Notes on Water Supply= in new Countries. By F.W. STONE. 18
    plates, 42 pp. crown 8vo. (_1888_)

               5  0

    =The Principles of Waterworks Engineering.= By J.H.T. TUDSBERY
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    illus. 447 pp. demy 8vo. (_1905_)

    _net_   1  1  0


    WORKSHOP PRACTICE.

    =A Handbook for Apprenticed Machinists.= By O.J. BEALE. Second
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    _net_      2  6

    =Bicycle Repairing.= By S.D.V. BURR. Sixth edition, 200 illus.
    208 pp. 8vo. (_New York, 1903_)

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    =Practice of Hand Turning.= By F. CAMPIN. Third edition, 99
    illus. 307 pp. crown 8vo. (_1883_)

               3  6

    =Calculation of Change Wheels for Screw Cutting on Lathes.= By
    D. DE VRIES. 46 illus. 83 pp. 8vo. (_1908_)

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    =Milling Machines and Milling Practice.= By D. DE VRIES. With
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    =French-Polishers' Manual.= By a French-Polisher. 31 pp. royal
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    =Art of Copper Smithing.= By J. FULLER. Third edition, 475
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    =Saw Filing and Management of Saws.= By R. GRIMSHAW. New
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    =Paint and Colour Mixing.= By A.S. JENNINGS. Fourth edition. 14
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    =The Mechanician=: a Treatise on the Construction and
    Manipulation of Tools. By C. KNIGHT. Fifth edition, 96 plates,
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    =Turner's and Fitter's Pocket Book.= By J. LA NICCA. 18mo,
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    =Tables for Engineers and Mechanics=, giving the values of the
    different trains of wheels required to produce Screws of any
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    =Screw-cutting Tables.= By W.A. MARTIN. Seventh edition, royal
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    =Metal Plate Work=, its Patterns and their Geometry, for the
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               9  0

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    =Modern Machine Shop Construction=, equipment and management.
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    =Turner's Handbook on Screw-cutting=, Coning, etc. By W. PRICE.
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    =Introduction to Eccentric Spiral Turning.= By H.C. ROBINSON.
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    =Manual of Instruction in Hard Soldering.= By H. ROWELL. Sixth
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    _net_      3  0

    =Pocket Book on Boilermaking, Shipbuilding=, and the Steel and
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    =Power and its Transmission.= A Practical Handbook for the
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    =Spons' Mechanics' Own Book=: A Manual for Handicraftsmen and
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               6  0

    Ditto       ditto    half morocco

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    =Spons' Workshop Receipts for Manufacturers, Mechanics and
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    _each net_ 3  0

    Vol. I. ACETYLENE LIGHTING _to_ DRYING. 223 illus. 532 pp.

    Vol. II. DYEING _to_ JAPANNING. 259 illus. 540 pp.

    Vol. III. JOINTING PIPES _to_ PUMPS. 256 illus. 528 pp.

    Vol. IV. RAINWATER SEPARATORS _to_ WINES. 250 illus. 520 pp.

    =Gauges at a Glance.= By T. TAYLOR. Second edition, post 8vo, oblong,
    with tape converter. (_1900_)

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    =Simple Soldering=, both Hard and Soft. By E. THATCHER. 52
    illus. 76 pp. crown 8vo, limp. (S. & C. SERIES, NO. 18.) (_New
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    _net_      1  6

    =The Modern Machinist.= By J.T. USHER. Fifth edition. 257
    illus. 322 pp. 8vo. (_New York, 1904_)

    _net_     10  6

    =Practical Wood Carving.= By C.J. WOODSEND. 108 illus. 86 pp.
    8vo. (_New York, 1897_)

    _net_      4  6

    =American Tool Making= and Interchangeable Manufacturing. By
    J.W. WOODWORTH. 600 illus. 544 pp. demy 8vo. (_New York, 1905_)

    _net_     17  0


    USEFUL TABLES.

    =Weights and Measurements of Sheet Lead.= By J. ALEXANDER.
    32mo, roan

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    =Tables of Parabolic Curves= for the use of Railway Engineers
    and others. By G.T. ALLEN. Fcap. 16mo

               4  0

    =Barlow's Tables of Squares=, Cubes, Square Roots, Cube Roots
    and Reciprocals. Crown 8vo

               6  0

    =Tables of Squares.= By E.E. BUCHANAN. Ninth edition, 12mo

    _net_      4  6

    =Land Area Tables.= By W. CODD. Square 16mo, on a sheet mounted
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    =Tables for Setting out Curves= from 101 to 5000 feet radius.
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    _net_      2  6

    =Transition Curves.= By W.G. FOX. 18mo, boards. (_New York_)

    _net_      2  0

    =Tables of some of the Principal Speeds= occurring in
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               0  6

    =Calculating Scale.= A Substitute for the Slide Rule. By W.
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    =Planimeter Areas.= Multipliers for various scales. By H.B.
    MOLESWORTH. Folding sheet in cloth case.

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    =Tables of Seamless Copper Tubes.= By I. O'TOOLE. 69 pp. oblong
    fcap. 8vo. (_1908_)

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    =Rownson's Iron Merchants' Tables= and Memoranda, Weights and
    Measures. 86 pp. 32mo, leather

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    =Spons' Tables and Memoranda for Engineers.= By J.T. HURST,
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    Ditto   ditto    in celluloid case

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       *       *       *       *       *


  Transcriber's Notes

  Obvious punctuation and spelling errors and inconsistent hyphenation
  have been corrected.

  Italic text is denoted by _underscores_ and bold text by =equal signs=.

  The OE ligature has been replaced by the separate characters.

  The fractions ¼, ½ and ¾ are represented using the Latin-1 characters,
  but other fractions use the / and - symbols, e.g. 3/8 or 2-5/8.

  The exponents 2 and 3 are represented using ² and ³ respectively, but
  other exponents are indicated by the caret character, for example,
  v^{1·85}

  Subscripts are simply enclosed in braces, e.g. W{0}.

  Other symbols that cannot be represented have been replaced by words
  in braces: {alpha}, {pi}, {therefore}, {square root} and
  {proportional to}.

  The skin friction formulæ given on pages 11 and 128 have been corrected
  by comparison with other sources. Respectively, the formulæ were
  originally printed as
      _f_ = 0·00000778_l_^{9·3}_v_^{1·85}
  and
      _f_ = 0·00000778_l_ - ^{00·7}_v_^{1·85}

  In ambiguous cases, the text has been left as it appears in the
  original book.