[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.