The Theory and Practice of Model Aeroplaning Part 3

-- 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.

[Ill.u.s.tration: 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.

[Ill.u.s.tration: 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 const.i.tute 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.

[Ill.u.s.tration: 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 Penaud first used elastic (rubber) for model aeroplanes, and during that time no better subst.i.tute (in spite of innumerable experiments) has been found. Nor for the smaller and lighter cla.s.s 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_. Gla.s.s 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 surpa.s.ses 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 inch up to 24-5/8 inches. Graph drawn in Fig.

14, No. B abscissae 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.

[Ill.u.s.tration: 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--6 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 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.

[Ill.u.s.tration: 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 3 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 princ.i.p.al 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, 3 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.)

[Ill.u.s.tration: FIG. 16.--TORQUE GRAPHS OF RUBBER MOTORS.

Abscissae = 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, 3 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.]