Chapter X: 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.

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.

§ 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.)

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.

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.