# Aircraft in Warfare (1916)/Appendix

APPENDIX I.
THE LEWIS GUN AS AN AEROPLANE ARM.
The Lewis Machine Gun has features which render it especially suitable for employment as an aeroplane arm. These are in brief:— The absence of water jacket. The lightness obtained by the adoption of pressure in place of recoil actuation. The self-contained magazine.
The abandonment of the water jacket is effected by resort to direct air cooling, a gilled jacket being applied to the barrel; the problem is closely analagous to that of the air cooled petrol motor. In aeronautical fighting a machine gun is never required to work continuously for any length of time, and the problem under these conditions presents no difficulty: in other fields of usefulness the reverse is the case, and calculations given later in the present appendix give some idea of the real difficulty of the problem, the solution of which has been achieved by the inventor of this weapon. The advantage of pressure actuation in place of recoil actuation lies in the fact that if the former be adopted the total weight of the weapon can be designed to the minimum possible, whereas in a recoil actuated gun the mass of the portion which acts as " abutment " to the recoil mechanism has to be far greater than considerations of strength alone would warrant: thus the total weight is ​greater in the older recoil actuated gun than in the Lewis type.
The importance of the self-contained magazine in a weapon to be handled from aircraft is obvious, and is so great as to make this feature almost a sine qua non. In the Lewis Gun each magazine contains 47 rounds, and can be replaced with but a few seconds pause in the discharge of the weapon. The resulting "breaks" in the continuity of discharge do not seriously affect the value of the arm in general usage, and in aeroplane fighting they count for nothing. The advantage, on the other hand, of a gun with no "appendages," which can be directed upward or downward or to any point of the compass at will, is one of real and decisive value.
The Problem of Direct Air Cooling. A Study of the Lewis System. Some Approximate Figures. The cooling of the barrel of a machine gun by air in place of the more usual water jacket is a problem of no mean difficulty. It is not ordinarily realised how great is the output of a machine gun in continuous firing expressed in horse power. Thus in the case of the M.VI service ammunition the muzzle energy is 2,000 ft. lbs., and the power represented by the energy of the stream of projectiles is approximately 0.06 horse power per shot per minute. At a maximum rate of fire of 800 per minute this gives 48 h.p, or at a normal speed of fire—say 480 per minute—29nbh.p. The problem of air cooling a machine gun then, is comparable to that of air cooling an internal combustion engine, of roughly 50 b.h.p., approximately the power of an aeronautical motor such as until recently in general usage.
The comparison with an ordinary petrol motor is closer than might be supposed, since the energy and heat account, in the rifle barrel and the motor cylinder ​respectively, is almost identical, in spite of the diversity of the conditions. Thus the thermal efficiency in the region of 25%, in other words, about one quarter of the heat energy of the fuel on the one hand, or explosive on the other, is converted into mechanical work.
Now we know how formidable is the difficulty of air cooling in the case of the petrol motor; the difficulty in the machine gun is augmented by the fact that the surface of the barrel on which to attach the cooling fins or gills is only about half a square foot, as compared with say two or three square feet or more in the petrol motor of equivalent output. On the other hand the condition as to temperature is not so exacting in the case of the gun barrel, and the degree of durability demanded is incomparably less.
The approximate energy account of the service rifle and ammunition is as follows:—
| Kinetic energy of bullet | 28% |
| Friction as heat imparted to bullet | 5% |
| Friction„ as„heat„imparted„to„ barrel | 5% | $\scriptstyle {\left.{\begin{matrix}\ \\\ \end{matrix}}\right\}\,$ Total barrel heat 30%. |
| Heat directly imparted to barrel | 25% | $\scriptstyle {\left.{\begin{matrix}\ \\\ \end{matrix}}\right\}\,$ Total barrel heat 30%. |
| Kinetic and heat energy of "exhaust" powder gases | 37% |
| | 100% |
Thus thirty per cent. of the total heat equivalent of the charge is imparted to the barrel and has to be dispersed by the cooling means employed. The actual heat equivalent of the service charge is approximately 7,000 ft. pounds, therefore the barrel heat per charge represents 2,100 ft, pounds, and taking the ordinary maximum rate of continuous fire as 600 per minute—10 per sec.—we have 21,000 ft. pounds per sec. as the ​equivalent rate of heat loss; this may otherwise be expressed as
37 Fah. H.U, per sec. or 15 Centigrade H.U, per sec. or 6,600 (gram) calories per sec. or 38 horse power.
Now, the actual form taken by the Cooling surface in the Lewis Gun is that of a number of radial gills of aluminium, whose aggregate surface is approximately 6 sq. ft., hence we have to dispose of the equivalent of $^{38}$⁄$_6$ or, say, 6 h.p, per square foot.
Following the method laid down in the author's recent " James Forrest " Lecture, the above betokens both a very considerable temperature difference and a high velocity of air over the cooling gills; the product of these (deg. Fah.) being 84,000. Thus the temperature is currently given (under the conditions in question) as about 440 deg. Fahrenheit, which means a temperature difference of 400 deg. Fahrenheit; this corresponds to a velocity of the air through the jacket, say, 200 ft, per second, in order that the heat shall be disposed of with sufficient rapidity by the surface of the gills. This appears unexpectedly high, but there are two ways in which the figure may be checked. Firstly, it is clearly necessary that the total mass of air passing shall be adequate, and more than adequate, to carry off the waste heat; in other words, the air entering the jacket at the one end at atmospheric temperature must be able to absorb the whole of the waste heat before leaving the jacket, and this without its temperature being raised to such an extent as to prevent its being active as a cooling agent. Secondly, we may compare the calculated resistance of the jacket to the passage of air, with the known recoil as due to the powder gases; since the former is ​overcome by the momentum of the latter, it is manifest that the jacket resistance can never exceed the mean recoil force as due to the gases: thus we have a limit to the possible velocity of the air blast.
As to the first of these, we have the combined area of the air passages, about 5 square inches, or volume per second at 200 ft. per second = $^{200×5}$⁄$_{144}$ = 7 cubic ft. = 0.54 lbs., equivalent in heat capacity to 0.13 lbs. of water. Now, the heat units to be taken up = 27, hence the air will be increased in temperature $^{27}$⁄$_{0.13}$ = 208 Fahrenheit. This result is concordant. Evidently no velocity much less than 200 ft. a second will pass the volume necessary.
Next as to the recoil calculation. If we take the resistance of the jacket as calculable on the basis of skin-friction we may fairly assume the single surface coefficient as .005, and at 200 ft, per second this gives 0.3 lbs. per square foot, or, on a total surface of 6 square feet, the resistance is 1.8 lbs.; this is the mean force which must be applied by the exhaust blast of the powder gases to maintain an air current of 200 ft. per second velocity.
It has been established by experiment that the mean recoil as due to the powder gases in the service cartridge is 0.28 that of the projectile; now the latter already calculated amounts to 2 lbs, per shot per second, or 20 lbs, at 10 shots per second. Thus the mean force due to the momentum of the powder gases is .028×20 = 5.6 lbs. But the air leaving the jacket muzzle retains approximately its mean velocity, and this represents by its momentum a force of 0.54 × 200/32.2 = 3.35 lbs., so the account becomes: ​
| Cr. | | | Dr. | | |
| Recoil due to powder gases | 5.6 | lbs. |
| | | | Resistance of jacket | 1.8 | lbs. |
| | | | Efflux momentum of air | 3.35 | lbs. |
| | | | Total | 5.15 | lbs. |
| | | | Credit Balance | .45 | lbs. |
| | 5.6 | lbs. | | 5.6 | lbs. |
There is, consequently, nothing inconsistent in the velocity of 200 ft. per second, though the margin of driving force as due to the momentum of the powder gases seems narrow. It is to be remembered, however, that the figure taken for the gas momentum is based on experiments made with the ordinary service rifle; it is without doubt considerably augmented by the special nozzle with which the barrel of the Lewis Gun is fitted, so that in reality there should be an ample margin.
It is worthy of note that the work done by the blast represents approximately 2 horse power, and the actual work done against the skin-friction on the gilled surface is about two-thirds of a horse power; an appreciable and valuable return for so simple an expedient as the muzzle ejector.
Summarising the foregoing, we have, under conditions firing, at 600 rounds per minute:—
* The mean velocity of the induced air current in the cooling jacket is approximately 200 feet per second.
* The temperature difference has a mean value of about 420 degrees Fah., that is to say the ordinary temperature of the gills is in the region of 500 Fah.
* The momentum represented by the exhaust powder gases is a measure of the force available for ​impelling the induced air current, and is consistent with the above.
In any actual measurements the jacket temperature recorded will depend very much upon where the bulb of the thermometer is placed, for there is a very steep temperature gradient from the surface of the bore of the barrel outward. Rough calculation shows that there must be a difference of about 200 degrees Fah. between the inner and outer surfaces of the barrel alone, apart from the difference in the gills themselves; thus it is improbable that the temperature of the rifled surface of the barrel when the gun is in continuous usage can be less than 700 Fah., but this does not seem to have any marked effect on its durability. Even in the case of a water cooled gun, when the water is on the boil, the internal temperature of the barrel at a high rate of fire is probably not less than 400 Fah.
The aggregate sectional area of the aluminium gills taken normal to the radius is approximately 250 sq. c. m., and the quantity of heat being 6,600 gram calories, we have the mean temperature gradient about 52 deg. C. per centimetre, or 240 Fah. per inch (measured radially): this means a difference between the root of the gills and the outer casing of roughly 300 Fah. Hence the total difference of temperature between the outer casing and the rifling, under conditions of continuous fire, will be about 500 Fah. This is quite sufficient to give rise to uncertainty when jacket temperature is under discussion; the portion of the jacket must be specified.
* ↑ For description see "Engineering," November 8th, 1912.
* ↑ M. VII ammunition is higher.
* ↑ Compare § 58.
* ↑ The conductivity of aluminium has been taken at 0.5 in C.G.S. Units; this is a fair average value. It is on the safe side.