468 



NATURE 



{Sept. 13, 1888 



CALCULATION OF RANGES, ETC., OF 

 ELONGATED PROJECTILES. 

 T7ROM time to time it has been suggested to me that 

 -*- some reduction in the coefficients of resistance 

 deduced from my experiments made in 1867-68, is 

 required to adapt them for use in connection with the 

 improved guns of more recent times. I do not agree 

 with those suggestions. My coefficients were most care- 

 fully deduced from experiments made with ogival-headed 

 shot fired at very low elevations so as to secure ranges of 

 about 500 or 600 yards, and the observations were made 

 near the gun. The 5-inch gun was a remarkably good 

 gun, and from the numerous records it gave had a pre- 

 ponderating effect on the final result ; while an un- 

 steady shot cut only a few screens, and had a very 

 trifling influence. It seems, therefore, that the co- 

 efficients were derived from shot moving very nearly in 

 the direction of their axes. I have applied these co- 

 efficients to calculate ranges for comparison with Com- 

 mander May's (R.N.) range-table for the 12-inch muzzle- 

 loading gun (based on practice 1885) ; muzzle velocity, 

 1892 f.s. ; "jump," 6 minutes. 



Elevation i° 2 ° 3° 4 ° 



Exp. range ... 1200 2267 3200 4057 yards. 

 Calc. range ... 1206 2249 3192 4039 „ 



Difference ... +6 -18 -8 - 18 



I will now do the same for the 4-inch breech-loading 

 gun, which was the gun chosen by the authorities to be 

 used in testing my coefficients on a long range ; muzzle 

 velocity, 1900 f.s. ; range-table founded on experiments 

 made in 1884 ; "jump," 6 minutes. 



Elevation io 2 ° 30 ,0 



Exp. range ... 1086 181 1 2400 2917 yards. 

 Calc. range ... 1049 1817 2410 2895 ,, 



Difference 



-37 +6 +10 



Thus it appears that my coefficients give very satis- 

 factory results when applied under the conditions of the 

 original experiments. Commander May's table stops at 

 a range of 4000 yards. As the elevation of the 4-inch 

 gun was gradually increased, the calculated ranges fell 

 shorter and shorter of the experimental ranges. At an 

 elevation of 15 the calculated range was 6364 yards, and 

 the experimental range 6608 yards, giving a difference 

 of 244 yards. The explanation of this seems to me to 

 be as follows : — 



When an elongated shot is fired from a rifled gun at 

 high elevations, the shot endeavours to preserve the 

 parallelism of its axis. This causes the axis of the shot 

 to become sensibly inclined to the direction of the motion 

 of its centre of gravity. Thus the pressure of the air 

 acts from below and raises the shot bodily, so as to give 

 its trajectory an increased elevation. This would naturally 

 increase the range of the shot. After a short time the 

 shot inclines sideways, as explained by Magnus, and the 

 shot continues to move with its axis inclined to the direc- 

 tion of its motion, which is the cause of the lateral " drift " 

 of the shot. This shot having had its axis so much in- 

 clined to the direction of its motion, would encounter a 

 greater resistance from the air than another shot fired 

 at a lower elevation, because this latter would move with 

 its axis more nearly in the direction of its motion. 



Hence it is clear that, in order to apply any rational 

 correction to the calculated ranges for high elevations, 

 it would be necessary slightly to increase both (1) the 

 elevation, and (2) the values of the coefficients of 

 resistance. 



Major Mackinlay, R.A., warns us that the published 

 range-tables are not to be "blindly followed," a very 

 necessary caution, when it is considered that we cannot 

 be quite certain about the muzzle velocity, the "jump," 

 the elevation, and the precise form of the head. The height 

 of the barometer is seldom mentioned. My only sur- 



prise is that such good agreement between calculation and 

 experiment should be found as above. The only question 

 seems to be whether it is worth while to trouble about the 

 correction of calculated ranges for high velocities and 

 high elevations, when the reason for some little dis- 

 crepancy is so evident. But to reduce coefficients would 

 be to make matters worse. 



Having been requested to calculate the range of a 9^2- 

 inch shot weighing 380 pounds, fired at an elevation of 

 40 with a muzzle velocity of 2360 f.s., I could not feel satis- 

 fied till I had completed the calculation of a range-table 

 for elevations o° to 45 ° on a horizontal plane 27 feet below 

 the muzzle. I give the result. Gravity and the tempera- 

 ture of the air were considered constant. The air was 

 supposed to be at rest, and the shot was assumed to move 

 in the direction of its axis ; head ogival, struck with a 

 radius of \\ diameter. When the results of experiment 

 are published I shall be ready to discuss the matter, but 

 there are so many things uncertain at heights of 10,000, 

 15,000 feet, &c, that I doubt whether any theoretical 

 advantages will result. It will, however, be interesting 

 to know what can be done in an extremity. 



It will be seen that the ranges go on increasing up to 

 an elevation of 45 , and would probably go on beyond an 

 elevation of 50 before reaching a maximum. 



