NO. 2 METHOD OF REACHING EXTREME ALTITUDES O3 



APPENDIX E 



CHECK ON APPROXIMATE METHOD OF CALCULATION, FOR 

 SMALL CHARGES FIRED IN RAPID SUCCESSION 



Consider a rocket weighing lO lbs., having 2 lbs. of propelling 

 material, fired two ounces at a time, eight times per second, with a 

 velocity of 6,000 ft./sec. — much less than the highest velocity 

 attained in the experiments, either in air or in vacuo. 



Let us suppose that, for simplicity, the rocket is directed upward 

 and that each shot takes place instantly (a supposition not far from 

 the truth) ; the velocity remaining constant between successive shots. 



After the first shot, the mass, 9f lbs., has an upward velocity Vq 

 due to the downward velocity of the ^ lb. expelled. This velocity, 

 Vq, is at once found by the Conservation of Momentum. But it is 

 decreased by gravity until, at the end of ^ sec, it is reduced to 



the space passed over during this time being 



s = Vot-^gt2. 



We have then, Vo' = 7i.8 ft./sec, and 8 = 9.23 ft. 



At the beginning of the second interval of ^ sec, an additional 

 velocity is given the remaining mass, of 76.8 ft./sec, and the final 

 velocity and space passed over may be found in the same way. By 

 comnleting the calculations for the remaining intervals we shall have 

 for time just under ^ sec, v' = 293.1 ft./sec; s= 91.98 ft. 

 for time just under i sec, Yo'= 603.8 ft./sec; s= 33548 ft. 

 and 

 for time just under 2 sec, Vo'=:i284.i ft./sec; 5=1315.68 ft./sec 



These figures compare well with those in table V, for s^. In the 

 present check, air resistance would doubtless be unimportant until the 

 velocity had reached 1,000 ft./sec. or so ; but the velocity would, even 

 if decreased somewhat by air resistance, compare favorably with that 

 of a projectile fired from a gun. 



No more elaborate calculation is necessary to demonstrate the 

 imijortance of the device, even for military purposes alone ; for it 

 comljines portability and cheapness (no gun is required for firing it) 

 with a range which compares favorably with the best artillery. 

 Further, all difficulties of the nature of erosion are, of course, 

 avoided. 



