NO. 2 METHOD OF REACHIIsfG EXTREME ALTITUDES 5 1 



ward, with a velocity of 7,000 ft./sec. at the first shot ; one-third of 

 the remaining mass, at the second shot ; and so on, for successive 

 shots. From' the principle of the Conservation of Momentum it will 

 be evident that the mass that remains is given an additional upward 

 velocity of 3,500 ft./sec. after each shot. 



Thus, after the fourth shot, the mass that remains is ^f, or prac- 

 tically ^, of the initial mass, and the velocity is 14,000 ft./sec. This 

 velocity is sufficient, if we neglect air resistance, to raise the part of 

 the rocket that remains to an altitude of ^80 miles (by the familiar 

 relation. v- = 2gh). Although the range would be much reduced if 

 air resistance were considered, it should nevertheless be remembered 

 that the values in table VII are calculated for the condition under 

 which air resistance is a minimum. 



The above simple case is not realizable in practice because of the 

 large mass of propellant for each shot compared with the total mass — 

 i. e., provision is not made for the mass of the chamber. The result 

 will be the same, however, if smaller charges are fired in rapid suc- 

 cession, as will be evident from a calculation similar to the above, 

 which is carried out in Appendix E, page 63, under the assumption 

 of smaller charges for successive shots. 



RECOVERY OF APPARATUS ON RETURN 

 A point of considerable practical importance is the question of 

 finding the apparatus on its return, and of following it during flight, 

 both of which depend in a large measure upon the time of flight. 



Concerning the times of ascent, table VII shows that these are 

 remarkably short. For example a height of over 230 miles is reached 

 in less than 6^ minutes (s^; a = 50). The reason is, of co'urse, that 

 the rocket under present discussion possesses the advantage of the 

 bullet in attaining a high velocity, with the added advantage of start- 

 ing gradually from rest. In fact, the motion fulfills closely the ideal 

 conditio'ns for extremely rapid transit — namely, starting from rest 

 with the maximum acceleration possible, and reversing this accelera- 

 tion, in direction, at the middle of the journey. 



The short time of ascent and descent is, of course, highly advan- 

 tageous as regards following the apparatus during ascent, and 

 recovering it on landing. The path can be followed, by day, by the 

 ejection of smoke at intervals, and at night by flashes. Any distinc- 

 tive feature, as for example, a long black streamer, could assist in 

 rendering: the instruments visible on the return. 



