NO. 2 METHOD OF REACllFNG EXTREME ALTITUDES 43 



is 6,000 ft. /sec.'-. The reason for this state of affairs is evident at 



once from the fact that the density ratio, — — is verv small for s-, 



and also from the fact that a occurs in the denominator of the term 

 containing R in ec[uation (6), so' that the large acceleration counter- 

 balances the increase in R. 



Thus, in order that the initial mass for s- shall be a minimum, the 

 acceleration must become very large, with consequent severe strains 

 in the rocket apparatus and instruments carried by the rocket, to 

 say nothing of the difficulty of firing with sufficient rapidity to 

 produce such large accelerations. It thus becomes advisable to 

 choose a moderate acceleration in s^ and Sg, and not to assign a 

 velocity, v^, as was done in the preceding intervals. Two accelera- 

 tions are chosen: 50 ft./sec.^ and 150 ft. /sec.-, respectively. The 

 interval Sg, also calculated for assigned accelerations, will be ex- 

 plained in detail below. In all cases, when either one of these 

 accelerations is mentioned in connection with Sg and Sg, this accelera- 

 tion will be understood as having been taken also in the preceding 

 intervals, beyond Sg. 



In order to see how far the effective velocity, c(i— k) may fall 

 short of 7,000 ft. /sec. and still not render the rocket impracticable, 

 a few additional columns for M are calculated. 



In the first of the additional columns. Mo, the effective velocity is 

 taken as 3,500 ft. /sec, namely, half that of the preceding calcula- 

 tions. This allows of considerable inefficiency of the apparatus, in a 

 number of ways. For example, the product 



c(i-k) =3.500, 



may be given by the same proportionality, k, as before, but with 

 a velocity of ejection of the gases as low as 3,750 ft./sec. On the 

 other hand, the velocity of ejection may be as large as before {i. e., 

 7,500 ft./sec); and the proportionality, k, increased to 0.533; 

 meaning, of course, that the rocket now consists more of mechanism 

 than of propellant. 



The second additional calculations, ^Ir^, are carried out under 

 the assumption that a reloading mechanism is used, with k as in the 

 original calculations (k=Y^g-), but that the velocity of expulsion of 

 the gases is the mean found by experiment for the Coston ship 

 rockets, namely 1029.25 ft./sec. In this case the effective velocity is 



c(i— k) = 1029.25(1— y\) =960 ft./sec 



