NO. 2 -METHOD OF REACHING EXTREME ALTITUDES 65 



NOTES 



^" A step-by-step method of solution similar to that herein employed can 

 evidently be used for oblique projection — other conditions remaining the same. 



^ If the efficiency is estimated by the kinetic energy of the rocket itself 

 (from the velocity the average mass of the rocket would acquire, by virtue of 

 the recoil of the gases ejected with the "average velocity" measured), the 

 efficiencies will, of course, be less than the two values given in table I, being, 

 respectively, 0.39 and 0.50 per cent. 



" Since this manuscript was written, rockets with a single charge, con- 

 structed along the general lines here explained, have been considerably further 

 developed. 



" Chambers of considerably reduced weight have since been made and 

 tested for velocities comparable to those here mentioned. For two particular 

 types of loading device, the ratio of weight of chamber to weight of charge 

 (here, 120) were, respectively, 63 (also 30 for this case, but at a sacrifice of 

 velocity) and 22 ; the ratio, for the nozzles, being reducible to comparatively 

 small values. In neither of these cases was any special attempt made to reduce 

 the weight of the chambers. 



" Later experiments support this prediction, and also demonstrate that 

 firing of the charges can take place in rapid succession. 



^^ The values of c and ( i — k) , here assigned, were chosen as being the largest 

 that could reasonably be expected. Later experiments have shown that lower 

 values are more easily realizable, but it should at the same time be understood 

 that no special attempt has been made to obtain experimentally the highest 

 values of these quantities. The numbers chosen may, then, be considered as 

 at least possible limiting values. 



It is well to mention, in this connection, that the developments with tlie 

 multiple-charge rocket have, so far, exceeded original expectations. This is 

 in accord with the fact that the experimental results have, from the start, been 

 more favorable than were expected. Thus an efficiency of 50 per cent was at 

 first considered the limit of what could be attained, and 4,000 to 5,000 ft/sec, 

 the highest possible velocity. Further it was naturally not expected that the 

 velocities obtained in vacuo would actually exceed those in air ; nor were 

 chambers as light as those at present used considered producible without con- 

 siderable experimental difficulty. 



^^Distribution of mass am.ong the secondary rockets for cases of large 

 total initial mass. — For very great altitudes, secondary rockets will be neces- 

 sary, as already explained, in order to keep the proportion of propellant to 

 total weight sensibly constant. The most extreme cases will require groups of 

 secondary rockets, which groups are discharged in succession. 



There are, under any circumstances, two possibilities : either the secondaries 

 may be small, so that each time a secondary rocket, or group of secondaries, is 

 discarded, the total mass is not appreciably changed, as indicated schematically 

 at (a), figure 8 ; or a series of as large secondaries as possible may be used, 

 (b), figure 8, in which case the empty casings constitute a considerable frac- 

 tion of the entire weight at the time the discarding takes place. 



