NO. 2 METHOD OF REACHING EXTREME ALTITUDES 45 



The third additional calculations, Mr^, are carried out for the case 

 of a rocket built up of Coston rockets in bundles (shown in section 

 in fig. 22), the lowest bundle of which is fired first and then released ; 

 after which the bundle above is fired and then released, and so on. 

 For the Coston ship rocket (having a range of a quarter of a mile, 

 with the charge of red fire removed, as already stated) the ratio of the 

 powder charge to the remaining mass of the rocket is found to be 

 closely ^. Hence the " efifective velocity " in this case is only 



c(i-k)= 1029.25(1 -I) =257.3 ft/sec. 



The M's in the last two cases are calculated only for the accelera- 

 tions that make M minima for the first case (effective velocity, 7,500 

 ft./sec). Hence in these cases, the M's are not minima, although 

 only in the last two cases is there probably much discrepancy from the 

 actual minima. 



The cross-section, throughout any interval, is taken as one square 

 inch except for interval Sg. It will be seen from the table that this 

 is justifiable, as the largest mass in intervals s^ to Sg does not dififer 

 much from one pound. 



CALCULATION OF MINIMUM MASS TO RAISE ONE POUND TO 

 VARIOUS ALTITUDES IN THE ATMOSPHERE 



The " total initial masses " required to raise one pound from 

 sea-level to the upper end of intervals Sg, s^ and Sg are given in 

 table Vn. They are obtained by multiplying together the minimum 

 masses (marked by stars in table V), from s^ up to and including the 

 interval in -question, and represent, as already explained, the mass in 

 pounds of a rocket which, starting at sea-level, would become re- 

 duced to one pound at the altitude given. 



The highest altitude attained by the one pound mass is not, 

 however, the upper end of the interval in question, but is a very 

 considerable distance higher. This, of course, follows from the 

 fact that the one pound reaches the upper end of each interval with 

 a considerable velocity, and will continue to rise after propulsion has 

 ceased until this velocity is reduced to zero, by gravity and air 

 resistance. 



If we call Vn the velocity with which the pound mass reaches the 

 upper end of the particular interval where propulsion ceases, h the 

 distance beyond which the one pound will rise (the cross-section 

 still being one square inch), and p the mean air resistance in poundals 



4 



