A METHOD OF REACHING EXTREME ALTITUDES 



By ROBERT H. GODDARD 



(With io Plates) 



OUTLINE 



A search for methods of raising recording apparatus beyond the 

 range for sounding balloons (about 20 miles) led the writer to 

 develop a theory of rocket action, in general (pp. 6 to 11), taking 

 into account air resistance and gravity. The problem was to deter- 

 mine the minimum initial mass of an ideal rocket necessary, in order 

 that on continuous loss of mass, a final mass of one pound would 

 remain, at any desired altitude. 



An approximate method was found necessary, in solving this prob- 

 lem ^pp. 10 to 11), in order to avoid an unsolved problem in the 

 Calculus of Variations. The solution that was obtained revealed 

 the fact that surprisingly small initial masses would be necessary 

 (table VII, p. 46) provided the gases were ejected from the rocket at 

 a high velocity, and also provided that fnost of the rocket consisted of 

 propellant material. The reason for this is, very briefly, that the 

 velocity enters exponentially in the expression for the initial mass. 

 Thus if the velocity of the ejected gases be increased five fold, for 

 example, the initial mass necessary to reach a given height will be 

 reduced to the fifth root of that required for the lesser velocity. (A 

 simple calculation, p. 50, shows at once the effectiveness of a rocket 

 apparatus of high efficiency.) 



It was o'bviously desirable to perform certain experiments : First, 

 with the object of finding just how inefficient an ordinary rocket is, 

 and secondly, to determine to what extent the efficiency could be 

 increased in a rocket of new design. The term " efficiency " here 

 means the ratio of the kinetic energy of the expelled gases to the heat 

 energy of the powder, the kinetic energy being calculated from the 

 average velocity of ejection, which was obtained indirectly by obser- 

 vations on the recoil of the rocket. 



It was found that not only does the powder in an ordinary rocket 

 constitute but a small fraction of the total mass (^ or J), but that, 

 furthermore, the efficiency is only 2 per cent, the average velocity of 

 ejection being about 1,000 ft./sec. (table I, p. 12). This was true 



Smithsonian Miscellaneous Collections, Vol. 71, No. 2 



