282 Table 68 (continued) 



NACA STANDARD ATMOSPHERE, TENTATIVE PROPERTIES OF THE 

 UPPER ATMOSPHERE 



the various equations used in computing the properties of the upper atmosphere. These 

 additional assumptions are: 



(a) the air is dry, 



(b) the air behaves as a perfect gas and hence obeys the general gas law which may 



be written 



JP.-tJj^L (1) 



p 9 pa T Mo 



(c) the air is at rest with respect to the earth and hence obeys the basic law for fluid 



statics 



dp = — gpdh (2) 



(d) the acceleration of gravity is constant with height. (Reference 1 also contains 



tables based on the assumption of a variation in the acceleration of gravity 

 inversely with the square of the distance from the center of the earth.) A 

 method for correcting to true height is given below (see p. 283). 



By means of equations (1) and (2) and equations representing the adopted specifica- 

 tions for temperature and composition, relationships may be deduced between pressure 

 and height. The equations representing the adopted specifications are 



T=:Ti + L(h-hi) (3) 



where L is the vertical temperature gradient AT/ Ah, and 



M 1 



Mo 1 - K (h - h m ) 

 where 



(4) 



* = - . V \ (5) 



h a — h m 



which represents the vertical gradient of the existing volume of molecular oxygen per 

 unit initial volume of normal dry air. 



Pressure-height relationships. — The equations that are based on a constant value of 

 g are as follows : * 



For combination A (constant temperature and constant composition) : 



log.-£ = Ct {h-h A ) (6) 



P* 



where 



C A== _gpT±M (7) 



po T Mo 

 For combination B (constant temperature gradient and constant composition) : 



log-£-=C B log-^- (8) 



pB IB 



where 



f gapoTo M /q\ 



po L Mo 

 For combination C (constant temperature and constant volume gradient of dissociation) : 



log ±- = Co log M. (10) 



ra Ma 



C = -f^ (11) 

 Po Kl 



where 



* See footnote 6, p. 266. 



(continued) 



SMITHSONIAN METEOROLOGICAL TABLES 



