256 Table 63 (continued) 



NACA STANDARD ATMOSPHERE, LOWER ATMOSPHERE 



(c) gravity is constant at all altitudes with the standard value, 8 



(d) the temperature of the isothermal atmosphere is — 55 C C. or — 67 C F., 



(e) equation (1) holds true for altitudes up to the isothermal atmosphere; the 



gradient vanishing at the lower limit of the isothermal atmosphere. 



The last assumption not only simplifies the standard atmosphere but it also appears to be 

 a very close approximation to actual conditions at any given time. 7 The altitude of the 

 lower limit of the isothermal atmosphere is found from equation (1) by substituting the 

 isothermal temperature : 



z _ 288-218 _ 10769 meters 

 .0065 



Z t = 51 8- 4 ~ 392 - 4 = 35332 feet 

 .00356617 



Since the air is assumed to be a perfect gas, the difference in pressure between two 

 levels is due to the weight of a column of air of unit cross section between the two 

 levels or 



dp = — gpdZ (3) 



Calculation of pressures and densities. — At any altitude in the standard atmosphere 

 the air temperature is known. The corresponding pressure is calculated from 



z =^£) ,og "(7) =A ' T - log "(y) (4) 



where : 



PogMTo 

 For metric measures K' = 67.4072 and for English measures K' = 122.862. 



Calculation of mean temperature. — The mean temperature T m which appears in 

 equation (4) is a harmonic mean given by 



f dZ 



T m =^ a (5) 



dZ_ 

 T 



whence below the isothermal region 



r m = 



log 



and in the isothermal region 



T m =- aZ (6) 



1 



To — aZ 

 Z 



(6a) 



Z« (Z-Zj) 



T m * T 



Useful relationships. — In the levels below the isothermal layer the following relation- 

 ships will prove useful : 



T^-(P_\ aR 



To \Po) 



l j_ 



L — ( T_\aR — (P \l~aR — i\ _ a 7 \aR 

 Po 





where aR = .190284. 



9 This is tantamount to using as the unit of "height," the unit of geopotential equal to 0.980665 

 dynamic meters, or 9 ^° 6 p 65 geopotential meters (gpm.), where 1 dynamic meter = 10 s cm.' sec.- a . 

 T See Table 68 for altitudes above 20,000 m. 



{continued') 

 SMITHSONIAN METEOROLOGICAL TABLES 



