for WD)m.z, a change in altitude will produce 
the following relationships: 
where 
condition (I) applies to some known condi- 
tion of velocity and power required for 
W’),,,,,z at some original, basic altitude 
condirion (2) applies to some new values of 
velocity and power required for (L/D),, 
at some different altitude 
and 
V= velocity, knots (TAX, of course) 
Pr=power required, h.p. 
o=altitude density ratio (sigma) 
Thus, if flight is conducted at 22,000 ft. 
(o=O.498), the airplane will have: 
a 42 percent higher velocity 
a 42 percent higher power required 
than when operating at sea level. Of course, 
the greater velocity is a higher TAS since the 
airplane at a given weight and lift coefficient 
will require the same PAS independent of 
altitude. Also, the drag of the airplane at 
altitude is the same as the drag at sea level but 
the higher TAS causes a proportionately 
greater power required. Note chat the same 
straight line from the origin tangent to the sea 
level power curve also is tangent to the 
altitude power curve. 
The effect of altitude on specific range can be 
appreciated from the previous relationships. 
If a change in altitude causes identical changes 
in velocity and power required, the proportion 
of velocity to power required would be un- 
changed. This fact implies that the specific 
range of the propeller powered airplane would 
be unaffected by altitude. In the actual case, 
this is true to the extent that powerplant specif- 
ic fuel consumption (c) and propeller efficiency 
(qp) are the principal factors which could 
cause a variation of specific range with altitude. 
NAWEPS oo-EOT-80 
AWPLANE PERFORMAhlCE 
If compressibility effects are negligible, any 
variation of ~peci)c range with altitude is strictly a 
function of engine-propeller pcrformanCC. 
The airplane equipped with the reciprocating 
engine will experience very little, if any, 
variation of specific range with altitude at low 
altitudes, There is negligible variation of 
brake specific fuel consumption for values of 
BHP below the maximum cruise power rating 
of the powerplant which is the auto-lean or 
manual lean range of engine operation. Thus, 
an increase in altitude will produce a decrease 
in specific range only when the increased power 
requirement exceeds the maximum cruise power 
rating of the powerplants. One advantage of 
supercharging is that the cruise power may be 
maintained at high altitude and the airplane 
may achieve the range at high altitude with 
the corresponding increase in TAS. The prin- 
cipal differences in the high altitude cruise and 
low altitude cruise are the true airspeeds and 
climb fuel requirements. 
The airplane equipped with the turboprop 
powerplant will exhibit a variation of specific 
range with altitude for two reasons. First, 
the specific fuel consumption (c) of the turbine 
engine improves with the lower inlet tem- 
peratures common to high altitudes. Also, 
the low power requirements to achieve opti- 
mum aerodynamic conditions at low altitude 
necessitate engine operation at low, inefficient 
output power. The increased power require- 
ments at high .altitudes allow the turbine 
powerplant to operate in an efficient output 
range. Thus, while the airplane has no 
particular preference for altitude, the power- 
plants prefer the higher altitudes and cause 
an increase in specific range with altitude. 
Generally, the upper limit of altitude for 
efficient cruise operation is defined by airplane 
gross weight (and power required) or com- 
presslbility effects. 
The optimum climb and descent for the 
propeller powered airplane is affected by 
many different factors and no general, all- 
inclusive relationship is applicable. Hand- 
book data for the specific airplane and various 
163