Generalized Power-Required Curve

In flying (or flight testing) an airplane, one rarely finds a standard atmosphere. In addition, the gross weight of the airplane is generally different from that used by the manufacturer to quote performance. The following method is useful for interpreting power measurements taken at any gross weight and density altitude.

Few and Pew are defined as the velocity and required power at sea level, where “ew” signifies equivalent weight. These quantities are related to a standard weight, by,

(7.23)

(7.24)

For any other density or gross weight, the velocity and power are given

I’hus, at the same lift coefficient, V and Vcw are related by

(7.25)

Similarly,

(7.26)

A graph of Pew versus Vew will simply be the sea level power required curve at the standard gross weight. As an example, take the Cherokee Arrow at a gross weight of 2400 lb, a density altitude of 5000 ft and an airspeed of 100 kt. Using Figure 7.15 as the standard,

At 5000 ft, <T equals 0.861. Therefore,

Vew = 97.5 kt = 164.8 fps

From Figure 7.15,

Pew = 73 hp

Therefore, from Equation 6.26,

Pr = 67.8 hp

In this manner, given a sea level power required curve at a standard gross weight, one can easily determine the power required at any altitude, airspeed, and gross weight.

P V ■* ew ‘ Є’

These relationships are particularly useful in flight testing. Power – fequired data taken at any altitude and gross weight are reduced to a plot of PewUew versus Vew – Such a plot will be a straight line having a slope proportional to / and an intercept proportional to Це. Thus all of the data collapses to a single, easily fitted line enabling one to determine accurately e and /. The equation of this straight line follows directly from Equation 7.21.

Timet

4

Г*» dh R/C

The time required to climb from one altitude, h, to another, h2, can be determined by evaluating the integral

Knowing the R/C as a function of h, this integral can easily be evaluated numerically. A solution in closed form can be obtained if one assumes that the rate of climb decreases linearly with altitude. A feeling of how valid this assumption is can be gained from Figures 7.13 and 7.14.

Let

R/C = (R/C)0(l – hlhabs) (7.29)

where habs = absolute ceiling.

Equation 7.28, for h = 0, then reduces to

___ ^abs j _________________ |________

~~ (R/C)0 n 1 – hlhabs

This represents the time required to climb from sea level to the altitude, h. The time required to climb from one altitude to another is obtained directly from Equation 7.30 by subtracting, one from the other, the times required to climb from sea level to each altitude.

Time to climb is presented for the Cherokee Arrow in Figure 7.16. This curve was calculated on the basis of Equation 7.30. For this particular example, it requires approximately 42.5 min to climb to the service ceiling.