The evaluation of an airplane’s flying quality is one of subjectiveness. It is difficult to quantify how an airplane feels to a pilot. An airplane may even have an unstable mode (as we will see in the next chapter) and yet feel fine to the pilot if the time to double amplitude is sufficiently long.

Figure 9.10 (taken from Ref. 9.1) presents the latest revision of the so-called Cooper-Harper Scale for evaluating airplane flying qualities Obviously, with adjectives such as “excellent,” “good,” “fair,” “moderate,” “considerable,” and “extensive,” different pilots will give the same airplane different ratings. Nevertheless, this system does provide a rational and somewhat objective base for measuring an airplane’s flying quality. Because of the subjective nature of the Cooper-Harper Scale, Reference 9.1 mainly emphasizes three levels within the scale.

Level 1: Cooper-Harper scale = 1-3.5 Level 2: Cooper-Harper scale = 3.5 – 6.5 Level 3: Cooper-Harper scale = 6.5 – 9+

In order to assure that an airplane lies within one of these levels (level 3 is really undesirable but flyable), Reference 9.1 specifies definite dynamic characteristics that the airplane should possess.

Figure 9.10 Cooper-Harper scale for rating airplane handling qualities. Phugold Mode

First, with regard to the phugoid mode,

Level 1: £>0.04 (9.96a)

Level 2: f > 0 (9.96b)

Level 3: Г2> 55 sec (9.96c)

C is the damping ratio, and T2 is the time to double amplitude.

The damping ratio, £, for a particular mode, is related to the roots of the characteristic equation as follows. Let the roots defining an oscillatory mode be given by

(t12 = — а ±іш

Now consider the product

(a – a,)(cr – a2) = 0

Expanded, it is

cr2 + 2acr + a2 + ш2 = 0


Comparing Equation 9.97 to Equation 9.50, it is obvious that

(o„2= a2 + co2


i = —


(9.98 b)

For the example of the Cherokee 180, in real time, a = 0.0265 and (o = 0.248 for the phugoid. Hence, the damping ratio, £, equals 0.106 and the undamped natural frequency, ton, equals 0.249 rad/sec. Thus, according to the criteria of Equation 9.96, the Cherokee falls within level 1.

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