NUMERICAL EXAMPLE—STEP RESPONSE

Analog computations were made for the airplane and flight condition of the previous example, with ДСТі_ = .0125 and with г/с = Oand.3 The results for F, a, and у are shown on Figs 10.7 and 10.8. The motion at this time scale is clearly dominated by the lightly damped phugoid. Consider Fig. 10.7

NUMERICAL EXAMPLE—STEP RESPONSE

NUMERICAL EXAMPLE—STEP RESPONSE

Fig. 10.7 Response to throttle (ДCj, = .0125). Jet transport erasing at high altitude. Thrust line passing through C. G.

Подпись: Да- 0.5° -

1—-

NUMERICAL EXAMPLE—STEP RESPONSE

Aass = 0.29* —S – t, sec

(zjc = 0) first. We see that the speed begins to increase immediately, before the other variables have time to change. It then undergoes a damped oscil­lation, returning finally to its initial value. The angle of attack varies only slightly, and у makes an oscillatory approach to its final positive value yss. The ultimate steady state is a climb with Д1? = Да = 0, the numerical value of yss being correctly given by (10.3,4). For the case zjc = .3, Fig. 10.8, the results differ from the preceding in several significant ways. Although the speed does begin to increase at first, the increase is small and is quickly followed by a reduction of order 10% Ve. The final value is 5% less than Ve, a rather large change. The initial response in a is rapid, being dominated

by the short-period mode, and is not seen in detail at this time scale. Because of the rapid increase in a, and the excess lift that goes with it, there is a much more rapid response in y. than is the case in Fig. 10.7. The amplitude of the у oscillation is also larger than on Fig. 10.7, and the final state is a climb of appreciably larger inclination. The steady states are again correctly predicted by (10.3,3).