Vertical Flight Performance of the Autogiro

A conventional momentum theory analysis of the autorotating rotor breaks down when the rotor is at large angles of attack to the relative wind. For larger disk angles of attack it is possible to equate the resultant force on the rotor to the weight of the autogiro (i. e., R ~ W). Furthermore, the resultant velocity, Уж, can be written as Vqo = y/Vf + Vd so that

W

CR = 1———————– . (12.7)

-p(.Vj + Vj)A

Harris (2003) shows that for large operational angles of attack it is possible to write

In pure vertical descent Vf = 0, so the vertical rate of descent in autorotation will be

at sea level, which compares favorably with the result given previously in Eq. 12.4 and also with results by Glauert (1926). The autorotative rate of descent, however, decreases quickly with increasing forward speed but only to a point, as has been shown previously in Fig. 12.2. For a series of horizontal velocities, V/, at the steeper angles of attack where Cr = Cd = 1-25, the rate of descent in autorotation, Vd, can be solved using

(12.10)

or in nondimensiohal terms

(12.11)

for which the predictions made using this latter equation are shown in Fig. 12.2. Note that for Vf = 0 this predicts Xd/kh = 1.79, which is consistent with the results shown in Section 2.13.7. While not exact, this equation does give a reasonably good result for Vd as a function of forward speed, V/, when the rotor disk is at steep angles of attack to the relative wind.