# The Flap Wing in Compressible Flow

Lift and moment The theory of the flap wing of infinite span in compressible flow may be derived approximately from the profile theory of compressible flow as given in Sec. 4-3. There solutions were obtained for subsonic incident flow using the subsonic similarity rule (Prandtl, Glauert) and for the supersonic incident flow using the supersonic similarity rule (Ackeret). The following formulas apply for fixed flap chord ratios = Afinc.

For subsonic incident flow (.Ma« < 1),

УМа^ – 1

In Fig. 8-14, the changes in zero-lift angle and zero moment caused by the flap deflection are given as a function of the flap chord ratio.

By using the above coefficients, the position of the flap neutral point can be computed with Eq. (8-6), where it has to be considered that dcLlda= lit! Vl —Mala for Maa° < 1 and dcLjdot= AjjMaL — 1 for Ma„ > 1. The position of the flap neutral point is given in Fig. 8-15 against the flap chord ratio fy. Here the relationships xNf = c/4 + (AxN)f applies for Маж < 1 and xNу = cj2 4- (AxN)f for Afecc > 1.

At supersonic velocities the flap neutral point lies much farther back than at subsonic velocities, as should be expected. The following expressions are obtained for the coefficients of the flap moment (control-surface moment) at subsonic incident flow (Mr*, < 1):

dCm f ( dCmf dcL dcL /inc

Figure 8-15 Position of the flap neutral point vs. the flap chord ratio for compres­sible flow (subsonic and supersonic veloci­ties).

dcmf______ 1___ /Эст A

dVf ~ Vl-Md 9i?/ Anc

Again, the coefficients marked inc are those of incompressible flow from Eq. (8-14) and Fig. 8-13. Corresponding relationships are found for the coefficients of flap loading.

For supersonic velocities (Mzoo > 1), the Ackeret rule yields (see Sec. 4-3-3)

dcmf____ 3_

dcL ~ 2

The coefficients of flap loading are determined immediately as cXf = 2cmf by realizing that the pressure distribution over the flap chord is constant.