# Aerodynamic Coefficients of the Flaps and Control Surfaces

The following aerodynamic coefficients are introduced for the wing with control surface:

 Lift: L c lA q oo (8-1) Pitching moment: M = cMAcqx (8-2) Control-surface moment: Mf = cmfAfCfq oo (8-3)

Here the lift coefficient and the pitching-moment coefficient are referred to the geometric quantities of the wing, as in the case of the wing without control surface [see Eq. (1-21)]; The control-surface moment Mf (flap moment, hinge moment) is referred to the axis of rotation of the control surface; its sign can be seen from Fig.

8- 1. The coefficient of the control-surface moment cmf is referred to the geometric
quantities of the control surface. These three aerodynamic coefficients depend on the angle of attack a and the control-surface angle rjf.

As an example of measurements, the lift coefficient Ci of a simple flap wing is plotted against the angle of attack in Fig. 8-5a for several flap angles rjf. The flap deflection T]f causes, corresponding to Fig. 2-24, an additive camber and thus, at constant angle of attack, an increase in lift. The curves cL(a) for several angles rjf are parallel to each other. The dependence of the lift coefficient on a and rjf for small angles may be expressed as

(84a)

(8 ЛЬ) where da/drif indicates the change in the zero-lift direction of the wing because of the flap deflection (flap effectiveness) [see Eq. (7-3&)]. The coefficient da/drjf depends strongly on the control-surface chord ratio. Data on this effect have been given in Fig. 2-25a for a flap wing of infinite span.

In Fig. 8-5b, the lift coefficient cL is plotted against the moment coefficient cM for several flap angles rjf- The flap angle causes a parallel shift of the moment curves. The dependence of the moment coefficient cM on cL and rjf for small values of these parameters may be expressed as

486 AERODYNAMICS OF THE STABILIZERS AND CONTROL SURFACES

Here, dcMldr)f gives the change of the zero moment with the flap deflection. This coefficient depends strongly on the flap chord ratio. Data on the wing of infinite span have been given in Fig. 2-25b.

Frequently it is advantageous to specify the location of the aerodynamic center of the additional forces generated by the flap deflection. This point is termed the flap neutral point. The distance of the flap neutral point from the neutral point of the wing without flap deflection (= neutral-point displacement) is obtained from Eqs. (8-5) and (84) as

(A xN)f _ _ bcMjbrif c dcLfbrif

where 3cLbrf may be taken from Eq. (8-4a).

In Fig. 8-6, cL is shown as a function of the control-surface moment coefficient cmf for several values of rjy. Here, too, a linear relationship applies of the form

The dependence of this coefficient on the flap chord ratio will be discussed in Sec.

8- 2. The condition cmf= 0 determines a certain coordination of щ and cL and thus also of 7у and a for self-setting of the free control surface.