Effect of Trim on С^1Х

In order to calculate the stalling speed of an afrplane in steady flight, one must consider that, in addition to the weight, the wing’s lift must support any download on the horizontal tail required to trim the airplane around its pitching axis. In order to determine this additional trim load, refer to Figure

Figure 3.61 Longitudinal trim of an airplane.

3.61. Here, tfae wing lift L, the tail lift, LT, the pitching moment about the wing’s aerodynamic center, Ми, and the weight are all shown in a positive sense. With the aerodynamic center of the tail located a distance of lT behind the center of gravity and the wing’s aerodynamic center a distance of (xcg-дсас)с ahead, the tail lift to trim is given by

г Afac T C. .

LT – —I – Lyixcg – xac)

It It

In addition, static equilibrium in the vertical direction requires that

L + LT = W

Therefore, it follows that

W = L[ l+^(*Cg-*ac)]+^

In coefficient form this becomes

CL = CLw [l + f<xct – xac)] + Cnjfc (3.82)

Here, CL is taken to mean the trim CL-

CLw refers to the untrimmed wing lift coefficient corrected for the fuselage.

It was mentioned earlier that the added drag caused by flaps must sometimes be considered in the trim of an airplane. If A CD denotes this increment in the drag coefficient and if the flaps are located a distance of h above the center of gravity, Equation 3.82 modified to account for the flap

(3.83)

ACd can be obtained experimentally or estimated on the basis of Equations 3.45 and 3.46.

CMac is normally negative and greater in magnitude than the moments resulting from CLw and ДC/> Thus CL is normally less than CLw. Since Equation 3.83 holds for maximum lift conditions, it follows that the trim is normally less than the wing C^.

In calculating CMac for use in Equation 3.83, the section aerodynamic moment determined from CMac, including the increment because of the flaps, is integrated over the wing excluding the part submerged in the fuselage.