FLIGHT MECHANICAL COEFFICIENTS OF THE WING

3-5-1 Contributions of the Wing to Stability

The methods for the computation of the aerodynamic forces on a wing have been discussed in detail in Secs. 3-2-3-4. This section will show how these methods can be applied to the determination of the flight mechanical coefficients of the wing. A survey on these coefficients has been given previously in Sec. 1-3-3.

The flight mechanical coefficients are determined by the motion of the wing

Figure 3-60 Drag polars of circular wings of various degrees of leading-edge rounding, accord­ing to measurements of Hansen [4-4]. Theory according to Kinner [44]. The drag at = 0 has been subtracted from the measured values. Disks I and II: cDp= 0.012; disk III: cDp = 0.008. Curve 1, with suction force from Eq. (3-125); CD = cDp + 0.274cjr. Curve 2, without suction force from Eq. (3-1446); Cjq = cjjp + Q,55c.

and the wing geometry. In the following discussions, only those coefficients will be considered that are significant for airplane stability. The coefficients that determine maneuverability will be treated later in Chap. 8.

In addition to the wing, the other parts of the airplane (fuselage, empennage) contribute, sometimes considerably, to these flight mechanical coefficients. These contributions will be discussed later, too. In the present section, only the contributions of the wing will be discussed.

The flight mechanical coefficients of the wing depend on numerous geometric parameters of the wing, such as wing planform (aspect ratio, taper, sweepback), twist, and dihedral (see Sec. 3-1-1). The dependence of the flight mechanical coefficients on wing geometry is too varied to attempt a complete description of all these interrelations. In some cases the contribution of the wing to the stability coefficients of the whole airplane is small. Further investigations will be restricted to the cases in which the wing makes an essential contribution. Reference will be made to the summary reports of Betz [6], Schlichting [72], and Multhopp [61].

Of the two axis systems of Fig. 1-6, the experimental system will be used.[19] The coefficients are defined in Eq. (1-21).

The motion of the airplane can be divided into a longitudinal motion and a lateral motion, as has been explained in Sec. 1-3-3. During longitudinal motion, the position of the plane of symmetry of the airplane does not change. This motion is characterized by three parameters: flight velocity V, angle of attack a, and pitching angular velocity cov (Fig. 3-61). The lateral motion is defined by sideslip angle (3, rolling angular velocity со*, and yawing angular velocity coz (Fig. 3-61). The stability coefficients are understood to be the changes of force and momentum coefficients with the above motion parameters.