CONTRIBUTIONS OF A TAIL

There is an approximate method for evaluating the contributions of a tail surface, which is satisfactory in many cases. This is based on the concept of the lag of the downwash. It neglects entirely the nonstationary character of the lift response of the tail to changes in tail angle of attack, and attributes the result entirely to the fact that the downwash at the tail does not respond instantaneously to changes in wing angle of attack. The downwash is assumed to be dependent primarily on the strength of the wing’s trailing vortices in the neighborhood of the tail. Since the vorticity is con­verted with the stream, then a change in the circulation at the wing will not be felt as a change in downwash at the tail until a time At — l,/u0 has elapsed, where l, is the tail length. It is therefore assumed that the instantaneous downwash at the tail, e(r), corresponds to the wing a at time (t — At). The corrections to the quasistatic down – wash and tail angle of attack are therefore

(5.5,9)

Cz of a Tail

Za

The correction to the tail lift coefficient for the downwash lag is

The correction to the airplane lift is therefore

AC, = a. a

Therefore

dCz dCL де l, S,

and

Cm. of a Tail

ma

The correction to the pitching moment is obtained from ACLt as

Эе l,

ACm = ~VH ACL = —a-jCt — VH

da u0

Therefore

5.2 The P Derivatives (Cyp, Clp, Cnp)

These derivatives all are obtainable from wind-tunnel tests on yawed models (Camp­bell and McKinney, 1952). Generally speaking, estimation methods do not give com­pletely reliable results, and testing is a necessity.

THE DERIVATIVE Cyp

This is the side-force derivative, giving the force that acts in the у direction (right) when the airplane has a positive /3 or v (i. e., a sideslip to the right, see Fig. 3.11). Cyp is usually negative, and frequently small enough to be neglected entirely. The main contributions are those of the body and the vertical tail, although the wing, and wing – body interference, may modify it significantly. Of these, only the tail effect is readily estimated. It may be expressed in terms of the vertical-tail lift-curve slope and the sidewash factor (see Sec. 3.9). (In this and the following sections the fin velocity ra­tio VFIV is assumed to be unity.)

or

(5.6,1)

The most troublesome component of this equation is the sidewash derivative dcr/d/3, which is difficult to estimate because of its dependence on the wing and fuselage geometry (see Sec. 3.9).

THE DERIVATIVE Clp

C, p is the dihedral effect, which was discussed at some length in Sec. 3.12.

THE DERIVATIVE Cnp

C,4, is the weathercock stability derivative, dealt with in Sec. 3.9.