Linear Model for the Tail

With the classical configuration, the tail is influenced by the downwash of the main wing. The downwash varies from ww at the wing (x = 0) to wT = 2ww in the Trefftz plane (x = +ro). The coefficient of downwash, ki = wt/ww| at the tail location is between -1 and -2. A study of the downwash induced by the vortex sheet of an elliptically loaded wing, provides a quantification of this effect, as shown in Fig. 11.2.

One also assumes a rectangular tail with an elliptic loading. This is a valid approx­imation since the tail has a low aspect ratio ARt = bt /ct where bt and ct are the tail span and chord, respectively. The tail mean camber is dt. The tail lift coefficient is given by

Подпись: Cbt = 2n

Linear Model for the Tail

dt

a + aim + ait + tt + 2 (11.7)

ct

Подпись:Подпись: (11.8)

Linear Model for the Tail Подпись: (11.9)

where aim represents the induced incidence due to the wing downwash at the tail lifting line and ait that due to the tail downwash on itself. Using the results of Prandtl Lifting Line

The linear decomposition for the tail lift consists of

dCLt 2n A + ki dCLm

da 1 + Ar n ARm d a

2n dt ki

CLt0 (tt) = 2 tt + 2- + *- CLm0 (11.10)

1 + Ar, Ct П ARm

Note that the tail setting angle tt, which controls the airplane flight operation, does not appear in the tail lift slope. The reference area for the tail lift is the tail area At = btct.

The tail drag is the sum of the friction drag CDt0 and the induced drag CDit calculated with formulae similar to those used for the wing. The area of reference for the tail drag is At.

Подпись: dCM,ot d a Подпись: xact dCLt cat d a Подпись: CM,ot0(tt) = —П - CLt0 (tt) ct cat Подпись: (11.11)

The moment coefficient for the tail can be decomposed as

Again, we note that the moment slope for the tail is independent of the tail setting angle.

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