FORCES ON THE WING

The vertical velocity of the wing section distant у from the center fine is

z = h(y)zT (7.13,2)

and the corresponding change in wing angle of attack is

A«(») = Цу)&тІГ (7.13,3)

This angle-of-attack distribution can be used with any applicable steady-flow wing theory to calculate the incremental local section lift. (It will of course be proportional to z^/F.) Let it be denoted in coefficient form by C’l(y)zT/V, and the corresponding increment in wing total lift coefficient by Cxio^y/F. G’t(y) and C’Lw are thus the values corresponding to unit value of the non­dimensional quantity zr/F.

FORCE ON THE TAIL

The tail experiences a downward velocity h(0)zT, and also, because of the altered wing lift distribution, a downwash change (dejdzT)zT. Hence the net change in tail angle of attack is

Aoq = h(0)zTIV—————— — zT

dzT

This produces an increment in the tail lift coefficient of amount

THE DERIVATIVE Ц

ZT

This derivative describes the contribution of wing bending velocity to the lift acting on the airplane. A suitable nondimensional form is dCLjd(zTjV):

THE DERIVATIVE An

nct

This derivative (see 5.12,12) represents the contribution to the generalized force in the bending degree of freedom, associated with a change in the angle of attack of the airplane. A suitable nondimensional form is obtained by defining

n — З’

* ipv2s

Then the appropriate nondimensional derivative is.

Let the wing lift distribution due to a perturbation oc in the angle of attack (constant across the span) be given by Сг^(у)а. Then in a virtual displacement in the wing bending mode bzT, the work done by this wing loading is

rb/2

— a G,(y)h(y) bzTpV{y) dy

J-b/2

The tail also contributes to this derivative. For the tail lift associated with a is

?£Ha

and the work done by this force during the virtual displacement is

3e

Therefore the contribution to G *• is and to is

^ a

The total value of Cis then the sum of (7.13,7 and 8.)

THE DERIVATIVE b,, (SEE 5.12,12)

This derivative identifies the contribution of zT to the generalized aero­dynamic force in the distortion degree of freedom. We have defined the associated wing load distribution above by the local lift coefficient С[(у)гт1У. As in the case of the derivative An above, the work done by this loading is calculated, with the result that the wing contributes

эсу _ 1 d2W

d(zT/V) ipV28 dzT d(zT/V)
f Gi(y)h(y)c(y) dy (7.13,9)

8 J-D/2

Likewise, the contribution of the tail is calculated here as for Anx, and is found to be

The total value of dC^jd{zTjV) is then the sum of (7.13,9 and 10.).