THE DERIVATIVE

The change in aileron hinge moment due to yawing velocity is a consequence of the velocity differential between the right and left ailerons. Let the hinge- moment coefficient of the right-hand aileron, at zero aileron angle, be СЫа. Then the corresponding hinge moment, with no yawing, is Ghao(pj2)V28aca. This hinge moment is normally balanced by that on the left aileron, so that no load is carried to the pilot’s control. Now, when yawing is added, the mean forward velocity at the right-hand aileron is changed from V to (F — rya), so that the hinge moment is approximately Cna(>(pj2)(V — гуа)2$аса. To the first order in r, the incremental hinge moment is

Д Ha = – ChaiipryaV8aca

On the left-hand side, the increment in H is equal to the above but opposite in sign, so that the two are additive with respect to the stick force, just as though the ailerons were deflected through a small positive angle. The coefficient of ДHa is

Art лр гУа____________________ У a rt

ha — ~ ~

Since Cha is defined as the hinge moment on one aileron then

rt лУа ft

°haT — + °ha0

Summary—Lateral Derivatives

	Су	Cl	Cn	Cjia	chr
p	-e-f)	F 8 Ь dp}	*	Neg.
p		N. A.6	* / ^ 3cr aFVvy b 0a)	2?c4	a /2 — -"i 7"Ц 6 Эр/
r	* S*,/ l. jj, da	* &F Z_F_ /„ l_F j|f S b 6 + Sr)	/ сгЭ —apVyl2 — + (tail) V I2 -2Cr y: p (iet)	4 6 °л“о	c /2— + —’і С7"Ц2 Ь +
8a	Neg. c	N. A.	N. A.	Chag	Neg.
8r	Sp – ar s	S’jfi Zp ar s T	—arFF	Neg.	Chrg

Table 8.1

a * denotes a contribution from the tail only.

6 N. A. means no convenient formula available. c Neg. means usually negligible.

THE DERIVATIVE ChTr

The change in the vertical-tail angle of attack (8.7,1) induces a change in the rudder hinge moment. This is given by

where Ghr is the derivative, with respect to the vertical-tail angle of attack of the rudder hinge-moment coefficient. Hence

c – = av(2T+l) <8V)

8.8 SUMMARY OF THE FORMULAE

Table 8.1 contains a summary of useful formulae used for estimation purposes.