Sudden Increase of Incidence
Let us assume the aircraft to be flying steadily and horizontally, so that if CL’ is the lift coefficient:
CL ^ 2 pV2S^j = W,
a sudden increase of incidence will increase the lift coefficient to:
cL( 2 pvs)
and the aircraft will acquire an upward acceleration f given by:
C – Сь)(1PV 2 S) = gf
so that it will begin to describe a curved path of radius of curvature r given by f = V2/r, where:
_ 2W 1 _ 2w 1
Г = SSP (Cl – Cl’) ~ ~SP (CL – CL’) ‘
In this analysis we ignore the change in drag. If the speed is high, CL’ is small and CL cannot exceed CLmax for speed V. Thus the absolute minimum value of r is given by:
where VS is the appropriate stalling speed. Since CLmax is accompanied by a rather large drag, the theoretical value of rmin in Equation (10.4) cannot be attained.
An aircraft weighing 200 kN, wing span 12 m and mean chord 2misin steady level flight at sea level, at a speed of 120 m/s. If the lift coefficient is suddenly increased by 10%, determine the upward acceleration causing the lift increase.
Given, W = 200 kN, 2b = 12 m, c = 2 m, V = 120 m/s.
1 2 ,
L = W = – pV2SC’L.
At sea level, p = 1.225 kg/m3. Therefore:
2 pV 2S
200 x 103
= 1 x 1.225 x 1202 x (12 x 2) = 0.945.
The new lift coefficient is:
Cl = 1.1 x C’L = 1.1 x 0.945 = 1.04.
The expression for upward acceleration f is:
W, ,4 1 2
– f = Cl – CL) – pV2S. g 2
(Cl – CL) 2pV2Sg
(1.04 – 0.945) 2 x 1.225 x 1202 x 24 x 9.81
200 x 103