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.

Example 10.2

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.

Solution

Given, W = 200 kN, 2b = 12 m, c = 2 m, V = 120 m/s.

In level flight:

1 2 ,

L = W = – pV2SC’L.

At sea level, p = 1.225 kg/m3. Therefore:

L

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

Hence:

(Cl – CL) 2pV2Sg
W

(1.04 – 0.945) 2 x 1.225 x 1202 x 24 x 9.81
200 x 103