Page 243 - Aerodynamics for Engineering Students

226 Aerodynamics for Engineering Students

Fig. 5.17
5.3.3 Ground effects

In this section, the influence of solid boundaries on aeroplane (or model) perform-
ance is estimated and once again the wing is replaced by the equivalent simplified
horseshoe vortex.
Since this is a linear problem, the method of superposition may be used in the
following way. If (Fig. 5.17b) a point vortex is placed at height h above a horizontal
plane, and an equal but opposite vortex is placed at depth h below the plane, the
vertical velocity component induced at any point on the plane by one of the vortices
is equal and opposite to that due to the other. Thus the net vertical velocity, induced
at any point on the plane, is zero. This shows that the superimposition of the image
vortex is equivalent in effect to the presence of a solid boundary. In exactly the same
way, the effect of a solid boundary on the horseshoe vortex can be modelled by
means of an image horseshoe vortex (Fig. 5.17a). In this case, the boundary is the
level ground and its influence on an aircraft h above is the same as that of the
‘inverted’ aircraft flying ‘in formation’ h below the ground level (Figs 5.17a and 5.18).
Before working out a particular problem, it is clear from the figure that the image
system reduces the downwash on the wing and hence the drag and power required, as
well as materially changing the downwash angle at the tail and hence the overall
pitching equilibrium of the aeroplane.

Example 5.2 An aeroplane of weight Wand span 2s is flying horizontally near the ground
at altitude h and speed V. Estimate the reduction in drag due to ground effect. If
W = 22 x 104N, h = 15.2m, s = 13.7m, V = 45m s-’, calculate the reduction in Newtons.
(U of L)
With the notation of Fig. 5.18 the change in downwash at y along the span is Aw t where

On a strip of span by at y from the centre-line,
lift I = pvro sy
and change in vortex drag
law
Ad,=-
V
(5.20)