Page 241 - Aerodynamics for Engineering Students

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224 Aerodynamics for Engineering Students

'11 '

'12

d2 I dl

b'

Fig. 5.15

components from the trailing vortices a2b2 and qd3. The net result is an
upwash on the leader.
(ii) These wings have additional influences to their own trails due to the leader and
the other follower. Bound vortex alcl and trailing vortices albl, a2b2 produce
downwashes. Again the net influence is an upwash.
From these simple considerations it appears that each aircraft is flying in a regime in
which upward components are induced by the presence of the others. The upwash
components reduce the downward velocities induced by the aircraft's own trail and
hence its trailing vortex drag. Because of the reduction in drag, less power is required
to maintain the forward velocity and the well-known operational fact emerges that
each aircraft of a formation has a better performance than when flying singly. In
most problems it is usual to assume that the wings have an elliptic distribution, and
that the influence calculated for mid-span position is typical of the whole wing span.
Also any curvature of the trails is neglected and the special forms of the Biot-Savart
law (Section 5.2.2) are used unreservedly.

5.3.2 Influence of the downwash on the tailplane
On most aircraft the tailplane is between the trailing vortices springing from the
mainplanes ahead and the flow around it is considerably influenced by these trails.
Forces on aerofoils are proportional to the square of the velocity and the angle of
incidence. Small velocity changes, therefore, have negligible effect unless they alter
the incidence of the aerofoil, when they then have a significant effect on the force on
the aerofoil.
Tailplanes work at incidences that are altered appreciably by the tilting of the
relative wind due to the large downward induced velocity components. Each particu-
lar aircraft configuration will have its own geometry. The solution of a particular
problem will be given here to show the method.

Example 5.1 Let the tailplane of an aeroplane be at distance x behind the wing centre of
pressure and in the plane of the vortex trail (Fig. 5.16).
Assuming elliptic distribution, the semi-span of the bound vortex is given by Eqn (5.18) as
s' = (&
7r