Page 61 - Aerodynamics for Engineering Students

44 Aerodynamics for Engineering Students

D

V
Fig. 1.22 Flow conditions and forces at a section of a three-dimensional lifting wing

The further apart the wing-tip vortices the less will be their effectiveness in producing
induced incidence and drag. It is therefore to be expected that these induced quantities
will depend on the wing aspect ratio, (AR). Some results obtained in Chapter 5 below are:

where am is the lift curve slope for the two-dimensional wing, and the trailing vortex
drag coefficient CD, is given by

c =- Dv -- " (1 +S) (Eqn(5.50))
-
Dv 4pPS ?r(AR)
where S is a small positive number, constant for a given wing.

1.5.8 Lift-dependent drag
and
It has been seen that the induced drag coefficient is proportional to G, may exist
in an inviscid fluid. On a complete aircraft, interference at wing/fuselage, wing/
engine-nacelle, and other such junctions leads to modification of the boundary layers
over the isolated wing, fuselage, etc. This interference, which is actually part of the
profile drag, usually vanes with the lift coefficient in such a manner that it may be
treated as of the form (a + Xi). The part of this profile drag coefficient which is
represented by the term (bC2) may be added to the induced drag. The sum so
obtained is known as the lift-dependent drag coefficient. The lift-dependent drag
is actually defined as 'the difference between the drag at a given lift coefficient and
the drag at some datum lift coefficient'.
If this datum lift coefficient is taken to be zero, the total drag coefficient of a
complete aeroplane may be taken, to a good approximation in most cases, as
CD = CO, + kC?;

where Coo is the drag coefficient at zero lift, and kC2 is the lift-dependent drag
coefficient, denoted by CD,.

1.5.9 Aerofoil characteristics
Lift coefficient: incidence
This variation is illustrated in Fig. 1.23 for a two-dimensional (infinite span) wing.
Considering first the full curve (a) which is for a moderately thick (13%) section of