Page 266 - Aerodynamics for Engineering Students

Finite wing theory 249

For (b):

and since S”_,ritfl(z) = 0 in Eqn (5.53)

(5.55)

Comparing Eqns (5.54) and (5.55)

and since fl(z) is an explicit function of z,

J_:(fl(Z))2dZ > 0

since (f1(z))2 is always positive whatever the sign of fl(z). Hence DV(b) is always
greater than Dv(~).

5.6 Determination of the load distribution
on a given wing

This is the direct problem broadly facing designers who wish to predict the perform-
ance of a projected wing before the long and costly process of model tests begin. This
does not imply that such tests need not be carried out. On the contrary, they may be
important steps in the design process towards a production aircraft.
The problem can be rephrased to suggest that the designers would wish to have
some indication of how the wing characteristics vary as, for example, the geometric
parameters of the project wing are changed. In this way, they can balance the
aerodynamic effects of their changing ideas against the basic specification - provided
there is a fairly simple process relating the changes in design parameters to the
aerodynamic characteristics. Of course, this is stating one of the design problems in
its baldest and simplest terms, but as in any design work, plausible theoretical
processes yielding reliable predictions are very comforting.
The loading on the wing has already been described in the most general terms
available and the overall characteristics are immediately to hand in terms of the
coefficients of the loading distribution (Section 5.5). It remains to relate the coeffi-
cients (or the series as a whole) to the basic aerofoil parameters of planform and
aerofoil section characteristics.

5.6.1 The general theory for wings of high aspect ratio

A start is made by considering the influence of the end effect, or downwash, on the
lifting properties of an aerofoil section at some distance z from the centre-line of the
wing. Figure 5.34 shows the lift-versus-incidence curve for an aerofoil section of