Page 248 - Aerodynamics for Engineering Students

Finite wing theory 231

For large aspect ratios s >> cy so provided z1 is not close to fs, i.e. near the wing-tips,

giving

Thus Eqn (5.23) reduces to the two-dimensional result, Eqn (4.103), i.e.

(5.24)

Lifting effect
To understand the fundamental concepts involved in modelling the lifting effect of
a vortex sheet, consider first the simple rectangular wing depicted in Fig. 5.21. Here
the vortex sheet is constructed from a collection of horseshoe vortices located in the
y = 0 plane.
From Helmholtz's second theorem (Section 5.2.1) the strength of the circulation
round any section of the vortex sheet (or wing) is the sum of the strengths of the

vortex filaments

CL\

Fig. 5.21 The relation between spanwise load variation and trailing vortex strength