At high angles of attack, several phenomena usually distinct from the
cruise flow appear. Usually part of the wing begins to stall (separation
occurs and the lift over that section is reduced). An approximate way to
predict when this will occur on well-designed high aspect ratio wings is
to look at the C_{l} distribution over the wing and determine the wing
C_{L} at
which some section (the critical section) reaches its 2-D maximum C_{l}. In
the example below the outboard sections have C_{lmax} = 1.5 so
the wing begins
to stall near the tip when C_{L} = 1.24

The effects of wing sweep must be taken into account when using critical
section theory as the outboard flow of the boundary layer acts to reduce
the maximum C_{l} available over the outboard sections.

When the sweep is very large, separation tends to occur near the leading
edge of the wing, but unlike in the low sweep situation, the separated region
is not large and does not reduce the lift. Instead, the flow rolls up into
a vortex that lies just above the wing surface.

Rather than reducing the lift of the wing, the leading edge vortices, increase
the wing lift in a nonlinear manner. The vortex can be viewed as reducing
the upper surface pressures by inducing higher velocities on the upper surface.

The net result can be large as seen on the plot here.

The effect can be predicted quantitatively by computing the motion of the
separated vortices using a nonlinear panel code or an Euler or Navier-Stokes
solver.

This figure shows computations from an unsteady non-linear panel method.
Wakes are shed from leading and trailing edges and allowed to roll-up with
the local flow field. Results are quite good for thin wings until the vortices
become unstable and "burst" - a phenomenon that is not well predicted
by these methods. Even these simple methods are computation-intensive.

However, a simple method of estimating the so-called "vortex lift"
was given by Polhamus in 1971. The Polhamus suction analogy states that
the extra normal force that is produced by a highly swept wing at high angles
of attack is equal to the loss of leading edge suction associated with the
separated flow. The figure below shows how, according to this idea, the
leading edge suction force present in attached flow (upper figure) is transformed
to a lifting force when the flow separates and forms a leading edge vortex
(lower figure).

The suction force includes a component of force in the drag direction. This
component is the difference between the no-suction drag:

C_{Di} = C_{n} sin α,
and the full-suction drag: C_{L}^{2} / π AR

where α is the angle of attack.

The total suction force coefficient, C_{s}, is then:

C_{s} = (C_{n} sin α - C_{L}^{2}/π AR) / cos Λ

where Λ is the leading edge sweep angle. If this acts as an additional normal
force then:

Cn' = C_{n} + (C_{n} tan α- C_{L}^{2}/π AR) / cos Λ

= C_{n} + (C_{n} sin α - C_{L}^{2}/π AR) / cos Λ

so, Cn' = C_{n} + (C_{n} sin α - C_{L}^{2}/π AR) / cos Λ

and in attached flow:

C_{L} = C_{La} sin α with C_{n} = C_{L} cos α

Thus, Cn' = C_{L} cos α + (C_{L} cos α sin α - C_{L}^{2}/π AR) / cos Λ

= C_{La} sin α cos α + (C_{La} sin α cos α sin α - (C_{La} sin α)^{2}/π AR) / cos Λ

= C_{La} sin α cos α + C_{La}/ cos Λ sin^{2} α cos α - C_{La}^{2}/(π AR cos Λ) sin^{2} a

C_{L}' = C_{La} [sin α cos^{2} α + sin^{2} α cos^{2} α /cos Λ - C_{La}/(π AR cos Λ) cos α
sin^{2} α]

= C_{La} sin α cos α (cos α + sin α cos α/ cos Λ - C_{La} sin α /(π AR cos Λ))

If we take the low aspect ratio result: C_{La} = π AR/2, then:

C_{L} '= π AR/2 sin α cos α (cos α + sin α cos α/ cos Λ - sin α /(2 cos Λ) )

The plot below shows this computation compared with experiment for a 80°
delta wing (AR = 0.705)

Attached flow computations, Polhamus suction analogy, and experiment for
lift on a 80° delta wing.

A flow pattern, similar to that of the highly swept delta wing, is found
at the tips of low aspect ratio wings and over fuselages. The vortex formation
significantly increases the lift in these cases as well. Especially in the
case of fuselage vortices, the airplane stability is affected and interaction
with downstream surfaces is often important and hard to predict.

Vortices generated by the fuselage and leading edge stakes of an F-18 are
visible in the photo below and this QuickTime video
clip of NASA's High Alpha Research Vehicle, used to investigate these
phenomena and ways to control them.