In this Chapter
This section covers wings for all speeds: low speed, transonic, supersonic, hypersonic, and in ground effect. While the wing geometry is a complex aerodynamic problem that must take into account several non-aerodynamic constraints, we will focus on those characteristics that are unequivocally set by the speed range, namely Reynolds and Mach numbers.
At low speeds (e.g. subsonic) only the Reynolds number is
the relevant scale parameter for the speed.
Following Küchemann (1965), the various aircraft types can be classified
according to the ratio of their semi-span to their length, b/L (the inverse of the
aircraft slenderness).
Aircraft for low subsonic cruise flight (e.g.
Douglas DC-3)
have a b/L of about 0.5; faster aircraft, in the transonic range are characterized by
a b/L = 0.3, whereas supersonic aircraft (Concorde) have a ratio b/L = 0.25.
At constant aircraft length this means that the wing gets shorter, partially because of
the aspect-ratio and partially because of the back sweep and the change of geometry
(delta wing, instead of a rectangular wing).
The Space Shuttle is the only hypersonic vehicle in service at the present time. It
has a b/L=0.3, while one would argue that this figure should be lower. In fact the
Shuttle is not designed to cruise under steady conditions for a long range.
As shown below, the requirements for flying efficiently at subsonic and supersonic
speeds are conflicting (e.g. supersonic fighters); for hypersonic vehicles in
particular, there is an enormous problem in designing a configuration that can take
off and land at low speeds.
Wing loading is in the range of 120-140 lb/ft² (580-680 kg/m²) on most
subsonic commercial transport aircraft.
The Planform Problem
Related Material
Speed and Wing Sweep
The unswept wing is the best balanced configuration for low speeds (subsonic). This type of wing is well understood, and relatively easy to compute, even with two-dimensional airfoil theory (or lifting surface).
As the speed increases toward transonic regimes aft sweep is required to have a
subsonic leading edge. Aft sweep, in fact, alleviates the normal component of the
speed, which is most responsible for the shock development, Fig. 1. This idea was
first introduced by Busemann in 1935.
As a general rule, a wing aft-sweep of less 30 degrees is required at subsonic
speeds, and a sweep of 50 to 60 degrees is appropriate for supersonic cruise. The
range of values in between is proper of wings in the transonic cruise regime, with
the upper values characteristic of transonic wings with good supersonic manoeuvre.
Wings with variable in-flight sweep have been proposed for a long time, sometimes they have also been developed (exclusively for fighter aircraft), but they pose challenging problems, such as the shift in the aerodynamic center, with consequences to the whole aircraft stability.
Longitudinal stability of the wing deteriorates with the increasing sweep also
for fixed wing, because of the increased loads in the outboard sections, which leads
to loss of lift and eventually to tip stall. This particular problem has been
investigated also for the forward-swept wing.
The table below is a summary of wing sweeps of some transport aircraft.
The leading edge radius assumes critical values that are related to the sweep angle
and to the wing aspect-ratio. The problem is fairly complicated, because it also
involves different types of separation (from the leading- or trailing edges).
Sometimes, like in the highly swept delta wings, separation from the leading edge is
desirable, therefore very small leading edge radii are used.
Wing thickness (or airfoil thickness) is strictly related to the drag
characteristics at all speeds. At subsonic speeds relatively thick wings (up to 20 %)
can be beneficial, since they increase the maximum lift.
As the speed increases thick wings are a major cause of shock waves, which lead to
leading edge separation, shock-induced separation, transonic drag rise, buffeting,
and eventually shock stall.
Figure 3: Force coefficients vs wing thickness
The above sketch is quite general. Wing thickness can be manipulated in the
so-called supercritical wing design to provide shock-free (or almost) wings at
transonic speeds. These wings can be almost as thick as subsonic wings.
Another effect of the wing thickness is on the transonic drag rise. An example is
given in the figure below
The use of ground effect is generally regarded as a very efficient means to increase
the lift and decrease the drag. This is not always true. However, for the cases where
ground effect is of any aerodynamic value, it is fully exploited. This is the case of
wings for racing cars, wings for wing-ships, and possibly remotely piloted vehicles.
The ground effect is measured as the ratio of the lift near ground and the lift in
unbounded stream, and is generally related to the ground clearance. Effective ground
clearances are of the order of 5-10 % wing chords. At values less than 5 % chord the
wing can be lifted or sinked, depending on various combinations of camber, thickness
and angle of attack. The most evident effects are the so-called ram-effect and
Venturi effect.
Here is a summary of special wings, from low- to hypersonic speeds, covered in this
section:
There is a number of other wings that at present are limited to research
papers (ring-wing, C-wing, joint wing, etc.)
Aircraft 
M Lockheed Tristar 35 deg 0.72 Airbus A-300 28 deg 0.73 Boeing B-737 25 deg 0.75 Douglas DC-9 24.5 deg 0.71 Fokker 100 23 deg 0.77 Speed and Leading-Edge Geometry
Speed and Wing Thickness
Figure 4: Effect of thickness on transonic drag rise
Related Material
Wings in Ground Effect
Summary of Wings
Selected References
