#### 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.

### The Planform Problem

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.

### 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.

Figure 1: Swept wing relationships

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.

Figure 2: Sweep angle versus Mach number

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.

Table 1: Wing Sweep Data (avaiable on CD-ROM)
Aircraft M

### Speed and Leading-Edge Geometry

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.

### Speed and Wing Thickness

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

Figure 4: Effect of thickness on transonic drag rise

#### Related Material (available on CD-ROM)

• Transonic Aerodynamics
• Supercritical Wings

### Wings in Ground Effect

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.

Figure 5: ground effect

#### Summary of Wings (available on CD-ROM)

Here is a summary of special wings, from low- to hypersonic speeds, covered in this section:

• Forward Swept Wing
• Oblique Flying Wing
• Delta Wing
• Low Aspect-Ratio Wing
• Hypersonic Waveriders
• Non-Planar Wing Systems
• Interference Problems

#### Selected References

• Ashley, H. and Landahl, M., Aerodynamics of Wings and Bodies, Addison-Wesley Publ. Company, Reading, Mass. 1965.

• Schlichting H. and Truckenbrodt E., Aerodynamics of the Airplane, McGraw-Hill, New York, 1979.

• Jones RT. Wing Theory, Princeton Univ. Press, Princeton, NJ. 1990.

• Abbott IH, Von Doenhoff A. Theory of Wing Sections, Dover Publ. Inc., New York, 1959.

• Katz J, Plotkin J. Low Speed Aerodynamics, McGraw-Hill, Inc., New York, 1991.

• Nickel K, Wohlfahrt M. Tailless Aircraft in Theory and Practice, Edward Arnold, London 1994 (also available from AIAA).
[Top of Page]