Wing Design Parameters






Span

Selecting the wing span is one of the most basic decisions to made in the design of a wing. The span is sometimes constrained by contest rules, hangar size, or ground facilities but when it is not we might decide to use the largest span consistent with structural dynamic constraints (flutter). This would reduce the induced drag directly.

However, as the span is increased, the wing structural weight also increases and at some point the weight increase offsets the induced drag savings. This point is rarely reached, though, for several reasons.
  1. The optimum is quite flat and one must stretch the span a great deal to reach the actual optimum.

  2. Concerns about wing bending as it affects stability and flutter mount as span is increased.

  3. The cost of the wing itself increases as the structural weight increases. This must be included so that we do not spend 10% more on the wing in order to save .001% in fuel consumption.

  4. The volume of the wing in which fuel can be stored is reduced.

  5. It is more difficult to locate the main landing gear at the root of the wing.

  6. The Reynolds number of wing sections is reduced, increasing parasite drag and reducing maximum lift capability.


On the other hand, span sometimes has a much greater benefit than one might predict based on an analysis of cruise drag. When an aircraft is constrained by a second segment climb requirement, extra span may help a great deal as the induced drag can be 70-80% of the total drag.

The selection of optimum wing span thus requires an analysis of much more than just cruise drag and structural weight. Once a reasonable choice has been made on the basis of all of these considerations, however, the sensitivities to changes in span can be assessed.

Area

The wing area, like the span, is chosen based on a wide variety of considerations including:
  1. Cruise drag

  2. Stalling speed / field length requirements

  3. Wing structural weight

  4. Fuel volume

These considerations often lead to a wing with the smallest area allowed by the constraints. But this is not always true; sometimes the wing area must be increased to obtain a reasonable CL at the selected cruise conditions.

Selecting cruise conditions is also an integral part of the wing design process. It should not be dictated a priori because the wing design parameters will be strongly affected by the selection, and an appropriate selection cannot be made without knowing some of these parameters. But the wing designer does not have complete freedom to choose these, either. Cruise altitude affects the fuselage structural design and the engine performance as well as the aircraft aerodynamics. The best CL for the wing is not the best for the aircraft as a whole. An example of this is seen by considering a fixed CL, fixed Mach design. If we fly higher, the wing area must be increased by the wing drag is nearly constant. The fuselage drag decreases, though; so we can minimize drag by flying very high with very large wings. This is not feasible because of considerations such as engine performance.

Sweep

Wing sweep is chosen almost exclusively for its desirable effect on transonic wave drag. (Sometimes for other reasons such as a c.g. problem or to move winglets back for greater directional stability.)
  1. It permits higher cruise Mach number, or greater thickness or CL at a given Mach number without drag divergence.

  2. It increases the additional loading at the tip and causes spanwise boundary layer flow, exacerbating the problem of tip stall and either reducing CLmax or increasing the required taper ratio for good stall.


  3. It increases the structural weight - both because of the increased tip loading, and because of the increased structural span.


  4. It stabilizes the wing aeroelastically but is destabilizing to the airplane.

  5. Too much sweep makes it difficult to accommodate the main gear in the wing.

See section 9.2.5 for more detail on simple sweep theory and the effects of sweep.
Much of the effect of sweep varies as the cosine of the sweep angle, making forward and aft-swept wings similar. There are important differences, though as discussed further in the section on forward swept wings.

Thickness

The distribution of thickness from wing root to tip is selected as follows:
  1. We would like to make the t/c as large as possible to reduce wing weight (thereby permitting larger span, for example).

  2. Greater t/c tends to increase CLmax up to a point, depending on the high lift system, but gains above about 12% are small if there at all.

  3. Greater t/c increases fuel volume and wing stiffness.

  4. Increasing t/c increases drag slightly by increasing the velocities and the adversity of the pressure gradients.

  5. The main trouble with thick airfoils at high speeds is the transonic drag rise which limits the speed and CL at which the airplane may fly efficiently.

Taper

The wing taper ratio (or in general, the planform shape) is determined from the following considerations:
  1. The planform shape should not give rise to an additional lift distribution that is so far from elliptical that the required twist for low cruise drag results in large off-design penalties.

  2. The chord distribution should be such that with the cruise lift distribution, the distribution of lift coefficient is compatible with the section performance. Avoid high Cl's which may lead to buffet or drag rise or separation.

  3. The chord distribution should produce an additional load distribution which is compatible with the high lift system and desired stalling characteristics.

  4. Lower taper ratios lead to lower wing weight.

  5. Lower taper ratios result in increased fuel volume.

  6. The tip chord should not be too small as Reynolds number effects cause reduced Cl capability.

  7. Larger root chords more easily accommodate landing gear.

Here, again, a diverse set of considerations are important.

The major design goal is to keep the taper ratio as small as possible (to keep the wing weight down) without excessive Cl variation or unacceptable stalling characteristics.

Since the lift distribution is nearly elliptical, the chord distribution should be nearly elliptical for uniform Cl's. Reduced lift or t/c outboard would permit lower taper ratios.

Evaluating the stalling characteristics is not so easy. In the low speed configuration we must know something about the high lift system: the flap type, span, and deflections. The flaps- retracted stalling characteristics are also important, however (DC-10).

Twist

The wing twist distribution is perhaps the least controversial design parameter to be selected. The twist must be chosen so that the cruise drag is not excessive. Extra washout helps the stalling characteristics and improves the induced drag at higher CL's for wings with additional load distributions too highly weighted at the tips.

Twist also changes the structural weight by modifying the moment distribution over the wing.

Twist on swept-back wings also produces a positive pitching moment which has a small effect on trimmed drag. The selection of wing twist is therefore accomplished by examining the trades between cruise drag, drag in second segment climb, and the wing structural weight. The selected washout is then just a bit higher to improve stall.