Drag is usually considered to be divided into the minimum drag, frequently called zero lift drag, C_D0, and the drag due to lift. The drag due to lift is further broken up into induced drag and additional profile drag. The induced drag is a function of the wing spanload only, and is independent of the details of the particular airfoil shape used in the wing. The additional profile drag is associated with the airfoil used in the wing. At low lift coefficients this drag should be small, only becoming important as flow separation starts to develop on the airfoil section. The additional profile drag becomes large as wing stall is approached.

Wing performance is evaluated based on the ability to obtain a high value of the lift to drag ratio, (L/D), relative to the maximum possible for that planform, and the ability to achieve a high maximum lift coefficient. Essentially, the wing should be designed to allow the airfoil to achieve its full performance. Recalling that in potential flow theory a two-dimensional airfoil has no drag due to lift, the maximum performance should occur by adding the induced drag, assuming an elliptic spanload, to the zero lift drag (this would be known as the 100% suction polar, since the airfoil section has no additional profile drag due to lift, and is thus achieving 100% of the leading edge suction required to eliminate the drag force in a two-dimensional flow), DC_D = C_L²/(AR). At the other extreme, the worst case occurs when the airfoil fails to produce any efficient lift, such that the only force is normal to the surface and there is no edge or suction force (0% leading edge suction). In this case the entire lifting force on the wing is the normal force, and the polar can be determined by resolving that force into lift and drag components {DC_D = C_L tan(a - a₀)}. In any experimental evaluation of wing performance both the 100% and 0% polars should be constructed, and used to establish bounds on the experimental polar. For unswept wings, the span efficiency, e, predicted based on lifting line analysis should also be contained on the drag polar estimate.

It is difficult to identify the initial flow breakdown using the drag polar. A better way of examining wing performance is available by plotting axial force as a function of normal force. In this plot the axial force should initially decrease. When the airfoil section starts to lose leading edge suction (in essence a failure to fully enforce the Kutta condition, leading to less circulation than theoretically required) the data should display a sharp "break." This can be used to identify the initial loss of airfoil performance. This illustrates the loss of aerodynamic efficiency due to flow separation.

The stability of the wing is determined by measuring the pitching moment characteristics and examining the slope of the pitching moment with respect to angle of attack and lift coefficient. At low angles of attack the curve should be linear, and the slope of the curve with respect to the lift coefficient can be used to determine the aerodynamic center of the wing. The behavior of the pitching moment curve at wing stall and the "break" of the lift curve with angle of attack play a major role in determining the aircraft flight characteristics at stall.

Stall characteristics are important. The pilot should have a warning that the stall is about to occur. At stall, the loss of lift should be gradual and the airplane should remain controllable. Stall is caused by flow separation on the wing. The characteristics of the stall will be associated with the initial flow separation location and the manner in which the separation develops as the angle of attack is increased. Mild wing stall is associated with a separation that occurs at the upper surface trailing edge, which then moves forward with increasing angle of attack in a systematic, smooth fashion. In addition, this type of stall will lead to flow unsteadiness that the pilot will sense as a buffeting of the airplane prior to stall. This can frequently be observed as model vibration during wind tunnel tests. For the aircraft to remain controllable, the ailerons should remain effective at stall. This can be a problem, and is a key consideration in aerodynamic wing design.

Abrupt stall characteristics are the result of a sudden separation at the wing leading edge, leading to separation over the entire upper surface of the wing. This type of stall provides little warning to the pilot. The loss of lift is large due to the massive flow separation. Wing flow separation characteristics can be examined directly using surface flow visualization techniques, typically tufts, to observe the separation pattern, or inferred by examination of the force and moment characteristics. The airfoil section and wing planform, camber, and twist, determine the stall characteristics.

In addition to the lift characteristics, the character of the pitching moment must also be carefully examined at wing stall. It is quite likely that the pitching moment curve slope will change dramatically at stall. If the slope suddenly becomes unstable, the pitching moment behavior is termed an "unstable break," and the airplane will tend to pitch nose up at stall. At best this is undesirable, and if insufficient control authority is available to bring the nose down the airplane will suffer a departure from controlled flight, possibly leading to a spin. If the pitching moment curve has a "stable break" the wing design is likely to be acceptable from a stability and control standpoint. For complete aircraft many factors other than the isolated wing characteristics influence the pitching moment behavior near stall.

Lift, drag, and pitching moment examples illustrating these characteristics are provided in Figure 1. Additional information on wing aerodynamics is contained in your aerodynamics text, Bertin (Ref. 1). The book by Abbott and von Doenhoff (Ref. 2) not only contains a wealth of information on airfoils, but also information on wing characteristics.

Figure 1a. Lift Coefficient

Figure 1b. Pitching moment

Figure 1c. Drag polar

Figure 1. Typical wind tunnel force and moment results plots

Key issues in testing a wing in a wind tunnel to predict full scale flight performance are the problem of maintaining Reynolds number similarity, accounting for possible flow nonuniformities in the wind tunnel, and making corrections to the wind tunnel data to account for the effects of the wind tunnel walls and the effect of the model support system on the measurements. In most cases the full scale flight conditions will result in turbulent flow. In wind tunnels the low Reynolds number may result in a significant amount of laminar flow. To achieve a boundary layer similar to the one that exists at the flight Reynolds number, the boundary layer is frequently "tripped" to force transition to turbulent flow. A discussion of forcing boundary layer transition by "tripping" (known as "fixing," because the boundary layer transition location is known to be at a specified fixed location) is provided in Appendix 3.

The flow in the wind tunnel is not perfectly uniform. To account for flow angularity, the experimental data taken in the test must be corrected after the test (this is sometimes built into the data reduction systems for modern online real time data reduction systems). The correction depends on the wind tunnel user knowing the flow angularity. Other wind tunnel corrections are also discussed in Appendix 3, which is based on the book by Barlow, Rae and Pope, Ref. 3.

Cavitation: This occurs most frequently on propellers. However, it can also occur on rudders, struts and hydrofoils. Whenever the ambient pressure at a point in the liquid equals or falls below the vapor pressure, the liquid will begin to "boil" and cavitation bubbles will appear. The bubbles move to areas of higher pressure and collapse. If they collapse while in contract with a solid surface, the surface will be eroded. The accumulation of bubbles on the propeller surface will form a vapor cavity. The pressure in this cavity will be approximately uniform altering the pressure distrubution across the blade and the flow pattern. As this cavity grows nothing to covering a large fraction of the chord with increasing flow speed, it will initially increase lift (with a small drag penality) but it soon significantly reduces lift and increases drag. The result for a propeller is reduced thrust and effeciency. Similarly, lift is lost on a hydrofoil. The effects of cavitation on the propeller will also lead to erosion of the propeller surface. Furthermore, noise (a high pitched hiss) is generated by the collapse of cavitation bubbles.

A the load on a propeller is increased, a typical sequence in the development of cavitation on a propeller begins at a tip vortex and spreads down the leading edge on the back (or suction side) of the propeller to the root of the blade. It then progresses along the back surface to the trailing edge until the whole back surface is enveloped by a cavity. A cone vortex may also be formed at the end of the hub. At this point, the thrust is wholly generated by the positive pressure acting on the face of the propeller.

Operation under cavitating conditions should be avoided, and in the design of a propeller this has to be checked. Most of the information on the cavitation characteristics of propellers is obtained from model tests. They are typically conducted in cavitation tunnels where the ambient pressure can be reduced to properly scale the cavitation number.

Ventilation: Any surface-piercing foil system tends to suffer from air entrainment. This is generally known as ventilation and also called entry. Ventilation by a hydrofoil is usually an unmitigated nuisance. It arises from the fact that the hydrodynamic pressure over the top of the foil is considerably below atmospheric pressure, so that any air that is offered the chance of being sucked into this region will rush in immediately. The result is a sudden and severe loss of lift. In bad cases the effect is as if the foil had broken off. If the supply of air is limited, or if it rushes in for only a brief moment of time, a single transient bubble forms on the dorsal surface of the foil and is shed into the slipstream. The effect is as if the ship had run over a rut. A much more serious situation occurs when air can enter continuously. This has often posed a problem in the development of a foil mounted on a hollow strut, or a variable-incidence foil driven by a push-pull rod, because these arrangements tend to provide a path for the air. It is endemic in all surface-piercing foils by their very nature, because air can leak in down the surface of the foil itself. Low fences or screens running chordwise on struts and foils are used to stop this leakage.

1. Bertin, J.J., Aerodynamics for Engineers, Prentice-Hall, Englewood Cliffs, 2001.
2. Abbott, I.H., and von Doenhoff, A.E., Theory of Wing Sections, Dover, New York, 1959.
3. Barlow, Jewel B, Rae, William H., Jr., and Pope, Alan, Low-Speed Wind Tunnel Testing, Wiley & Sons, New York, 1999.
4. Hilbert Schenck, Jr., Ed., Introduction to Ocean Engineering, McGraw-Hill, 1975.
5. Riegels, F.W., Airfoil Sections, Butterworths, London, 1961 (English translation from German)
6. Warner, E.P., Airplane Design: Performance, McGraw-Hill, New York, 1936.
7. Hoerner, S.F., Fluid-Dynamic Drag, 1965, now published by the Author's estate, PO Box 65283, Vancouver, WA 98665, phone (206) 576-3997. This information is from page 6-6.
8. Pittman, J.L., Miller, D.S., and Mason, W.H., "Body and Canard Effects on an Attached-Flow Maneuver Wing at Mach 1.62," NASA TP 2249, February 1984.