Copyright © A. Filippone (1999-2003). All Rights Reserved.

Wings for All Speeds

Low Aspect-Ratio Wings


Wings of low aspect-ratio are known for having poor aerodynamic efficiency L/D at low speeds, along with stability problems, both static and dynamic.

The high angle of attack stall of the low aspect-ratio wings has been known since the early days of aerodynamics. Why short wings, then ? – There can only be practical limitations to use such wings.

The most interesting case is the wing-in-ground ship (AR = 1 ÷ 3); there are also short wings in racing cars (typical aspect ratios AR < 3); short wings are also part of control devices in competition sailing boats and micro air vehicles. Low aspect ratios (about 2 ÷ 3) in fighter aircraft are necessary to maintain a high degree of manouvrability, though at the expense of some stability (see below).

We define a low aspect-ratio wing a wing having AR < 5. Squared wings and wings with even lower aspect ratios are still interesting from a theoretical point of view, but of uncertain application.

Theoretical analysis was performed by Betz in the 1920s. Later a number of non-linear lifting line theories (Multhopp, Gersten, Truckenbrodt, and others) provided simple means to predict the vortex lift created by the leading edge separation.

Fig. 1 below shows a qualitative example of how strong an influence the leading edge vortex can have on the lifting characteristics of a short wing.

Figure 1: Lift characteristics at very low aspect-ratios

Wing Performance at Low Speeds

Short wings for low speeds have been studied for a long time. The high angle of attack stall of the low aspect-ratio wings has been known since the early days of aerodynamics. Handley-Page (1911) found that a squared wing (AR=1) stalled at angles above 40 degrees, while a moderately slender wing (AR=6.25) stalled at incidences as low as 10 degrees.

Experimental Data

A large body of data was published in the 1920s as a result of a series of experiments at Gottingen, Germany. Data for different aspect-ratios can be correlated quite well using the Prandtl-Lanchester formula, originally derived for elliptic spanwise loading. Having reference data at aspect-ratio AR=5, one can derive the polar characteristics of shorter wings with remarkable precision, at least in the linear range.

Maximum Lift Coefficients

The values of the maximum lift coefficient are largely independent from the aspect-ratios at aspect-ratios above 2 and a Reynolds number 1 million. At aspect-ratios 1 < AR < 2 the most evident effect is the shift of the angle of attack at which maximum lift is reached. This angle increases progressively and easily reaches 30 degrees. Squared wings show Clmax as high as 1.3.

At even lower aspect ratios the wing is subject to strong vortex flows and CL increases at a faster rate than that predicted with a linear theory. This is due to the presence of the strong tip vortices that separate closer to the leading edge, according to a mechanism similar to that governing the delta wing.

The spanwise distribution of lift is another interesting aspect of these wings. The lift is mostly concentrated in the inboard sections and reaches high values. Aft sweep moves the point of maximum lift outboard, which on turns may promote undesirable tip stall.

Pressure Characteristics

Experimental investigations showed that the root sections do not experience high LE pressure peaks. In addition, the spanwise pressure gradients are such as to cause an outward drain of the boundary layer from the root sections. The combined influence of these two effects is such as to make the root sections highly resistant to flow separation and therefore capable of developing local lift coefficients of such large magnitude as to more than compensate for the lift losses that occur when the tip sections of the wing stall.

Stability Characteristics

Longitudinal and lateral stability of low aspect-ratio wings have been investigated over the years. One important aspect is the behavior of the pitching moment with the lift coefficient, that is strongly dependent on the wing sweep and various technical devices (tip devices, fences, nacelles, etc.).

Longitudinal stability depends mostly on the aspect-ratio and the sweep angle (Shortal-Maggin, 1951). The stability limit is approximated in the figure below for untapered wings (tapered wings have less conservative limits).

Longitudinal Stability

Figure 2: Longitudinal stability limits (empirical data).

Leading-edge separation due to induced camber in the three-dimensional wing may cause a bubble of large spanwise extent, so that airfoils that ordinarily stall from the trailing-edge actually stall from the leading-edge. This phenomenon is dependent (at least) on the sweep, on the leading edge radius and the twist.

Inflection Lift

In the study of wing stability it is useful to define the terms inflection lift and usable lift. The inflection lift is the point at which there is a change in the pitching moment without consequences to the stability. Usable lift is the point at which the pitching moment breaks away and leads to a shift of the aerodynamic center with major consequences for the longitudinal stability.

Figs. 3 and 4 below show examples of pitching moment behavior at constant aspect-ratios and at constant sweep, respectively. The data are qualitative, but they are compiled from experimental works reported in Ref. 1.

Figure 3: Pitching moment at constant sweep angle (45 deg)

Figure 4: Pitching moment at aspect-ratio (AR=4.)

The ratio between inflection lift and maximum lift is of the order 0.5-1.0, with the lowest values approached by low aspect-ratio wings, and the largest values proper of slender wings.

Means for Improving Performances

Tip stall is one of the problems encountered by short wings (Fig. 2), especially at take-off and landing. One very effective way to delay or even remove the stall is the use of fences (or vanes), which are vertical surfaces aligned with the flight direction.

The fences provide a physical bound to the spanwise pressure gradients and constrain the boundary layer drain toward the tip, which is the prime cause of the tip stall.

Effect of Fences

Figure 5: Effect of fences on CL of swept back wing.

Other methods include: nacelles, stores, extensible leading- edge flaps, droop nose, boundary layer control, chord extension, variable sweep, camber, and twist. Vertical/ horizonal tail and wing-body combinations make up for additional effects.

Performances at Supersonic Speeds

Wing sweep and aspect ratio at supersonic speeds have a rather precise correlation, showing the stability limits of the wing. In this correlation the aspect-ratio decreases as the sweep increases.

For sweeps of 40 to 60 degrees the aspect-ratios range is 2 to 4, although this limit can be occasionally exceeded by accurate design of the tails and other control surfaces. Since high sweep is required to fly with agility at supersonic speeds, the aspect-ratio is set as a consequence.

The Table below shows a summary of fighter aircraft wing aspect-ratio and maximum speeds (data compiled from Jane’s Information System).

Table 1: Aspect-Ratios of Fighter Wings
Aircraft AR M
US F-15 (McDonnell-Douglas) 3.0 2.5
US F-18 (McDonnel-Douglas) 3.5 1.8
Dassault Mirage 2000 2.0 2.2
Dassault Rafale MO2 2.6 2.0
Sukhoi Su-27 3.5 2.3
Mapo Mig-29 3.4 2.3

The wings of the aircraft on Table 1 are all swept back. Development of swept forward wings is still at the research stage, except for one prototype fighter (X-29).

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Selected References

  • Fink MP, Lastinger JL, Aerodynamic Characteristics of Low-Aspect Ratio Wings in Close Proximity to the Ground, NACA TN D-926, 1961.

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

  • Jane’s: All the World’s Aircraft, 1999-2002, edited by P. Jackson, 1999 (published fully update every year !)
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Copyright © A. Filippone (1999-2003). All Rights Reserved.