Low Aspect-Ratio Wings
Summary
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
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.
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.
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.
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.
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).
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.
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.
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.
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.
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).
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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Wing Performance at Low Speeds
Experimental Data
Maximum Lift Coefficients
Pressure Characteristics
Stability Characteristics
Inflection Lift
Means for Improving Performances
Performances at Supersonic Speeds
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
Related material
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Selected References