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To clarify the question, I mean the type of wing used on a Concorde or a fighter jet, vs a glider's long and thin ones. What is the aerodynamic reason for using a short wing when the plane is faster?

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Another reason to have shorter wings on high-speed or maneuverable aircraft deals with the aircraft's aspect ratio, which is the ratio between its length to is breadth/chord. Longer wings (high aspect) bend more under load, and may twist, which causes structural issues. Additionally, aircraft with shorter wings (low aspect) can roll much quicker. This means that a fighter jet with short wings may roll at rates up to 720 degrees/second while a large airliner or cargo plane may roll at 15-60 degrees per second.

A third reason is parasitic drag. From the linked wikipedia article above:

While high aspect wings create less induced drag, they have greater parasitic drag, (drag due to shape, frontal area, and surface friction). This is because, for an equal wing area, the average chord (length in the direction of wind travel over the wing) is smaller. Due to the effects of Reynolds number, the value of the section drag coefficient is an inverse logarithmic function of the characteristic length of the surface, which means that, even if two wings of the same area are flying at equal speeds and equal angles of attack, the section drag coefficient is slightly higher on the wing with the smaller chord. However, this variation is very small when compared to the variation in induced drag with changing wingspan. For example, the section drag coefficient $c_d$; of a NACA 23012 airfoil (at typical lift coefficients) is inversely proportional to chord length to the power 0.129: $$ c_d \varpropto \frac{1}{(\text{chord})^{0.129}}.$$

Since parasite drag increases with airspeed, and high aspect wings have higher parasite drag, it makes sense for high-speed aircraft to have the wing that creates less drag at high speeds, and the slower aircraft to have the wing that creates less induced drag. You can see this in a simple graphic of the drag curves:

enter image description here

(Since the induced drag is lower at high speeds anyway, there is little point in minimizing that, rather minimize the type of drag that is a much larger factor at high speeds)

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You may want to take a look at this and this but generally it has to do with the fact that many things change at super sonic speeds mainly

The primary advantage of the delta wing is that, with a large enough angle of rearward sweep, the wing’s leading edge will not contact the shock wave boundary formed at the nose of the fuselage as the speed of the aircraft approaches and exceeds transonic to supersonic speed.

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  • $\begingroup$ Thanks! Though I'm not so sure what a "rearward sweep" refers to. $\endgroup$ – Ewen W. Apr 7 '15 at 1:20
  • $\begingroup$ @EwenW. - simply, where the wings sweep to the rear (the wingtips are aft of the wing root) $\endgroup$ – SSumner Apr 7 '15 at 1:22
  • $\begingroup$ The opposite of en.wikipedia.org/wiki/Forward-swept_wing $\endgroup$ – Dave Apr 7 '15 at 1:27
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At low airspeed, the aerodynamics of long thin wings are great. The longer and thinner, the lower the induced drag (the drag inherent in creating lift, very dominant at low speeds). However, aero requirements always seem to be contrary to structures requirements. Savings in aerodynamics are often offset by increased weight of structures, and a balance needs to be struck for the best fuel economy.

enter image description here

The wing shape is very dependent on the maximum design speed of the craft, roughly as follows:

  • Subsonic < Mach 0.6: long, thin and straight please. Induced drag is the dominant design factor.

  • High subsonic < M0.85: friction drag becomes more dominant, induced drag is less due to higher speed, and compressibility effects start introducing quite a bit of extra drag. Wing sweep is introduced. A long, thin, swept wing creates a high amount of torsion, heavier structure etc, so unfortunately we need to keep the wings a bit shorter and stubbier. New materials and wing profiles enable longer and thinner wings again with less of a weight penalty.

  • Transsonic between M 0.85 and M1.2: Compressibility is such a dominant factor that the area rule is much more important in reducing drag than the wing shape. Whichever wing shape fits the area rule is best. But fuel economy in this speed region is always questionable, either slow down like all pax planes or speed up like Concorde.

  • Supersonic > M 1.2. Compressibility drag is all dominant, and now we want to mainly limit this form of drag. Induced drag is of no concern anymore. A very good way of limiting shock wave drag is to make sure that all of the wing stays within the shock cone streaming from the nose tip: within this cone, airspeed is lower than outside the cone. Even for military planes where fuel economy is not the dominant design factor, the performance penalty of having the wing stick out of the shock cone is considerable.

enter image description here

Source

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Short wing means less structural weight. But an airplane needs an optimum wing surface area (optimum for its weight, in other words the wing it needs to generate enough lift for the size of the airplane). So for the same lift, a shorter wing would be lighter, but study have shown that lift is not generated on the full span of the wing, so a short wing would not be efficient. A longer wing is much more efficient (generate more lift for its surface) but at the expense of weight (you need a beefier structure to maintain the integrity of the wing, so there is a sweet spot in between)

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