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In aerodynamics, the aspect ratio of a wing is the length of the wing compared with the breadth (chord) of the wing. A high aspect ratio indicates long, narrow wings, whereas a low aspect ratio indicates short, stubby wings. [1]

For most wings, the length of the chord varies along the wing so the aspect ratio AR is defined as the square of the wingspan divided by the area of the wing planform.[2][3]

AR = {b^2 \over S}

where

b is the wingspan, and
S is the area of the wing planform.

Contents

Aspect ratio of airplane wings

Low aspect ratio wing (AR=5.6) of a Piper PA-28 Cherokee
High aspect ratio wing (AR=12.8) of the Bombardier Dash 8 Q400
Very low aspect ratio wing (AR=1.8) of the Concorde
Very high aspect ratio wing of the Glaser-Dirks DG-808 glider(AR=27.4)

Aspect ratio and planform can be used to predict the aerodynamic performance of a wing.

For a given wing area, the aspect ratio is proportional to the square of the wingspan, and the wingspan is of particular significance in determining the performance. An airplane in flight can be imagined to affect a circular cylinder of air. The diameter of that cylinder is equal to the wingspan. [4] A large wingspan is working on a large cylinder of air, and a small wingspan is working on a small cylinder of air. For two aircraft of the same weight but different wingspans the small cylinder of air must be pushed downward by a greater amount than the large cylinder in order to produce an equal upward force. The aft-leaning component of this change in velocity is proportional to the induced drag. Therefore the larger downward velocity produces a larger aft-leaning component and this leads to larger induced drag on the aircraft with the smaller wingspan and lower aspect ratio.

The interaction between undisturbed air outside the circular cylinder of air, and the downward-moving cylinder of air occurs at the wingtips, and can be seen as wingtip vortices.

This property of aspect ratio AR is illustrated in the formula used to calculate the drag coefficient of an aircraft C_d\;[5][6][7]

C_d =C_{d0} + \frac{(C_L)^2}{\pi e AR}

where

C_d\; is the aircraft drag coefficient
C_{d0}\;   is the aircraft zero-lift drag coefficient,
C_L\; is the aircraft lift coefficient,
\pi\; is the circumference-to-diameter ratio of a circle,
e\; is the Oswald efficiency number
AR is the aspect ratio.

There are several reasons why all aircraft do not have high aspect wings:

  • Structural: A long wing has higher bending stress for a given load than a short one, which requires stronger structure to withstand. Also, longer wings have greater deflection for a given load, and in some applications this deflection is undesirable (e.g. if the deflected wing interferes with aileron movement).
  • Maneuverability: a high aspect-ratio wing will have a lower roll rate than one of low aspect ratio, because in a high-aspect-ratio wing, an equal amount of wing movement due to aileron deflection (at the aileron) will result in less rolling action on the fuselage due to the greater length between the aileron and the fuselage. A higher aspect ratio wing will also have a higher moment of inertia to overcome. Due to the lower roll rates, high aspect ratio wings are usually not used on fighter aircraft.
  • Parasitic drag: 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,[8] 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}}.
    A 20 percent increase in chord length would decrease the section drag coefficient by 2.38 percent.
  • Practicality: low aspect ratios have a greater useful internal volume, since the maximum thickness is greater, which can be used to house the fuel tanks, retractable landing gear and other systems.


Variable aspect ratio

Extending the trailing-edge wing flaps causes a decrease in aspect ratio because extending the flaps increases the wing chord but with no change in wingspan. This decrease in aspect ratio causes an increase in induced drag which is detrimental to the airplaneā€™s performance during takeoff but may be beneficial during landing.

Aircraft which approach or exceed the speed of sound sometimes incorporate variable-sweep wings. This is due to the difference in fluid behavior in the subsonic and transonic/supersonic regimes. In subsonic flow, induced drag is a significant component of total drag, particularly at high angle of attack. However, as the flow becomes transonic and then supersonic, the shock wave first generated along the wing's upper surface causes wave drag on the aircraft, and this drag is proportional to the length of the wing - the longer the wing, the longer the shock wave. Thus a long wing, valuable at low speeds, becomes a detriment at transonic speeds. If the aircraft design can fulfil its mission profiles with the extra weight and complexity of a moveable wing, the swing-wing provides a solution to this problem.

Aspect ratio of bird wings

High aspect ratio wings abound in nature. Most birds that fly long distances have wings of high aspect ratio, and with tapered or elliptical wingtips. This is particularly noticeable on soaring birds such as albatrosses and eagles. By contrast, hawks of the genus Accipiter such as the Eurasian Sparrowhawk have wings of low aspect ratio (and long tails) for maneuverability.

See also

Notes

  1. ^ Kermode, A.C. (1972), Mechanics of Flight, Chapter 3, (p.103, eighth edition), Pitman Publishing Limited, London ISBN 0 273 31623 0
  2. ^ Anderson, John D. Jr, Introduction to Flight, Equation 5.26
  3. ^ Clancy, L.J., Aerodynamics, sub-section 5.13(f)
  4. ^ Clancy, L.J., Aerodynamics, section 5.15
  5. ^ Anderson, John D. Jr, Introduction to Flight, section 5.14
  6. ^ Clancy, L.J., Aerodynamics, sub-equation 5.8
  7. ^ Anderson, John D. Jr, Fundamentals of Aerodynamics, Equation 5.63 (4th edition)
  8. ^ Dommasch, D.O., Sherby, S.S., and Connolly, T.F. (1961), Airplane Aerodynamics, page 128, Pitman Publishing Corp. New York

References

  • Anderson, John D. Jr, Introduction to Flight, 5th edition, McGraw-Hill. New York, NY. ISBN 0-07-282569-3
  • Anderson, John D. Jr, Fundamentals of Aerodynamics, Section 5.3 (4th edition), McGraw-Hill. New York, NY. ISBN 0-07-295046-3
  • Clancy, L.J. (1975), Aerodynamics, Pitman Publishing Limited, London ISBN 0 273 01120 0
  • John P. Fielding. Introduction to Aircraft Design, Cambridge University Press, ISBN 978-0-521-65722-8
  • Daniel P. Raymer (1989). Aircraft Design: A Conceptual Approach, American Institute of Aeronautics and Astronautics, Inc., Washington, DC. ISBN 0-930403-51-7
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