Aspect Ratio (wing) - Aspect Ratio of Aircraft Wings

Aspect Ratio of Aircraft Wings

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. 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

where

	is the aircraft drag coefficient
	is the aircraft zero-lift drag coefficient,
	is the aircraft lift coefficient,
	is the circumference-to-diameter ratio of a circle,
	is the Oswald efficiency number
	is the aspect ratio.

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

• Structural: A long wing has higher bending stress for a given load than a short one and therefore requires higher structural-design (architectural and/or material) specifications. 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, the section drag coefficient of a NACA 23012 airfoil (at typical lift coefficients) is inversely proportional to chord length to the power 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.

• Airfield Size: Airfields, hangars and other ground equipment define a maximum wingspan, which cannot be exceeded, and to generate enough lift at the given wingspan, the aircraft designer has to lower the aspect-ratio and increase the total wing area.