A finite wing with an elliptical lift distribution has an aspect ratio of 6. The airfoil of the wing has a lift slope of 0.15 per degree. Find and compare the lift slopes for a straight wing and a swept wing with a half-chord line sweep of 30^{\circ}.

A finite wing with an elliptical lift distribution has an aspect ratio of 6. The airfoil of the wing has a lift slope of 0.15 per degree. Find and compare the lift slopes for a straight wing and a swept wing with a half-chord line sweep of 30^{\circ}.

Worldtech Asked on 12th August 2021 in Aeronautics.
Add Comment
  • 1 Answer(s)

    High aspect ratio straight wingHigh aspect ratio straight wing

    Using Helmbold’s equation, for calculating the lift slope for straight wing, a = \frac{a_{0}}{\sqrt{1+\left ( \frac{a_{0}}{\pi AR} \right )^{2}}+\left ( \frac{a_{0}}{\pi AR} \right )} Lift slope for the airfoil = a_{0} = 0.15\,/degree = 8.5944\,/radian.

    Therefore,

    a = \frac{8.5944}{\sqrt{1+\left ( \frac{8.5944}{\pi \left ( 6 \right )} \right )^{2}}+\left ( \frac{8.5944}{\pi \left ( 6 \right )} \right )}=1.4569\,per\,radian

    Swept wingSwept wing

    Using Helmbold’s equation, for calculating the lift slope for a swept wing ,a = \frac{a_{0}cos\Lambda }{\sqrt{1+\left ( \frac{a_{0}cos\Lambda}{\pi AR} \right )^{2}}+\left ( \frac{a_{0}cos\Lambda}{\pi AR} \right )}Here, \Lambda = 30^{0}, is the sweep angle of the wing referenced to the half-chord line.  Therefore,  a = \frac{8.5944cos30^{0}}{\sqrt{1+\left ( \frac{8.5944cos30^{0}}{\pi \left ( 6 \right )} \right )^{2}}+\left ( \frac{8.5944cos30^{0}}{\pi \left ( 6 \right )} \right )}=1.4436\,per\,radianOn comparing the lift slopes of straight wing and swept wing, we can see that there is a reduction in  lift slope for the swept wing.

    Wing sweep is decreasing the lift slope, and it affects lift slope to a larger degree for a high aspect ratio wings than for a lower aspect ratio wings.

    techAir Answered on 27th August 2021.
    Add Comment
  • Your Answer

    By posting your answer, you agree to the privacy policy and terms of service.