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.
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    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,  \[a = \frac{8.5944cos30^{0}}{\sqrt{1+\left ( \frac{8.5944cos30^{0}}{\pi \left ( 6 \right )} \right )^{2}}+\left ( \frac{8.5944cos30^{0}}{\pi \left ( 6 \right )} \right )}=1.4436\,per\,radian\]On 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.
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