# 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 $$30^{\circ}$$.

Asked on 12th August 2021 in

High 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 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.