The aerodynamic performance of wings is sometimes presented as CL vs. CD with the angle of attack a being the free parameter that varies along the curve. The relationship between CL and CD is known as a drag polar and such plots are called polar plots. Replot the aerodynamic results in Figure 14.26

Question

The aerodynamic performance of wings is sometimes presented as $C_L$ vs. $C_D$ with the angle of attack a being the free parameter that varies along the curve. The relationship between $C_L$ and $C_D$ is known as a drag polar and such plots are called polar plots. Replot the aerodynamic results in Figure 14.26 to create a polar plot, and compare with the drag polar for an elliptical lift distribution, (14.26), evaluated with an aspect ratio of Λ = 6.5.

$C_{D_{ i }}=\frac{D_i}{(1 / 2) \rho U^2 A}=\frac{C_L^2}{\pi\left(s^2 / A\right)}=\frac{C_L^2}{\pi \Lambda}$ , (14.26)

[latex]C_{D_{ i }}=\frac{D_i}{(1 / 2) \rho U^2 A}=\frac{C_L^2}{\pi\left(s^2 / A\right)}=\frac{C_L^2}{\pi \Lambda}[/latex], (14.26)

Accepted Answer

Using an angle of attack increment of 2°, the curves provided in Figure 14.26 are approximately described by:

α (°)	[latex]C_D[/latex]	[latex]C_L[/latex]
-8.0	0.060	-0.22
-6.0	0.027	-0.07
-4.0	0.015	0.07
-2.0	0.014	0.22
0.0	0.017	0.36
2.0	0.022	0.50
4.0	0.030	0.64
6.0	0.040	0.78
8.0	0.052	0.92
10.0	0.066	1.04
12.0	0.083	1.14
14.0	0.103	1.20
16.0	0.133	1.21
18.0	0.175	1.07

The polar plot for this data is shown in Figure 14.28, along with the curve predicted by (14.26) for an aspect ratio of 6.5. The horizontal shift between the plotted drag polar and the predicted curve is the profile drag coefficient, [latex]C_{D,o}[/latex], of the wing. Here, [latex]C_{D,o}\approx0.01[/latex] and it is less than half of the total drag coefficient, [latex]C_D[/latex], when [latex]C_L> 0.5[/latex].

Question 14.7: The aerodynamic performance of wings is sometimes presented ...

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