The theoretical lift-curve slope for a 2D, thin airfoil in inviscid flow is given by the equation:
\[ \frac{dC_L}{d\alpha} = 2\pi \]
This value is expressed in terms of per radian. To convert it into per degree, you can use the conversion factor \( \frac{180}{\pi} \):
\[ \frac{dC_L}{d\alpha} = 2\pi \cdot \frac{180}{\pi} = 360 \quad \text{(per degree)} \]
Now, for an elliptic wing, the lift-curve slope can be calculated using the aspect ratio \( A \). The lift-curve slope for a finite wing can be approximated by:
\[ \frac{dC_L}{d\alpha} = \frac{2\pi}{1 + \frac{A}{2}} \]
Given that \( A = 12 \):
\[ \frac{dC_L}{d\alpha} = \frac{2\pi}{1 + \frac{12}{2}} = \frac{2\pi}{1 + 6} = \frac{2\pi}{7} \]
To express this value in per degree:
\[ \frac{dC_L}{d\alpha} \text{ (per degree)} = \frac{2\pi}{7} \cdot \frac{180}{\pi} = \frac{360}{7} \approx 51.43 \quad \text{(per degree)} \]
Thus, the lift-curve slope for the elliptical wing with an aspect ratio \( A = 12 \) is approximately 51.43 per degree.
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