Question

Consider a finite wing of aspect ratio 10 with span effectiveness factor 0.95. Its airfoil section has a lift slope of 0.106 per degree and a zero-lift angle of attack of -1.5\(^{\circ}\). The lift coefficient of the wing at an angle of attack of 3.5\(^{\circ}\) is ________ (rounded off to 2 decimal places).

Hint:

Use the finite-wing lift-slope correction a = a0/(1 + a0/(pi e AR)), convert a0 to per radian, then multiply by (alpha - alpha_L0).

Answer 1

Correct Answer: 0.44

Step 1: Keep everything in radians from the start.
Rather than switching between degrees and radians midway, convert the angle of attack range to radians up front and carry the calculation through in radians.

Step 2: Convert the section lift slope and the angle of attack change to radians.
$a_0 = 0.106 \times (180/\pi) = 6.073$ per radian (same as before).
$\Delta\alpha = \alpha - \alpha_{L0} = 3.5^{\circ}-(-1.5^{\circ}) = 5^{\circ} = 5 \times \dfrac{\pi}{180} = 0.0873$ rad.

Step 3: Apply the finite-wing correction.
$\pi e AR = \pi \times 0.95 \times 10 = 29.845$.
$a = \dfrac{a_0}{1+a_0/(\pi e AR)} = \dfrac{6.073}{1+6.073/29.845} = \dfrac{6.073}{1.2035} = 5.046$ per radian.

Step 4: Multiply the finite-wing slope by the angle change, both in radians.
$c_l = a \times \Delta\alpha = 5.046 \times 0.0873 = 0.4405$.

Final Answer:
Rounded to 2 decimal places, $c_l \approx 0.44$, matching the degree-based calculation.
\[ \boxed{c_l \approx 0.44} \]