The Cessna Cardinal, a single-engine light airplane, has a wing with an area of 16.2 m2 and an aspect ratio of 7.31. Assume that the span efficiency factor is 0.62.
(a) If the airplane is flying at standard sea-level conditions with a velocity of 251 km/h, what is the induced drag when the total weight is 9800 N?
(b) What is the induced drag when the airplane is flying at 85.5 km/h (this is the stall speed at sea level when the aircraft is in landing configuration, with flaps down).
(a) Induced drag = \(C_{D_i} = \frac{C_L^2}{\pi e AR}\)
\[ L = \frac{1}{2} \rho v^2 S C_L \]
\[L = W = 9800 \, \text{N},\]
\[V = \frac{251000}{3600} = 69.7 \, \text{m/s},\]
\[S = 16.2 \, \text{m}^2,\]
\[e = 0.62,\]
\[AR = 7.31\]
\[\Rightarrow C_L = \frac{9800}{\frac{1}{2} (1.225) (69.7 \times 69.7) (16.2)} = 0.203\]
\[\Rightarrow C_{D_i} = \frac{(0.203)^2}{(3.14)(0.62)(7.31)} = 0.002894\]
\[q_\infty = \frac{1}{2} (1.225) (69.7)^2 = 2975.58\, \text{N/m}^2\]
\[\Rightarrow D_i = q_\infty S C_{D_i} = (2975.58)(16.2)(0.215) = 10363.95\, \text{N}\]
(b)
\[V_\infty = 85.5 \, \text{km/h} = 23.75 \, \text{m/s}\]
\[q_\infty = \frac{1}{2} (1.225) (23.75)^2 = 345 \, \text{N/m}^2\]
\[\Rightarrow C_L = \frac{L}{q_\infty S} = \frac{9800}{345 \times 16.2} = 1.75\]
\[\Rightarrow C_{D_i} = \frac{C_L^2}{\pi e AR} = \frac{(1.75)^2}{(3.14)(0.62)(7.31)} = 0.215\]
\[\Rightarrow D_i = q_\infty S C_{D_i} = (345)(16.2)(0.215) = 1202 \, \text{N}\]
