Question 10.3: A small aircraft has a wing area of 30 m², a lift coefficien......
A small aircraft has a wing area of 30 m², a lift coefficient of 0.45 at takeoff settings, and a total mass of 2800 kg. Determine (a) the takeoff speed of this aircraft at sea level at standard atmospheric conditions, (b) the wing loading, and (c) the required power to maintain a constant cruising speed of 300 km/h for a cruising drag coefficient of 0.035.
Wing area = 30 \mathrm{m^{2};\;C_{L}=0.45;\;\rho_{a i r}=1.23~\mathrm{kg/m^{3};\;C_{D}=0.035}}
Total weight, W = 2800 x 9.8 = 27440 N
(a) Lift force, F_L = Total weight, W
C_L × 0.5 × ρ × U² × area = 27440
0.45 × 0.5 × 1.23 × U² × 30 = 27440
U = 57.5 m/s
Therefore, takeoff speed = 57.5\times{\frac{18}{5}}=207 km/h
(b) Wing loading, w={\frac{\text{Total weight}}{\text{Wing area}}} \\ =\;\frac{W}{30}=\frac{27440}{30}=915\,\mathrm{Nm}^{-2}
(c) Cruising speed, U = 300 km/h = 300\times{\frac{5}{18}}=83.33 m/s
Drag force, F_{D}=C_{D}\times0.5\times\rho\times U^{2}\times\text{area}
= 0.035 × 0.5 × 1.23 × 83.33² × 30
= 4484.1 N
Power required = F_D × U = 4484.1 × 83.33 = 373660 watts = 373.66 kW
= 501 HP (1 horse power = 746 watts)