A twin-engined propeller aircraft is equipped with two engines, each rated at 98 kW shaft power. During cruise flight at 72 m/s at an altitude of 3400 metres, the aircraft experiences a lift coefficient of 0.555. Its wing surface area is 28 square metres, with an average chord length of 2 metres. Its zero-lift drag coefficient is 0.01 and its span efficiency (or Oswald) factor is 0.7.

Answer 1

To determine the total engine power required by the aircraft during cruise flight, we need to consider the four main forces acting on the aircraft: lift, drag, weight, and thrust.

1. Lift force (L) can be calculated using the lift coefficient (CL), air density (ρ), velocity (V), and wing surface area (S):
L = 0.5 * CL * ρ * V^2 * S

2. To find the air density (ρ) at an altitude of 3400 meters, we can use the International Standard Atmosphere (ISA) model. At this altitude, the air density can be approximated as:
ρ = ρ0 * e^(-h/H)
where ρ0 is the air density at sea level (1.225 kg/m³), h is the altitude (3400 m), and H is the scale height (7000 m):
ρ = 1.225 * e^(-3400/7000)

3. Drag force (D) can be calculated considering two components: induced drag (Di) and parasite drag (Dp). The sum of these two components is the total drag (D).
D = Di + Dp

a. Induced drag (Di) is related to lift force (L) and the span efficiency factor (e):
Di = L^2 / (0.5 * ρ * V^2 * S * π * AR * e)
where AR is the aspect ratio of the wing. Since the aspect ratio is not given, let's assume it to be 8 (a common value for general aviation aircraft).

b. Parasite drag (Dp) is related to the zero-lift drag coefficient (CD0):
Dp = 0.5 * CD0 * ρ * V^2 * S

4. Weight force (W) can be calculated using the mass (m) and acceleration due to gravity (g):
W = m * g

5. Finally, the total power required (P) can be determined by multiplying the total drag force (D) with the velocity (V):
P = D * V

Let's calculate each of these quantities step by step:

1. Lift Force:
L = 0.5 * CL * ρ * V^2 * S
= 0.5 * 0.555 * (1.225 * e^(-3400/7000)) * (72)^2 * 28
≈ 38573 N

2. Air Density:
ρ = ρ0 * e^(-h/H)
= 1.225 * e^(-3400/7000)
≈ 0.785 kg/m³

3a. Induced Drag:
AR = 8
e = 0.7
Di = L^2 / (0.5 * ρ * V^2 * S * π * AR * e)
= (38573)^2 / (0.5 * (0.785) * (72)^2 * 28 * π * 8 * 0.7)
≈ 1147 N

3b. Parasite Drag:
CD0 = 0.01
Dp = 0.5 * CD0 * ρ * V^2 * S
= 0.5 * 0.01 * (0.785) * (72)^2 * 28
≈ 792 N

Total Drag:
D = Di + Dp
= 1147 + 792
≈ 1939 N

4. Weight:
Assuming the mass (m) of the aircraft is not given, we cannot directly calculate the weight force. However, we can find the power required to overcome the weight force by using the following formula:
P_w = m * g * V
The power required to overcome the weight force should be equal to the total power required (P) calculated in step 5.

5. Total Power Required:
P = D * V
= 1939 * 72
≈ 139,608 N·m/s (or Watts)

Please note that the mass (m) of the aircraft is not given in the provided information, so the specific weight forces or power required to overcome the weight force cannot be determined without this information.