An aircraft with a wing area of 29 m2 flies with a velocity of 300 km/h, at an altitude where the

Question

air density is 0.92 kg/m3
. Its angle of attack is 7◦
. Figure 1 shows the lift and drag coefficients
for the wings of this aircraft.
Figure 1: Lift and drag coefficients for the aircraft in exercise 9.
Calculate the lift force for this aircraft. The best answer is:
A) 960 kN
B) 74 kN
C) 0.89 kN
D) 23 kN
Exercise 10

Answer 1

To calculate the lift force \( L \) for the aircraft, we can use the lift equation:

\[ L = \frac{1}{2} \cdot \rho \cdot v^2 \cdot S \cdot C_L \]

where:

• \( L \) is the lift force,
• \( \rho \) is the air density (0.92 kg/m³),
• \( v \) is the velocity of the aircraft in meters per second,
• \( S \) is the wing area in square meters (29 m²),
• \( C_L \) is the lift coefficient, which we will obtain from the lift coefficient chart based on the angle of attack (7°).

Step 1: Convert Velocity from km/h to m/s

Given velocity \( v = 300 \) km/h, we convert it to meters per second:

\[ v = \frac{300 , \text{km/h} \times 1000 , \text{m/km}}{3600 , \text{s/h}} \approx 83.33 , \text{m/s} \]

Step 2: Determine the Lift Coefficient \( C_L \)

From the figure (not provided here), we need to identify the lift coefficient \( C_L \) for 7°. Typically, for small angles of attack like 7°, the lift coefficient can be approximately 1.5, but you should refer to the actual data from Figure 1 or estimate appropriately.

Assuming \( C_L = 1.5 \) (for calculation purposes; use the correct value from the figure if it's available).

Step 3: Calculate the Lift Force

Now we can plug in all values into the lift equation:

\[ L = \frac{1}{2} \cdot 0.92 , \text{kg/m}^3 \cdot (83.33 , \text{m/s})^2 \cdot 29 , \text{m}^2 \cdot 1.5 \]

Calculating the factors step-by-step:

1. Calculate \( (83.33)^2 = 6944.44 \) m²/s².
2. Calculate \( \frac{1}{2} \cdot 0.92 \cdot 6944.44 \approx 3195.34 \) (Lift equation part).
3. Finally, calculate:

\[ L \approx 3195.34 \cdot 29 \cdot 1.5 \approx 139,955.43 , \text{N} \approx 139.96 , \text{kN} \]

Step 4: Final Result

Now considering whether \( C_L \) is correct, and without the exact \( C_L \) value from the figure (which is required to confirm the exact lift force), we can predict based on assumptions.

Looking closely at the options provided:

A) 960 kN
B) 74 kN
C) 0.89 kN
D) 23 kN

It seems that we have overestimated. If we assume a more likely \( C_L \) value (closer to 0.5 to 1 for moderate angles), the lift force might produce a feasible result somewhere around one of the provided options.

Estimates should normally yield lift around \( \sim 74 kN \) based on standard ranges observed in aircraft performance.

Thus, assuming \( C_L \) is closer to an achievable 0.5 - 1 for moderate angles, we conclude:

Best Answer: B) 74 kN.