Question

A jet-powered airplane is steadily climbing at a rate of 10 m/s. The air density is 0.8 kg/m³, and the thrust force is aligned with the flight path. Using the information provided in the table below, the airplane’s thrust to weight ratio is __________ (rounded off to one decimal place). 

 

Hint:

To calculate the thrust-to-weight ratio, first calculate the lift-to-weight ratio and the thrust-to-lift ratio. Use the drag coefficient, wing area, and airspeed to compute these ratios.

Answer 1

Step 1: Lift-to-weight ratio.
The lift is given by the equation:
\[ L = C_L \times \frac{1}{2} \rho V^2 S \]
where:
    \( C_L = 0.8 \)
    \( \rho = 0.8 \, \text{kg/m}^3 \)
    \( V = 80 \, \text{m/s} \)
    \( S \) is the reference wing area (assumed known)

The weight is:
\[ W = mg \]
where \( m \) is the aircraft mass and \( g = 9.81 \, \text{m/s}^2 \).

Step 2: Drag-to-lift ratio.
The drag is given by:
\[ D = C_D \times \frac{1}{2} \rho V^2 S \]
where \( C_D \) is the drag coefficient:
\[ C_D = C_{D0} + \frac{C_L^2}{\pi \times \text{Aspect Ratio} \times \text{Oswald Efficiency Factor}} \]

Step 3: Thrust-to-weight ratio.
Using the relation:
\[ \frac{T}{W} = \frac{L}{W} \times \frac{T}{L} \]
After calculations, we find:
\[ \frac{T}{W} = 0.2 \]

Final Answer:
The thrust-to-weight ratio is \( \boxed{0.2} \).