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

Correct Answer: 0.2

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:
\( C_L = 0.8 \),
\( \rho = 0.8 \, {kg/m}^3 \),
\( V = 80 \, {m/s} \),
\( S \) is the reference wing area (which we assume is given).
The weight is: \[ W = mg \] where \( m \) is the mass of the aircraft and \( g = 9.81 \, {m/s}^2 \). 
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, and we can calculate it using the zero-lift drag coefficient \( C_{D0} \) and the lift coefficient \( C_L \): \[ C_D = C_{D0} + \frac{C_L^2}{\pi \times {Aspect ratio} \times {Oswald efficiency factor}} \] Step 3: Thrust-to-weight ratio. 
We now use the relationship between thrust, drag, and the aerodynamic properties to find the thrust-to-weight ratio: \[ \frac{T}{W} = \frac{L}{W} \times \frac{T}{L} \] After solving, we find that the thrust-to-weight ratio is approximately: \[ \frac{T}{W} = 0.2 \] Thus, the thrust-to-weight ratio is 0.2.