A medium-sized jet has a 3.8-m-diameter fuselage and a loaded mass of 85,000 kg. The drag on an airplane is primarily due to the cylindrical fuselage, and aerodynamic shaping gives it a drag coefficient of 0.37. How much thrust must the jet’s engines provide to cruise at 230 m/s at an altitude where the air density is 1.0 kg/m3?

Fthrust = 110.99 kN

Explanation:

Model:

Ignore the drag on the wings and focus on the cylindrical fuselage.

Visualize:

The net force is zero as the jet cruises at 230 m/s, so the thrust must be equal in magnitude to the drag. The  gravitational and lift forces are equal in magnitude and opposite in direction.

Given

D = 3.80 m  ⇒ R = D / 2 = 3.80 m/ 2 = 1.90 m

C = 0.37

ρ = 1.0 kg/m³

v = 230 m/s

m = 85,000 kg

Fthrust = ?

We show the Free Body Diagram in the pic.

Then, we apply

∑Fx = 0  (→+)

Fthrust = Fdrag = (1/2)*C*ρ*A*v²

A = π*R² = π*(1.90 m)² = 11.34 m²

⇒  Fthrust = (1/2)*(0.37)*(1.0 kg/m³)*(11.34 m²)*(230 m/s)²

⇒  Fthrust = 110990.159 N = 110.99 kN

hi

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