An aircraft executes a horizontal loop at a speed of 720 km/h with its wings banked at $15^{\circ}$ . What is the radius of the loop?

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Solution

Speed of the aircraft, $v = 720 k m / h = 720 \times \frac{5}{18} = 200 m / s$
Acceleration due to gravity, $g = 10 m / s^{2}$
Angle of banking, $θ = 15^{\circ}$
For radius r, of the loop, we have the relation:
$t a n θ = \frac{v^{2}}{r g} r = \frac{v^{2}}{g t a n θ} = \frac{200 \times 200}{10 \times t a n 15} = \frac{400}{0.268} = 14925.37 m = 14.92 k m$

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An aircraft executes a horizontal loop at a speed of 720 km/h with its wings banked at 15∘. What is the radius of the loop?

Speed of the aircraft, v=720km/h=720×518=200 m/s Acceleration due to gravity, g=10m/s2 Angle of banking, θ=15∘ For radius r, of the loop, we have the relation: tan θ=v2rgr=v2g tanθ=200×20010×tan15=4000.268=14925.37 m=14.92 km

An aircraft executes a horizontal loop at a speed of 720 km/h with its wings banked at $15^{\circ}$ . What is the radius of the loop?