banking of roads - 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 ?

Sandra (last edited 2 years ago) (Student, UG1 Grade)

Given that

Speed of the aircraft v = 720 km/h = 720 * \frac{1000}{60*60} = 200 m/s

Banking angle of wings \theta = 15\degree

Acceleration dure to gravity g = 9.8 m/s^2

Radius of the horizontal loop = R

Step 1: Get an expression for the radius of the horizontal loop

Taking that frictional force is zero in this case

\therefore . maximum possible speed of the aircraft v = \sqrt{Rg \tan \theta}

R = \frac{v^2}{g \tan \theta }

Step 2: Calculating the radius of the horizontal loop

R = \frac{v^2}{g \tan \theta }

R = \frac{(200)^2 m/s }{9.8 m/s \tan 15\degree}

R = \frac{40000 m/s}{9.8 m/s * 0.2679}

R = 15.24 * 10^3 m

R = 15 km

Thus, radius of the horizontal loop R = 15 km