Question

An aircraft in level flight completes a circular turn in 100 second.

1) What is the radius of circular turn?

2) What is angle of banking, if velocity of aircraft is 40m/s ?​

Answer 1

Given,

An aircraft in level flight completes a circular turn in 100 seconds.

To find,

the radius of circular turn.

angle of banking if the velocity of aircraft is 40ms.

angular velocity, ω = 2π/T =2π/100 = 0.02π rad/s.

radius of the circular turn, r = v/ω

= (40 m/s)/(0.02π)

= 2000/π

= 636.94 ≈ 637 m

angle of banking, θ = tan¯¹(v²/rg)

= tan¯¹(40²/637 × 9.8)

= tan¯¹(1600/6242.6)

= 14.3756 °

Therefore radius of circular turn is 637 m and angle of banking is 14.3756°

Answer 2

r = 637 m

θ = 14.38°

Explanation:

Given:

t = 100s

velocity = 40 m/s

Find:

Radius of circular turn

Angle of banking

Solution:

Angular velocity ω = 2π/t = 2π/100 = 0.02π rad/s.

Radius of the circular turn r = v/ω

 = 40 / 0.02π

 = 637 m

Angle of banking θ = tan¯¹(v²/rg)

 = tan¯¹(40² / 637*9.8)

 = 14.38°