The diameters of the main rotor and tail rotor of a single-engine helicopter are 7.53 m and 1.06 m, respectively. The respective rotational speeds are 443 rev/min and 4,120 rev/min. Calculate the speeds of the tips of both rotors. Compare these speeds with the speed of sound, 343 m/s.

Main motor= 174.66 m/s

Tail motor=228.66 m/s

Explanation:

✓Main motor

Diameter of the main motor= 7.53 m

rotational speeds = 443 rev/min

The speed of the trip= rotational speed × radius

Radius of the main rotor= diameter/ 2

= 7.53 /2=3.765 m

The speed of the trip= (443 ×2π ×3.765)

= 10479.69 meter per minutes

We can convert to metre per seconds as

10479.69/ 60

= 174.66 m/s( less than speed of sound)

✓ Tail motor

Diameter of the main motor= 1.06 m

rotational speeds = 4120 rev/min

The speed of the trip= rotational speed × radius

Radius of the main rotor= diameter/ 2

= 1.06/2

= 0.53m

The speed of the trip= (4120 ×2π ×0.53)

= 13719.96 meter per minutes

We can convert to metre per seconds as

13719.96/ 60

= 228.66 m/s( less than speed of sound)