Question

A five metre tall, 1 m diameter Flettner rotor mounted on a small cargo vessel, spins at 50 rpm in a steady beam breeze of 15 knots. What is the thrust generated by the rotor? The air density and viscosity may be assumed constant at 1.22 kg/m3 and 1.79 x 10‐5 Pa.s respectively. Note also that 1 knot = 0.514 m/s.   Which direction must the rotor spin to produce forward thrust?

Answer 1

The following formula may be used to calculate theoretical thrust (TFRT) produced by the Flettner rotor in Newton (N):

TFRT = ρ x v x 2π x ωr² x L

where ρ = air density (kg/m3)

v = maximum wind speed (m/s)

ω = rotational speed (rad/s)

r = rotor radius (m)

L = length of the rotor (m)

Given:

ρ = 1.22 kg/m³

v = 15 knots = 15 x 0.514 m/s = 7.71 m/s

ω = 50 rpm =   rad/s = 5.23 rad/s

r = 0.5 m

L = 5 m

TFRT = ρ x v x 2π x ωr² x L = 1.22 x 7.71 x 2 x 3.14 x 5.23 x 0.5² x 5 N = 386.17 N

A) Thurst generated by the rotor 386.17N.

B) The rotor should spin in clockwise direction to produce forward thrust, as shown in image above.