Ships with rotating sails

The ships are returning to have sails. Not like sails from centuries ago, but with rotating sails, which are this post’s subject.

Why rotating sails?

Ships with rotating sails save fuel and reduce emission of polluting gases. Many ships use gas turbine and diesel motor to propulsion, which are derivatives from oil. Therefore, this is a solution to reduce environmental impact by ships and fossil fuel consumption. The rotating sail also is called Flettner rotor. Which were invented in 1922 and used in a ship to tests in 1924.

In that time, were more economically viable to use diesel motors to ships. But now, with composites materials and more urgent environmental questions, the interest for these sails returned and it is possible to build sails with good resistance and weight light enough to install with cranes quickly in ships.

The Magnus effect

The Magnus effect is the principle behind the rotating sail. When the air, or a fluid, is in contact with a rotating object, is created a pressure difference between the opposite sides of the object. Creating a thrust force in the direction of low pressure side.

This is the Kutta-Joukowski theorem, which calculates the thrust in a cylinder spinning in the presence of an air flow.

$L=\rho \cdot G\cdot V$

Where,

$L$ is the lift force in $N/m$ ;
$\rho$ is the air density in $kg/m^3$ ;
$G$ is the vortex strength in $m^2/s$ ;
$V$ is the air flow speed in $m/s$ .

To calculate $G$ , must use this formula.

$G=2\pi \cdot r\cdot V_r$

Where,

$r$ is the cylinder radius;
$V_r$ is the rotational speed.

The rotational speed is cylinder circumference times the angular speed $\omega$ in revolutions per seconds.

$V_r=2\pi \cdot r\cdot \omega$

The theorem shows that to increase lift force, must increase the radius, length and cylinder speed. However, bigger the radius and length, heavier the sail, which limits the size. The Magnus effect is the explanation why balls make curves in the air when spin.