When you think of sailing boats, you will generally think of beautiful sculptured wooden pieces of art, with long white sails, dancing in wind of the ocean.

However, at one point and another, some engineers have and do make boats slightly differently. Sails were replaced with long rotating cylinders, and so the rotor ship was born. However, how did these boats work? Let’s talk about everything related to the Magnus effect.

Magnus Effect Explained

The Magnus effect is a fluid dynamics phenomenon that occurs when a cylindrical shape spins and has a velocity through a fluid. The rotational velocity of the cylindrical shape going through the fluid causes one side of the cylinder to have high pressure, with the other side having a low pressure. This exerts a perpendicular force on the cylindrical shape, to the velocity of the object through the fluid it is traveling through.

This works, in part, due to Bernoulli’s theorem on fluid dynamics: the faster the velocity of a fluid, the lower the pressure of the fluid.

When a cylinder moves through a fluid, it will have an equal velocity of fluid passing over it, on both sides. Introduce a rotational velocity to the cylinder, and the velocity of the fluid around each side of the cylinder changes:

  • The side that is rotating in the same direction as the motion through the fluid has an increased fluid velocity – low pressure
  • The side that is rotating against the direction of motion through the fluid has a decreased fluid velocity – high pressure

This occurs due to the interaction of the fluid environment and the surface of the cylindrical object in friction with the fluid.

Detailed diagram of the Magnus effect

Friction of the cylinder rotating with fluid → increased/decreased fluid velocity around each side of cylinder → perpendicular force to motion of travel through fluid

What is interesting regarding the Magnus effect is that the science of it has not been explored as in-depth as other areas of fluid dynamics, potentially due to the lack of capability of utilizing the physics behind it.

History Behind the Magnus Effect

 Heinrich Gustav Magnus was the first person to describe the Magnus effect, back in 1852. Later, other physicists would describe the phenomenon, such as Isaac Newton and Benjamin Robins.

The Magnus effect was only truly industrialized in the 20th century by Anton Flettner, who utilized the experience of the likes of Albert Einstein to create the first ship that utilized the physical phenomenon with rotor sails. Hence, the name ‘Flettner rotor ship’ was born.

The Magnus effect was also used in World War II, by Barnes Wallis and the bouncing bomb he invented. It was made sure that the bomb had 500 rpm of backspin to give the cylindrical bomb lift to make it bounce several times over 700-800 meters.

Why do some Boats use the Magnus Effect?

Due to the nature of the Magnus effect, it was explored by some boats to replace sails and other forms of propulsion with rotating cylinders and still is. But, why?

  • Efficiency – Combining a rotor sail with a typical propeller propulsion system, powered by a motor, can improve the efficiency of a vessel. The Viking Grace Ferry, actually estimated an improved efficiency of 6% from installing a rotor sail.
  • Improved tacking course – The angle of tack is the direction of motion a sailed ship has to go, ‘zig-zagging’ due to the direction of the wind. Typically, sailing boats have to tack at an angle of 45 degrees to the wind. With sailing boats that utilize the Magnus effect, the angle of tacking can be greatly reduced down, to 20-30 degrees. This results in less severe ‘zig-zagging’.
  • Quicker journeys – Due to an improved angle of tacking, the distance traveled is reduced, resulting in quicker and more efficient journeys.
  • More robust – In heavy storms, sails can easily get damaged, and require maintenance throughout the journey. With rotor sails, they are much stronger and can withstand storms much better than sails, whilst also requiring less maintenance during the journey.

Examples of Boats Utilizing the Magnus Effect

E Ship 1

Owned by Germany’s Enercon GmbH, the cargo ship had four large rotor sails that generated the force from the Magnus effect. The boat was built in 2010 and, to accompany the Flettner rotors, had two propellors too.

Buckau Flettner Rotor Ship

Buckau Flettner Rotor Ship

Built by Anton Flettner, and even assisted by Albert Einstein, the Buckau was finished in 1924. It proved advantageous to sailed ships, in the sense that it could tack into the wind at 20-30 degrees, as opposed to sails at 45 degrees to the wind. The rotors were also less likely to be damaged in storms than the sails, adding to the reliability of the ship, powered by an electric motor.

Viking Grace Ferry Ship

Viking Grace Ferry Ship

A ferry ship with one 24 meter high rotor sail, the Viking Grace Ferry is relatively new compared to the above, finished in 2014. It is expected that the rotor sail will help save up to 6% of the fuel: the equivalent of €180,000 and 900 tones of carbon dioxide a year.

Magnus Effect in Sports

We’ve all seen those curling free-kicks from the likes of David Beckham, ‘bend it like Beckham’, and Lionel Messi. That’s done by the Magnus effect, from Beckham and Messi hitting the ball in such a way to provide a spin on the ball through the air.

Another great example is with Cristiano Ronaldo, that hits the ball with topspin. Instead of getting a sideways force on the ball to make it spin left/right, a topspin enables the ball to have a force exerted on it towards the ground. This ultimately allows the ball to dip very quickly, so Ronaldo’s free kicks are able to get up and over the walls very easily, whilst applying a lot of power.

Another example that uses the physics phenomenon is with another type of free-kick, by the likes of Gareth Bale and Cristiano Ronaldo again. This is where the ball is kicked in such a way, that the ball has a very little spin on it, if any, at all. This ultimately provides a very uncertain path of travel for the ball, since any brief spin on the ball will cause a such a force – if the spin changes ever so slightly in different directions, the motion of the ball can suddenly change too, making it even more difficult for the goalkeeper to predict the direction of travel.

Jabulani Ball – Germany 2006 World Cup

Jabulani ball, known for being an unpredictable World Cup ball

The Magnus effect was actually at fault during the Germany World Cup, where Adidas designed a ball, called the Jabulani ball, which had the seems stitched on the inside. This made the surface of the ball incredibly smooth, which made the ball much more unpredictable – the boundary layer of air influenced by the ball was reduced. This meant the effect of the Magnus effect was reduced, and natural variations in the ball/wind and other external factors had a greater influence. This is generally why you will see many balls in sports have a textured surface: to prevent such unpredicted behavior.

Other sports that utilize the Magnus effect include:

  • Formula One – Using bodywork to direct the airflow away from the tires, not only due to the frontal area of the tires causing resistance but the high-pressure zones above the tires, caused by the Magnus effect.
  • Baseball – Spinning the ball in different directions to put off the batsman.
  • Tennis – Hitting a ball with topspin so that the ball dips quicker over the net. Slicing the ball allows for the ball to float more, giving more time for the player to recover/reposition.

Magnus Effect Experiment

Far and few experiments have been conducted on the Magnus effect to determine the physics behind it, and how the main variables involved with the Magnus effect affect the force exerted. Such variables include:

  • Rotational velocity of the cylindrical object
  • Surface friction coefficient of the cylindrical object
  • Velocity of object through the fluid

Other variables can have an impact, including the fluid density and diameter of the cylindrical object.

Magnus Effect Equation

The Magnus Force’s equation is notorious online. For example, Wikipedia had an equation, which had been removed (as of 2013). This makes clear that to model the Magnus effect with an equation is an extremely difficult task. Nasa has attempted to model the Magnus effect through the following equation (for a cylindrical object):

F­m = Ժ4π²r²sv

Magnus effect equation for a cylindrical object (source: Nasa)


  • Ժ = fluid density.
  • r = radius of the cylinder.
  • s = rotational speed.
  • v = fluid velocity.

However, this equation cannot be used because it does not take into account the surface coefficient of the cylinder which is a fundamental element to the Magnus effect: it is the interaction between the surface of the cylinder which will determine the size of the boundary layer which will affect the size of the force.

To look into this crudely, an experiment was conducted to see how the surface coefficient of friction of the cylinder affects the Magnus effect:

The cylindrical barrel will roll from a set displacement from the ramp into the water. As it enters the water it will, therefore, have a fixed velocity and rotational speed. The barrel, when spinning through the water, will produce a Magnus Force causing is to deflect to the left of the ramp (at the point of impact with the water).

Ultimately, although a crude experiment, it provides the basis that the Magnus effect equation, even supplied by NASA, is incomplete. There is still a lack of true clarity between the variables that affect the force exerted.

The Magnus effect works through creating a boundary layer/vortex of air around the cylinder which spins in sync with the cylinder. The problem is that with a smooth surface, the friction between the first layer of air and surface of the cylinder is minimal. Therefore, the boundary layer will be much smaller. The results, make clear, as the surface coefficient of friction increases, so does the boundary layer and Magnus force exerted.

Utilizing the Magnus Effect for the Future

The proof is in the pudding that the Magnus effect is a hard physical phenomenon to utilize in an effective way – the issue comes that there are cheaper alternative ways to gain propulsion or force.

The biggest issue surrounding the Magnus effect is the resistance it creates to achieve the force. Not only is the area of the cylindrical object generally on the larger side, but it also requires an external power source to rotate the object.

However, when installed in the correct manner, there is the hope of improving the efficiency of large ships. The Viking Grace Ferry is a prime example of this. However, without a firm grasp of the physical equation behind the Magnus effect, it is difficult o fully utilize it. For example, the surface coefficient of friction that the rotor ships use for their rotor sails is a question that clearly has not been explored, and, therefore, has no basis as to how much that can influence efficiency (instead of spinning the rotor quicker).

As well as this, the issue stems also with the upfront design, manufacturing, and testing cost. With the world moving towards becoming more eco-friendly, maybe the Magnus effect is something we will start to see on more and more on small and large ships alike…

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