The Magnus Effect

1) The Physics

The Magnus Effect is a physical phenomenon that causes an object rotating in a stream

of liquid or gas to move in a direction perpendicular to the direction of the stream.

How does it work?

The round object rotates clockwise as shown by the two arrows. It floats in a stream

of liquid or gas – either the fluid flows in the direction indicated by the arrows on the right side

of the picture, or the object itself moves in the opposite direction (or a combination of both

cases). As for the effect, both situations are equal. The relative velocity of this movement is

marked V. The surface of the spinning object drives the fluid along, thus influencing the

velocity of the fluid flowing around it. The flow velocity and tip velocity of the spinning object

combine: they add where they go in the same direction and subtract where their directions

are opposite. This means that the relative velocity of the fluid flow on the opposite sides of

the object is different as well as the fluid pressure associated with it: the higher the velocity,

the lower the pressure. The difference in pressure on the opposite sides of the object causes

a force moving from the higher pressure area to the lower pressure area. This force is

marked F in the picture with an arrow showing its direction. It causes the perpendicular

movement of the object, thus for example changing the original trajectory of a ball flying

through the air as shown below.

2) (More or Less) Everyday Life

2.1) Sports – Ball Games

Let us illustrate the result of the Magnus Effect on something as ordinary as a shot on

goal in football.

The ball rotation and original direction, the relative air flow velocity as well as the

direction of resulting force action are indicated by arrows. The air is not, in fact, moving but

the movement of the ball causes relative air flow in the direction opposite to the ball

movement.

So what happens? Instead of moving directly to the point you aim it to, the direction of

the ball is deflected by the Magnus Effect to the same side as the direction in which the ball

spins. This can be a great disadvantage for an unpractised player. However, if you

understand it, it can explain some famous sports mysteries like the well known goal from

a direct kick of Roberto Carlos.

Roberto Carlos da Silva Rocha, a Brazilian football player known for his hard shots is

the author of a famous goal from July 1997. During a match between Brasil and France

which took place in Lyon, Roberto standing 35 m from the goal hit the ball with the outer part

of his foot, thus making it circle a wall of three players, hit a goalpost and end in the goal of

a very surprised French goalkeeper. Some of the eyewitnesses still probably consider it

random chance against the laws of physics.

This effect is especially well observed in table-tennis, where the ball is small and

very light. The surface of a racket is made of rubber specifically to enable experienced

players to send the ball spinning and take advantage of the Magnus Effect.

The combination of the rotation of a golf ball around its vertical axis and the Magnus

Effect causing a horizontal force causes the same sideways movement, here known as

“slice” or “hook”. In combination with so-called back-spin (when the ball rotates around its

horizontal axis as if it wanted to roll back to the point it has left) the Magnus Effect helps the

ball to stay airborne a little longer as the force caused by the air-pressure difference

counteracts gravity.

2.2) External Ballistics

Ballistics is the part of mechanics that describes the flight of a projectile. External

ballistics deals with the part of the flight between the bullet leaving the barrel and hitting the

target.

Upon leaving the barrel, the bullet performs a very complicated motion. Its trajectory

is subject to gravity and possible crosswind, the bullet itself spins in order to gain better

stability, it is tilted from the trajectory axis because of inaccurate balancing of the centre of

gravity etc. Because of this, the bullet axis describes a cone with the summit in the centre of

gravity around the axis of its flight direction, its tip moving in a small circle.

This

means that it always experiences some sideways wind component regardless of other

conditions and together with its rotation it becomes subject to the Magnus Effect. It can

cause an observable deflection in the bullet’s path added to the deflection caused by external

conditions.

However, the Magnus Effect in external ballistic does not have to be necessarily a

disadvantage. In airsoft, players are encouraged to use the so-called Hop-up mechanism in

order to lengthen the projectile’s fight. As the projectiles they use are in the shape of a ball,

they do not have to trouble themselves with the cone-shaped movement of a standard bullet.

They use the Hop-up mechanism to add the back-spin mentioned above to the projectile and

reduce the effect of gravity via the Magnus Effect.

3) Engineering

3.1) Flettner ship

Fletter ship, also known as Rotor ship, uses the Magnus Effect for propulsion. Instead of

sails or a screw-propeller, it is driven by so-called rotor-sails. These are huge vertical

cylinders run by their own engines or motors and their spin exerts the tractive effort the ship

needs to go forward.

Buckau (Baden-Baden)

The picture shows the first rotor

ship ever built, called Buckau. It

was designed by a German

engineer Anton Flettner, who

applied for a German patent for a

rotor-driven ship in 1922. The ship

was finished in 1924 and set out on

its first voyage in February 1925. In

1926, the ship, now renamed

Baden-Baden, sailed to New York

via South America in 40 days. It performed flawlessly even in stormy weather and was able

to sail into the wind, or tack, at 20-30 degrees, while ships equipped with standard sails could

tack at 45 degrees at most. However, there was a major disadvantage: the ship needed

more energy to rotate its rotor-sails than a propeller-driven ship would need for its propulsion.

In spite of this fact, the idea has not

been forgotten and rotor ships are still built

these days. The German University of

Flensburg is developing a rotor-driven

catamaran, the German wind-turbine

producer Enercon have built E-Ship 1 which

they want to use to transport wind-turbines

and equipment around the world.

E-

ship 1

Discovery Project Earth

Discovery Project Earth is a project supported by

the Discovery Channel that introduces means of fighting

global warming. In these terms, Stephen H. Salter,

Emeritus Professor of Engineering Design at the University

of Edinburgh, and John Latham, an atmospheric physicist

based at the National Center for Atmospheric Research in

Colorado, built a prototype of a robotic rotor-ship that was

able to spray sea-water into the air in order to enhance

cloud reflectivity. The rotors were made of carbon fibre and

attached to a trimaran which they were able to pilot steadily at a speed of six knots (more

than 11 km per hour). The efficiency of the propulsion was not mentioned, however, the ship

was able to run, emissions free, and complete its task according to the scope of the project.

Still, one question remains: as I could not find out what exactly was this emission-free drive,

the amount of emissions let into the atmosphere to produce this environmentally friendly

propulsion is yet to be compared with its benefits.

3.2) Flettner airplane

Some flying machines use the Magnus Effect to help create the necessary lift by

adding a rotating cylinder on the front part of their wings. But it gets better than that.

Inspired by his rotor ships, Anton Flettner decided to build an airplane that had no

wings at all and relied solely on the Magnus Effect to lift it into the air. The 921-V shown in

the picture, the first or one of the first prototypes was built in 1930. It is said to have flown at

least once, though not for long. Its short career ended with a crash landing. It is probably the

only aircraft with rotor-wing that ever made it into the air. However, the concept does have

some potential: when Ludwig Prandtl, a German scientist of the time, experimented with

rotating cylinders in a wind tunnel, he found out that they can create up to ten times more lift

than standard wings.

3.3) iCar 101 – roadable aircraft

And some French enthusiasts have decided to use this potential. They introduced a

refined digital model of the “first roadable aircraft with "Magnus effect" telescopic spinning

wings”.

Flying cars, first considered to be pure sci-fi, gradually become interesting for more

and more serious scientists and researchers. But they have always been forced to a halt

faced with two serious problems. First, even small conventional airplanes have a wingspan

wide enough to block a highway successfully – so how could we fold them to make them

small enough for the flying car to fit on the road and, at the same time, strong enough so that

they will be reliable in the air? Second, airplanes with flat wings need a fast and long start-up

before they can actually take off which would make them useless in a traffic jam you hoped

to avoid by flying over it.

The single-seater aircraft called iCar seems to solve both problems effortlessly.

Instead of a conventional wing, it is designed to fly by means of four telescopic rotors. When

folded, they are small enough to fit on the road. They should be fine in the air, too, as a

cylindrical construction like this one, even one not made of one piece, has lateral stiffness

much higher than a flat one, especially when considering it is composed of more movably

connected pieces. Also, if Prandtl’s experiments in the wind tunnel were correct, the much

higher lift provided by the Flettner rotors should reduce the necessary start-up significantly.

The authors obviously believe in their design: a French patent application was filed in

July 2009. It should protect the use of telescopic spinning wings on vehicles and on wind

turbines. One would say their belief is well placed; if you look at its characteristics, you will

see it makes the sci-fi matter much more science and much less fiction.

iCar’s characteristics

Folded width 2.50 meters

Unfolded width (wingspan) 4.50 meters

Length 6 meters

Height 2 meters

Empty mass 550 kilograms

Fuel mass 130 kilograms

Payload mass 120 kilograms

Takeoff speed (at sea level) 180 km/h

Takeoff distance (at sea level) 500 meters

Cruise speed (at 10000 feet) 310 km/h

Range 800 to 1000 km

iCar’s virtual takeoff (screenshots)

1. 2.

3. 4.

5. 6.

3.4) MARS - a high altitude wind turbine

MARS stands for Magenn Air Rotor System. It is a high altitude wind turbine designed

by Magenn Power Inc., a Northern America power company. Following their slogan “wind

power everywhere”, they decidet to build a wind turbine that was to outclass the conventional

ones.

It is a balloon filled with helium tethered to the ground. Its cloth “blades” allow it to turn

in the wind about its horizontal axis, thus generating electrical energy that can be used

directly or stored in batteries. One of its greatest advantages is its ability to work at heights

much greater than those of conventional turbines. This is a result of helium and the Magnus

effect, which also adds extra stability to its position.

4) Sources

http://cs.wikipedia.org

http://en.wikipedia.org

http://sk.wikipedia.org

http://dsc.discovery.com

http://tech-wiki.webnode.sk

http://tripatlas.com

http://vat.pravda.sk

http://www.icar-101.com

http://www.infovek.sk

http://www.magenn.com/

http://www.nennstiel-ruprecht.de

http://www.physicsforums.com

http://www.pilotfriend.com

Vladimír Schwarcz – Teória streľby (2000)

fyzika.utc.sk, text published by RNDr. Jozef KÚDELČÍK, PhD.