the magnus effect
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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.
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