The Magnus effect is the phenomenon whereby a spinning object flying in a fluid creates a whirlpool of fluid around itself, and experiences a force perpendicular to the line of motion. The overall behaviour is similar to that around an aerofoil (see lift force) with a circulation which is generated by the mechanical rotation, rather than by aerofoil action.
In many ball sports, the Magnus effect is responsible for the curved motion of a spinning ball. The effect also affects spinning missiles, and is used in rotor ships and Flettner airplanes.
German physicist Heinrich Magnus described the effect in 1852. However, in 1672, Isaac Newton had described it and correctly inferred the cause after observing tennis players in his Cambridge college. In 1742, Benjamin Robins (1707-1751), a British artillery engineer, explained deviations in the trajectories of musket balls in terms of the Magnus effect.
When a body (such as a sphere or circular cylinder) is spinning in a fluid, it creates a boundary layer around itself, and the boundary layer induces a more widespread circular motion of the fluid. If the body is moving through the fluid with a velocity V, the velocity of the fluid close to the body is a little greater than V on one side and a little less than V on the other. This is because the induced velocity due to the boundary layer surrounding the spinning body is added to V on one side, and subtracted from V on the other. In accordance with Bernoulli's principle, where the velocity is greater the fluid pressure is less; and where the velocity is less, the fluid pressure is greater. This pressure gradient results in a net force on the body, and subsequent motion in a direction perpendicular to the relative velocity vector (i.e. the velocity of the body relative to the fluid flow).
The Kutta–Joukowski theorem relates the lift generated by a right cylinder to the speed of the cylinder through the fluid, the density of the fluid, and the circulation.
The following equation demonstrates the lift force induced on a ball that is spinning along an axis of rotation perpendicular to the direction of its translational motion:
F = ρωrVACL
F = lift force
ρ = density of the fluid
ω = angular velocity
r = radius of the ball
V = velocity of the ball
A = cross-sectional area of ball
CL = lift coefficient
The lift coefficient CL may be determined from graphs of experimental data using Reynolds numbers and spin ratios. For a smooth ball with spin ratio of 0.5 to 4.5, typical lift coefficients range from 0.2 to 0.6.
The Magnus effect is commonly used to explain the often mysterious and commonly observed movements of spinning balls in sport, especially association football, table tennis, tennis, volleyball, golf, baseball, cricket and in various paintball marker brands.
The Magnus effect can also be found in advanced external ballistics. Firstly, a spinning bullet in flight is often subject to a crosswind, which can be simplified as blowing either from the left or the right. In addition to this, even in completely calm air a bullet experiences a small sideways wind component due to its yawing motion. This yawing motion along the bullet's flight path means that the nose of the bullet is pointing in a slightly different direction from the direction in which the bullet is traveling. In other words, the bullet is "skidding" sideways at any given moment, and thus it experiences a small sideways wind component in addition to any crosswind component. (yaw of repose)
Topics of Interest
Some flying machines use the Magnus effect to create lift with a rotating cylinder at the front of a wing that allows flight at lower horizontal speeds.
A flettner or rotor airplane is an airplane that has no wings but instead uses the Magnus effect to create lift. Thus it is similar to the Flettner rotor used in a Flettner ship. Such airplanes were first built by Anton Flettner.
The Coandă effect is the tendency of a fluid jet to be attracted to a nearby surface. The principle was named after Romanian aerodynamics pioneer Henri Coandă, who was the first to recognize the practical application of the phenomenon in aircraft development.
A Rotor ship, also known as a Flettner ship, is a ship designed to use the Magnus effect for propulsion. To make advantage of this effect, it uses rotorsails which are directly connected to a propeller. The Magnus effect is a force acting on a spinning body in a moving airstream, which acts perpendicularly to the direction of the airstream. German engineer Anton Flettner was the first to build a ship which attempted to tap this force for propulsion.
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