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A brief history of theory leading to the
"Magnus Effect": Newton in 1672 noted
how a ball's flight was affected by spin. In
1742, Robins showed that a transverse
aerodynamic force could be detected on a
rotating sphere. Earlier theories also gave
a simple analysis for a "frictionless
fluid," which showed that the side force was
proportional to the free stream velocity and
the rotational speed. In 1853, the first
explanation of the lateral deflection of a
spinning ball or cylinder is credited to
German physicist Heinrich Magnus from which
the phenomenon derives it
name, the "Magnus Effect". This, all
presented well before the introduction of
the boundary-layer concept by Prandtl in
1904.
The commonly accepted explanation is that
a spinning object creates a whirlpool of
rotating fluid about itself. On the side
where the motion of the whirlpool is in the
same direction as that of the direction of
flow to which the object is exposed, the
velocity will be increased. On the opposite
side, where the directions are opposed, the
velocity will be decreased. Then, according
to Bernoulli's principle, the pressure is
lower on the side where the velocity is
greater, and consequently there is an
unbalanced force at right angles to the
fluid flow. This is the Magnus effect.
Studies agree that the Magnus force
results from the asymmetric distortion of
the boundary layer displacement thickness
caused by the combined spinning and flow
past the sphere. The motion imparted by the
spinning cylinder to the boundary layer
affects the manner in which the flow
separates from the surface at the rear.
Boundary layer separation is delayed on the
side of the spinning object that is moving
in the same direction as the free stream
flow, while the separation or shear occurs
prematurely on the side moving against the
free stream flow creating turbulence in the
down stream wake. The resulting turbulent
wake then shifts toward the side moving
against the free stream flow. As a result,
flow past the object is deflected, and the
resulting change in momentum flux causes a
force in the opposite direction (see
figure 1).
This phenomenon is influenced by the
conditions within the layer next to the
body, known as the boundary layer. Certain
results of the force of the spinning body
introduce anomalies within the layer, such
as creating turbulent flow on one side and
not the other.
The following equation demonstrates the
manipulation of characteristics needed to
determine the lift force generated by
inducing a mechanical rotation on a
cylinder:
F = 1/2 . ρ . V2. A . Cl
F = lift force
V = velocity of flow
A = cross-sectional area of cylinder
Cl = lift coefficient
ρ = density of the fluid

The lift coefficient is the ratio between
the weight of the cylinder and the fluid
density, the velocity squared, and the
cross-sectional area of the cylinder. Lift
coefficient is dependent on:
Spin ratio = RPM.Dia
2.V
The Lift coefficient may be determined
from graphs of experimental data using
Reynolds number and spin ratio. Typical lift
coefficients of a cylinder with smooth
surface range from 0.2 to 0.6 with spin
ratios ranging from 0.5 to 4.5. |