All that is necessary to create lift is to
turn
a flow of air. The airfoil of a
wing turns a flow, but so does a spinning ball. The exact
details are fairly complex and are given on a
separate slide.
Summarizing the results, the amount of force generated by a spinning
ball depends on the amount of spin, the velocity of the ball, the size of the ball,
and the density of the fluid.
The figure shows a view of the flow as if we were moving with the
ball looking down from above. The ball appears stationary, and the
flow moves from left to right. As the ball spins,
the air near the surface of the ball moves with the surface of the ball.
If there was no free stream flow and the ball was stopped and spinning,
there would be circular flow around the ball which would match the speed
of rotation at the surface and die away to nothing far from the ball.
When the free stream flow is added to this circular flow, the resulting
flow has a net turning and produces a force. On the figure the ball
spins counterclockwise, so the free stream flow over the top of the
ball is opposed by the circular flow; the free stream flow below the
ball is assisted by the circular flow. In the figure we can see that
the streamlines around the ball are
distorted because of the spinning. The net turning of the flow has
produced a downward force.
As the force acts on the ball, it is deflected along it's
flight path.
The mathematical details of the ball's trajectory are
given on a separate slide.
Be particularly aware of the simplifying assumptions that have
gone into this analysis. The type of flow field shown in the figure
is called an ideal flow field. We have produced the ideal flow field
by superimposing the flow field from an ideal vortex centered on the
ball with a uniform free stream flow.
There is no viscosity
in this model, no
boundary layer
on the ball, even though viscosity is the
real origin of the circulating flow! In reality, the flow around a
spinning baseball is very complex. The ball isn't even smooth; the
stitches used to hold the covering together stick up out of the
boundary layer. In addition, the flow off the rear of the ball is
separated and can even be unsteady. BUT, the simplified model
helps us to determine the important parameters and the dependence of
the lift force on the value of the parameters. To obtain an accurate
value for the force, engineers typically use a
lift coefficient
that is determined experimentally and accounts for the details
that are too complex to model in the analysis.
You can investigate the effect of
aerodynamics on throwing a curve ball by using the
CurveBall Java Applet.
Have fun !
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