As an object moves through the air, the air is disturbed by
the object. The disturbance generates an
on the object. Since a force is a
having both a magnitude and a direction, we can
the aerodynamic force into two components.
Drag acts in the direction
of travel of the object.
Lift acts perpendicular
to the direction of travel.
are capable of generating a lift force.
In particular, a
generates a force that is perpendicular to both the flow
direction and to the axis of rotation.
The lift force generated by a spinning baseball is the origin of the
curve ball thrown by big league pitchers.
For a curve ball, the direction of the lift force is used to
move the ball parallel to the surface of the earth, from side to side.
The lift force on a baseball is too small to overcome the
weight of the ball.
On this page we will discuss some of the details of the lift of a baseball.
The details of how a moving baseball creates lift are fairly complex.
If we move with an object through the air,
the object appears to stand still and the
air moves past the object at the speed of the object.
Next to the surface of the object, the molecules of the air
the surface, as discussed in the
properties of air slide. This thin
layer of molecules entrains or pulls the surrounding flow
For a spinning ball the external flow is pulled
in the direction of the spin. If the ball is not
we have a spinning, vortex-like flow set up around
the spinning ball, neglecting three-dimensional and
viscous effects in the outer flow.
If the ball is translating through the air at
some velocity, then on one side of the ball the entrained flow opposes
the free stream flow, while on the other side of the ball, the
entrained and free stream flows are in the same direction.
Adding the components of velocity for the entrained flow to the free
stream flow, on one side of the ball the net velocity is less
than free stream; while on the other, the net velocity is
greater than free stream. The flow is then turned by the
spinning ball, and a force is
generated. Because of the change to the velocity field, the pressure
field is also altered around the ball. The magnitude of the
force can be computed by
the surface pressure times the area around the ball.
The direction of the force is
perpendicular (at a right angle) to the flow direction
and to the axis of rotation. On
we develop the mathematical equation for the ideal theoretical lift of a
spinning, smooth ball.
L = (4 * pi^2 * b^3 * s * rho * V) * 4 / 3
where b is the radius of the ball, s is the spin of the ball,
rho is the density of the air, V is the velocity of the ball,
and pi is the standard 3.1415...
The equation given above describes the theoretical lift force generated
on a smooth, rotating ball. The ideal
around a smooth ball are shown on the figure at the top left, marked
But in reality, the flow around a spinning baseball is very complex
and looks more like the "Reference" flow shown on the figure.
Viscosity generates a boundary layer on the ball and
the stitches used to hold the covering of the ball together
stick up out of the boundary layer and disturb both the boundary layer
and free stream flow.
On the ball, the boundary layer transitions to
which affects the amount of
The stitches are not symmetrically distributed around the ball.
So the real flow around the ball is separated, unsteady, and
We can use the theoretical lift as a first order,
or preliminary, estimate of the lift on a baseball.
But to account for these real-world effects that we have neglected
in our ideal flow model, we define a
The lift coefficient is an experimentally determined factor that
is multiplied times the ideal lift value to produce a real lift value.
The ideal simplified model
tells us the relative importance of the
that affect the lift force on the baseball, while all of the complex factors
are modeled by the lift coefficient.
Using experimental data for the
of a big league curve ball, we have determined the value of the
coefficient to be .15.
You can further investigate the lift of a spinning baseball
by using the
The lift force on the baseball is very similar to the lift
generated by an
You can also
your own copy of CurveBall.
The figure on this web page was created by Elizabeth Morton, of Magnificat
High School, during a "shadowing" experience at NASA Glenn during May of 2007.
- NASA Baseball Home Page
- Beginner's Guide Home Page