Boundary Layers and Life in Velocity Gradients
Wind velocity aloft is greater than at the surface, causing this cumulus cloud, viewed perpendicual to the wind direction, to have its upper parts displaced in the downwind direction, called shear.
For years, many scientists believed that the curveball was an optical illusion. As we shall see, this is not true. In fact, physicists have long been aware of the fact that a spinning ball curves in flight, going back to Isaac Newton, who wrote a paper on the subject in 1671. In 1852, the German physicist Gustav Magnus revived the topic when he demonstrated in an experiment that when a spinning object moves through a fluid it experiences a sideways force. This phenomenon, now known as the Magnus Effect, is the fundamental principle behind the curved flight of any spinning ball.
The Physics Of A Curveball
| The theory of the Magnus Effect is a relatively simple exercise
in aerodynamics. When any object is moving through the air, its surface
interacts with a thin layer of air known as the boundary layer. In the case
of a sphere, which has a very poor aerodynamic shape, the air in the boundary
layer peels away from the surface, creating a "wake" or low-pressure
region behind the ball. The front-to-back pressure difference creates a
backward force on the ball, which slows its forward motion. This is the
normal air resistance, or aerodynamic drag, that acts on any object moving
through the air. However, if the sphere is spinning as it moves, the boundary
layer separates at different points on opposite sides of the ballfurther
upstream on the side of the ball that is turning into the airflow, and further
downstream on the side of the ball turning backward. As a consequence, the
air flowing around the ball is deflected slightly sideways, resulting in
an asymmetrical wake behind the ball. The effect is to generate a pressure
difference across the ball, creating a lateral force component that pushes
the ball sideways. This lateral force, at right angles to the forward motion
of the ball, is known as the Magnus force. |
The strength of the Magnus force is in direct proportion to the rate of spin as well as the forward speed of the ballthe greater the forward speed, the greater the force. It will also be proportional to the air density, which means that a ball will tend to curve less at higher altitudes where the air is thinnera boon to hitters in a high-altitude city like Denver. The stitches on the baseball also help to increase the Magnus forcenot only by increasing the thickness of the boundary layer, but also by providing a place for the pitcher to put his fingers so that he can put more spin on the ball. It should be noted, however, that stitches are not required to make a ball curve. Even a smooth-surfaced table tennis ball will curve if it is given enough spin.
On the other hand, the direction of the Magnus force depends only on the direction of spin. As shown in the diagram, the force is always directed toward the side of the ball that is turning backward. In other words, the Magnus force always points in the same direction that the front of the ball is turning toward.
By properly orienting the spin direction, a pitcher can make the
Magnus force point in any directionleft, right, up, down and so on.
For example, the natural clockwise rotation of a righthander's wrist creates
a leftward force (from the pitcher's perspective), which causes the ball
to curve away from a righthand batter. When thrown with a three-quarters
overhand motion, the same pitch will curve down and away from the batter.
Conversely, a lefthand pitcher's natural wrist rotation (which is counterclockwise)
causes the ball to curve left to rightthat is, into a righthand batter
and away from a lefthander. In order for a righthand pitcher to imitate
this motion of throwing the pitch known as a screwball, he must turn his
wrist counterclockwise as he releases the ballan unnatural, uncomfortable
motion that frequently leads to elbow trouble. Much of the strategy of baseball
is a direct consequence of the fact that righthanders and lefthanders throw
different pitches, simply because of the quirk of human physiology that
our hands rotate more easily in one direction than the other.
|( Popular Mechanics, August 1997 issue )|
|The airflow around a smooth ball breaks at the top and bottom, slowing down the ball. On a dimpled ball, it breaks farther back, producing less drag. The dimples also provide spin that shifts the backdraft down, creating negative pressure above the ball and generating lift.|
|Obtained from Popular Mechanics website at http://www.popularmechnics.com|