The Mechanics of a Curve Ball

Wil Seely-Kirk

Writer’s comment: As a kid, I loved when my dad took me to watch the Giants play. The way the pitchers made the baseball dance on its way to home plate amazed me. I first picked up a baseball when I was three, and even then I wanted to be a pitcher. When I was seven, I’d throw a tennis ball against the front steps repeatedly, trying to make the ball curve (it rarely did). As I grew older, I realized that most people—including me—did not know how or why a curve ball curves. Our third paper in Elizabeth Davis’ English 101 (Advanced Composition) class happened to be an explanatory essay. I figured this was a great time to learn what makes a curve ball tick. I hope those who read this find the information as interesting as I did.
- Wil Seely-Kirk

Instructor’s comment: Sir Isaac Newton and Wil Seely-Kirk make a good pair in this classic Explanation Essay written for English 101: Advanced Composition. Wil’s essay includes vivid “insider information” from physics (and from that other exciting and arcane discipline—American baseball) while he familiarizes lay readers with concepts and terminology from a subject obviously close to his heart. Wil may throw a curve ball now and then, but the tone is reader-friendly throughout. Isaac Newton, professor of mathematics at Cambridge in the late 1600s, was said to have been a modest individual. He once remarked: “I do not know what I may appear to the world, but to myself I seem to have been only like a boy playing on the seashore, and diverting myself in now and then finding a smoother pebble or a prettier shell than ordinary, whilst the great ocean of truth lay all undiscovered before me.”There is a charming modesty to Wil’s essay—much to the credit of a certain late 1900s’ UCD undergraduate writer.
- Elizabeth Davis, English Department

In 1671, long before home runs, no-hitters, and sacrifice bunts, Sir Isaac Newton wrote a paper on the fact that a spinning ball curves in flight. In 1852, German physicist, Gustav Magnus, while studying the forces which act on the rotating blades of windmills, expanded on Newton’s work and demonstrated that a spinning object moving through a fluid experiences a sideways force. Known as the Magnus effect, this phenomenon is not only the basis for a substantial amount of today’s wind-generated energy, but also the fundamental principle behind the curve ball.
     The Magnus force is actually not incredibly complicated—it’s just a relatively simple exercise in aerodynamics. The surface of an object traveling through the air interacts with the thin layer of air surrounding it; this layer of air is known as the boundary layer. For a spherical baseball (a very poor aerodynamic shape), the boundary layer peels off as the ball moves, creating a low pressure area, or wake, behind the ball. The pressure difference from front to back creates a force in the direction of the side with lower pressure. This force is the normal everyday air resistance or drag force which affects everything from cars to birds to rocket ships. When a baseball is traveling with no spin, its wake is symmetrical and the drag force and gravity are the only acting forces. But when the ball is spinning, the wake becomes asymmetrical and a new force enters the picture (Fig. 1).

Figure 1
     The side of the baseball which happens to be spinning into the oncoming air will make the airflow past this side slower due to the friction between the surface of the ball and the onrushing air molecules. Meanwhile, on the opposite side, the ball is spinning in the same direction as the approaching air. In this case friction between the baseball and air molecules produces faster airflow. Faster airflow creates lower pressure, while slower airflow produces higher pressure. A pressure gradient will form across the ball. This difference in pressure will result in a force—the Magnus force—which will again point toward the side with lower pressure (Fig. 2). This force is similar to lift, the phenomenon that enables airplanes to become airborne. As a plane taxis down the runway, air moves faster across the top of the wing than the bottom, and the difference in pressure produces a force in the upward direction.

Figure 2
     The magnitude of the Magnus force depends on three factors: the rate of spin (faster spin, bigger force), the forward velocity of the ball (more velocity, more force), and the density of the air the ball travels through (higher density, higher Magnus force). In Denver, where the Colorado Rockies play, the air is much less dense and balls will not curve nearly as much as in other cities. Not surprisingly, each year the Rockies are near the bottom of the league in pitching and near the top in hitting.
     In the context of curve balls, the Magnus force must point downward, meaning that the ball must be thrown with a forward rotation, or top spin. Spin of this type causes the air to move faster past the bottom of the ball, creating lower pressure, and (surprise) a downward force. The Magnus force is not limited to pointing only downward; actually, a simple rule to remember is that the force will always point to the side of the ball that is spinning backwards. So if a ball has a reverse rotation or backspin, the Magnus force will point up. This is why every hitting coach, be it in little league, high school, or the majors will teach a young player to swing downward on the ball to produce backspin and thus attain maximum distance (Fig. 3).

Figure 3
     Baseballs also have the extra benefit of having stitches—216 to be exact—which protrude one or two millimeters from the ball’s surface. These seams act to create more friction between the ball surface and the boundary layer to induce a sharper curve. The stitches also enable a pitcher to get a better grip on the ball and impose a faster rotation on the old cowhide, which will again produce more curve.
     Finally, the big question: how is a curve ball thrown? First, the ball is gripped by the seams with the thumb on one side and with the middle and index fingers on the other (Fig 4). The ball is thrown like a fastball except as the ball is released, a downward snapping of the wrist in conjunction with the fingers imparts a twelve-to-six o’clock rotation on the ball. This results in top spin and the desired downward Magnus force. It may not be enough to strike out Big Mac, but it’s a start.

Figure 4