In addition to gravity pulling them down, all flying objects’ horizontal motion is opposed by friction from the air, the strength of which is described by a drag coefficient. While bullets, pop flies and other projectiles are merely slowed while gravity pulls them down, the combination of a non-uniform surface and high rate of rotation causes the resistance of air to be uneven across the profile of the ball, pushing it sideways as well as straight backward. That unevenness is the basic reason that a curve ball curves.
When a fastball leaves the pitcher’s hand, the ball rotates relatively slowly, from the top backward. But by flicking the wrist instead of letting the ball slide off his fingertips, a pitcher can cause the ball’s rotation to be right to left or left to right, depending on whether the pitcher is right or left-handed. Consider a ball spinning from left to right, from the batter’s perspective. In effect, the left side of the ball is moving faster than the left side of it, which causes the air resistance to be stronger on the left side of the ball than the right. Meanwhile, the right side of the ball is spinning away from the direction of the ball’s travel, in the same direction as the air pushing the ball backward, so the air resistance is less on the right side of the ball. As a result, instead of directly opposing the ball’s initial direction, air resistance opposes the ball from slightly left of center. That opposition, applied at every point of the ball’s trajectory from the pitcher to the catcher’s mitt (or to the bat, depending on the quality of the pitch), continuously pushes the ball to the batter’s right, and is what causes a curve ball to curve.
Besides not rotating very fast, a fastball does not “curve” vertically because its rotation is parallel to its direction of travel. If the air resistance to a fastball is at all off-center, it is somewhat below the front of the ball, but not nearly enough to cause the ball to lift, because gravity is so much stronger than the minor asymmetry of the air resistance. A fastball certainly drops from the elevated pitcher’s mound to the level plate, and gravity probably causes it to curve down slightly in addition, but its forward motion is so great in comparison that any curving is unnoticeable.
Because the stitches protrude slightly from the uniform leather surface of the rest of the surface of the ball, they encounter greater air resistance. In addition to flicking their wrists as they release the ball, pitchers can maximize the curve of their pitch by gripping the ball such that the greatest number of stitches are perpendicular to the direction of the ball’s rotation. The cost of maximizing the air resistance this way is that the pitch is also slower, so pitchers use a variety of grips to obtain different balances of pitch velocity and curve, with names like “slider” and “circle curve” which refers to the shape of the pitcher’s fingers as he grips the ball.
