Using physics to throw, kick, and hit balls further

A common goal in many sports is to throw, kick, or hit a ball as far as possible. To reach this goal is simple: you apply all the force you have to the ball. But that’s not all. You also have to choose the best launch angle. The angle plays an important role in determining the distance that flying objects travel.

Trajectories of a thrown ball: Throw parabola

Without air friction

If you ignore air friction, a launch angle of exactly 45° yields the largest distance due to the physics laws of motion. The launch angle is measured between the ground and the direction of movement directly at releasing. At this angle, the athlete’s energy is applied equally into the ball’s horizontal movement and its vertical movement. You need the horizontal component for the forward direction, and the vertical movement to give the ball some hang time in the air. The result is a nice parabolic path on which the ball travels. In reality though, you can’t ignore air friction. Because of this, the best angle is a little bit below 45°. To be very exact, you also have to take into account the height in which you release the ball. The perfect angle would be decreased further by a small amount. In most sports, however, you can neglect this because the roughly 2 m (ca. 6 ft) at which you release the ball doesn’t matter if you throw more than 20 m (ca. 60 ft). So let’s have a closer look at the physics of the flight of a ball.

With air friction

As it travels through the air, a ball has to push air molecules away. This takes away some of the ball’s moving energy and deforms the flight parabola. In physics classes in school, you often ignore the air friction because it is very difficult to calculate. But if you neglect air friction in sports, your results won’t be as good. Don’t worry, you don’t have to calculate it. It’s enough just to know about it. Because of the air friction, the optimal angle is decreased. The more the friction matters, the smaller the angle should be.

The air friction depends on the shape, size, texture, and the speed of the ball. The bigger, rougher and faster the ball is, the stronger the air friction will be. But how much the friction matters also depends upon the relation between the energy of the flying object (which is higher for heavier objects) and the energy lost because of the friction.

The optimal angles to send balls flying the farthest distances are around 40°. For example, for kicking or punting a football, you yield the largest distance at a launch angle between 35° and 40°. If you throw a small ball, such as one used in track and field events or a baseball, the ball is much smaller. Thus, the friction plays a smaller role in the movement. Then the best angle is almost 45°.