How to kick a "banana shoot"?

Everyone was holding his breath after the referee gave a free kick, and the defensive wall was built in front of the free kick taker. At this moment, the player shot a rotating ball that finely detoured the wall, and he scored a beautiful goal before the goalkeeper can react! Then, you may wonder why did the football not obey Newton's law of motion. You may think that since the football is shot under gravity, it should move in projectile motion. However, the football moved in a horizontal curve, showing that it experienced a horizontal force. Where did this force come from?

The football moves horizontally

The football in rotation

Banana shoot

Fig. 1  The football moves horizontally without rotation (The ball is moving downwards in this figure).

Fig. 2  The football in rotation without horizontal motion.

Fig. 3  The football in both horizontal and rotational motion.


Let us look at the figures. The lines represent the flow of air. In Fig. 1, the football moves horizontally without rotation. When the ball moves forward, air moves backward relative to the ball. Fig. 2 shows the football in rotation without horizontal motion. The rotation of the ball mobilizes the surrounding air to perform a cyclone-like motion. Fig. 3 shows the football in both horizontal and rotational motion, which is exactly the "Banana Shoot". In this case, the speed of air on the right-hand side of the ball is greater than that on the left-hand side. According to Bernoulli's equation of fluid mechanics ( constant), fluid flowing at a larger speed has a smaller pressure. Therefore, the pressure on the right-hand side of the ball is smaller than that on the left-hand side. Because of the differences in pressure, a force pointing to the right is produced and it acts on the ball. As a result, the ball is not only moving forward but is also right turning as it experiences the horizontal force. In fact, this principle is widely applied in daily life to change the direction of motion of objects in fluids. For example, the operations of flights and yachts are based on this principle.