Behind many of the great feats we see performed by athletes are small and efficient physical tricks that enable them to run faster, jump higher and even make a ball change direction in mid-air. In honor of the 2020 Olympic Games, which are being held in Tokyo these days, we will review the small secrets behind the greatest feats of athletes and the physical principles behind them - and no, we are not going to talk about banana kicks.

## Higher – the Fosbury Flop

When we want to jump high, the intuitive way to do this is simply to run and jump, raising our legs as high as possible. This was indeed the accepted method of doing it even in Ancient Greece. In the 1960s, a young athlete named Dick Fosbury revolutionized the high jump by developing a new jumping technique – he jumped backwards, with his back facing down. The novel technique enabled him to collect the gold medal in the 1968 Olympic Games held in Mexico City. Today, you will no longer see athletes jumping any other way but this.

So what’s so great about the Fosbury method? The keyword is the center of gravity. The center of gravity is an imaginary point representing the center of mass of the whole body, so that on average the mass above it is equal to the mass below it and the mass on the left is equal to the mass on the right, and so on. For the average person, the center of gravity is found approximately in the umbilical region. If we take a sphere of uniform density, the center of gravity point will be in its center, but in bodies with a more complex shape, it can be elsewhere and even entirely outside the body, as in the example of a banana or a bagel.

When we do a high-jump, we strive to lift our center of gravity as high as possible. In the traditional method, the jumpers would transfer their center of gravity above the bar, but Fosbury “cheated the system”. With his backwards jump, he arched his body so as to manage to keep his center of gravity lower than the height of the bar as he was passing over it.  If you look at a jumper who uses this method, you will see that at any given moment the center of his body mass is found below the bar, but the part of the body that passes the bar at that very moment is above it. Thus, he had to invest less effort on his way uphill and over the bar. The new method did not significantly raise the height to which the center of gravity could reach, but the body had passed the bar nonetheless.

A comprehensive explanation about the Fosbury jump and its history can be found in the following video, by Assaf Bar-Yosef.

The video was produced by TEDed.

## Taking down the opponent

In judo, too, the center of gravity plays an important role. If we lean sideways, our center of gravity will move as well and if we lean too far, our center of gravity will no longer be above our feet and we will lose our balance and fall down. It is not uncommon to see two opponents in judo with one larger and heavier than the other, but his opponent still manages a takedown. There are two main methods of doing this - by tilting or by using leverage.

In the first method, the judoka (a judo practitioner) tilts the opponent’s body forward using the foot, in a movement called a grip. This maneuver causes the opponents’ center of gravity to move forward (or backwards) and to fall due to loss of balance.

Judo sweep | Illustration: Shutterstock

The second method employs the leverage principle, or the fulcrum. Archimedes is credited with saying “Give me a lever long enough and a fulcrum on which to place it, and I shall move the world”. When we grasp the arm of the opponent and lean it on our shoulder, we create a fulcrum and a lever in the form of the opponents’ own arm, and thus need much less energy to throw down the opponent. A slight movement is enough to change his center of gravity and then his way to the floor is paved. It is somewhat similar to a seesaw in which a light-weight child is sitting on one end and a heavier child on the other. If they are both sitting at the edges of the seesaw, the heavier child will surely tilt the seesaw, lifting the lighter child, but if he sits closer to the fulcrum at the center of the seesaw, the lighter child will find it easier to lift him.

Judo throw | Illustration: Shutterstock

## The art of the spin – the trifecta

In basketball, there are moments in which a single basket made outside the three-point arch scores three points and can determine an entire game - remember ‘Zalgiris’ miracle’? Shooting into the hoop involves many physical variables, such as the intensity and angle of the shot and the rotation of the ball around its axis, all of this during motion and under the protection of a defender.

A study published a few years ago analyzed the ideal conditions for scoring a three-point field goal. According to this study, if the ball is slightly spun backwards during the shot (self-rotation), and not just thrown in an arc, there is a better chance of it getting in the basket. The slight spin exerts a slight lift on the ball at the end of its trajectory, allowing the player to throw it a little weaker and still reach the hoop. This slows the ball down and reduces the risk of it bouncing back off the ring of the basket.

The same researcher also calculated the ideal angle and force required for the shot. According to this, it is best to make a 45-degree throw, from a distance of seven meters from the basket, at a speed just shy of 32 km/h and a spin of two rotations per second. This can definitely be something to practice but it would be  hard to apply it facing a tough defense with only a few seconds left on the 24-second clock.

## The banana’s sister – a curveball in baseball

The most famous example of a move that seems to contradict the rules of physics is the spectacular banana kick in soccer, but instead I will tell you about it’s younger and cooler sister from the United States – the curveball in baseball.

Similar to the banana kick, here, the pitcher throws the ball forward, and just before it reaches the batter, the ball suddenly changes its trajectory. The reason this happens is due to the spin the pitcher puts on the ball - the ball is thrown straight at a high speed and with a strong spin. As the ball advances, friction with the air slows its movement, and its rotation in the air creates pressure differences causing it to eventually change its direction.

This is exactly what happens in the banana kick as well, but here the pitcher has a lot more options. In soccer, the player kicks the side of the ball and its trajectory curves sideways. In baseball, a ball can be given spin in any direction we want, creating interesting routes of movement, such as a rotation that will make it rise due to pressure differences above and below it, or rather fall down much faster in the middle of its trajectory.

Throwing a curveball in baseball | Animation: AtomicRED, Wikipedia

The geography of the racket – the ‘sweet spot’ in tennis

On any kind of racket, whether in tennis, baseball or golf, there is a wonderous point  - known as the ‘sweet spot’ - a place in which a ball hit ensures maximum momentum. It may not sound very exciting, but in reality it is sometimes what makes the difference between winning or losing a game.

As opposed to what one might think, this point is not in the center of the bat but rather closer to the bottom. The exact location and size of this point are dependent on the structure of the racket, the strength of the fibers, their make and more. Today, using advanced fiber technology, rackets are manufactured with a larger ‘sweet spot’ that increases the chance that the player will hit it. In fact, a more accurate definition for it would be the ‘sweet zone’ rather than just a  ‘sweet spot’.