And what ChatGPT says about the data:
Throw in billiards refers to the deflection of the object ball from its expected path when hit with spin or at an angle by the cue ball. This effect is influenced by the friction between the balls and the way the cue ball transfers spin or “english” to the object ball.
Here’s why 30 degrees is significant:
1. Optimal Friction and Spin Transfer: At angles around 30 degrees, the frictional forces between the cue ball and the object ball are often at a maximum. This is because at smaller angles, there’s less side spin imparted to cause deflection (throw), and at larger angles, the cue ball glances off more sharply, reducing the direct transfer of spin.
2. Empirical Studies: Studies and empirical observations in billiards have demonstrated that the maximum throw effect generally occurs at around 30 degrees when no sidespin is applied to the cue ball. Players often use this knowledge to their advantage when aiming for a precise shot that requires the cue ball to make a specific angle with the object ball.
3. Player Experience: Experienced billiard players recognize that shots near this angle are more likely to induce the maximum throw, which they use strategically depending on the situation in the game.
Here’s a breakdown of why lower speeds might result in higher throw:
1. Increased Contact Time: At lower speeds, the cue ball remains in contact with the object ball for a slightly longer duration. This increased contact time allows the frictional forces between the balls to have a more significant effect, transferring more spin or “english” from the cue ball to the object ball. The greater the spin imparted, the more the object ball is deflected from its original path, resulting in higher throw.
2. Frictional Effects: Throw is largely a result of friction between the cue ball and the object ball. At lower speeds, the frictional forces have more time to act effectively. This friction causes more lateral movement (deflection) of the object ball, increasing the throw. At higher speeds, the balls make contact for a shorter period, reducing the amount of frictional force exerted, and thus, the throw is less.
3. Less Momentum Overcomes Spin Effects: At lower speeds, the momentum of the cue ball is lower, meaning it doesn’t easily overcome the side spin or english applied to it. Therefore, the spin has a more pronounced effect on the object ball, increasing throw. Conversely, at higher speeds, the cue ball’s momentum is greater, and it tends to continue along its initial trajectory more forcefully, reducing the effect of spin and thereby decreasing throw.
4. Cushioning and Elasticity: Lower speeds also mean less forceful impacts, which reduces deformation of the balls and the table’s cloth. At higher speeds, the elasticity and bounce-back effects of the collision can reduce the effectiveness of frictional forces, diminishing the spin transfer.