How to bowl a strike–mathematically
A bowler’s chance of scoring a perfect 300 is about 1 in 11,500. So, unless you are dedicated to improving your game, it is best to enjoy the strikes as they come. You can either use a system of differential equations developed by MIT and Princeton to find the optimal placement of bowling balls, or you can refer to a newly-developed system. The formula is universal across all fields of physics, engineering and mathematics. It could be a breakthrough in the bowling game. The study, published in AIP Advances on April 15, was a collaboration between experts from University of New Mexico and Loughborough University as well as Swarthmore College. Prior to their work, the majority of bowling strategies were based on statistical analyses performed by professional bowlers. These methods were helpful but did not include more in-depth investigations into the physics of a bowling ball, the conditions on lane, and the pins. This meant that even the slightest variation on form could dramatically alter a player’s performance.
A USBC-approved bowling lane has 39 boards, each measuring approximately 2.73 cm (1.07 in). The x-axis measures in boards. The y-axis aligns with the axis of minimum inertia of the weight block. Credit: Simon Ji
However Hooper, along with his colleagues, decided to take a different route based on the underlying principle of Euler’s Formula. The equation was created by Swiss polymath Leonhard Euler in the 18th century. It establishes a link between trigonometric and complex exponential functions. Euler’s work is used to calculate compound interest, determine the half-lives for radioactive isotopes and many other mathematical calculations. Now, let’s talk about bowling. The new model, unlike previous works, takes into account various physical conditions in a game such as lane oils. Oil is applied to a lane in an initially thin and relatively even layer. However, the oil spreads out unevenly, creating a friction surface that is unique. “Our model offers a solution for both problems, by building a bowling simulation that can accurately calculate bowling trajectory when inputs are given for all factors that could affect ball movement,” explained Hooper. “A ‘miss-room’ is also calculated to account for human inaccuracies which allows bowlers to find their own optimal targeting strategy.”
Determining their new equations required accounting for multiple difficult-to-describe factors, such as describing the tiny asymmetries on a bowling ball’s surface. They also had to find a way to translate the complex mathematical inputs they used into language that was useful for bowlers, coaches and industry professionals. In the end, they believe that their new equations will soon be applied across training regimens, manufacturing processes, and professional events.
For now, it’s probably best for the average bowler to stick with the “practice makes perfect” mentality.
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