Mathematical modelling of oil patterns in tenpin bowling

The sport of tenpin bowling has many hidden intricacies that are not immediately obvious. One such feature is the thin film of oil that is applied to the lane by sophisticated lane machines. It is there first and foremost to protect the lane surface from the friction generated with the bowling balls. However, the placement of the oil in leagues and tournaments, known as the oil pattern, dictates how easy it is for bowlers to achieve high scores, where abouts on the lane they should play and with what type of bowling ball they should use. In this paper we shall discuss a mathematical model consisting of two coupled first order differential equations that describes the process of the application of oil to a bowling lane by lane machines manufactured by Kegel. The results of the model show a novel 3-dimensional representation of the oil pattern which can be used to guide the design of oil patterns as well as helping bowlers devise their optimal strategy for playing on them. We will discuss how to make oil patterns more difficult for bowlers to score on without simply increasing the volume of oil applied to the lane which causes problems for the pin setters and lane machinery.