# A Finite Element Investigation into the Effect of Slope of Grain on Wood Baseball Bat Durability
## 1 Introduction  
In the early years of baseball, bats were made from a wide variety of wood species as players explored various woods in their quest to find the perfect wood. Eventually, northern white ash became the wood of choice as it had the best combination of density, stiffness, and impact resistance properties. For example, hickory has better impact resistance than the northern white ash, but it is denser than ash, thereby making for a relatively heavy bat. In the late 19 th century, the [PERSON] family in Louisville, Kentucky cemented the central role of ash bats in baseball when it began manufacturing northern white ash bats for a number of professional teams [1]. Ash remained the wood of choice until the late 1990s when maple bats were introduced to players by [PERSON], and a small number of players transitioned from ash to maple [2]. As the popularity of maple bats increased, the rate at which bats were breaking into multiple pieces during games was perceived to be increasing as well. However, there were no data to support whether this phenomenon was real or perceived. To obtain concrete data on the phenomenon, Major League Baseball (MLB) in cooperation with the Major League Baseball Players Association (MLBPA) authorized the collection of all bats that broke in games during a 2\(\frac{1}{2}\)-month portion of the 2008 MLB regular-season. Visual inspection of these broken bats concluded that the slope-of-grain (SoG) of the wood in each of the bats played a major role in the likelihood of a bat breaking into multiple fragments [3]. Slope-of-grain is defined to be the angle of the grain of the wood in the bat with respect to a line parallel to the longitudinal axis of the bat. As a result of the SoG observations from the field-collection bats and the understanding of the mechanical behavior of maple from a wood-science perspective, the wood-science experts on the team recommended new regulations be implemented after the 2008 season with respect to (1) setting the allowable range of SoG to be \(\pm 3^{\circ}\) and (2) changing the hitting surface for maple bats from edge grain to face grain. Before limiting the allowable range of SoG to be \(\pm 3^{\circ}\), many bat manufacturers were not closely monitoring SoG, and therefore, allowing wood with SoGs of up to \(\pm 10^{\circ}\) to be used in bats. After the 2009 season, additional regulations were implemented to restrict the minimum allowable wood density to 0.0245 lb/in\({}^{3}\) (678 Kg/m\({}^{3}\)) for maple wood species that could be used to manufacture baseball bats. Before this limitation was implemented, any species of maple was allowed to be used to make a wood bat. Without a list of specific maple species, maple species with poor impact properties were sometimes being used. After the introduction of the strict limitation to a single species of maple and greater awareness and compliance with the new regulations, the MPF rate dropped an additional 15-20% between the 2009 and 2010 seasons [4]. Each of the new regulations had the benefit that the improvements in bat durability came with changes that were fairly transparent to the players, i.e., there were no bat geometries or popular wood species that were prohibited from use. The combination of (1) setting the allowable range for SoG to be \(\pm 3^{\circ}\), (2) changing the impact surface from the edge to face grain for maple, and (3) the restriction on the minimum allowable wood density of 0.0245 lb/in\({}^{3}\) (678 kg/m\({}^{3}\)) for the wood species of maple resulted in a measurable decrease of \(\sim\)65% in the MPF rate per game [5]. Of these three changes, the only one that has an option to offer any additional drop in the MPF rate without any increase in bat weight is a further tightening of the allowable SoG from \(\pm 3^{\circ}\).