# A Finite Element Investigation into the Effect of Slope of Grain on Wood Baseball Bat Durability
## 2 Background  
Baseball bats are comprised of four major regions, as shown in Figure 1. The barrel is the intended ball impact region. The barrel of a typical 34.0 in. (86.4 cm) long baseball bat extends from the tip of the barrel to 10.0-12.0 in. (25.4-30.5 cm) down the length of the bat. The taper region is where the diameter of the bat transitions from the large diameter of the barrel to the small diameter of the handle. The taper region of a 34.0-in. (86.4 cm) bat runs from the end of the barrel section to about 20.0 in. (50.8 cm) from the tip of the barrel. Manufacturers are required to place their company label on this region of the bat, and the location of the label should be located 90\({}^{\circ}\) away from the intended hitting surface of the bat such that a batter can follow the protocol of hitting with the label up or label down. The handle of a baseball bat is the section that a player grips when swinging. The handle of a 34.0 in. (86.4 cm) bat extends from the end of the taper region to about 33 in. (84 cm) from the tip of the barrel. The final \(\sim\)1 in. (\(\sim\)2.5 cm) of a wood baseball bat is the knob, which has a diameter a bit larger than that of the grip area so as to help the player maintain his hold on the bat during the swing. Upon the wide acceptance of northern white ash as the wood of choice, the players also settled on holding the bat such that the ball would impact the edge grain of the wood as opposed to the face grain (Figure 2). As a result, bat manufacturers located their logo on the face grain of the bat, i.e., 90\({}^{\circ}\) away from the edge grain. Thus, players would commonly hit with the logo up or logo down. Figure 1 shows an example of the location of the Louisville Slugger logo on the face-grain surface of an ash bat. Figure 1: Ash baseball bat with logo on the face-grain surface of the bat. The knob, handle, taper and barrel sections of the bat are identified. Figure 3 shows the respective directions of positive and negative SoGs for a label-up orientation of the bat and the ball traveling from the pitcher to home plate. In Figure 3, the bat is shown situated in a finite element model of the bat durability testing system at the University of Massachusetts Lowell Baseball Research Center (UMLBRC). An SoG of \(0^{\circ}\), i.e., the grain of the wood is aligned with the long axis of the bat, is alleged to be the optimal condition for bat durability. As the SoG deviates from \(0^{\circ}\), the effective break strength, i.e., the modulus of rupture, of the wood decreases [6; 9; 10; 11]. [PERSON]'s equation can be used to quantify the effect of SoG on wood mechanical properties,  
\[N=\frac{\text{PQ}}{\text{P}\sin^{n}\theta+\text{Q}\cos^{n}\theta}\,, \tag{1}\]  
where \(N\) is the strength at an angle \(\theta\) to the fiber direction, P is the strength perpendicular to the fiber, Q is the strength parallel to the fiber, and n is an empirically determined constant [10]. Different  
Figure 3: Finite element model of a baseball and the bat in the test fixture. The annotations denote the directions of positive, negative and \(0^{\circ}\) SoGs. Figure 2: Face-grain and edge-grain surfaces of an ash wood baseball bat. properties follow different curves (Figure 4), and these curves are average relationships developed across many species. The Wood Handbook states that the modulus of rupture (MOR) falls very close to the curve Q/P = 0.1 and n = 1.5. Using these values, the Hankinson Equation for a 3\({}^{\circ}\) SoG results in \(N\) = 0.895, meaning that the strength of a 3\({}^{\circ}\) SoG specimen is 89.5% of a specimen with a 0\({}^{\circ}\) SoG. The MOR curve in Figure 4 shows that an SoG of \(\pm\)10\({}^{\circ}\) will result in a 60% drop in MOR--thus, the motivation to tighten the allowable SoG range to be \(\pm\)3\({}^{\circ}\). The motivation for the change in hitting surface was based on the knowledge that the impact resistance of map, a diffuse porous wood, is better on the face grain than on the edge grain.