# A Finite Element Investigation into the Effect of Slope of Grain on Wood Baseball Bat Durability
## 5 Discussion
Figure 13 is an overlay plot of the boundaries denoting the transition from NF to SPF (solid lines) and for the transition from SPF to MPF (dashed lines), respectively, for all three wood species when impacted at the 14.0 in. (35.6 cm) location. The yellow birch bats transition from NF to SPF at much lower velocities in comparison to the maple bats and slightly lower than the ash bats. For example, the transition velocities from NF to SPF for a bat with a \(-3^{\circ}\) SoG for maple and ash are 115 and 110 mph, respectively, while the yellow birch is 100 mph. However, the yellow birch bats once again had a much better durability window (for both velocity and SoG span) in their transition from SPF to MPF than the other two species. This 14.0-in. (35.6-cm) modeling implies that the rate of MPFs due to outside pitches could be reduced if the SoG range for all three kinds of wood were decreased from \(\pm 3^{\circ}\) to \(\pm 2^{\circ}\). There are several general observations that can be made from the analysis of the models. Negative-SoG bats in the range of 0\({}^{\circ}\) to \(-1^{\circ}\) exhibit a higher SPF durability than positive-SoG bats for all three wood species for a 2.0 in. (5.1 cm) impact. As the impact speed increases to the MPF boundary, the best durability is at a 0\({}^{\circ}\) SoG. Positive-SoG bats in the range of +1\({}^{\circ}\) to +2\({}^{\circ}\) exhibit a higher SPF durability than negative-SoG bats for all three wood species for a 14.0 in. (35.6 cm) impact. This phenomenon continues for yellow birch bats as they transition from an SPF to an MPF. As the impact speed increases to the MPF boundary, the best durability is at a 0\({}^{\circ}\) SoG for ash and maple bats. The bias of the peak durabilities to be for negative-SoGs for outside-pitch (2.0 in., 5.1 cm) impacts and to be for positive SoGs for the inside-pitch (14.0 in. 35.6 cm) impacts supports that a 0\({}^{\circ}\)-SoG bat is the most versatile with respect to bat durability. Based on the Hankinson equations as plotted in Figure 4, it was expected that bat durability would decrease as the magnitude of SoG increases. Thus, it is unexpected to see the results of increased bat durability for small nonzero SoGs, i.e., increase in bat durability for small negative SoGs for the 2.0 in. (5.1 cm) outside-pitch impact and the increase in bat durability for small positive SoGs for the 14.0 in (35.6 cm) inside-pitch impact. The respective increases with opposite SoGs may be a consequence of the respective deformation mode and location of the maximum strain for each of the two impact conditions. For the outside-pitch condition, the bat exhibits a diving board mode shape, i.e., like that of a beam clamped at one end with a backward tip deflection--see Figure 8a. For the inside-pitch condition, the bat bends in the reverse direction of that described for the outside-pitch situation with the zero-slope near the middle of the length of the bat--see Figure 8b. Thus, for the outside pitch, the front side of the bat is in tension with the maximum strain in the handle section near the knob. For the inside pitch, the back side of the bat is in tension with the maximum strain developing in the taper section of the bat. This bat response was visually confirmed during high-speed video recordings of impacts and could be validated experimentally through digital image correlation (DIC) or by placing strain gauges along the length of the bat. The difference in the sensitivity of the range of SoG may be a consequence of the respective bat section that is experiencing the maximum strain for the respective impact location. With respect to how the material behavior contributes to this increase in bat durability for small non-zero SoGs, a plausible explanation may be at what magnitude of bending do the wood fibers become fully engaged in the deformation process. Future studies will look at extreme changes in bat profiles to see if the trends found for this bat profile are also seen in those other profiles.