# Finite Element Analysis of Athletic Equipment

As we continue our series on stress analysis in athletic equipment, we will take a closer look at hockey sticks and baseball bats.  Mechanical engineering plays an expanded role in the designing and testing of athletic equipment.  Mechanical engineers use both computer aided design (CAD) and finite element analysis (FEA) to determine that the stresses seen in hockey sticks and baseball bats is different from the stresses seen in the shoes and helmets worn by the players.  Shoes and helmets repeatedly experience smaller stresses, while hockey sticks and baseball bats will experience a sudden very high concentration of stress as they collide with a ball or puck. In this blog we will discuss how the strength of this equipment is determined using FEA.

## FEA is one tool used in analysis

A baseball bat is arguably the most important tool throughout the course of a baseball game. Coincidentally, it is also the piece of equipment that is most likely to be broken. the first is that the grain near the handle is subjected to too much force and the second being the bat reaches its failure stress at the critical point. A finite element analysis of the bat showed that a bat-ball collision that is about 5 inches away from the sweet spot, known as the critical point, can result in stress upwards of 4 times higher than the stress at the sweet spot itself

[1].  The dynamic stress in the handle can reach over 30,000 psi for about 0.007 seconds, which is about twice the average strength of most hardwoods that are used to make bats. Due to the natural elasticity of wood and its shock absorbing nature it is able to survive stresses like this, but after repeated impacts fatigue will begin to set in. Fatigue starts with micro cracks in the bat and as the stress cycle is repeated, these cracks grow until they cause a fracture in the bat [2].  A large impact on bat strength obviously comes from the wood that the bat is made of. The most popular choice used to be white ash because it was less dense than most other woods, but after Barry Bonds’ record breaking homerun season, where he used a maple bat, many abandoned the white ash in hopes of finding more power. The cons of using a maple bat though, are that it is much stiffer and cannot handle the same stresses that a white ash bat could due to ash’s natural ability to flex. Other than the natural strength in maple and ash wood their grain patterns have a large impact on the breaking point of the bat. An ash bat has two types of grain in a bat, edge-grain and flat-grain, while a maple bat’s grains all run the length of the bat. The edge-grain is seen running parallel to the length of the bat, while the flat-grain is the semi-circular lines that run perpendicular to the length of the bat. If an ash bat contacts the ball on the edge-grain it transfers the impact forces solidly to the ball, however if it makes contact with the ball on the flat-grain the bat is likely to flake because the stress is too high. The flat-grain of the bat can’t handle as much stress and experiences fatigue at a much faster rate than the edge-grain of the bat, but the edge-grain can handle more stress than any part of a maple bat.

A hockey stick is designed very differently than a baseball bat and doesn’t fail quite as often. A hockey stick has the ability to bend and snap to create a whipping type action to send the puck towards the goal. A shot of 100 mph puck speed would require a stick to undergo 560 N of force that would cause a 300 deflection, or about 15 cm. The majority of wooden hockey sticks are made using rock elm for the shaft which has a maximum tensile stress of 15 MPa and a maximum compression stress of 11 MPa. However new sticks are normally made with a polyetuylene fiber which has a maximum tensile stress of 3500 MPa and are therefore much stronger [3].  The newer stick designs require less force to create more deflection and therefore can shoot the puck faster. Similar to baseball bats, hockey sticks experience fatigue over time, but because of the synthetic nature of the material, fatigue leads to a weakening of the fibers instead of micro cracks in the material which allows for greater durability and a longer lifespan.

[1]  Sherwood, James “Characterizing the Performance of Baseball Bats Using Experimental and Finite Element Methods” University of Massachusetts, Lowell Massachusetts [2]  Boucher, Kyle “Impact Stresses in Wooden Baseball Bats” Worcester Polytechnic Institute

[3]  Hache, Alain “The Physics of Hockey” The Johns Hopkins University Press, Baltimore, MD. 2002