On Monday evening Hampden-Sydney’s three COMAP teams successfully completed the arduous Mathematical Contest in Modeling (MCM), capping off a banner year in which H-SC competed in math contests at the regional, national, and international levels. H-SC’s Team Alpha, consisting of Matthew Carrington, Miguel Mogollon, and Tian Shihao, submitted their paper, entitled “Give Me a Bat, and I’ll Give You the Sweet Spot“, which analyzed the problem of modeling the “sweet spot” on a baseball bat.
Team Alpha’s paper used a moment of inertia approach to calculate the speed of the batted ball as a function of the point of contact between the ball and the bat. They were then able to identity the sweet spot as the point along the bat that resulted in the greatest batted ball speed.
Team Beta, made up of Cameron Auker, Nathan Parr, and Douglas Vermilya, analyzed the problem of predicting the next location where a serial criminal will strike. Their paper, “A Simple Approach to Geographical Modeling: The Circle-Decay Overlay Model“, used spatial distribution and probability distance strategies to predict the location of the next crime.
Team Beta tested their model on historical data from known serial killers such as David Berkowitz and Peter Sutcliffe. Their results were good, predicting the location of the criminal’s last crime with over 90% accuracy at the lowest level of spatial resolution, and 30% to 60% accuracy at the highest level of resolution.
Team Gamma, consisting of Paul Cottrell and Ke Shang, also analyzed the problem of explaining the sweet spot on a baseball bat. Their paper, “Mathematical Portraits of Baseball Bat Vibration“, analyzes the problem from the point of view of Euler-Bernoulli beam theory, the basic idea being that the sweet spot occurs at the “nodes” of the bat, where energy loss due to vibration is minimized. This approach is complicated by the non-constant cross-section of baseball bats, and the team developed a heuristic to address this situation.
Results from the COMAP competition should be in by early April. In the meantime, the Math/CS department congratulates all the H-SC students who have participated in the contests this year!