A Mathematical Approach to Modeling Physics for the Vertical Position in Synchronized Swimming

In Synchronized Swimming, arguably the most demanding sport known to man, one of the most basic positions is called a vertical. In this position a swimmer’s upper body is submerged in water and their legs are held above the surface while their body is kept in a straight line. Along with the buoyancy forces of the surrounding water and the air in the lungs, swimmers must also support themselves by making movements called sculls with their arms that propel them upwards. This additional force is the applied force. The goal of this research is to use physics principles to create a mathematical model that will help assist synchronized swimmers in maximizing their scores for the vertical position. The math done in this model confirmed that the amount of applied force inversely correlates with the buoyancy force needed to lift the synchronized swimmer out of the water. Additionally, the total force pushing the synchronized swimmer upwards is the same at each level. When the collected data is fitted to a second-order polynomial comparing applied sculling force to desired score, the graph shows that the data had an R2 fit of 0.984. This knowledge could ultimately inform athletes about how to use buoyancy and other forces to their advantage which could increase their performance levels.