Mechanical and Mathematical Modeling of Sport Archery Arrow Ballistics

Mechanical and mathematical model of external ballistics of the modern sport bow has been proposed. The force of air drag, shear friction, and drag on the fletching, and the additional force that depends on the angle of attack have been taken into account in the model. The corresponding Cauchy problem was stated and solved using the Runge-Kutta method and the program NDSolve from the software packet Mathematica 5. The model was applied to the example of the modern sport bow and arrow within the framework of the International Archery Federation Standard. Quantitative dependencies of kinematic parameters of arrow ballistics were obtained as a function of bow and arrow system adjustment. As a result of computer simulation based on the model, estimates were calculated for the difference in the vertical coordinate of the arrow tip on a target for the Olympic distance (70 m) caused by the initial angle of attack and initial angular velocity.