Medieval Trebuchet Range Calculation: A Physics Problem Based on Energy Conservation

This article estimates the range of a medieval trebuchet by calculating energy conservation. The author first analyzes the process of converting the potential energy of the counterweight into the kinetic energy of the projectile, taking into account energy losses. Then, using a simplified integration method (avoiding complex calculus), the author calculates the flight time of the projectile in the air and ultimately estimates the range of the trebuchet, comparing it with data from historical documents, with surprisingly consistent results. The article points out that the range of the trebuchet is independent of gravitational acceleration, which is counterintuitive, but the author explains this phenomenon through analysis.