Catapulting Through Time
Julian Ding, Olivia Harvey
David Thompson Secondary
Floor Location : S 063 D
Before the invention of gunpowder cannons, catapults were the most powerful projectile-launching devices in existence. Through advancements in engineering, their designs evolved over time until the ultimate form was reached: the trebuchet. In our project, we endeavoured to unlock the secrets of trebuchet motion by constructing a mathematical model for trebuchet motion and a physical trebuchet to experiment with.
To design the theoretical model, we used the physics principles of conservation of energy and angular velocity to derive an equation to approximate the launch velocity of the projectile. The model assumes total energy retention within the trebuchet system and calculates the projectile's launch velocity from the final angular velocity achievable by the throwing arm as a function of the counterweight mass. We then used this approximation in a kinematics-based model for projectile motion to reach a final estimation for projectile range, putting air resistance into consideration.
By constructing a trebuchet frame, we wanted to determine if utilizing a swinging versus fixed counterweight and a free-sliding versus fixed frame would increase the trebuchet’s efficiency. This was achieved by attaching masses of 0.500, 1.00, 1.50, and 2.00 kilograms to the throwing arm of the trebuchet and testing the range of the projectile with all combinations of upgrades.
Our experimental results proved that the swinging counterweight decreased the energy efficiency of the trebuchet over the fixed counterweight configuration, however the sliding frame increased energy efficiency when compared to the fixed frame. Our hypothesis to explain the decrease in energy efficiency caused by the swinging-counterweight arm is that its double-pendulum nature was less efficient than the single pendulum of the fixed-counterweight arm and also had a greater moment of inertia. Furthermore, the validity of our theoretical model as a model for the motion of fixed-counterweight trebuchets was verified from our experimental results through graphical analysis.