Analyzing the Trebuchet As a Lever

Analyzing the Trebuchet as a Lever This is a very simple analysis of the fundamental operation of a trebuchet

The trebuchet develops the force necessary to accelerate the projectile through the imbalance of forces acting on a (class1) lever.

The unbalanced forces acting on the lever create a torque or turning motion at the pivot or fulcrum of the lever.

The counter weight, fulcrum and projectile are positioned in a manner that serves to increase the speed of the projectile. The counterweight is positioned relatively close to the fulcrum, and the projectile is positioned relatively far from the fulcrum.

12 Oz Lead Ball

10 gram Wood Ball Tether Hook

Note: The wooden ball is tethered to a hook on the end of the throwing arm. As the counterweight drops, the ball rotates on it’s tether, effectively increasing the ball’s distance from the fulcrum. As the ball rotates further from the fulcrum, it undergoes an increasing acceleration. This is similar to the effect of a water skier being whipped through turn behind a power boat.

10 gram 12 Oz Wood Ball Lead Ball

The imbalance of forces can be calculated at any moment during the trebuchet’s throw by determining the net torques acting about the lever arm.

F x Distance = Force x Distance

50 Newton centimeters = 8.8 Newton centimeters The net torque is the difference between these 2 torques The net torque acting on the wooden ball = approximately 41 Newton centimeters Example. Assume that at a given moment during the trebuchet throw, these conditions exists;

Counterweight arm = 15 centimeters Counterweight = 12 Ounces Projectile arm (effective) = 90 Centimeters Projectile weight = 10 grams

Because the counter weight and projectile weights are given in different units. It is necessary to convert the ounce units to grams.

12 ounces = 340.2 grams

The counter weight torque = 340.2 grams force x 15 cm Which can be converted to 50 Newton centimeters torque.

The projectile torque = 10 grams force x 90 centimeters which can be converted to 8.8 Newton centimeters torque.