We took the formulas from this site here. This simulation ignores sensible things like friction, drag, and the counterweight slamming into the ground.
The first formula calculates the distance the weight falls. The weight should fall in a straight line. A is the starting angle of the counterweight to the pivot, and B is the ending angle, which is assumed to be 45 because that is the optimal release angle.
`"Weight distance" = "Counterweight arm length" * sin(A) + "Counterweight arm length" * sin(B)`
The second formula calculates the torque for both sides of the arm. The larger the distance between these torques, the more the arm moves and the further the projectile goes. In the simulation, we are assuming the trebuchet itself weight nothing, mostly because we really didn't want to add more sliders.
`"Counterweight arm torque" = "Counterweight arm length" * "Counterweight mass"/2`
`"Projectile arm torque" = "Projectile arm length" * "Projectile weight"/2`
The third formula determines the velocity of the counterweight (and therefore the projectile) from the torques found earlier.
`"Counterweight acceleration" = "Gravity acceleration" * (1 – ( "Projectile arm torque" / "Counterweight arm torque"))`
The fourth formula determines the acceleration of the counterweight (and therefore the projectile, in our model) from it's velocity and how far it falls.
`"Counterweight Velocity" = root * ("Counterweight acceleration " * " Counterweight drop distance")`
Finally, we determine the distance of the projectile by a formula found at this website.
`"Projectile distance" = "Projectile acceleration"^2 / "Gravity acceleration"`
"IS THAT A TREBUCHET!?" "No, its just their tree bucket."
