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• The Range of a trebuchet fired on a horizontal plane is
  • = 2V Sin(a)Cos(a)/g
    • Where g is the acceleration of gravity, V is the velocity of the projectile, and "a" is the release angle of the sling.
• The ideal release angle for the sling is 45 degrees.
• This velocity "V" can be calculated in an ideal system as potential energy=kinetic energy.
• This is demonstrated in the following equations:
  • 
  • 

• Due to conservation of energy,
  

• Solving and substituting equations:
  

 

This is for an ideal, frictionless system, the addition of air resistence, friction, and other such variables (tapered throwing arms etc), will influence this range.