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The Math behind the Trebuchet
Transcript of The Math behind the Trebuchet
TREBUCHET Equations Many of the results of a trebuchet can be determined by equations The arm The arm is the key part in the trebuchet, as it provides the momentum, the height, and contributes to the angle of release. The key ratio of an arm is anywere between 3:1 and 5:1. The arm is split into two parts by the fulcrum. The longer side is responsible for throwing, acceleration quickly due to the dropping weights. The shorter side of the arm is resobonsible for holding the weights, and distancing the weights from the fulcrum. The base The base of a trebuchet provides the stability, the support, and the elevation needed to create the trebuchet. While there is no throwing mechanism involved, it must be sturdy and sportive to support the weight and momentum of the counter-weight. Angles When building a trebuchet, angles are included in almost every aspect. The magical angle is 45˚, This is both a strong angle to create supports, but also the critical angle in throwing. The Hook The hook is both the simplest and the most complicated part of the trebuchet.
It controls the release of the sling, the trajectory, and the distance of the throw
It must be adjusted so that the release of the projectile is launched at a 45 degree angle. This is a diagram of the supports for the main arm of the trebuchet. The angles are 45˚ and 90˚, and create strong and solid supports. This is the conversion between potential energy to kinetic energy
√(mgh/1/2m) = v
√[(68)(9.8)(2)/(1/2)(1)] = v
51m/s ≈ v This equation calculates the maximum range based on the masses of objects.
R = 2 (68/1)(2)
R = 272m Ratios Many key calculations to the effectivness of the trebuchet relies on ratios.
The most important ratio is the of the arm, and the placement of the fulcrum. The ratio can be 3:1, 4:1, or 5:1
Another ratio is that of the weight to the counter weight to that of the projectile. The key weigt is 70:1, and we came close with 68:1 The Sling -The sling provides a secondary motion, maximizing the power from the weights and giving it a final flick
-It's meant to mimic the forearm motion that a human makes when throwing a ball.
-Too short or too long will ruin the launch.
-For optimal distance, the sling should be 85% of the length of the arm from the fulcrum to the hook. 0.85 x 7.5=6.4 feet from the end of the line to the centre of the pouch.
-One side is connected, one side is hooked on
-When the hook passes 90 degrees, the sling will fly open, launching the payload. THE COUNTERWEIGHT The counterweight pivots around a much shorter distance than the payload end. Payload end will reach higher velocity. This is the principal of mechanical advantage. Its weight must be much greater than the weight of the payload, to get a high launch velocity. However, increasing the mass of the counterweight beyond a certain point will not help, since the limiting speed of the falling counterweight is free-fall speed. Counterweight 100x greater than payload TYPE Trebuchet is First class type lever - payload attached to one end and weight to the other Type II (Second Class) - like a wheel barrow. The long handles of a wheel barrow are really the long arms of a lever. Type III (Third Class) -