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Pumpkin Ballistics Software

Underlying Assumptions:

Level Ground In the professional version of this software, I will take hills into consideration.  However, for now, we will assume that the ground is level.  Indeed, hurling contests are almost always held on flat farmland and the distances involved (200+ meters) are so much greater than the height of the trebuchet’s release point (2+ meters) that assuming away changes in altitude do not create much lose of accuracy. 
Low Speed The professional version will address homemade mortars firing steel balls at velocities up to 375 m/s. In this version, if you input parameters for your trebuchet that describe cannon-like velocities (roughly, anything over 100 m/s), the software will respond with an error message.
Low Apex Both this software and the professional version ask the user to input the altitude and then it looks up the air density for that altitude.  Air density is re-calculated at every point during the ball’s flight so, if it flies so high that the air is significantly thinner at its apex, this is taken into consideration.  In this version, it is assumed that the pumpkin does not go high enough to experience different air densities.
No Wind The professional version will take wind speed, from any angle, into consideration.  But, for the purpose of comparing different types of pumpkins or different trebuchet designs, one should do all of one’s testing in still air.  It is only when creating a range table for field use in target shooting that one must consider wind conditions.
No Weather The professional version will allow the user to input air pressure and temperature.  In this version, it is assumed that the pressure is 29.92 inches of mercury and the temperature is 15° Celsius.  Neither version takes humidity into consideration, as it has a negligible effect.
No Spin  I see no evidence that the opening of a nylon pouch imparts spin to pumpkins.  Balls are given spin when they roll; for example, a baseball rolls off the pitcher’s fingertips or a golf ball rolls up the angled face of a club.  A golf ball is violently struck by a steeply angled clubface made of unyielding steel and with very aggressive grooves cut into it to gain traction and assure that the ball rolls rather than slides up the face.  It accelerates from a standstill up to speeds over 60 m/s in less than one millisecond, which is a very different thing than a pumpkin gently nestled in a smooth nylon pouch and taking about 500 to 600 times longer to accelerate up to speed, at which point the pouch just opens, without any twisting motions.  Anyway, pumpkins lack the raised stitches or dimples that cause baseballs or golf balls to curve.  Note.

Definition of Variables:

Efficiency How much of the potential energy contained in the suspended counterweight is transferred to kinetic energy in the flying pumpkin.
Angle The angle in which the pumpkin is launched, measured in degrees.
Range The distance over which the pumpkin is hurled, measured in meters.

Leave one variable (efficiency, angle or range) blank and it will be calculated.

Important Note

The height of the counterweight is NOT the distance from its apex to its nadir. It is the distance from its apex to its position at the moment the pumpkin is released. Further movement of the counterweight after the pumpkin is gone will not add any distance to its range.

A lot of hurlers measure the counterweight's apex when their treb is cocked. Then they measure its nadir after all movement has ceased. Then they take the difference of those two measurements, call it "height" and never think about that parameter again. This is not right. If the model is to be accurate, one must re-measure both launch angle and height every time a change is made to the treb's design.