Figure 2
Mc=30, Mp=0.5
Lc=0.321 or 0.5, Lp=Variable
Sa=-46
In figure 2 we can see range of the trebuchet as a function of the ratio between the length of the two arms. Mc=30, Mp=0.5, Sa= -46, and Lc=0.321 or 0.5. The curves shows the best ratio between the arms to be 2.3 : 1 no matter what the length of the counterweight arm within the range 0.321 - 0.5 m considered for my needs. This graph came from the same set of data as the previous one and can be explained in the same manner. The data fed into the computer to achieve these graphs was such that the results can be applied to my trebuchet. My trebuchet has a counterweight arm length of 0.321 m and so we know that the best length of projectile arm is 0.74 m. Both the first and the second graph were drawn using data for a varying projectile arm length.
Figure 3
Mc=30, Mp=variable
Lc=0.321, Lp=0.8
Sa=-46 or -11
In figure 3, the variation of the range of the trebuchet with the mass of the projectile is shown. Mc=30, Lc=0.5, Lp=0.8 and Sa=-46 or -11. This figure allows us to see that as small a projectile as possible must be used to obtain maximum range. It also shows how big a feat it is to throw a huge boulder a few hundred metres. It is interesting to note that the graph does not go down to 0 slowly when the mass of the projectile is increased but falls suddenly, like the first graph. This is probably due to the same reasons: When the trebuchet can only just lift the projectile, it has some time to accelerate, firing a certain distance. When the trebuchet can no longer lift the counterweight with the starting angle specified, the range falls to 0.
Figure 4
Mc=30, Mp=variable
Lc=0.321, Lp=0.8
Sa=-46
Figure 4 shows the curve with the starting angle of -46 degrees from the previous graph but on an exponential scale. We can see that most of the curve is a straight line, that is the range varies exponentially with the projectile mass. The equation given for this particular part of the curve is:
The range of values of Mp to which this applies is 2 < Mp < 9. This allows us to see just how great the effect of increasing the projectile mass is on the range.
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© Filip Radlinski 1996, 1997