Figure 12
Mc=30, Mp=0.5
Lc=0.321 or 0.5, Lp=0.8
Sa=-46 or -11
Figure 12 shows the evolution of the angular velocity of the trebuchet projectile arm with time. The constants used are the same as for figure 11. First, the slope rises slightly indicating a greater acceleration, then as time progresses, the slope curves downward, indicating a lower acceleration. The curve illustrating the behaviour of the trebuchet with a 32 cm counterweight arm and a starting angle of -11 degrees even shows us the beginning of the deceleration of the trebuchet arm, with the slope being negative right at the end of the curve. The maximum velocity of the three curves shows what we would expect: that the bigger trebuchet and the trebuchet with the smaller starting angle would reach a greater maximum velocity, and thus be able to send a projectile a greater distance. Figure 11 is actually a graph of the values of slopes of the curves from figure 12.
Figure 13
Mc=30, Mp=0.5
Lc=0.321 or 0.5, Lp=0.8
Sa=-46 or -11
Figure 13 presents the range of the trebuchet in function of the time of release of the projectile. The values of the constants are the following: Mc=30, Mp=0.5, Lc=0.5 or 0.321, Lp=0.8 and Sa=-46 and -11. The figure shows how critical the timing for the release of the projectile is. If the projectile is released just 50 milliseconds early or late, the range is practically 0 with the trebuchet specifications used. Probably a bigger trebuchet would allow a greater time span for the release of the projectile. This graph shows us that if a small trebuchet seems not to be able to throw a projectile farther than 5 metres, it could just be a matter of timing to get the range up to 27 metres. An interesting point the graph shows is that the range does not increase steadily with time and then decreases steadily but it starts by growing very slowly, then suddenly shoots up, slows down for a few milliseconds and then shoots back down. The negative range shown by two of the trebuchets just means that the projectile is flung into the ground when the arm comes around and should be considered as a range of 0 m. It is also interesting to note that the change in the rate of change of the range is much smaller with the smaller trebuchet put at the higher starting angle. This is probably due to the higher starting angle: On the other trebuchets, until the arm reaches past 0 degrees, the range is 0 but on the above described trebuchet this happens much faster. This is not however a solution that should be used to make it easier to time the release of the projectile right because making the starting angle higher greatly decreases the maximum range.
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© Filip Radlinski 1996, 1997