Figure 10
Mc=30, Mp=0.5
Lc=0.321 or 0.5, Lp=0.8
Sa=-46 or -11
Figure 10 shows the variation of the angle of the projectile arm of the trebuchet with the ground in function of time. The constants are: Mc=30, Mp=0.5, Lc=0.321 or 0.5, Lp=0.8 and Sa=-46 or -11. The slope of the curve gets larger with time because the trebuchet is accelerating. Unfortunately, data was not calculated for a trebuchet which just barely manages to lift its projectile. Such a curve would probably have a bend at the end, showing how the trebuchet slows down and comes back in a swing back movement. The curve illustrating the behaviour of the trebuchet with a counterweight arm of 50 cm is much steeper than the others and this is the way we would expect it: The counterweight arm is longer so the angular acceleration is greater. The other two curves look similar only the trebuchet with the lower starting angle is 'behind' on the other one. They both have the same acceleration at each angle and so both curves have the same slope when the arm is at a certain angle. This explains the 'delay' of the curve with the starting angle of -46 degrees.
Figure 11
Mc=30, Mp=0.5
Lc=0.321 or 0.5, Lp=0.8
Sa=-46 or -11
In figure 11 is presented the variation of the angular acceleration of the projectile arm of the trebuchet with time. The values of the constants are the following: Mp=0.5, Mc=30, Lc=0.5 or 0.321, Lp=0.8 and Sa=-46 and -11. By comparison to figure 10, this graph illustrates the way in which the acceleration is greatest near 0 degrees and smaller farther away. The curves where the trebuchet starts at -46 degrees show this very well. At t=0 the trebuchet is at -46 degrees and the acceleration has a certain value. As time progresses, the acceleration gets bigger: The trebuchet nears and gets to 0 degrees. When the trebuchet passes 0 degrees, the acceleration gets smaller: This is because the perpendicular forces acting on the trebuchet arm get smaller and so their sum gets smaller. The trebuchet continues to accelerate until it reaches a certain point. At this point, it slows down, starting the 'swing back' action it would make if we allowed it to continue. The trebuchet is at this point trying to balance itself. The trebuchet which starts at -11 degrees also shows this evolution of the acceleration, only it is almost at maximum acceleration from the start, thus the curve does not rise as much as for the other two 'test shots'. This trebuchet also falls into 'swing back' faster because it has a smaller range of angle to go through before it should swing back.
BackNextHome
© Filip Radlinski 1996, 1997