Figure 8
Mc=30, Mp=0.5 or 1.5
Lc=0.5, Lp=0.8
Sa=variable
Figure 8 shows the calculated range of the trebuchet in function of the starting angle of the projectile arm with the ground. The values of the constants are: Mc=30, Mp=0.5 or 1.5, Lc=0.5, and Lp=0.8. The starting angle is described on the diagram below. The starting angle being smaller gives the trebuchet more time to accelerate. However acceleration depends on the angle and since the acceleration near -90 degrees is very small this is not a very 'important' angle. The slope is not steep at the top end of figure 8. If the starting angle is only slightly increased or decreased around this point, it will not greatly affect the range. The same goes for +90 degrees. At 0 degrees the acceleration is the greatest and thus 0 degrees is a very 'important' angle. If the starting angle is adjusted only very slightly in has a great effect on the range of the trebuchet. A heavier projectile makes this curve less sloped in general but it keeps the same form. We can safely assume that any trebuchet would give the same form of graph. This graph shows that the starting angle should be around -45 degrees or slightly less, but making it much smaller won't have a great effect on the range. However this effect may be slightly larger once the sling is added to the trebuchet.
Figure 9
Mc=30, Mp=0.5
Lc=0.5, Lp=0.8
Sa=variable
Figure 9 displays the best shooting angle in function of the starting angle. The constants had the following values: Mc=30, Mp=0.5, Lc=0.5 and Lp=0.8. The graph shows that even though the best shooting angle depends on the velocity of the projectile and the acceleration of the trebuchet, it also depends on the starting angle. The starting angle cannot be higher than 90 degrees or the projectile will just fall out. Even at 90 degrees or a little bit less, the acceleration is so small than the projectile doesn't go anywhere. The graph allows us to see that the best angle rises up to almost 90 degrees but always stays below. When the starting angle is small, the projectile stays on the trebuchet through a long range of angles, from -80 to 50 at the start. As the starting angle increases, the range of angles through which the projectile is 'not shot' gets smaller until it is only about 10 degrees when the starting angle nears 90 degrees. The rise of the curve increases steadily, that is the slope grows. This is probably because the projectile needs to be on the trebuchet for a certain amount of time to accelerate and the firing angle is increasing to allow this range as the starting angle increases. An interesting note is that when the projectile mass changes from 0.5 kg to 1.5 kg the curve barely changes.
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© Filip Radlinski 1996, 1997