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Traction trebuchets were the earliest kind of trebuchet, where instead of the more familiar counterweight, the force came from lots of men pulling ropes attached to the short arm:

traction trebuchet https://en.wikipedia.org/wiki/Trebuchet#/media/File:SiJiao_Pao-t1.jpg

I'm not familiar with the physics, but since the force is provided via direct manpower, wouldn't it be difficult to manage its accuracy, such as when the men pulling the ropes get tired?

How did siege engineers manage accuracy for such a device? Were there any special techniques, or did they just try to get everyone to pull with the same force?

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    An advantage of seige artillery is that your target isn't moving. If you miss with one shot you can try again (and again). Rate of fire usually isn't too much of an issue either. So the men pulling aren't going to get tired all that quickly. Of course, the whole concept of accuracy is also different when your target is a large city wall or tower compared to say shooting at a man or unit of men. – Steve Bird Aug 23 '16 at 6:30
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    More important is the rope which would need to hold the weave when wet. As the rope dries out it would tighten providing truly enormous tension and creating a near ballistic trajectory for whatever it was they were hurling. Absolutely devastating weapon against any fixed fortification. – Doctor Zhivago Aug 23 '16 at 14:04
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As Steve Bird implied in his comment, firing at a very large target that isn't moving doesn't require pinpoint accuracy. Nonetheless, some degree of accuracy would undoubtedly have been desirable.

W. T. S. Tarver, in The Traction Trebuchet: A Reconstruction of an Early Medieval Siege Engine (this link downloads a pdf) makes several observations "based on five years of experience with this kind of machine". Among them are:

  1. One discovery was that

By shooting as fast as possible (a bit over four shots per minute) the operator and the crew fall into a rhythm which makes the shots more powerful and consistent.

  1. Later in the trials,

an even more effective method of shooting was discovered. Very simply, the crew counts to three, giving a light tug on each of "one" and "two," and hauling through on "three." This slightly slows the rate of shooting but coordinates the pull of the crew to a remarkable extent.

  1. Tarver also realised that

consistently sized ammunition is crucial for accurate shooting because the mass of the projectile is an integral part of the dynamic system which propels it.

On this last point, Tarver gives some examples of cluster patterns achieved by a team of 16 pullers:

with a 41-inch sling and a 5-inch hook set at 40 degrees discharged six 4.7-kg balls in one minute and ten seconds to distances of 81, 79, 76, 77, 76, and 76 m

and

a different crew of fifteen pullers using the same hook and sling settings shot six 4.7-kg balls to distances of 100, 90, 105, 100, 105, and 93 m. The second 100-m ball landed on the first, destroying both.

Travers also states that

….In 1989, I could usually strike a round target 10 m in diameter a distance of 90 m away on the second shot given consistent ammunition, and accuracy improved in 1991. Medieval artillerists took great care to control the weight of their shot, having each projectile chiseled to a near-perfect sphere.

Although "identical ammunition is best", Travers believes a skilled operator should be able to "compensate for variations of up to plus or minus 10 percent in mass".

In building and operating the traction trebuchet, Tarver made use of medieval illustrations and, most importantly, "the military manual of Mardi b. 'Ali b. Mardi al-Tarsisi, written around A.D. 1187", but he also points out that (being made primarily of wood) none have survived so it is impossible to be sure exactly how they were constructed.

traction trebuchet

This illumination from the Bible de Maciejowski shows how, sometimes, the operator didn't release until he was off the ground. Attrib: The Morgan Library & Museum [Public domain], via Wikimedia Commons

A final point worth making is that traction trebuchets had a faster rate of fire than the more accurate counterweight ones so there was some compensation there.

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