Oh not discrepancies. Here is what happens
The trebuchet made by Sascha only has one arm, for that particular case if it does not move then more momentum is transferred to the rock.
I you observe the real model they have a double arm so the ball gets more velocity because it has a longer arm. The wheels allow the double arm mechanism to fully extend by moving forward when the counter weight fall.
The trebuchet with the double arm is just using more of the potential energy left, by allowing the arm to fully expand, but the wheels are stealing momentum from the system by allowing the base to slide, that energy can not come from the vacuum.
If not wheels are added then arm does not expand and the energy is eaten by the friction with the ground, and the ball does not travel too far.
The double arm trebuchet is like a sling shot that by tuning the resonance you can make so it uses the most possible energy of the system.
If they made the trebuchet with a very long single arm of a length equivalent to the length of the double arm extended, then ball would travel even farther than the double arm on wheel but this was physically implausible because the was not way to get a light material that long and that strong. If you notice the second arm is a wire with very little weight.
Here is what I predict:
Double arm not wheels – very short range
Double arm on wheel – medium range for the rock
Single arm equivalent to double arm fully extend not stopper– medium range for the rock
Single arm equivalent to double arm fully extend – the longest range
Here is a site that show and explains why the double arm wheels had longer range,
http://www.pbs.org/wgbh/nova/lostempire ... heels.html
but remember the comparison is to other double arm without wheels, there was not way to make a trebuchet with a really long arm.
Sascha: beautiful isn't the Law of conservation of momentum beautiful.
You can almost feel it when you can see it so close in action.