Thinking this approach out, could someone correct me if I have this wrong.
So he gradually increases the energy transfer from the weight to the arm over the course of the drop. But that arm swinging around must have a lot of energy loss due to friction and air resistance.
This loss will rise exponentially with the speed increase right? So in a sense he is holding his energy budget in a very inefficient phase, with high losses.
Two things support this. A) he spent a lot of time trying to make the arm more arodynamic. B) The spool widening at the end, which is essentially changing back down gears, applying more torque, right at the end when you want speed.
An alternative would be to drop the weight, and let it fall unrestricted until it gets to it's highest speed (this would minimise friction and air resistance) and only at the end of its fall, transfer the energy into the arm.
In this case the arm would only need to rotate 180 degrees or whatever, and not waste energy rotating right?
And then, to take this a step further to make this work there would need to be some flexibility or elasticity in the system to take energy from the high speed falling weight to the arm.
And what you have ended up with is something that looks like.... A whip!
If I'm picturing what you're explaining correctly, I think this would be difficult. Suddenly accelerating the arm from zero to hundreds of mph would put immense stress on the arm, not to mention whatever you're planning on using to transfer that energy (you kinda hand waved that bit).
I think your assessment is correct about the energy losses. I'm just not sure about the fix.
I think the fix is essentially a whip, that's what I meant by elasticity and flexibility.
If you want to accelerate a weight quickly in a single swipe, (simplified) gradually reducing the mass along the length of the whip imparts more kenetic energy at the end (the whip crack).
So the arm would no longer be rigid, although you can see in the OPs video it isn't actually fully rigid.
Energy loss from air resistance typically is quadratic, not exponential, with regard to velocity. So it’s worth much less than you’re arguing. And the arm has to rotate from what I can understand, so the end rotational velocity - and hence, rotational energy - would be the same?