Any Mechanical Engineers willing to lend some advice?

Actually, the 300 m/s could be right.

The sling acts as a velocity multiplier depending on its length. IE turns a short radius into a long radius with an additional whip action when it reaches full extension due to moment of inertia.

Your weight has massive amounts of inertia and very little drag. In bullet/artillery land, we would say your cross sectional energy density is high and therefore why the ballistics are impressive.

Think about it simplistically:

Velocity of dropping weight is ~30m/s, your arm multiplier is 4. Sling length multiplier is another 4. Sling whip at end due to kinematic dynamics would only need to have a multiplier factor of 2. For a total velocity multiplying factor of 10.

Now the tension in the sling cable might not be able to withstand the stress along with the trebuchet in question, but, the math says it should be possible.

I think i know what your talking about allready there. I was taught it as vector math. In short the arm will be imparting X force whilst centripetal force will be imparting Y force and those will balance out when the sling is at a specific angle relative to the arm. As rotation speed increases those forces will favour centripetal more and more. By using force vector math you can determine at what angle the sling will be really at, and from that it's true radius, inertia, e.t.c.

Also yes i'm aware 300m/s is possible in theory, the science is easy to understand on that. But i saw a system that at a different arm ratio, (closer to the real world experimentally confirmed ideal ratio), was providing just 100 to jumped suddenly to 300. That's suspicious.

Anyway thanks for the help, i'll probably take a swing at the whole vector math thing eventually however. Though to be fair as i said i don't need an accurate to the decimal output, just an estimate that will if inaccurate allways come out on the low side velocity wise.

Carl wrote:I think i know what your talking about allready there. I was taught it as vector math. In short the arm will be imparting X force whilst centripetal force will be imparting Y force and those will balance out when the sling is at a specific angle relative to the arm. As rotation speed increases those forces will favour centripetal more and more. By using force vector math you can determine at what angle the sling will be really at, and from that it's true radius, inertia, e.t.c.

Also yes i'm aware 300m/s is possible in theory, the science is easy to understand on that. But i saw a system that at a different arm ratio, (closer to the real world experimentally confirmed ideal ratio), was providing just 100 to jumped suddenly to 300. That's suspicious.

Anyway thanks for the help, i'll probably take a swing at the whole vector math thing eventually however. Though to be fair as i said i don't need an accurate to the decimal output, just an estimate that will if inaccurate allways come out on the low side velocity wise.

The velocity will approach the drop velocity x (radial+whip) multiplier when the drop weight energy is >> slung weight and the imparted moment of inertia of the arm.

I believe if you take your example and drop the weight mass by a power of 10 or two you will get your lower velocity. I have not played with the numbers, but I believe you added way too many 000's to the weight dropped.

I didn't read all the reply's but: I believe your problem may be a physics issue. Your calculating the force using rotational acceleration. The force applied (Gravity) is linear acceleration, the force of gravity pulling strait down. The rotational motion of the hopper is caused by centripetal force, a conservative force that adds no additional energy to the projectile. If you use rotational distance, then you add additional distance traveled side-to-side which cancels-out. The distance used to calculate the force is only the height of the hopper at the start ( H0 ) minus the height of the hopper when the stone is released ( Hf ).
If you took all the same components (projectile, hopper, weight, etc...) & built a ramp at the same angle the trebuchet releases at (with minimum friction surface). put the projectile on it with the sling. attach them to the hopper with ropes and pulleys and mount the hopper on a set of vertical rails with a height = to the vertical distance (Y only) the trebuchet's hopper drops. the projectile would leave the end of the ramp with the same force as the trebuchet. Of-course the end of the ramp would have to be the same height as the trebuchet's sling, at release, to have the same range.

@MAD-4A: What your suggesting is basically the reverse method of how i did it. Put all components in a linear reference frame first, I chose to put them all in a rotational as only the counterweight wasn't allready in such.

@Relax: Duh silly me, conservation of momentum. So basic.

And no there's no extra zero's. UI dug up on the web that the ideal throw weight to counterweight mass ratio is 133.33 to 1 and the no-sling part of the sheet backs this up. Move away from it and the system efficiency plummets like, well, a stone.

That said late last night my inner engineer finally told my inner writer to shut up sit down and let him actually think. As a consequence i realised a couple of things.

First having the weight act via a drum or cam may be more efficient in it's transfer of energy to the system, it changes the system parameters from a centripetal force PoV in some problematic way.

Second, subject to fixing the above point and subject to a throw arm to machine height ratio less than 1.0 there's nothing limiting the throw arc to a partial revolution as their is in a traditional trebuchet. Such a setup actually allows for even easier sums and produces even higher system efficiencies than a much longer armed trebuchet style design.


I'm still playing with a few engineering concepts for improving the basic design but it's allready a lot better than an actual trebuchet as overall system mass despite the centripetal counterweight is a lot lower. my estimate of the moving component mass of a trebuchet with a 1500Kg throw weight was about 250 tons. The new design can throw a stone 50% heavier at a third again the velocity of the no sling form on 175 tons.

Still i appreciate all the help, sorry if it feels like i wasted your time a bit. Just wish my inner engineer had given me a kick about not needing to use a trebuchet modification if the basic principles could be put to use more effectively in an alternate configuration. Got it stuck into my head the trebuchet design was close to ideal, when reality is it can be improved on, or at least approximated by a design with several technical side benefits in this case.

Oh, don't feel sorry at all.

A picture is worth 10,000 words in this case. Without one trying to "describe" is nay impossible or from the other end, even trying to decipher what the person is doing, or not doing, while not impossible, might as well be.

The ability to actually show the real equations would be worth several thousand more words, but forums are not a good medium for that at all.

Carl wrote:@MAD-4A: What your suggesting is basically the reverse method of how i did it. Put all components in a linear reference frame first, I chose to put them all in a rotational as only the counterweight wasn't allready in such.

It is linear all the rotation is through conservative forces. The only non-conservative fore is the dropping of the weight which is caused by the linear acceleration of gravity applying force on the weight which is then transmitted through conversion & re-conversion to the linear motion of the projectile at the moment it leave the sling so all of the rotational energy cancels out & is effectively nil. Its a linear drop producing a linear flight at x degrees & y height, which after the moment of release becomes a ballistic path due to the linear acceleration of gravity then applied to the projectile.

There is not one part of this problem that is linear, other than the acceleration due to gravity. All of the kinematics are best solved in r-theta by hand. By computer? Cartesian is easier as you can plot them easier in Excel. Would require TK-solver, Mathcad, etc to use r-theta. Of course the easiest would be Solidworks, ProE, Catia etc, as all you have to do is draw the system and hit go. Setting simple pins and lines in ProE or Solidworks is a cinch. Never had to use that part of the program in Catia when I have worked either for or with Boeing.

Relax wrote:There is not one part of this problem that is linear, other than the acceleration due to gravity.

No - there is nothing in this, energy wise, that is not linear, that does not cancel out. the only thing needed rationally, is to calculate the position of the sling at the moment of release - which tells the height & angle of the projectile. all, non-conservative, energy calculations are linear.

MAD-4A wrote:

Relax wrote:There is not one part of this problem that is linear, other than the acceleration due to gravity.

No - there is nothing in this, energy wise, that is not linear, that does not cancel out. the only thing needed rationally, is to calculate the position of the sling at the moment of release - which tells the height & angle of the projectile. all, non-conservative, energy calculations are linear.

Think ya might want to remember what LINEAR means. d/dx d/dv and d/da are what again???


d/dx, d/dv, d/da are certainly not linear at ANY point. One can white wash WAG the dropped weight as linear(its not) but nothing else is even close.