Any Mechanical Engineers willing to lend some advice?

First, i've actually got a fair amount of mechanical engineering training myself. The problem is i've stepped into waters my degree of training doesn't quite cover and searches on google have failed to turn up anything useful. Probably because i don't quite know what keywords to use.

Second whilst this IS for a fictional setting i'm working on i'm not going to stray into fanfiction territory. It's purely engineering but it explains partly why certain existing tools for the job on the web don't quite cut the mustard.

Third, the other reason the online tools don't quite work is that most of them just aren't accurate at larger scales and throw up all kinds of warnings about that.



So what am i trying to do and what is my problem?


Okay the basics is i'm trying to math out the performance of a variation on the basic Trebuchet. The main difference being the counterweight acts through chains on a continuous radius cam. Which means torque over the whole action equals the peak torque of a standard design trebuchet. It's also the easiest way to set up an excel spreadsheet to solve it


The methodology is clear. If you know the system rotational inertia and the system torque and the system actuation arc in radians you can use fairly basic mechanical engineering formulas to determine the final rotational velocity of the system. Specifically, (assuming initial velocity is zero and can so be dispensed with in the equations), the final velocity in radians per second is equal to the the square root of; (twice the rotational acceleration multiplied by the rotational distance covered, units of rad's per second and rads respectively).

Otherwise expressed as: w2 = 2aq.

With the full form being w2 = wo2 + 2aq

But as noted if zero wo2 can be ignored.

If you know rotational velocity at the moment of stone release and the radius of the stone from the axis or rotation you can determine it's linear velocity and thus it's release velocity and energy.

Currently i'm fudging slings and including separate sling and no sling values in the spreadsheet while i work on calculating slings properly, but that's something i'll ask for help on if i get stuck.


This brings me onto my problem. The problem i'm running into with the spreadsheet is that for very small designs it's producing output energy's greater than the input energy. That's clearly wrong .


Now I'm confident that I'm handling Acceleration, torque, moment of inertia of the arm and stone, and the distance value of the rotation correctly.

Acceleration is T/I where T is torque and I is moment of inertia.

Moment of inertia is r^2*M where r is the average radius.

Torque is r*f, where r is radius and f is force, (or r*9.81*m where r is radius, 9.81 is gravity, and m is the counterweight mass)

And rotational distance is (Degrees/360)*2*pie



Where i suspect the issue is and want the help is in accounting for the system inertia component of the counterweight. I've so far treated it as a rotating mass affixed to the cam as that seemed like the closest i could think of as to how it might work. The problem is this is one type of problem i was never taught how to solve and all Google searches turned up no answers. The result is that presumable the overall system inertia is on the severely low side.

I'm hoping someone can at least confirm the cause if not provide me with the appropriate formulae.


If anyone wants the spreadsheet to check my sums with feel free to ask.

Your counterweight accelerates. The force it applies is reduced to:

r * M * (9.81 - A)

Also, I don't think you can just call its linear motion angular velocity.
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Ma Lemming: If all your friends jumped off a cliff
into the sea, would you....oh....um....nevermind.

Your counterweight accelerates. The force it applies is reduced to:

r * M * (9.81 - A)

Also, I don't think you can just call its linear motion angular velocity.

The first part i'm aware of but excel throws a hissy fit if you try and use a formulae that references itself.

The latter point is what i'm stuck with, the only way to solve a problem like that is to bring the inertia values of the linear and rotational components into the same frame of reference. But i have no clue how to actually do that and google's being no help.

Sorry for the double post, whilst i haven't solved the problem i did just spot an error in my sums. I'd forgotten to add the projectile inertia to the overall system inertia, (i'd calculated the projectile inertia, but when adding the values of the different components together in another cell i'd missed the relevant output). Which was producing a vastly lower overall inertia.

Thats at least got the whole system into the range where conservation of energy is now being obeyed, even if i'm confident the math is still fairly off.

EDIT: Major mathing boo boo. Corrected now.

Okay think i've solved this after running some idea's through my head and if i'm right it's laughably simple. But check my thinking/working for me.

Ok lets assume instead of trying to calculate the moment of inertia of a linear mass via it's mass and acting radius we instead use a known acceleration output and object mass and radius of acting wheel, (we'll assume for the math the wheel masses nothing as it's rotational inertia then becomes balanced out on both sides of the math where about to run).


Well that ends up kind of simple.

First lets assume a known acceleration on a known mass by a known radius wheel. That requires a force of F which requires a Torque T of F*r.

Now we know the torque and thanks to the known radius of the wheel and the known linear acceleration we can also calculate the radial acceleration of the wheel. Using that we can back calculate the effective moment of inertia of the linear mass.

2 quick examples:

Example 1:

1 meter radius, 1m/s acceleration, 1kg mass

The required force in a linear fashion is 1n so we need 1*1 torque for a total torque of 1nm.

For a given linear acceleration the rate of acceleration of the linear radius of the wheel at the force acting point must match the actual linear value, and using simple formulae you can convert this to actual radial acceleration equivalent.

The specific formulae is:

A, (linear, Al from here on out) = 2*Pie*R*RPS = Al/2*pie*r= RPS

RPS = A (radial)/2*Pie = RPS*2*Pie = Ar

That breaks down to Al/2*pie*r = Ar/2*Pie = Al/r = Ar

In this case equal to 1

T=IA so I = T/A so I = 1/1 = 1


If we Change the parameters to 0.5 radius 1kg mass and 1 m/2 of acceleration the numbers fall out as follows:

F=ma = 1*1 - 1n of force

T=Fr = 1*0.5 = 0.5

Radial Acceleration = 2 rads/s

I = T/a = 0.5/2 = 0.25


If we Change the parameters to 2 radius 1kg mass and 1 m/2 of acceleration the numbers fall out as follows:

F=ma = 1*1 - 1n of force

T=Fr = 1*2 = 2

Radial Acceleration = 0.5 rads/s

I = T/a = 2/0.5 = 4



What is being shown is that the equivalent rotational inertia is always equal to Mr^2 in accordance with the normal rotational inertia calculations. So i was right to start with which means the only error was my calculation boo boo, (twice).


It's painfully simple when you see it laid out like that.

So, in short you are in a trebuchet competition at school using a softball and want us to solve this inertia problem for you?

"fictional setting". Yea, no kidding. How stupid do you think we are?

Enjoy Dynamics class. How is Sophomore life treating you...

And NO, I will not run through the math for you.

HINT: Treat the whole system as time stepped inertia in Excel. You should not need any call functions for solving. If you do, something is very wrong. After all it is mgh(PE) turning into radial acceleration. Resisting this will be inertia. I suppose you could go retentive anal and add wind drag...

Key for obtaining maximum distance thrown: WILL require you to play with the release mech for throwing the softball. Quick hint, look no further than how the folks in medieval times built their release mechs. There are even shows on this mech release on the History channel which will show you how to build your equivalent for your softball.

You did not specify if they were allowing ratchet mechanisms which means spring eqns. Which makes this more complicated as then we get into deflection and efficiency in releasing said stored energy.

Anyways... Enjoy Dynamics class and stop lying to us that this is for some "fictional writing".

Relax: i can pointyou to a whole bunch of posts on another forum where i go into more details, but there aren't any real engineers over there, hence why i thought to ask here, we seem to have a few, (i've been an on and off lurker for a while actually). But i know these forum,s have a no-fanfiction clause so i can't talk about them here.

If i was trying to do what you claim i could just use this.

The problem is that works fine for stuff upto pumpkins. Try to throw around 1500 kg rocks and it goes and plays a hissy fit on us producing low confidence results with sometimes stupid output, like 300 m/s velocities).

Relax, why not try to be nice and polite? There is no indication of what you are accusing Carl of, and even if that was what he was doing, so what?

and even if that was what he was doing, so what?

As someone with collage level engineering training i can actually kinda understand this. Saw way too many students who could do it by rote, but couldn't apply it to real world problems. It6 can be really frustrating to see.

To be fair i discovered that excel does have a disabled by default method of handling circular references, you just need some IF arguments to avoid certain conditions that can totally cause the whole thing to fall apart.

The problem is having a college only level education meant i wasn't certain how to handle the counterweight. Given that since i fixed the error in the excel sheet regarding projectile moment of inertia being incorrectly and unintentionally not included the sums have always come out with an appropriate value and assuming my little math proof earlier on the counterweight is correct the spreadsheet should be producing sufficiently accurate values for my purpose. A step by step setup would be preferable and would allow for variable radius cam's. But overall i don't need a spreadsheet of that size and super fine grained accuracy. Just something close enough and who's error possibilities i'm aware of.

Daryl: It is impolite to cheat and frankly downright stupid. Maybe I was too sensitive: I have been asked many, many, many, many times to "help" budding engineers on everything from Trebuchets to ball drops, to bridge design in school competitions. Everything from school projects to international competitions(I have won a couple so why I get asked a ton). Now I will always be willing to POINT them in the correct direction, but having me solve their equations? Hell no. Engineering is all about trade-offs, and the pointing in directions of different INPUTS/OUTPUTS one must consider along with variable materials is what I will always tell them. Sure, I can tell them how to win, did that once to my shame(not that they took my blatant "advice") but that does not help them any.

CARL:

The problem with that program probably revolves around its Kinematics of the sling. Far more likely is that your sling is too long/short or the program has a tension release eqn in it that you violated with the excess weight or some such.

If you want to create your own, uh "accurate" version.

Calculating the rotational velocity at the end of the arm due the falling counterweight is easy. You already showed that. The sling on the other hand has non linear radial position, velocity, and acceleration. This requires kinematics. Effectively this just means lots and lots of high school geometry for position, velocity, and acceleration tied to the definition of a derivative:IE step function. IE Calculus chapter 1 and its base definition. IE everyone used to do this by HAND. Pity those clock makers! Thankfully we now have computers.

This is the main reason you MUST use time stamped iterations. Hope you remember your laws of sine and cosine... Thankfully you only have a 2d kinematics problem making life MUCH much much easier.

You must treat distance, velocity, acceleration in their derivative form for your step function in excel. 2d it is not hard.

Showing this over the internet is impossible. If you can get your hands on a kinematics book. Go for it. A college library should have old kinematics text books. You may have to ask as often old text books are "hidden".

PET PEEVE: All text books should be free electronic versions. Can't wait till someone just writes it and puts them on the web instead of having students paying $150 for a stupid book they will use 3 months and then can't sell them as the "publisher" changes 2 things in the book and calls it "new" and the jack ass professors go along with it as they are lazy and do not want to actually teach.