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This is just an idea off the top of my head: You could produce a maximum moment of inertia, based on the assumption that all the weight is on an infinitely thin band at the circumference of the disc. It wouldnt be perfect but it would be better than no measurement at all.
The only other way that you could measure a disks stored energy would be to measure the work required to accelerate the disk to a fixed velocity over a fixed time. Havent thought this through yet, but once a formula is thought out and equipment set up, measuring a new disk would simply be like balancing a wheel.
Not saying its easier, but should be more accurate, and require only the initial effort as opposed to having to take each disk from scratch, and as you say calculating each change of shape/part as you would have to. This may be easier for one or two, but over time still being laborious.
Dont have all the answers.
Roger
MOI of a disc rotating about its centre point = 1/2 x Mr^2
MOI of a bar rotating about one end = 1/3 Ml^2
where
M = Total Mass
r = radius
l = length
If the mass is not rotating about its centre of gravity then you have to use the parallel axis theorem to calculate the additional MOI. This is
(Total MOI) = (MOI about centre of gravity) + (Area of object) x (distance of axle from centre of gravity).
so for vortexs disc if modeled as a large disc (200mm) with a smaller disc cut out of the middle (140mm?) and a bar put across (width 30mm) then total x-sectional area = 0.068 m^2
mass per unit area = 43.9 kg/m^2
Total MOI = 0.03 kgm^2
Total KE = 3.3 KJ
Similarly for strip:
MOI = 0.095 (seems a bit large)
KE = 6.4 KJ
Ive just done these in a rush and am pretty sure one of them is wrong .If Anyone wants me to explain my methods or any thing then just post your e-mail or e-mail me and i will send you the full calculations
Joe Townsend
Also other ways to calculate moment of inertia are
1: to take the disk off, place it on a rotational pendulum and calculate the difference in period.
2: place the disc and axle on two bars at a slight decline. By timing the disc rolling measured distance at a measured angle you can calculate the MOI. If anyone wants a full explanation of these method please feel free to e-mail me and I will dig out my 2nd year lab books.
Joe Townsend
I found this,
http://homepages.which.net/~paul.hills/Spinningdisks/Disks.htmlhttp://homepages.which.net/~paul.hil...sks/Disks.html
I think that covers it all!
Many thanks to you Joseph for reinforcing the difference in KE between Vortex and strip (though not quite as extreme as I got - But probably much more acurately) I feel vindicated.
Geoff - Fantastic find - Everything needed, and by your component method.
Ed - Hope you are not too dissapointed in the KE produced by Vortex - Vortex speaks for itself. (compliment).
Roger.
Im impressed with the erudition of the above posts, but the purpose of this exercise must be to define a fairly simple limit for the KE of a spinner that is a bit cleverer than Mentorns 1500rpm rule. The limit needs to be crude enough to be checkable. That rules out any consideration of weight distribution. Here is how I would do it for heavyweights:-
Spinner weight(kg) * (Radius(m) * Speed(RPM)) squared 5,000,000
Then we get into the more interesting argument about whether 5 million is too much!
Jeremy
while finishing my final degree project.... which was to design a new robot arena, i went through all of the sums.
Ill have to pop into uni and pick up the report, but as far as i can remember it is very difficult to work out the ke,
You have to know what the time taken for the disc at full speed to decelerate to nothing in Milliseconds is )
Then you put that into a formula with the other values and hey presto, you have a value.
They do the same for crash tests and if you look in the books, they use experimental method to determine the time.
I will look it out.
jonno
That website says it perfectly, good find geoff. I think it may start to get misleading though if people start to talk (boast) about their spinners in terms of KJ of energy, to me it means very little as strip has far more KJ than vortex but if is far less destructive (from what ive seen). Does anyone know a good way to measure a discs effectiveness numerically?
Guys,
If you thought that section was cool...Just check out the rest of that site!! :)
http://homepages.which.net/~paul.hills/http://homepages.which.net/~paul.hills/