Falling Chain

[ken_roberts]

Yesterday I ran across a really neat paper, about the velocity and weight of a chain which is falling onto a scale. Now you might think it is obvious, the chain falls at the free fall rate due to gravity, but not so - it falls faster! Moreover, the weight on the scale is more than prior theory predicts

Comments

[torpidai]

Sorry didn't get the pdf yet, trying to sort out my back-ups before Doze 7 trial "times out"

However, Hamm and Geminard's experiment found that with their particular chain, the force was running more like 5.5*w(t), and the top of the chain was correspondingly falling faster than free fall

I wonder what the sample size was, and myself I'd suggest that as it's a chain, rather than a rope, with the random ways a chain could fall upon itself, wouldn't the extra speed be down to the "Whip effect"? I'm very sure that this could be easily tested for by having the chain land in a "Former" rather than (I assume) they would have used a flat plate-load cell rather than a scale? If they did similar to what you've described in a former that "Folds" the chain, The whip effect would be more obvious at or just after the folds, (I'd assume) no monies to try it :) I'll read the paper when I get a moment.

[ken_roberts]

Yes, it was a load cell, not a scale. That "scale" was my term. Actually, I'm not clear on the distinction between load cell and scale. The scale I have for lab measurements is just a load cell in a physical and electonic wrapper that adjusts for desired range as I understand it. But I know nothing per se about load cells

[torpidai]

if the chain falls on a hard surface, the individual balls cause impacts that make the weight reading very noisy.Yes, My bad and probably explains why I failed additional science GSCE miserably, I read "Chain" and automaticaly assumed Motorcycle/bicycle type chain ie only flexes significantly through one plane... I must read this paper soon

[torpidai]

The 2005 paper by Geminard, and others, discusses the whip effect, on the falling of a chain which is tethered in a U shape, and then one side of the U is cut loose to drop.

Sounds like you get to read all the fun stuff, For the U shape and testing for the "whip effect" (Which btw I just assumed existed, didn't believe people were researching it) I'd be dropping the u shaped chain on to raised bars, and table edges(Just measuring the end of chain w/o the table top support, though other end retention could make for an interesting engineering solution)

As for the Garden hose/rope... I'd assume less of a whip effect due to lower mass and lower flexibility, It's also be harder to test in the "Drop in differing densities of oil" I'd have moved the chain experiment on to, could make for a messy rope or a good candle though.

[ken_roberts]

The LIDAR is a neat idea. It might be cheaper to get a high speed camera and video the falling objects against a scale.

I read another paper yesterday, in which the authors started out dropping a styrofoam ball over a balcony and using a stopwatch to time its fall against the profile of a set of stair steps. At least that was what led them to their observation - later verified by using better equipment - that the ball's rate of fall from rest first speeds up, then slows down. They believe the effect is due to a fluid dynamics retardation, as the ball ends up pulling a "street" of vortices behind it, but those vortices do not form until it gets up some speed. So there is a period when the ball is falling faster than its terminal velocity. Their paper uses a digital video camera taking frames at 1/2000th second.

Your suggestion of dropping the chain to hit raised bars and table edges is an excellent idea.

ttyl - the week's errands etc need tending to!

3rd time lucky?

[torpidai]

Grr, I must get an LJ-client, IE seems to "Lose" posts if net connection interupted :S

Anyhaps, Lidar can be made real cheap from parts mostly easily obtainable from other peoples junk.

as for the styrofoam ball travelling faster than terminal velocity at some point (I'd actually assume that this would be just prior to it "Settling down and balancing to its final speed", seems pretty reasonable...

You say "Vortices", I'll assume that's the posh term for "eddie currents", or low pressure areas, thought to be caused by drag? I'd suggest that they take time to form so between the object forming them and their effects being able to "Work" to suck the object back to a stable speed... rather like a steam centrifugal regulator (or any mechanical regulator I guess)

I'd suggest the high speed camera should be used and the ball dropped in a large smoke-filled cylinder to test for this.

Your suggestion of dropping the chain to hit raised bars and table edges is an excellent idea.It was Just a thought, I'm so cynical that often, the next

Re: 3rd time lucky?

[ken_roberts]

Ah - still learning how to use LJ - yes, I see why you would not have gotten notification of my reply to your comment, as it was not known as such to LJ. I've been out-denting to deal with the excessive in-denting, but will try in future to be sure to reply to something by the person I'm communicating with

Re: 3rd time lucky?

[torpidai]

So, how would you go about making something to do Lidar? You're much more electronic capable than me, but I do have a soldering iron. I priced a high-speed camera, about $250-300 Cdn (that's maybe 200 in SI currency units??) which is a bit steep for just an experiment.

Ah, here again, I'm all very good at the theory ;), and after I've collected the parts for my 3d printer (I'm far too tight to spend the amounts wanted for the reprap mendel ;) Lidar is certainly something I was intent on trying, but...

I'd begin with an old computer (They fall on my lap for free these days, wifeies going spare ;)) then hook up an opto-isolator bank to the printer port (Though I'm presently also considering using a PIC18F4550 IC to run all through USB, like the stepper motor control Here but we'll see) to get a simple 8 i/o interface

Doh... and problem solved, you'll need your calculator :)

[torpidai]

Finaly started to read about the chain experiment, just as soon as it dawned on me, no need to download PDF's anymore :S

anyhaps... For example, consider a chain attached by its two
ends at the same height and separated horizontally by a certain distance [see Fig. 1(b)]. As
one of the ends is released the acceleration of the chain tip is greater than g, the acceleration
due to gravity.2-4Why is this any great surprise? as one end of the chain is "Fixed" the friction will never be equal in all links of the chain, (even a greased bicycle chain as I've previously suggested I'd use for such experiments.) but anyhaps, the rate of fall, I'd suggest, due to gravity, will, on links nearer the fixed end, be "wasted" on neglible heat due to friction of the links, the chain itself will be "trying", initialy to fall downwards, through a line plotted directly through it's centre f gravity (One would assume this would be the center of the chain) but no matter what type of release mechanism used (even electro-magnetic) there will be some friction