Re: [math-fun] breaking spaghetti
It occurs to me that the speed of bending may result is varying numbers of breaks. I imagine the breaking stress being nearly uniform over the noodle. When you continuously increase the stress it could occur that the duration of failure is long enough for other points to also fail before enough stress is released to stabilize the remaining noodle sections.
If I were researching this seriously, I would advance on two fronts. First, I would build a robotic spaghetti-bender so that the forces were more reproducible between trials. There are a good fistful of variables in the way you put stress on the noodle: each hand exerts a translational force on the piece of noodle it's gripping, as well as a torque; the robotic jig ought to provide controls for at least some of those variables. Second, it is clear to me that a thousand frames per second is at least an order of magnitude too slow. Everything interesting to this problem happens between two adjacent frames: in one frame, the noodle is in one piece, and in the next, three breaks have occurred and two pieces are spinning away wildly into the air. We need to resolve the breaks into distinct frames to see what order they happen in; it seems likely that rebound from early breaks causes the late ones. On Mon, Nov 24, 2014 at 5:29 PM, Hugh Everett <cche@heverett.net> wrote:
It occurs to me that the speed of bending may result is varying numbers of breaks. I imagine the breaking stress being nearly uniform over the noodle. When you continuously increase the stress it could occur that the duration of failure is long enough for other points to also fail before enough stress is released to stabilize the remaining noodle sections.
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We could investigate all the variables Allan mentions, but to keep things simple we could alternatively just imagine the strand beginning uncompressed between two parallel concave Teflon endpieces that just barely hold it in place: [(-----------)] . Then imagine the endpieces moving toward each other at a constant speed while remaining parallel. The result should essentially depend only on the speed. (Of course, compression at a variable speed could well produce other results.) But in the case of constant-speed compression, I'd guess that for any speed below some threshold speed, pretty much the same thing happens. It would be interesting to examine that case, and what happens in the cases where the constant speed is increased to higher values. --Dan
On Nov 24, 2014, at 3:07 PM, Allan Wechsler <acwacw@gmail.com> wrote:
If I were researching this seriously, I would advance on two fronts. First, I would build a robotic spaghetti-bender so that the forces were more reproducible between trials. There are a good fistful of variables in the way you put stress on the noodle: each hand exerts a translational force on the piece of noodle it's gripping, as well as a torque; the robotic jig ought to provide controls for at least some of those variables. Second, it is clear to me that a thousand frames per second is at least an order of magnitude too slow. Everything interesting to this problem happens between two adjacent frames: in one frame, the noodle is in one piece, and in the next, three breaks have occurred and two pieces are spinning away wildly into the air. We need to resolve the breaks into distinct frames to see what order they happen in; it seems likely that rebound from early breaks causes the late ones.
On Mon, Nov 24, 2014 at 5:29 PM, Hugh Everett <cche@heverett.net> wrote:
It occurs to me that the speed of bending may result is varying numbers of breaks. I imagine the breaking stress being nearly uniform over the noodle. When you continuously increase the stress it could occur that the duration of failure is long enough for other points to also fail before enough stress is released to stabilize the remaining noodle sections.
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This is a good idea. The spaghetto would tend to hang down between the endpieces. I imagine playing mostly with very slow speeds, and measuring the outward force carefully to see if there are any prior hints that the noodle is about to break. I don't know what the state of the art is for very high frame rates, but I understand that at very high rates you can only capture a few hundred frames, at most. So there needs to be a trigger of some sort to start the capture. The actual break feels like it would probably be too late to serve as a good trigger. On Tue, Nov 25, 2014 at 7:52 PM, Dan Asimov <dasimov@earthlink.net> wrote:
We could investigate all the variables Allan mentions, but to keep things simple we could alternatively just imagine the strand beginning uncompressed between two parallel concave Teflon endpieces that just barely hold it in place:
[(-----------)] .
Then imagine the endpieces moving toward each other at a constant speed while remaining parallel. The result should essentially depend only on the speed. (Of course, compression at a variable speed could well produce other results.)
But in the case of constant-speed compression, I'd guess that for any speed below some threshold speed, pretty much the same thing happens. It would be interesting to examine that case, and what happens in the cases where the constant speed is increased to higher values.
--Dan
On Nov 24, 2014, at 3:07 PM, Allan Wechsler <acwacw@gmail.com> wrote:
If I were researching this seriously, I would advance on two fronts. First, I would build a robotic spaghetti-bender so that the forces were more reproducible between trials. There are a good fistful of variables in the way you put stress on the noodle: each hand exerts a translational force on the piece of noodle it's gripping, as well as a torque; the robotic jig ought to provide controls for at least some of those variables. Second, it is clear to me that a thousand frames per second is at least an order of magnitude too slow. Everything interesting to this problem happens between two adjacent frames: in one frame, the noodle is in one piece, and in the next, three breaks have occurred and two pieces are spinning away wildly into the air. We need to resolve the breaks into distinct frames to see what order they happen in; it seems likely that rebound from early breaks causes the late ones.
On Mon, Nov 24, 2014 at 5:29 PM, Hugh Everett <cche@heverett.net> wrote:
It occurs to me that the speed of bending may result is varying numbers of breaks. I imagine the breaking stress being nearly uniform over the noodle. When you continuously increase the stress it could occur that the duration of failure is long enough for other points to also fail before enough stress is released to stabilize the remaining noodle sections.
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participants (3)
-
Allan Wechsler -
Dan Asimov -
Hugh Everett