# Looking for a sheet that resists

Discussion in 'Mathematics and Physics' started by jasonbe, Oct 30, 2008.

1. ### dknguyenWell-Known Member

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Yes, I also spent a great deal of effort and time explaining this to him in not one but TWO previous thread. It's just one more of the many questions where people have gone to great lengths to give him the answer and he just ignores it and asks the question again.

Last edited: Jul 13, 2009
2. ### jasonbeNew Member

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Sorry, the picture does look familiar. For the most part, along each individual path, does the current not change? Perhaps I should know this, but I just want to confirm it.

What shape defines the paths?

3. ### jasonbeNew Member

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This question was relevant to my previous threads. One reason is that I think that it can be discussed independently.

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5. ### jasonbeNew Member

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At Sheet resistance - Wikipedia, the free encyclopedia R is defined by the formula R = pl/A = pL/(Wt). Do you know of any formulas that define R in terms of resistivity, a current gradient, area, and a curve? I'm guessing according to Tesla23's picture that this curve might be defined as bunch of infinitesimal adjacent perpendiculars to the electric field lines. However, if this is so - there may be three or four types of curves - corresponding to when these lines are diverging, converging, and (a) combination(s) of when these lines are diverging and converging. And, my best guess is that all of these curves have to be added together in a different formula to calculate the total resistance between the source and the sink. Unless a distance gradient could be used. I don't know. But, if anyone knows what I am getting at, would you please explain to me how and why the resistance could be calculated between the source and the sink?

Last edited: Jul 13, 2009
6. ### MrAlWell-Known MemberMost Helpful Member

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Hi,

You know you could construct a discreet version of the sheet with resistors that
are all of equal value and connected in a grid pattern. You could then try to
find generalizations about what the resistance is between any two points.

Although you would want to use many more resistors, a very very rough approximation
would be four resistors forming a single square, where there are nodes at the corners.
Across any of the sides we would measure R in parallel with 3*R which equals (0.75*R), but across
any two corners diagonally we would measure 2*R in parallel with 2*R, which is
of course simply R. You could then generalize for positions x and y.

With more resistors you would find that the approximation becomes better and better,
and when R approaches zero ohms the solution approaches the exact solution.

I believe that for the application you are looking at it becomes very difficult to detect
multiple pieces even when they can inject their own frequency. For one such object
i think it would be a probable solution to detecting position, but for multiple objects
it becomes very difficult.

You might instead try using a grid of whatever resolution you need. You usually dont
need infinitesimal resolution anyway for detecting game pieces.

Alternately, maybe high frequency sound communication where the piece sends out its own id signal,

The resistive sheet method probably wont work for multiple pieces anyway unless there is something
unique about each one because you might end up with the position where there are pieces getting
in the way of other pieces similar to what would happen with cameras oriented on the right side
and upper side of the board for example. If one piece gets in the way of another piece along any
one axis, it works ok because you always have the other axis, but if both paths become obscured
you can not see the inside piece.

Last edited: Jul 13, 2009

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8. ### jasonbeNew Member

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I could have it set up so that signals resulting in continuous measurements were timed. Though I don't plan on making a discrete model, I'm thinking about your design.

9. ### jasonbeNew Member

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I don't remember having asked for it.

10. ### MrAlWell-Known MemberMost Helpful Member

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Hi,

Yes the discreet model is for developing the math for the real sheet.

I guess you could use timed signals, but then how would you have
each pieces time sync'ed to the other pieces?
Are you prepared to make each piece active...that is, having it's own
internal power source?
That is a main question to be answered: active or passive pieces?

Last edited: Jul 13, 2009
11. ### dknguyenWell-Known Member

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Suprise surpise. Rephrasing the question does not change the question. This time you said "current paths", the first time you said "current distributions".

We already went over this with him in the past 2 threads. He is not willing. He wants multiple passive pieces on a single resistive layer which is the whole problem and he's refused alternatives and has been running us around in circles.

Last edited: Jul 14, 2009
12. ### MrAlWell-Known MemberMost Helpful Member

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Hi DK,

Oh i see, well he should know then that that will not work, at least not
in the real world. There at least has to be some restrictions on the
positioning of the pieces. Some arrangements of pieces will not allow
2d detection, and still other arrangements will require extreme measurement
resolutions which would probably get lost in the noise of the uncertainty
of the resistive gradients of the sheet. Just how perfect a sheet can
you get anyway?
Take for example a 9 piece arrangement in a pattern similar to boxes
in a tic tac toe game. How to detect the center piece? Yes you can
alter the angles of measurements, but then that brings up the question of
how small the pieces are, and what if they are some day placed in the
same arrangement as the tic tac toe board but on a different angle?
You'd have to use multiple scanning angles, which would mean multiple
wires attached to the sheet.

Do yourself a favor and move to video scanning now, you'll save time.
Either that or you'll have to move to active pieces.

Last edited: Jul 14, 2009
13. ### jasonbeNew Member

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Your model seems even more interesting considering this use. So, the squares would represent units of distance or area through which current paths travel? And, a function of the resistors along each path would represent an amount of resistance that was related to the number of squares and therefore vary according to distance - as resistance would do if the material causing it had a uniform consistency? And then, if one made the model really large - as in a lot of pieces and not large pieces, maybe one could use Kirchhoff's laws to determine if and what resistors with different values could be substituted for each group of resistors in the original model. By only substituting groups of resistors in the original model - if this is what you meant or what it could mean, and not substituting any resistors already substituted; one could compare the different values of the resistors substituted. However, I'm not certain if a parallel circuit of resistors in series - the number of resistors in series corresponding to the length of continuous paths on the sheet, would be more representative. Still, it does seem to me that using resistors with equal values in the original model - before substituting resistors in the original model for resistors having a different value, would accurately represent equal units of distance. One thing that I've thought about - even though I may not be able to understand it in detail, is if the formula R = pL/A could be expanded to include a variable describing how much the wire was curved. I'm not sure if a formula describing the continuous paths on a sheet would have to take into consideration the curvature of the paths in addition to their length. However, I am curious about what defines their shape.

The pieces would not have to be synchronized with the other pieces - only with a unit that processed the signals as they were sent at different intervals.

At this time I'm thinking that the pieces will be passive.

Last edited: Jul 14, 2009
14. ### jasonbeNew Member

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The only equations that I can remember people posting - after searching through posts, are Ohm's law, two about sheet resistance, and - if I remeber correctly, a referece to Maxwell's equations. Ohm's law won't work by itself because resistance is a function of distance that I haven't been able to determine. I can't rely on the ones about sheet resistance because I haven't been able to determine what L means. Even if I knew if one of Maxwell's equations could work, I don't have enough information about the boundary and field lines to use any equations. If I were able to determine E, could I just muliply E by the area within a boundary defined by where the point electrical contacts effected magnetic field lines? The magnetic flux in the equation varies as a funtion of time. In my sheet, they seem as though they would vary as a function of distance. I could still use help with what the shape of the paths are in the model of the sheet - and how these shapes vary with different characteristics of materials.

15. ### jasonbeNew Member

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I see that three problems - some of which have been reiterated, have been presented: 1) detecting multiple pieces, 2) detecting the pieces at mulitple angles with multiple wires, and 3) the material not being of uniform composition and symmetrical.

The first and second problems are related. If I can detect one game piece, then I can detect two game pieces by opening part of the circuit to each piece at different times. This will allow more than two game pieces if done accordingly. This, however, may result in pieces equal distant from a contact on the sheet giving the same readings. If there were two contacts on the sheet - which I don't mind adding, the position of each game piece could be narrowed down - as far as I can tell, to two locations. To prevent two signals associated with the contacts on the sheet from interfering with each other, part of the circuit to each of the wires - of which these contacts could be comprised, could be opened at different times. In the same way, a third contact on the sheet could be used to pinpoint the locations of game pieces. In this way, to measure the location of two game pieces with three contacts on the sheet would require opening and closing the circuit in such a way that at any one time only one contact on the sheet and only one connection to a game piece would be part of the circuit that was closed - and the other contacts on the sheet and wires to the game pieces would be part of the open part of the circuit at that same time.

I don't mind experimenting with a sheet that may be imperfect.

Last edited: Jul 14, 2009