Hit and miss counter between a surface and a stick

Hello \

I am brainstorming about a project that involves a statistical count to calculate the number pi. The problem has a flat surface with very thin parallel lines on it separated a distance "s" from each-other. I now release a matchstick like piece on this surface that also has length "s". All I need to be able to do is to detect a hit if the matchstick is in contact with one of the lines on this surface. Dimension wise the distance s ~=2cm and the surface is a 10cmx10cm.

I am open to any suggestions from image processing to capacitor/resistance sensoring

To give it a little more twist. This whole process "could" also happen inside a water tank.

I d appreciate any help/ pointers on this.

http://en.wikipedia.org/wiki/Pi#Probability_and_statistics

Conductive paint and offcuts of piano wire? The idea would be that each ‘line’ consists of a thin gap in the paint which divides the overall area into several parallel areas. If the ‘stick’ intersects a ‘line’ then the areas on each side of the line would become connected together, which would be easy enough to detect electrically.

I assume that since you’re looking for statistical accuracy the sensing mechanism must be reasonably accurate and must not influence where the ‘sticks’ fall.

I guess you will want to take lots of samples. Do you have some scheme in mind for dropping and recovering the ‘sticks’?

PeterH:
Conductive paint and offcuts of piano wire? The idea would be that each ‘line’ consists of a thin gap in the paint which divides the overall area into several parallel areas. If the ‘stick’ intersects a ‘line’ then the areas on each side of the line would become connected together, which would be easy enough to detect electrically.

Possibly easier, and certainly cheaper, than conductive paint would be to etch a piece of PCB with the required lines.

The problem with conducting lines, however made, is that they won't register a miss.

Does the OP plan to drop the "matches" one at a time or several at the same time, and if so, how many?

...R

Thank you for getting back to me. I really like the "zoning" idea. I ll start doing some testings with different mediums.

Robin2: The problem with conducting lines, however made, is that they won't register a miss. Does the OP plan to drop the "matches" one at a time or several at the same time, and if so, how many?

Robin each trials will always involve a single drop. If its not hit then its a miss. however the accuracy part is very important as you mentioned. I am not sure how it will show its effect as the number of trials get bigger and bigger.

I have a few ideas about the trial repeating it self in pure randomness but honestly the more I think about the more I feel stuck within a pseudorandom boundary.

The idea is not to have an operator directly dumping the stick. Rather the procedure should have a repeat option "automode". Here are a few ideas:

a.Applied Electromagnetic field: to lift the stick up and randomly through it around in the box. b.Air bubbles: have the box filled with water and generate random bubbles coming out from the bottom to lift the stick randomly. c.Magnetic stirrer: again filled with water cause turbulence to through the stick around randomly.

Again from statistical point of view I will never get a pure random trial... Any suggestions is of course more than welcome

It may be useful if you describe what the apparatus is intended to achieve or demonstrate. I'm not a mathematician and I have no idea why you mentioned PI.

I can't conceive of a mechanical way of dropping the stick without feeding the dropper with pseudo-random numbers which (I presume) would defeat the object of the exercise.

Does it have to involve falling sticks or, for example, could it be done by directly detecting or counting bubbles or something else that "might" be more random? What about the location of raindrops on a plate? Or the intervals between them hitting a target?

...R

If you designed the landing area to be the bottom of a cylindrical chamber then you could physically shake the container at the start of each test to generate a new random landing position. Envisaging something a few inches across, it would be easy enough to automate the shaking if you didn't want to do it manually.

I’ve been thinking more about this …

It seems to me that it is impossible to design a machine that will produce random results although you could build pseudo random behaviour into it - such as shaking or moving part of the apparatus.

If I were designing the project so that a human dropped the stick (I would only have one) I would instruct her or him to drop it with the greatest repeated accuracy they could achieve and as fast as they could do it. Then there seems a possibility that the inevitable small variations will be random, or at least subconscious.

I think you may be able to apply the same logic to a machine. If you designed an incredibly precise machine and measured the results with extreme precision you would probably find a random variation due to the tiny effects of molecular disturbances. But such a machine would cost £100,000 +.

I suspect the problem with a less precise machine (I.e. an affordable machine) is to distinguish between its normal non-random (but perhaps very confusing) cycle of behaviour and the truly random variations in that cycle. I wonder if you carried out batches of (say) 1000 tests and looked for variations between the batches would that variation be random?

The best I can think of for a simple machine is one which drops the sticks on their end so that they bounce before they land on the stripes. But even then you would need to do a lot of tests to check whether there is a repeating non-random pattern. I’m not sure whether randomness would be improved by using the same stick all the time or several or a large number of sticks.

Interesting problem.

…R

Think of an old-fashioned pinball machine, where the ball randomly bounces about on several rows of pins before dropping into a cup. If you can arrange several springy pins (each of different 'springyness') in your drop zone that the stick will hit on its way down, it will introduce randomness. Maybe you could use different grades of piano wire for these. The pins will need to be further apart than the length of the stick, so that the stick doesn't get trapped part of the way down.

Why not use a 10x10 board, use a bottom layer piece of single wire (wish i could doodle here) to make a vertical mesh (side a of switch) & a top layer with individual horizontal strands (sides b of switch) each to a separate input, so when object hits top wire (b) it comes into contact with (a) and sends (true) to input.