strange question regarding complex shapes such as cones and hemispheres, for research

ineffable500

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Hi mathematics-interested:

I have a question regarding cones, parabolic curves, and hemisphere-type shapes which I am not even sure exactly how to ask. But, I think I can explain in a brief discourse.

I build water electrolyzer cells, aka HHO units, Brown's Gas generators, and a few other names. Usually these are built with flat plates which are held 1/8 inch apart from each other with 1/8 inch spacers between each plate. I would like to build a cell which uses some kind of 3-dimensional shape rather than a flat plate. But, the trick is going to be finding what kind of shape can produce a nested stack where each surface of each shape is exactly 1/8 inch away from the closest point on the shape next to it.

This is my question: what shapes, with what wall thickness (for these will have to be real items, not 2-dimensional hypothetical constructs), has this characteristic where nesting the shapes allows the surface of the lower shape to be exactly the same distance, and specifically 1/8 inch, away from the surface of the upper shape, at all points on its surface, when the shapes are translated apart (from the point at which the identical shapes would occupy exactly the same space were that possible) to the point where they become exactly 1/8 inch apart?

Hemispheres will not work: the lower edge will be closer than 1/8 inch when the top point is 1/8 inch away. Will cones work? Perhaps a cone could work except for the area above the tip of the lower cone--which would be fine because I would remove that area of material for my application anyway. Perhaps a parabolic dish or a parabolic curved sheet/bent sheet? One idea I had was to get flexible plate and stick two opposing edges into slits cut into a box which would cause the material to bend up or down. Each plate would bend in an identical fashion, and if the slits in the box for the edges of the plates were 1/8 inch apart, I would have succeeded in my intention, right?

It's clear to me that hemispheres won't work but I'm not sure what kind of deflection from the out-of-round will produce the qualities I need! I hope that I will be able to have the shapes manufactured, too, without terrible CAD-aided expense. I like the idea of the bent plates for this reason.

Also, I realize I can use hemispheres which share a bottom plane and in which each hemisphere is bigger. I plan to build a cell like this, with 1", 1.5", 2", etc. diameter hemispheres which have a wall thickness of 1/8 inch. However, the limitation in this method is the amount of current (amperage) I can use based upon the surface area of the smallest hemisphere.

Thanks!

with care,
Zarrin Leff
 
Hi mathematics-interested:

I have a question regarding cones, parabolic curves, and hemisphere-type shapes which I am not even sure exactly how to ask. But, I think I can explain in a brief discourse.

I build water electrolyzer cells, aka HHO units, Brown's Gas generators, and a few other names. Usually these are built with flat plates which are held 1/8 inch apart from each other with 1/8 inch spacers between each plate. I would like to build a cell which uses some kind of 3-dimensional shape rather than a flat plate. But, the trick is going to be finding what kind of shape can produce a nested stack where each surface of each shape is exactly 1/8 inch away from the closest point on the shape next to it.

This is my question: what shapes, with what wall thickness (for these will have to be real items, not 2-dimensional hypothetical constructs), has this characteristic where nesting the shapes allows the surface of the lower shape to be exactly the same distance, and specifically 1/8 inch, away from the surface of the upper shape, at all points on its surface, when the shapes are translated apart (from the point at which the identical shapes would occupy exactly the same space were that possible) to the point where they become exactly 1/8 inch apart?

Hemispheres will not work: the lower edge will be closer than 1/8 inch when the top point is 1/8 inch away. Will cones work? Perhaps a cone could work except for the area above the tip of the lower cone--which would be fine because I would remove that area of material for my application anyway. Perhaps a parabolic dish or a parabolic curved sheet/bent sheet? One idea I had was to get flexible plate and stick two opposing edges into slits cut into a box which would cause the material to bend up or down. Each plate would bend in an identical fashion, and if the slits in the box for the edges of the plates were 1/8 inch apart, I would have succeeded in my intention, right?

It's clear to me that hemispheres won't work but I'm not sure what kind of deflection from the out-of-round will produce the qualities I need! I hope that I will be able to have the shapes manufactured, too, without terrible CAD-aided expense. I like the idea of the bent plates for this reason.

Also, I realize I can use hemispheres which share a bottom plane and in which each hemisphere is bigger. I plan to build a cell like this, with 1", 1.5", 2", etc. diameter hemispheres which have a wall thickness of 1/8 inch. However, the limitation in this method is the amount of current (amperage) I can use based upon the surface area of the smallest hemisphere.

Thanks!

with care,
Zarrin Leff

I do not understand that!!

Concentric sets of hemispheres will be constant distance away. However, the surface areas will not be same - thus "density" of flow will not be constant (i.e. two concentric hemispheres do not have equal surface area.)

If you want equal surface area - I do not see any thing other than flat plates. One variation of flat plate could be wavy plates (like S shape)
 
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Well, regarding the nested hemispheres of the same diameter, the ones easily available are .13 inch thickness steel, which is just a hair bigger than 1/8 inch. So, putting one say 5" diameter hemisphere on top of another 5" hemisphere, the bottom edge of the top hemisphere will contact the bottom hemisphere in a circle at the point at which the lower hemisphere's outer diameter is 4.74 inches. But, the top points will not be touching I don't think. As I see it in my mind's eye, unless I have exactly the right ratio of outer/inner diameter of a shape which is close to a hemisphere but not exactly, and this matched to the wall thickness, it won't set correctly because I'm actually putting an inner surface of the top "hemisphere-like shape" with a diameter that is smaller, which means it will ride up high. I don't know how high up the "shoulder" it should ride, or what the shape would be as an off-hemisphere shape, in order to work with a given wall thickness of, say, .13 inches. I was hoping a parabola shape might work, or a hemisphere that was cut off to be only 1/3 of a sphere, or something like that, but I don't know, and I don't even know where to start to try to figure it out theoretically with math!

Thanks for your reply,
regards,
Zarrin

.
 
Well, regarding the nested hemispheres of the same diameter, the ones easily available are .13 inch thickness steel, which is just a hair bigger than 1/8 inch. So, putting one say 5" diameter hemisphere on top of another 5" hemisphere,
regards,
Zarrin

.

No I was thinking about 5" dia hemisphere on top of 4.75" dia hemisphere - concentrically placed.
 
I'm pretty sure cones will work. But I can't tell if any curved surfaces would work.

Cones - as I see it - will give you trouble at the apex. The perpendicular-distance between the sidewalls will not be same as apex-to-apex distance.
 
Subhotosh,

Thanks. I think you are right about the cones. The walls would be a little different than the apex , I think--all those points on the inner surface of the upper cone that were above the tip of the lower cone and also above the point at which a line drawn perpendicularly through the walls of both cones would strike the inner surface of the upper cone after it went through the tip of the lower cone. This latter line being relevant for the reason that the shortest distance between the walls of the upper and lower cone would be measured with this perpendicular distance.

Thus, armed with this knowledge, I think I have found a solution to this problem. I will get a stack of cones with the tip cut off. In addition, I am looking to incorporate the Great Pyramid dimensions into this stack. So, the cones will be 6 inches diameter at the base and 3.8184 inches tall if they went to a full tip. But I will have the tip cut off to leave a, perhaps, 3/8 inch hole. Then, around near the base will be an o-ring, and again at the top, inside of the hole, will be another o-ring with the same thickness. Thus, all the area of walls inbetween these o-rings will be the same distance apart, and I will have a workable area there which will be sealed so that it will hold gas and water. Then, through some other judicions designs and thinking I did, I will have a way, via holes and drilling and sealing the top hole of the bottom and top cones of the stack, to have a flow-through of water and gas through each cell in the cone stack array.

Thanks for your feedback and consideration, helping me to discover some things! Sometimes it just takes a little discussion for one to discover. Carl Jung said essentially the same thing when he was doing character analysis and psychotherapy: the most "magical and productive things happened when he as the therapist just listened and "got out of the way!"

with care,
Zarrin Leff
 
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