I agree it will have an X shaped region of zero field.
I think it will be more of a concave sided diamond than an X.
tombo wrote:I disagree that zero fields are fine.
If someone can point out the distinction in overall effect between a hole (cusp) due to 1 field (point cusp), due to two fields (line cusp), due to three fields (quasi-line, or maybe better put "terminating" line cusp) or due to four fields (funny cusp) I would greatly appreciate it. Until then, I maintain that a hole is a hole is a hole, and the smaller the better for all of them.
tombo wrote:DrB never drew it this way to my knowledge. [Although, I vaguely remember that one of the enclosed machines had vertex coils and did not work very well for reasons that Art Carlson was very eloquent and adamant about a few months back.]
DrB said it didn't work because of the metal in the way. Did I mis-read him?
When I look at it I see 48 vertexes, each with an odd number (3) of faces.
First, MARVELOUS image. I wish you had done it with the bowed coils, but I agree that your bottom image is what DrB proposed. Beautiful!
As to 48 vertices, that is interesting because I see 12 vertices of even number (4). I can also stretch it to see 48 with even number (2), but as I say, it is a stretch.
tombo wrote:Of interest there are irreconcilable geometrical issues with the shape.
If the hole is square then the straight to curved transitions cannot be in the same place for the two curves. If they are the same then the hole is very much longer than it is wide. I tried to make that work for hours.
Hmm. I never anticipated the hole to be square. I find that the centers of curvatures of the "round corners" will be situated ~2.5 and 3.5 coil x-section diameters away from the true vertex, resulting in a hole that is ~3 times as tall as wide. This results from taking lines normal to the incoming and outgoing arms of the "square" coil (when using the bowed, spherical layup in your MPG varient). Of course, the further the centers of rotation are away from the vertex, the more squarish the rectangle becomes.
If you would take your spherical MPG and simply copy and past with 90 degree rotations about the north pole, you will see it come out naturally.
Without the crossovers there are no zero field points:
True, but there are quasi-line cusps (maybe even true line cusps) that stretch from virtual point cusp to virtual point cusp. The void resulting from these long cusps seems much larger, and therefore worse at keeping relative density, than a small point like void.
tombo wrote:I believe that DrB referred to square plan form, round cross section coils like these. (Although maybe closer to touching than shown in this plot.)
I agree completely, but in order to hold these together there must either be a forest of supports outside the MaGrid, or nubs between the coils. My slight modification of his plan has coils (instead of nubs) between the coils and ALL
metal is protected. It also provides for adequate cooling, etc.
tombo wrote:IMO the funny cusp is an artifact of approximating the ideal infinitely sharp vertex points with the long rounded almost kissing regions of round coils like in WB6.
Actually, the funny cusp is what you get with my configuration (4 fields meeting together) and a quasi-line cusp is what the WB6 gives as the approximation. The WB6 is best approximated by 24 vertices of odd number (3).
tombo wrote:I further believe that the square plan form reduces it greatly.
This I agree with completely because it greatly shrinks the distance between each pair of the 24 three- field vertices, making them meld into effectively 12 four-field vertices.
tombo wrote:The sharper the bends can be made, the smaller the funny cusp becomes.
Abso-dang-lutely! (or more acurately, the less linear, more funny the cusp becomes.
tombo wrote:It reduces in size to approximately what it would be in a machine with round coils the same radius and spacing as the radius of the curved corners of the square coils.
Gotcha, I think.
As I said, BEAUTIFUL!!! No can you do the bowed MPG as I described? Should be fairly easy.