## Joule Heating and Ampère’s force law

30 11 2008

I’ve completed a first attempt at coding calculations for Joule Heating and Ampère’s force law. Joule Heating tells us how hot the copper coil will get when we pass a currant through it. Ampère’s force law tells us the mechanical force the coils exert on the chassis. No idea if these calculations are correct, going to review them with someone who knows better.  A shout out to ruby-units, this rubygem makes working with physical units very easy. Here is the source code for the calculations

Here are the calculations for the current dimentions:

• wraps: 225
• torus_tube_wall_thickness: 4.998 mm

Joule Heating

• drive_amps: 2000 A
• coil_length: 116507 mm
• specific_heat_of_copper: 24.44 J/mol*degK
• atomic_weight_of_copper: 63.546 g/mol
• coil_weight_in_moles: 53.9277 mol
• coil_weight: 3426.89 g
• wire_resistance: 5.21096e-06 Ohm/mm
• coil_resistance: 0.607114 Ohm
• joule_heating: 1842.54 degK

Ampère’s force law. I simplified the model. I’m calculating the force between two coils at a distance equal to the torus_midplane_radius.

• magnetic_constant: 1.25664e-06 N/A^2
• magnetic_force_constant: 2e-07 N/A^2
• seperation_of_wires: 0.192693 m
• coil_force_per_meter: 4.15167 N/m
• coil_force: 483.7 N

## Bugs

23 11 2008

This project has the best bugs. What other projects produces Dali-esce deconstructionist works of art when you fuck up your code?

soft deconstruction with baked beans:

## New Calculations

23 11 2008

Based on the new coil winding calculations, I am going to slim down the coils to hit a target of ~200 wraps. Now the coils appear to be proportioned like the coils on the WB6. Here is what the adjustment looks like:

• coil_length: 116,309.299858263 mm
• wraps: 225
• torus_tube_wall_thickness: 4.998 mm

Next we will calculate Forces_between_two_magnetic_dipoles, and Power_dissipation of the coils in the form of heat. This will give us some idea of the tensile strength and temperature envelope of the device.

21 11 2008

## Coil Winder

16 11 2008

I’m working on a computer controlled coil winder. I’ve started by using the midpoint circle algorithm to rasterize a circle. Each digit represents a wrap of 22 gauge wire inside a torus with a cross section about the size of a US quarter:

Here is an updated version. The wire is a more realistic 12 gauge. I knocked out the corners, so it’s true only where the coil should be. Now it’s much easier to iterate over. This coil would have 421 turns. With some additional code, I can now calculate the actual length of wire necessary for the coil, and in this case it comes out to ~200 meters! With this new information, I will have to adjust the model. I want to shoot for the same wire gauge and number of wraps as WB6.

Here we have the design for the bobbins. They split down the middle so you can remove the finished coil:

## Progress

16 11 2008

This iteration of the design is nearly ready for rapid prototyping. The chassis walls are thicker, and there is more room for the coils. Also the joints are hollow now, so the coils can be wired together. Specs:

• torus_tube_wall_thickness: 5.236 mm

Here is the corresponding array of 12 lids:

## Open Source

13 11 2008

Unless specified otherwise, all intellectual property generated by this project will be open sourced under the MIT license.

The decawell source code is available on github.

## NYC RESISTER

13 11 2008

Last night I attended NYC Resister for the first time… wow. Really impressive. Talented, well equipped, and fun. In 5 hours I went form zero knowledge to a working computer controlled stepper motor using the reprap electrical hardware. I can’t understate how much more productive and fun it is working with like minded individuals.

## Success

9 11 2008

Now we have the completed polywell shape, with connectors:

Now we can export to an STL file, and produce our first physical object (in plastic to begin with).

## New Approach

8 11 2008

I have successfully calculated the icosahedron inside the dodecahedron using an a simple formula and some ugly brute force.

Here is how I did this:

Starting with the vertices of a unit dodecahedron, I find the midpoint of each pentagon in the dodecahedron which defines the icosahedron. Given the vertices of each pentagon, you can easy find the midpoint by averaging the points in the pentagon. EASY!

What’s not as easy is grouping the vertices of the dodecahedron into pentagon faces. I used some ugly brute force to find this:

I tested every combination of 5 vertices to find the ones farthest from the center. These vertices define the related icosahedron.

Here we see the tori defined by the icosahedron nested inside the vertices of the dodecahedron:

Now we can just solve for the midpoint of each edge of the dodecahedron. Here are the edges: