The following computations are done with a 0.6-T field, in order to be conservative or allow the use of cheaper magnets.
Printed circuit disks are made of two networks, each made of 24 radial wires (shown in red and green in the previous figures), connected as “serpentines.” The series resistance of the wires is assumed to be the resistance of the radial axes, as the circular connections can be designed sufficiently thick for essentially zero resistance. The cross section of the radial wires is 2 mm2 (4 mm large x 0.5-mm thick) in the center part of the disk, up to 8 mm2 (16 mm x 0.5 mm) in the outer part.
The twin networks are powered with 90° phase difference, as shown below, in order to maintain the motor torque during the switching time of the current on the complementary phase.
The length of the 24 wires is 24 * 15 cm = 3.6m. The rotation force on these wires is:
F = B * I * l = 0.6 * 3.6 * I = 2.16 * I
This force is applied in the middle of the wires, at a distance from the axis of 12.5 cm. The motor torque per stack is
Γ = F * r = 2.16 * 0.125 * I = 0.27 * I
The total motor torque generated by the 12 stacks is:
Γtot = 12 * 0.27 * I = 3.24 * I
A 30A current generates a mechanical torque of 97.2 Nm.
A vehicle driven by four wheels has a total driving torque of 390 Nm, when 30A is flowing through all stacks. This corresponds to the driving torque of existing high-performance cars.
A 15-cm copper wire, with a cross section varying between 2 mm2
and 8 mm2
has a resistance of 6 µΩ. Assuming that interconnections between radial wires have a negligible resistance, the total resistance of a printed circuit disk wire is 24 * 6 = 0.145 mΩ.
A 30A current flowing through this wire generates a 4.5 mV voltage drop, and 130 mW power dissipation. The total power dissipation for the 12 stacks of a wheel, when 30A are flowing in all disks is 1.6W.
All wires of all stacks are connected to the command circuitry, located close to the axle. Each wire is connected to an electronic switch, with a series resistance of 0.2 Ω (conservative number, in order to take into account unexpected parasitic resistances). This switch represents the major contribution in the estimated total resistance of the electric circuit, and generates most of the joule losses (carefull selection of these MOS transistors has a direct impact on the energetic yield of the system).