Counter-Rotating Pairs at 120 — 8x the Force
What if you ran both configurations at once?
Previously
Earlier today I published Three at 120 — three co-rotating pulsed gyro assemblies at 120-degree spacing. The 120-degree symmetry cancelled angular momentum without counter-rotating pairs and focused all force onto a single axis. Clean result: Fy bias of -1.27 N pulsed, dead zero on all other axes.
But the original simulation used counter-rotating pairs. Two assemblies spinning opposite directions, cancelling angular momentum by brute force. That also worked.
The obvious question: what happens when you combine both? Three counter-rotating pairs, each pair at 120-degree spacing. Six assemblies total. Angular momentum cancelled at two levels — locally within each pair, and globally through the triangular symmetry.
The Setup
Forked the triangular sim. Six assemblies instead of three. Each pair shares a position on the triangle, one spinning forward, one spinning backward. Same offset race geometry, same pulse function, same ball count.
The only new parameter is pair separation — how far apart the two assemblies within each pair sit along the radial axis. Adjustable with Left/Right keys, defaulting to 0.3.
Visually, each pair shares a colour — bright for the forward assembly, dim for the reverse. Cyan, magenta, lime. Six sets of balls on six races, all converging on the centre.
The Result
The numbers came in fast and they came in big.
Pulsed (pulse 0.5, 33,609 samples, 672 seconds):
| Axis | Force | Torque | |------|-------|--------| | Fx | 0.00 N | 0.00 N.m | | Fy | +10.49 N | — | | Fz | 0.00 N | 0.00 N.m | | Ty | — | -20.47 N.m |
Constant spin control (pulse 0.0, 13,702 samples, 275 seconds):
| Axis | Force | Torque | |------|-------|--------| | Fx | 0.00 N | 0.00 N.m | | Fy | +0.28 N | — | | Fz | 0.00 N | 0.00 N.m | | Ty | — | -0.10 N.m |
Pulsed-to-constant ratio: 37x on force, clean control confirmation.
The 120-degree symmetry still kills every off-axis component. Fx, Fz, Tx, Tz — all dead zero. Everything concentrated on Fy.
The Comparison
Here's why this matters:
| Configuration | Assemblies | Fy bias (pulsed) | Fy bias (constant) | |---|---|---|---| | Counter-rotating pair | 2 | -3.05 N | ~0 N | | Co-rotating triangle | 3 | -1.27 N | -0.21 N | | Counter-rotating pairs at 120 deg | 6 | +10.49 N | +0.28 N |
The counter-rotating pairs produce 8.3 times the force of the co-rotating triangle. With only twice the mass. If the effect were purely additive — three pairs instead of one — you'd expect roughly 3x the original pair's output, so about 9 N. The actual 10.49 N is in that range, suggesting the forces stack linearly.
But compare to the co-rotating triangle: three assemblies producing 1.27 N, doubled to six assemblies producing 10.49 N. That's not 2x — it's 8.3x. The counter-rotation within each pair amplifies the effect significantly beyond just doubling the mass.
Why Counter-Rotation Amplifies
In the co-rotating triangle, all three assemblies spin the same direction. The pulse omega(t) = omega_base * (1 + pulse * cos(theta)) applies the same speed profile to all of them. The force asymmetry comes from each assembly independently.
In the counter-rotating version, the forward assembly pulses as cos(theta) and the reverse assembly pulses as cos(-theta). At any given moment, one assembly is in its fast phase while the other is in its slow phase. The forces don't cancel — they reinforce, because the offset geometry means the "fast" forces and "slow" forces point in the same direction on the frame even though the assemblies spin opposite ways.
The counter-rotating pair extracts more asymmetry from the same pulse profile than a single assembly can alone.
What I Learned
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Counter-rotation amplifies, it doesn't just add. Two assemblies at the same position spinning opposite directions produce more force bias per unit mass than either alone. The interaction between the opposing speed profiles extracts additional asymmetry.
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The 120-degree symmetry holds perfectly at double the assembly count. Six assemblies, three pairs, all off-axis forces still exactly zero. The geometry scales.
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Linear impulse growth is stable over 11 minutes. 7,051 N.s accumulated at a steady rate of +10.49 N. No sign of convergence, saturation, or drift.
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Pair separation is a new control parameter. The distance between forward and reverse assemblies within each pair affects the torque distribution. Another knob to tune for the physical prototype.
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The A/B control ratio is 37x. Pulsed vs constant on the same geometry gives a definitive answer. This isn't numerical noise.
What's Next
This is the configuration to prototype. Six assemblies, three counter-rotating pairs, 120-degree spacing. The simulation has explored the parameter space — pulse strength, offset angle, pair separation, assembly count, rotation direction. The counter-rotating triangular arrangement is the winner.
Physical build requirements:
- Three motor pairs, each pair driving two races in opposite directions
- Triangular frame at 120-degree spacing
- Adjustable pair separation for tuning
- Coupling medium (surface with anisotropic friction, or water)
The force is there. The geometry is clean. The control confirms it. Time to make it real.
Counter-rotating. Triangular. 10.49 N. Built with Claude Code. Published at indigo-nx.com.