“Tiny Orbo replication” 170% efficient

[Edit: See Holy grail tiny orbo replication to replicate.]

[2010/2/11 update: See "Tiny orbo replication 2" major update]

Today I took more detailed measurements to obtain the efficiency of my “tiny Orbo replication.”  Once again it was well over 100% efficient. My “tiny Orbo replication” has changed since the last measurements. The toroid was rotated 180 degrees around so that there are no wires directly facing the magnets. Also, the voltage was low, just 0.36 volts. Furthermore, I moved the toroid closer the magnets, so the inductance is different. The following math and results excludes joule heating from electrical wire resistance, as the goal is to see if there is any excess energy:

General info
Revolutions per second: 26.5 rps (1590 rpm)

Pulses per second: 53.0 pulses/s
Peak voltage pulse across coil: 0.36 V
Peak current pulse through coil: 1.26 A
Inductance of coil during pulse: 60 uH
Power input into inductance: 0.5 * 60 uH * 1.26² A * 53.0 pulses/s = 2.52 mW. Note, inductance was linear in this range. [2010/2/11 update: Nearly all of this inductance energy can be captured back. See "Tiny orbo replication 2" major update]

Deceleration control test:
Time duration: 0.33 s
Starting rps: 27.6 rps
Ending rps: 24.7 rps
Deceleration rate: (27.6 rps – 24.7 rps) / 0.33 s = 8.79 rps/s
Calculated rps from 26.5 rps in 0.1 s = (26.5 rps – 8.79 rps/s * 0.1 s) = 25.6 rps

NdFeB magnets
Quantity: 2
Density: 7400 kg/m³
Length: 0.0033 m
Radius: 0.0028 m
Total volume: [(pi * 0.0028² m) * 0.0033 m] * 2 = 1.63e-7 m³
Total mass: 7400 kg/m3 * [(pi * 0.0028² m) * 0.0033 m] * 2 = 1.20e-3 kg
Average distance from center of rotation: 0.016 m
Average velocity @ 26.5 rps: (2 * pi * 0.016 m) * 26.5 Hz = 2.66 m/s
Kinetic Energy @ 26.5 Hz: 0.5 * 1.20e-3 kg * 2.66² m/s = 4.25 mJ
Average velocity @ 25.6 Hz: (2 * pi * 0.016 m) * 25.6 Hz = 2.57 m/s
Kinetic Energy @ 25.6 Hz: 0.5 * 1.2e-3 kg * 2.⁵⁷² m/s = 3.96 mJ
Deceleration energy loss in 0.1 seconds: 4.25 mJ – 3.96 mJ = 0.290 mJ
Power output from friction @ 26.5 rps: 0.290 mJ / 0.100 s = 2.90 mW

Black plastic outer rim
Quantity: 1
Density: 1000 kg/m³
Height: 0.00635 m
Thickness: 0.000889 m
Distance from center of rotation: 0.0146 m
Volume: (2 * pi * 0.0146 m) * 0.00635 m * 0.000889 m = 5.18e-7 m
Mass: 1000 kg/m³ * [(2 * pi * 0.0146 m) * 0.00635 m * 0.000889 m] = 0.000518 kg
Velocity @ 26.5 Hz: (2 * pi * 0.0146 m) * 26.5 Hz = 2.43 m/s
Kinetic energy at 26.5 Hz: 0.5 * 0.000518 kg * 2.43² m/s = 1.53 mJ
Velocity@ 25.6 Hz: (2 * pi * 0.0146 m) * 26.5 Hz = 2.35 m/s
Kinetic energy at 25.6 Hz: 0.5 * 0.000518 kg * 2.35² m/s = 1.43 mJ
Deceleration energy loss in 0.1 seconds: 1.53 mJ – 1.43 mJ = 0.100 mJ
Power output from friction @ 26.5 rps: 0.100 mJ / 0.100 s = 1.00 mW

Black plastic flat top disc
Quantity: 1
Density: 1000 kg/m³
Radius: 0.0146 m
Thickness: 0.000686 m
[extra info: Volume: 9.19e-7 m^3]
[extra info: Mass: 0.000919 kg]
Integrated Kinetic energy at 26.5 Hz: 0.679 mJ
Integrated Kinetic energy at 25.6 Hz: 0.633 mJ
Deceleration energy loss in 0.1 seconds: 0.679 mJ – 0.633 mJ = 0.0460 mJ
Power output from friction @ 26.5 rps: 0.0460 mJ / 0.100 s = 0.460 mW

Total friction heating from both NdFeB & black plastic outer rim: 2.90 mW + 1.00 mW + 0.460 mW = 4.36 mW

Efficiency: 4.36 mW / 2.52 mW = 173%

Friction heating was calculated by doing a control experiment. During the control experiment, the “tiny orbo replication” was rotating over 28 rps. The deceleration rate was then recorded after turning the “tiny orbo replication” off. This showed how fast the machine decelerated between 27.6 rps and 24.7 rps. The deceleration rate along with mass and velocity of the pieces provides the loss in kinetic energy over time, which provides the friction heating output of the device at the operating speed.

This the circuit I’m using.

Click to enlarge image.

I am not affiliated with Steorn. Orbo is trademarked by Steorn

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