Configuration Variables
Mass & Geometry
2.5 lb
14 in
7.5 in
4.0 in
Wave Conditions
15°
8.0 s
Drive System
4:1
0.13 V/RPM
0.50
Predicted Output
Torque Analysis
Base torque (centered, no shaft)
0.00 N·m
Elevated torque (with shaft height)
0.00 N·m
Offset eccentric torque (with offset)
0.00 N·m
Torque improvement vs centered
0%
Generator Output
Track RPM (from tilt oscillation)
0 RPM
Generator RPM (after pulley ratio)
0 RPM
Predicted AC Voltage
0.0 V
Predicted DC Voltage (after rectifier)
0.0 V
Vector Force Analysis
Lateral force component (drives rotation)
0.00 N
Vertical force component (drives pendulum)
0.00 N
Vector balance ratio (1.0 = optimal 45°)
0.00
Distance from 45° optimum
0°
Vector diagram updates with tilt angle slider
Resonant Orbital Pumping
Energy per wave cycle
0.00 J
RPM after 10 pumping cycles
0 RPM
Pumped voltage (10 cycles)
0.0 V
Pumping multiplier vs passive
0x
Power Output
Passive mode power
0.0 W
Resonant pumping mode power
0.0 W
Scaling Projections
25x scale-up power (fourth power law)
0 kW
Configuration Comparison — Centered vs Offset Eccentric
| Parameter | Centered (offset = 0) | Offset Eccentric (current settings) | Improvement |
|---|---|---|---|
| Torque | 0 N·m | 0 N·m | +0% |
| Generator Voltage | 0 V | 0 V | +0% |
| Dead zones | Yes — zero torque at vertical | None — constant differential | Eliminated |
| Self-orienting | No | Yes — swivel finds gravity | New capability |
| Resonant pumping capable | Limited | Full — 5-10x energy amplification | +0% |
Experiment Data Logger
Record predicted values for each configuration. Compare against measured voltage from the actual demo to validate and refine the model.
No trials logged yet. Adjust parameters and click "Log Current Configuration" to record a trial.
Equations & Physics Reference
The mathematical models behind each output in the simulator. All equations use SI units internally (kg, meters, radians) and convert for display.
Constants
Gravitational acceleration
g = 9.81 m/s²
Unit conversions
1 lb = 0.4536 kg | 1 in = 0.0254 m
1. Torque Analysis
Base Torque (centered, no shaft):
τbase = m × g × sin(θ) × R
Elevated Torque (with shaft height):
τelevated = m × g × sin(θ) × (R + H × cos(θ))
Offset Eccentric Torque (OIMH):
τoffset = m × g × sin(θ) × (R + H × cos(θ) + d × cos(θ))
τbase = m × g × sin(θ) × R
Elevated Torque (with shaft height):
τelevated = m × g × sin(θ) × (R + H × cos(θ))
Offset Eccentric Torque (OIMH):
τoffset = m × g × sin(θ) × (R + H × cos(θ) + d × cos(θ))
Where: m = mass (kg), g = gravity (9.81 m/s²), θ = tilt angle (radians), R = track radius (m), H = shaft height (m), d = offset distance (m)
Key insight: The offset eccentric torque is always greater than the centered torque because the offset distance adds an additional moment arm. This is why the OIMH produces more rotational force than a centered mass.
Key insight: The offset eccentric torque is always greater than the centered torque because the offset distance adds an additional moment arm. This is why the OIMH produces more rotational force than a centered mass.
Torque improvement vs centered
(τoffset / τbase − 1) × 100%
2. Track RPM (Orbital Speed)
Base orbital speed (resonant):
RPMbase = 60 / T
With tilt energy multiplier:
RPMtrack = RPMbase × 2·sin(θ) × √(m / mref) × Hfactor × ζ
RPMbase = 60 / T
With tilt energy multiplier:
RPMtrack = RPMbase × 2·sin(θ) × √(m / mref) × Hfactor × ζ
Where: T = wave period (seconds), θ = tilt angle, mref = 2.5 lb reference mass, Hfactor = shaft height leverage factor, ζ = damping/swivel tension coefficient
Key insight: At resonance, the weight completes approximately 1 full orbit per wave cycle. Larger tilt angles pump more energy per cycle, increasing orbital speed. This is the principle of resonant orbital pumping — like pushing a child on a swing.
Key insight: At resonance, the weight completes approximately 1 full orbit per wave cycle. Larger tilt angles pump more energy per cycle, increasing orbital speed. This is the principle of resonant orbital pumping — like pushing a child on a swing.
3. Generator RPM & Voltage
Generator RPM (after gearing):
RPMgen = RPMtrack × Pulley Ratio
AC Voltage:
VAC = RPMgen × Kv
DC Voltage (after built-in rectifier):
VDC = VAC × 0.9
RPMgen = RPMtrack × Pulley Ratio
AC Voltage:
VAC = RPMgen × Kv
DC Voltage (after built-in rectifier):
VDC = VAC × 0.9
Where: Kv = generator voltage constant (0.13 V/RPM measured from bench demo), Pulley Ratio = gear multiplication (e.g., 3:1 triples generator RPM)
Measured data: Kv = 0.13 V/RPM was confirmed across multiple speeds (30 RPM = 4V, 60 RPM = 8V, 100 RPM = 13V). Linear relationship confirmed.
Key insight: The pulley/gear ratio is the simplest way to multiply voltage output without changing anything else. A 3:1 ratio triples the voltage.
Measured data: Kv = 0.13 V/RPM was confirmed across multiple speeds (30 RPM = 4V, 60 RPM = 8V, 100 RPM = 13V). Linear relationship confirmed.
Key insight: The pulley/gear ratio is the simplest way to multiply voltage output without changing anything else. A 3:1 ratio triples the voltage.
4. Vector Force Analysis (45° Sweet Spot)
Lateral force (drives lazy susan rotation):
Flateral = m × g × sin(θ)
Vertical force (drives pendulum swing):
Fvertical = m × g × cos(θ)
Vector balance ratio:
Ratio = min(Flateral, Fvertical) / max(Flateral, Fvertical)
Optimum:
At θ = 45°: sin(45°) = cos(45°) = 0.707 → Ratio = 1.0 (perfect balance)
Flateral = m × g × sin(θ)
Vertical force (drives pendulum swing):
Fvertical = m × g × cos(θ)
Vector balance ratio:
Ratio = min(Flateral, Fvertical) / max(Flateral, Fvertical)
Optimum:
At θ = 45°: sin(45°) = cos(45°) = 0.707 → Ratio = 1.0 (perfect balance)
Key insight: At 45° tilt, gravitational force splits equally into the lateral component (driving rotation) and the vertical component (driving pendulum swing). Both energy harvesting mechanisms peak simultaneously. Shallower angles favor one axis; steeper angles favor the other. 45° is the combined optimum.
Bench validation: The flat disc weight tilted to approximately 45° produced the most responsive orbital behavior during testing.
Bench validation: The flat disc weight tilted to approximately 45° produced the most responsive orbital behavior during testing.
5. Resonant Orbital Pumping
Energy per wave cycle:
Ecycle = τoffset × C × ζ
Moment of inertia:
I = m × (R + d)²
Angular velocity buildup per cycle:
Δω = (τoffset × ζ) / I × T × 0.7
RPM after N pumping cycles:
RPMN = RPMtrack + Σi=1N (Δω × 60 / 2π)
Ecycle = τoffset × C × ζ
Moment of inertia:
I = m × (R + d)²
Angular velocity buildup per cycle:
Δω = (τoffset × ζ) / I × T × 0.7
RPM after N pumping cycles:
RPMN = RPMtrack + Σi=1N (Δω × 60 / 2π)
Where: C = circumference of track (2πR), ζ = damping coefficient, I = moment of inertia, T = wave period, 0.7 = coupling efficiency factor
Key insight: Like pushing a child on a swing, each wave cycle adds energy to the orbital path. After 10 consistent wave cycles, the orbital speed can be 5–10x higher than a single passive cycle. This is why consistent ocean swells produce dramatically more power than isolated waves.
Key insight: Like pushing a child on a swing, each wave cycle adds energy to the orbital path. After 10 consistent wave cycles, the orbital speed can be 5–10x higher than a single passive cycle. This is why consistent ocean swells produce dramatically more power than isolated waves.
6. Power Output
Electrical power:
P = V² / Rload
Passive mode:
Ppassive = VAC² / Rload
Resonant pumping mode:
Ppumped = Vpumped² / Rload
P = V² / Rload
Passive mode:
Ppassive = VAC² / Rload
Resonant pumping mode:
Ppumped = Vpumped² / Rload
Where: Rload = assumed 10Ω load resistance
Key insight: Power scales with voltage squared. Doubling the voltage quadruples the power. This is why the gear ratio and resonant pumping have such a dramatic effect on power output.
Key insight: Power scales with voltage squared. Doubling the voltage quadruples the power. This is why the gear ratio and resonant pumping have such a dramatic effect on power output.
7. Fourth Power Scaling Law
Scaling projection:
Pscaled = Pbench × S4
Example (25x linear scale):
Pscaled = Pbench × 254 = Pbench × 390,625
Pscaled = Pbench × S4
Example (25x linear scale):
Pscaled = Pbench × 254 = Pbench × 390,625
Where: S = linear scale factor (e.g., 25x means all dimensions are 25 times larger)
Why fourth power? Mass scales as L³ (volume). Torque arm scales as L. Torque = Force × Distance = (mass × g) × arm = L³ × L = L4. Power is proportional to torque × angular velocity, and angular velocity is preserved at resonance, so power scales as L4.
Key insight: A 50-foot production buoy (approximately 40x scale from bench demo) would produce 404 = 2,560,000 times the bench demo power. This is why even a few watts on the bench translates to megawatts at production scale.
Why fourth power? Mass scales as L³ (volume). Torque arm scales as L. Torque = Force × Distance = (mass × g) × arm = L³ × L = L4. Power is proportional to torque × angular velocity, and angular velocity is preserved at resonance, so power scales as L4.
Key insight: A 50-foot production buoy (approximately 40x scale from bench demo) would produce 404 = 2,560,000 times the bench demo power. This is why even a few watts on the bench translates to megawatts at production scale.
Model Validation
Bench Demo Measured Data (April 4, 2026):
Generator: 3-phase brushless with built-in DC rectification
Generator constant: Kv = 0.13 V/RPM (confirmed linear across full RPM range)
Track: 15” aluminum lazy susan bearing
Mass: 2.5 lb cast iron flat disc at ~45° tilt
Shaft: 3/4” aluminum extension rod, 14” height
Generator: 3-phase brushless with built-in DC rectification
Generator constant: Kv = 0.13 V/RPM (confirmed linear across full RPM range)
Track: 15” aluminum lazy susan bearing
Mass: 2.5 lb cast iron flat disc at ~45° tilt
Shaft: 3/4” aluminum extension rod, 14” height
| Condition | Approx RPM | Measured Voltage | Predicted (RPM × 0.13) |
|---|---|---|---|
| Gentle tilt | ~23 | 3V | 3.0V |
| Realistic swell | ~30 | 4V | 3.9V |
| Moderate swell | ~42 | 5–6V | 5.5V |
| Active seas | ~60 | 8V | 7.8V |
| Storm conditions | ~100 | 13V | 13.0V |