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Water, loads and governor
Available power is rho g Q H eta. The drive must overcome the weight imbalance of the two vessels along the slope plus rolling resistance and damping; the governor sets the cruise speed and brakes near the end.
Operation
Model checks
The science
What is modelled
Two counterbalanced vessels on rails share a cable over a drive wheel on a 490 m slope rising 20.6 m. Water power from the sluice drives the wheel; a proportional controller tracks the speed setpoint within the available drive and brake limits.
Equations
- Available power
P = rho g Q H eta; usable drive forcemin(F_max, P / max(v, 0.32)). - Gravity imbalance
(mB - mA) g sin(theta); rollingmu (mA + mB) g cos(theta); dampingc v. - Governor: force
K (v_target - v)clamped to the available limits; slows to stop at the end with a fixed deceleration.
Checks run in the page
- Hydraulic power from flow, head and efficiency.
- Gravity imbalance from the slope geometry.
- A weak-stream stall against the available force.
- Steady cruise force balance.
Honest simplifications
An illustrative reduced-order model: historical geometry only, with the drive train, control law and operating numbers made up for teaching; no cable elasticity, no wheel dynamics and no real installation parameters. Not an engineering or safety tool.
What to try
- Press Weak stream: the drive cannot beat the imbalance and the haul stalls.
- Press Balanced, fast and watch the speed settle just under the setpoint where drive equals rolling plus damping.
- Press Reverse at the end to send the loaded vessel back.