This revision keeps the documented weighted-pendulum and pitman pump topology while limiting numerical outputs to ideal unloaded pendulum quantities.
Ideal Pendulum and Pump-Linkage Explorer
Choose pendulum length, bob mass and small half-amplitude. The worksheet reports ideal unloaded timing, bob rise and stored gravitational energy; the connected pump linkage is illustrative only.
Equation Used
- The bob is a point mass on a massless rigid arm.
- Half-amplitude is at most 15 degrees, the small-angle range stated by OpenStax.
- Air drag, pivot friction, pumping load and operator input are excluded from the outputs.
- The illustration uses a coupling radius 0.45L, slider offset 0.45L and rigid pitman length 0.75L.
- Pump displacement, valves, bore, head, leakage, flow, useful work and efficiency are not predicted.
Replaces unsupported flow and operating claims with ideal pendulum quantities and a connected, constant-length illustrative pitman.
A weighted pendulum linked to a pump shaft
US patent 1485664 shows a pendulum with an adjustable lower weight and a pitman connection to a pump crankshaft for hoisting water from a well. The animation retains that general idea as a declared rigid-link construction: a pin on the pendulum drives a vertical slider through a constant-length pitman.
The illustration solves the slider position so the coupling radius and pitman length remain invariant. It is not a reconstruction of the patent dimensions or a production pump.
A historical pump-drive concept
The patent describes intermittent farm-well use, where the pump continues while the pendulum oscillates. That supports the topology, not the former page's specific village systems, depth ranges, fatigue claims or named installations.
This page is an educational motion model and does not select a water-supply system.
Ideal unloaded pendulum quantities
OpenStax gives the ideal small-angle period and notes that it is independent of bob mass. The bob rises h=L[1-cos(alpha)] above the bottom of its swing, so its gravitational potential energy there is E=mgh.
These equations contain no pump bore, stroke, head, valves or losses and therefore cannot predict water flow or useful output.
A declared ideal example
For L=1.2 m, m=12 kg and alpha=10 degrees, the ideal period is about 2.198 s and frequency about 0.455 Hz. The bob rises about 18.2 mm and has about 2.15 J of gravitational potential energy above the bottom.
Stored motion is not free pumping work
A pump load removes energy from the oscillation. Maintaining motion requires external work equal to useful hydraulic work plus mechanical and hydraulic losses. A free-pendulum period alone does not set pump stroke rate under load.
The former flow predictions, depth and discharge ranges, ergonomic recommendations, alignment tolerances, service diagnoses, named installations and case study are not supported by the cited sources and are removed.
Pendulum water-lift questions
Does bob mass change the ideal period?
No. Mass cancels from the ideal simple-pendulum equation.
Does stored energy equal delivered water energy?
No. It is only the bob's gravitational potential above the bottom; useful output would be lower and requires a complete pump and loss model.
Why limit amplitude to 15 degrees?
OpenStax identifies that as the range where the small-angle sine approximation differs by less than one percent.
Does the model predict flow or operator effort?
No.
Pendulum water-lift references
- US patent 1485664A, Pendulum: adjustable weighted pendulum, pitman and pump-shaft application for hoisting water.
- OpenStax University Physics, Pendulums: ideal small-angle period and mass independence.
- OpenStax University Physics, Conservation of Energy: pendulum gravitational potential energy.
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