# Ideal lifting and adjustable support geometry

Reproduce with `python reproduce.py` using numpy and matplotlib. All masses, dimensions, times and efficiencies are hypothetical teaching inputs. No device was tested.

For a slow direct vertical lift at g = 9.81 m/s², total lifted mass m includes platform and payload. Force F=mg; useful work E=mgh; average useful power P=E/t; input energy Ein=E/eta; ideal pressure difference dp=F/A. Units are N, J, W and Pa. The pressure figure converts m² to cm² and Pa to kPa explicitly.

The model assumes constant gravity, no counterweight, no friction or acceleration, and equal initial/final speed. Efficiency eta is an assumed aggregate conversion efficiency, not a measured value. Pressure difference acts over a simple effective area; actual cylinders can have unequal areas and backpressure, which this model omits. This is not an actuator sizing or building safety calculation.

lift-grid.csv contains 1,701 combinations: three masses (50/100/200 kg), 21 heights (0–1 m by .05), three durations (10/20/40 s), three efficiencies (.5/.75/1) and three areas (.001/.005/.01 m²). pressure-area.csv contains 273 points for the three masses and 91 areas from .001 to .01 m² by .0001. No interpolation represents experimental evidence.

support-geometry.csv contains 81 purely geometric angles: left height .6 m, right height .4–1.2 m by .01, horizontal separation 1.2 m. Angle = atan2(right-left, separation), reported in degrees. These angles do not establish strength, comfort, contact pressure or stability.

The generator checks pA=F, Fh=E, Pt=E and eta*Ein=E on every lift row. It checks inverse tangent geometry, zero-height energy with nonzero support force, zero-mass outputs, and duration scaling. Negative mass/height, zero duration/area, invalid efficiency and nonfinite input are rejected. All checks appear in validation.json. There are 2,055 CSV rows overall.

A stationary load can require support force while doing zero ideal mechanical work. Holding electrical power, leakage and active control are not modeled. Lowering/regeneration is outside this model. A lock and a motion stop perform distinct functions; none is designed here.

Figures: lift-energy-power compares energy versus height and average useful power versus duration at a fixed 1 m rise; pressure-area shows the pressure/area tradeoff. The figures are analytic model curves, not measured performance or confidence intervals.

Sources: [NASA work and gravitational energy](https://pwg.gsfc.nasa.gov/stargaze/Senergy.htm); [NIST pressure measurement](https://www.nist.gov/news-events/news/2017/05/faster-way-calibrate-piston-gauges). These sources support the physical definitions, not the hypothetical equipment or its performance.