The universal predictor: three parameters from geometry to capacity
By DigiEntropy Engineering · 2025-12-25 · 8 min read
A closed-form capacity calculator built on the kinematic equation and the universal η_v(Π) curve reproduces vendor EN 12900 polynomials to a mean absolute error of ~4 % across multiple Bitzer reciprocating families on R134a and R404A — using only three universal parameters per refrigerant.
About this post — Authored by an AI assistant using DigiEntropy's polynomial corpus, the universal compressor predictor, and the project's chart-generation tooling. Charts are produced by Python scripts that read the same database the live site queries; tables and formulas are pulled from the same engineering modules. Findings reflect the project's current dataset and methodology — send corrections or deeper questions to admin@digientropy.com.
Abstract
Combining the kinematic mass-flow equation with the universal volumetric-efficiency curve $\etav(\Pi, \mathrm{ref})$ fitted in the geometry-collapse post yields a closed-form predictor of cooling capacity $Q$ and shaft power $P$ that requires no per-model polynomial coefficients. The predictor takes only the model name (which determines $N{\mathrm{cyl}}, D, L$), the operating point $(Te, Tc)$, and the refrigerant. On a representative validation set spanning two refrigerants and six Bitzer Octagon families, the predictor reproduces the vendor EN 12900 capacity polynomials to a mean absolute error of $\sim 4\%$ at the standard $Te = -10\,^\circ\mathrm{C}, Tc = 40\,^\circ\mathrm{C}$ point.
The predictor is also a live tool: the Universal Predictor tab of the God Theory lab. Enter a model and an operating point and it evaluates the closed form in the browser, side by side with the manufacturer's own polynomial.
3.9 % - mean absolute relative error - Bitzer Octagon validation set
Across the validation set, the mean absolute relative error is 3.9 %, with every cell falling inside the ±5 % band.
six - numbers per technology × refrigerant pair - three for ηv, three for ηis
The total parameter budget per (technology × refrigerant) pair is therefore six numbers: three for ηv and three for ηis.
+0.6% - 4HE-25Y capacity vs vendor - R404A at -10/40 C: 42.40 kW predicted
God Theory lab, Universal Predictor — 4HE-25Y on R404A at -10/40 C: predicted mass flow 1189 kg/h (+1.0% vs vendor), capacity 42.40 kW (+0.6%) and power 14.25 kW (-8.0%), all from geometry plus the two efficiency curves.
3.2 percent - cross-refrigerant spread - one parameter set, three refrigerants
The universality table, scored on a coarser grid, puts the cross-refrigerant spread at 3.2 percent and rates the geometry-plus-thermodynamics picture mostly universal.
3–5 % - BOCK HG/HGX and Hanbell RC2 - same kinematic equation
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