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. Since this post first appeared, the predictor has become a live, native 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. Method The predictor evaluates the system $\dot m \;=\; \rhos(Te, \mathrm{SH}, \mathrm{ref}) \cdot Vd \cdot N \cdot \etav(\Pi, \mathrm{ref})$ $Q \;=\; \dot m \cdot \Delta h{\mathrm{evap}}(Te, \mathrm{SH}, Tc, \mathrm{SC}, \mathrm{ref})$ $P \;=\; \dot m \cdot \frac{\Delta h{is}(\Pi, \mathrm{ref})}{\eta{is}(\Pi, \mathrm{ref})}$ State quantities ($\rhos$, $\Delta h{\mathrm{evap}}$, $\Delta h{is}$) come from CoolProp; the kinematic factor $Vd \cdot N$ comes from the parsed model name; $\etav$ comes from the three-parameter universal fit; $\eta{is}$ is a separate Gaussian-in-$\ln\Pi$ fit using three additional parameters $(\eta{peak}, \Pi{design}, \sigma)$. The total parameter budget per (technology $\times$ refrigerant) pair is therefore six numbers: three for $\etav$ and three for $\eta{is}$. We refer to the $\etav$ trio as the "core parameters" because the predictor's capacity error is dominated by the $\etav$ fit; the power error is split between the $\etav$ and $\eta{is}$ errors. Validation We compare the predictor's $Q$ output against the vendor's EN 12900 polynomial $Q$ output at $Te = -10\,^\circ\mathrm{C}, Tc = 40\,^\circ\mathrm{C}, f =…