A design tool is worth what its worst case is worth. This page lists the reference each physical model is measured against, the tolerance it must meet before a release ships, and the largest deviation actually found — named by the operating point that produced it.
Chamber conditions are found by Gibbs free-energy minimisation over the product species, with thermodynamic data from the NASA polynomial database. The reference is NASA CEA, the code the industry treats as ground truth for this calculation.
145 operating points across six propellant combinations — methalox, kerolox, hydrolox, ethanol, methanol and propane — sweeping mixture ratio, chamber pressure from 10 to 250 bar, and area ratio from 4 to 150. Nine quantities are compared at every point.
| Quantity | Worst | Tolerance | Worst case at | |
|---|---|---|---|---|
| Chamber temperature | 2.686 K | 10 K | OK | kerolox O/F 2.2, 60 bar, ε 16 |
| Molecular weight | 0.137 % | 0.5 % | OK | kerolox O/F 2.2, 60 bar, ε 16 |
| Isentropic γ | 0.010 % | 0.5 % | OK | kerolox O/F 2.6, 250 bar, ε 4 |
| Characteristic velocity c* | 2.923 % | 3 % | OK | kerolox O/F 2.6, 10 bar, ε 4 |
| Vacuum specific impulse | 0.029 % | 1 % | OK | kerolox O/F 2.6, 250 bar, ε 4 |
| Exit Mach number | 0.031 % | 1 % | OK | kerolox O/F 2.6, 250 bar, ε 150 |
| Exit temperature | 0.171 % | 1 % | OK | kerolox O/F 2.6, 250 bar, ε 150 |
| Throat temperature | 0.080 % | 1 % | OK | kerolox O/F 2.2, 60 bar, ε 16 |
| Pressure ratio pc/pe | 0.092 % | 1 % | OK | kerolox O/F 2.6, 250 bar, ε 150 |
2.923 % against a 3 % tolerance is the tightest margin on this page, and it is worth saying where it comes from: low chamber pressure with kerosene, where condensed-phase carbon matters most. Every other quantity sits an order of magnitude inside its limit. The gate is deliberately set where the model is weakest rather than where it looks best.
Regenerative cooling is only as good as the fluid properties behind it. CSTAR carries embedded property tables for five coolants — RP-1, methane, hydrogen, oxygen and ethanol — so the application runs entirely offline with no dependency to install. The reference is CoolProp.
1200 states per fluid, 6000 in total. Four properties are compared: density, specific heat, viscosity and thermal conductivity.
| Property | Worst | Tolerance | Worst case at | |
|---|---|---|---|---|
| Density ρ | 2.005 % | 3 % | OK | hydrogen, 34 K, 33 bar |
| Specific heat cp | 4.214 % | 6 % | OK | hydrogen, 45 K, 39 bar |
| Viscosity μ | 3.019 % | 4 % | OK | hydrogen, 45 K, 33 bar |
| Conductivity k | 2.036 % | 3 % | OK | hydrogen, 45 K, 33 bar |
Interpolation in a table is exact at the grid nodes. Sampling randomly therefore includes points that sit near nodes and flatters the result — an early version of this test reported errors several times smaller for exactly that reason. Every error above is measured at the cell centre, the point furthest from any node, where bilinear interpolation is at its worst. These are upper bounds, not averages.
Hydrogen dominates every row because it is the hardest case in the set: near its critical point the properties change violently over a few kelvin. The other four fluids stay under 1.3 % throughout.
Nozzle contouring uses the method of characteristics. Unlike the two gates above, this one has an exact analytic answer to check against — Prandtl–Meyer theory — so the tolerance can be far tighter.
| Check | Worst | Tolerance | Worst case at | |
|---|---|---|---|---|
| Exit Mach vs exact theory | 0.0031 % | 0.05 % | OK | γ 1.15, M 4.0 |
| Mass conservation | 0.0284 % | 0.1 % | OK | γ 1.15, M 4.0 |
Matching theory at one mesh density proves little on its own. The solution converges at the expected rate as characteristics are added, at γ = 1.22 and design Mach 3.0:
| Characteristics | Exit Mach | Change |
|---|---|---|
| 20 | 2.99869558 | — |
| 40 | 2.99969996 | 3.35 × 10⁻² % |
| 80 | 2.99992788 | 7.60 × 10⁻³ % |
| 160 | 2.99998231 | 1.81 × 10⁻³ % |
| 320 | 2.99999562 | 4.44 × 10⁻⁴ % |
The axisymmetric branch of the characteristics solver did not pass mass conservation, and the cause was not established with enough confidence to ship it. Rather than return a plausible-looking contour of unknown quality, that code path raises an error and refuses. The planar solver above, which is validated, is what the application uses.
A tool that quietly returns a wrong answer is worse than one that stops. This is the only place in CSTAR where a model was written and then deliberately withheld.
Not every model has a reference implementation to run against. These are implemented from the standard sources and stated as such, so you know exactly what you are relying on:
The demo runs the full flow solution on your geometry, not a fixed sample — the thermochemistry and nozzle results above are exactly what it computes. If your engine has known numbers, put them in and compare before you spend anything.