Bridge: relating gravity levels through flame stretch rate

HYPOTHESIS — NOT EVIDENCE

Stretch rate (per second) is how hard the surrounding gas flow pulls on a flame. Weak airflow in orbit and weak buoyancy on the Moon can stretch a flame by similar amounts. That is the bridge between them.

In PYRION, gravity is a regime barrier: a microgravity test and a lunar-gravity target are not comparable, and the verdict says so. NASA's own literature relates gravity levels through the flame stretch rate. Olson & T'ien write that the effect of partial gravity such as those found on the Moon (1/6 g) or Mars (1/3 g) on material flammability can be examined at Earth's gravity through equivalence of flame stretch rates (NTRS 20000004509, Combustion and Flame 121(3), 2000, p. 3). Quoted as written by NASA. PYRION uses 0.165 g for the Moon (the lunar-g setting of NASA's ground-test centrifuge, shown on p. 13 of the FM2 science presentation, NTRS 20260001966: “Upward Spread Lunar-g = 0.165 gE”; FM2, Flammability of Materials on the Moon, is a planned experiment, not a centrifuge) and 0.38 g for Mars (NASA NSSDC Mars Fact Sheet); the Envelope presets use 0.16 g (NTRS 20210020446). All round to the quoted fractions. This page uses that idea to point at the PSI tests whose stretch rate is closest. It does not change any verdict, and nothing here is a prediction of flame behavior on the Moon.

Gravity dial

One control for everything below. Four stops, not a continuous scale.

Gravity level 0.165 g. Source: Lunar-g = 0.165 gE (NTRS 20260001966, p. 13).

Stretch map

Stretch rate (s⁻¹, log scale) against ambient O₂. Solid lines: the forced stretch of PSI tests from BASS-II (Burning and Suppression of Solids II, a flame experiment on the International Space Station) on PMMA (acrylic plastic) rods, from each test's flow readings and rod radius. Hatched magenta band: the hypothesised buoyant stretch at the selected gravity, one band per rod radius.

The PSI table itself labels these rods only "clear rod" and "black rod". NASA states what they are: Microgravity experiments burning cast PMMA cylindrical rods in axial flow have been conducted aboard the International Space Station as part of the BASS-II experiment (NTRS 20150008961, Olson & Ferkul, p. 1). So the PMMA-in-air density factor applies (T*, the flame temperature at the limit, 865–990 K, Olson & T'ien), and axial flow is why the rod-tip formula is the default. The table does not say how each individual rod sat in the flow, so the formula stays a choice, shown with every result.

0 transfer analogs at Moon (0.165 g); 6 more only partly overlap the band. Analogs are hypotheses: they are never counted as APPLICABLE.

9 of 129 BASS-II tests in the derived table have a stated rod radius and a parsed flow. The others are not guessed (films and sheets have no radius; some flow cells are ambiguous).

6 tests whose flow sweep only passes through the band at Moon

Their stretch rate falls inside the band for part of the flow readings and outside for the rest: not analogs by the engine's rule (the whole range must lie inside), shown so nothing is hidden.

1/4" clear rod: stretch 4.7 to 94.5 s⁻¹, band 18.3 to 18.9 s⁻¹
1/4" clear rod: stretch 14.2 to 23.6 s⁻¹, band 18.3 to 18.9 s⁻¹
3/8" clear rod: stretch 0 to 15.7 s⁻¹, band 15 to 15.4 s⁻¹
3/8" clear rod: stretch 0 to 15.7 s⁻¹, band 15 to 15.4 s⁻¹
1/4" clear rod: stretch 0 to 52 s⁻¹, band 18.3 to 18.9 s⁻¹
1/4" clear rod: stretch 0 to 52 s⁻¹, band 18.3 to 18.9 s⁻¹

Limits

Geometry. The expressions are for stagnation-point flow on curved bodies. Flat fabric sheets (SIBAL, Nomex in BASS, BASS-II, Saffire) have no radius R: no stretch rate is computed for them.
Material dependence. The direction of the gravity effect depends on the material (NTRS 20250006779, pp. 18-19). An analog found for PMMA says nothing about Nomex.
Scale and time. Sample size and test duration differ between an ISS glovebox, a centrifuge drop (about 5 s) and the lunar surface.
Pressure. Stretch equivalence does not account for a pressure difference; pressure stays a separate axis.
It is a hypothesis. FM2 (lunar surface) is designed to test this kind of bridge. Until then, nothing here is a prediction of flame behavior on the Moon.

FM2 instrument balance

Closed-chamber mass balance, not a flame model. How much oxygen a burn can use before the chamber reaches a hypothesised limiting oxygen concentration (LOC, the lowest oxygen level at which a flame still spreads). It does not say where the limit is.

Inputs, with sources

Volume 14.4 L NTRS 20260001966, p. 6: Chamber volume 14.4 L
Pressure 8.2 psia (56.5 kPa) NTRS 20260001966, p. 10: Test 1: 8.2 psia (+/- 0.3 psi), 37% O2 , balance nitrogen
Starting O₂ 37 / 33 / 29 / 25 % (the four tests, same source, pp. 5–10)
Fuel for the PMMA rows: 1.9176 g O₂ per g derived by PYRION from C₅H₈O₂, not stated by NASA. FM2's planned sample is a fabric (Synergy Pro "Navy"; NTRS 20260001966, p. 10) whose composition PSI does not hold, so the PMMA columns illustrate the oxygen balance; the O₂ consumable column is the material-independent result.

Temperature 295.2 K (22 °C) assumed range 15–35 °C, not in the sourceHypothesised limiting O₂ 25 % hypothesis, not a measurementThe FM2 plan expects a lunar limit of 24–26 % (NTRS 20260001966, p. 5: Test a material with an expected Lunar LOC of 24-26% and an expected oxygen consumption of 0.08 mol fraction). That is an expectation, not a result.

Output per test (limit 25 %)

Start O₂	O₂ consumable	Final O₂	PMMA burned (illustration)
37 %	39.8 mmol (1.27 g)	25 %	0.66 g (0.64–0.68 over the T range)
33 %	26.5 mmol (0.85 g)	25 %	0.44 g (0.42–0.45 over the T range)
29 %	13.3 mmol (0.42 g)	25 %	0.22 g (0.21–0.23 over the T range)
25 %	none	25 %	—

A start at or below the hypothesised limit has nothing to consume in this model. Final O₂ is the limit reached, not a prediction of the flame.

Formulas and assumptions

n = P V / (R T)
O2 consumable = n (x_start - L)
fuel burned = O2 consumable x M_O2 / (g O2 per g fuel)
Ideal gas.
Fixed temperature and fixed chamber volume: the heat of combustion is not modelled.
The total number of moles stays constant: the moles of products (CO2, H2O, CO, soot) replace the moles of O2 consumed. The mole change from products is ignored.
The O2 demand per gram of fuel is the stoichiometric one given as input; incomplete combustion is not modelled.
The limit L is a hypothesis supplied by the caller; the balance does not predict it.

Check case: PMMA at 34 % O₂, 8.2 psia, up to 1.2 g burned

NASA estimates the final O₂ at 13 % to 21 % (NTRS 20260001966, p. 26: PMMA; 34% O2; 8.2 psi; up to 1.2 g burned Final O2 fraction 13% to 21%). This balance, burning 1.2 g of PMMA completely, gives 12.3 % at 295 K (11.4–12.8 % over the assumed temperature range): outside NASA's range.

Fuel mass that would bring a 34 % start to 21 %: 0.74–0.69 g; to 13 %: 1.19–1.11 g. The source gives the 13–21 % range without saying which burned mass or temperature belong to each end, so this check can show consistency of the instrument model, not that the model is right.

Sealed before FM2 flies

PYRION wrote down what it will and will not say about FM2 before any result is public. The fingerprint (SHA-256) of that text has a public timestamp (OpenTimestamps; technical details on the Proof page), so anyone can check later that the text was not changed after the results came out. Read the statements in the predictions README and the proof file SHA256SUMS.ots on GitHub.

Why this page exists