Source: https://guthlabs.ai/docs/instruments/rocket-equation-tsiolkovsky/mechanism/

instrument mechanism / verified-with-binding-errata

# Rocket Equation (Tsiolkovsky) mechanism

The inspectable method record for Rocket Equation (Tsiolkovsky), kept separate from implementation and qualification.

Status: **VERIFIED_WITH_ERRATA**Lifecycle: **verified-with-binding-errata**

## Model scope

The honest label correctly identifies this as a single-stage idealization that ignores gravity and drag losses. Verdict is NEEDS_REVIEW because the required-propellant inverse formula and the exhaust-velocity alternative are claimed but not explicitly defined, and the valid mass-ratio constraints are unstated.

- The stated formula is correct for ideal delta-v when Isp is in seconds and g0 is included, but the spec also claims required propellant mass and does not state the required inverse formula: m_propellant = mf·(exp(Δv/(Isp·g0))−1).

- The inputs allow exhaust velocity, but the displayed formula only uses Isp; the equivalent exhaust-velocity form Δv = ve·ln(m0/mf) must be specified, with ve in m/s.

- The mass-ratio domain constraint m0 > 0 and mf > 0, normally m0 >= mf, is not stated.

## Units and conventions

- Isp is in seconds.

- g0 is the standard gravity constant 9.80665 m/s².

- If exhaust velocity is used instead of Isp, it is in m/s and ve = Isp·g0.

- m0 and mf must use the same mass units; their ratio is dimensionless.

- Delta-v and exhaust velocity outputs are in m/s; propellant mass uses the same mass unit as mf.

- The natural logarithm ln and exponential exp are used.

## Inspectable vector

One of 4 source-bound review vectors:

````
{
  "inputs": {
    "Isp_s": 300,
    "m0_kg": 10000,
    "mf_kg": 4000,
    "g0_m_per_s2": 9.80665
  },
  "expected_outputs": {
    "delta_v_m_per_s": 2695.7228
  },
  "working": "ve = Isp·g0 = 300·9.80665 = 2941.995 m/s. Mass ratio = m0/mf = 10000/4000 = 2.5. ln(2.5) = 0.916290732. Delta-v = 2941.995·0.916290732 = 2695.7228 m/s."
}
````

## Failure boundary

**BREAK_CLAIMED** · SELF_FLAGGED

The zero-final-mass input creates a division-by-zero and undefined logarithm argument; the instrument must reject it rather than return a finite value. Directional and input-representation conventions can also produce sign or interpretation errors if not explicitly labeled.

## Other records

[01**Overview**](<https://guthlabs.ai/docs/instruments/rocket-equation-tsiolkovsky/>)[03**Implementation**](<https://guthlabs.ai/docs/instruments/rocket-equation-tsiolkovsky/implementation/>)[04**Qualification**](<https://guthlabs.ai/docs/instruments/rocket-equation-tsiolkovsky/qualification/>)

## Sources and evidence

These pointers bind the page to evidence. They do not grant authority or collapse verification into deployment.

- `VERIFIED_LEDGER.json`

- `evidence-tranche4/tranche4-results.json`

- `BOUNDARY_HAZARD_CATALOG.json`