Source: https://guthlabs.ai/docs/instruments/belt-pulley-speed-length-calculator/

instrument / verified-clean

# Belt & Pulley Speed/Length Calculator

The current ledger marks this instrument verified clean within the source-bound verification corpus.

Status: **VERIFIED_CLEAN**Lifecycle: **verified-clean**

## Inspectable records

[01**Overview**Purpose and lifecycle](<https://guthlabs.ai/docs/instruments/belt-pulley-speed-length-calculator/>)[02**Mechanism**Method and assumptions](<https://guthlabs.ai/docs/instruments/belt-pulley-speed-length-calculator/mechanism/>)[03**Implementation**Binding and validation](<https://guthlabs.ai/docs/instruments/belt-pulley-speed-length-calculator/implementation/>)[04**Qualification**Evidence and errata](<https://guthlabs.ai/docs/instruments/belt-pulley-speed-length-calculator/qualification/>)

## Ledger state

The current ledger marks this instrument verified clean within the source-bound verification corpus.

**Area**: Mechanical, Civil & Structural Engineering — Statics/Dynamics, Strength of Materials, Machine Design, Civil, HVAC, Vibration

**Tranche**: tranche-4

**Evidence ID**: t4-282

**Ledger rows**: 1

No ledger note is attached.

## Review findings

The formulas are acceptable for an ideal, no-slip, open-belt drive when all length units are consistent and C > (D1+D2)/2. Review is required because the specification does not define the direction of "speed ratio" and does not state that the belt-length result is approximate.

### Formula and scope findings

- The term "speed ratio" is ambiguous: it could mean N1/N2 = D2/D1 or N2/N1 = D1/D2. The specification must define the direction explicitly.

- The belt-length equation is the standard approximate open-belt-length formula, not an exact geometric belt-length calculation; the output should be labeled approximate.

- N1D1=N2D2 assumes no belt slip and that D1 and D2 are effective pitch diameters, not necessarily outside diameters.

### Unit assumptions

- D1, D2, and C must use the same length unit; the resulting L has that same unit.

- N1 and N2 must use the same rotational-speed unit, such as rpm.

- The test vectors interpret speed ratio as input speed divided by output speed: N1/N2 = D2/D1.

- The diameter-speed relation assumes ideal no-slip transmission using effective pitch diameters.

## Boundary hardening

**BREAK_CLAIMED** · SELF_FLAGGED

The calculator can encounter an undefined belt-length expression when C=0, can return a plausible but physically invalid length when C is below the open-belt geometric limit unless that limit is explicitly checked, and can disagree on the sign of N2 because the speed-direction convention is unspecified.

## Errata and corrections

No applied erratum is attached to this unique-name record.

## Inspectable example

4 review vectors are recorded. One source-bound sample is shown below.

````
{
  "inputs": {
    "D1": 100,
    "D2": 200,
    "C": 1000,
    "N1": 1200,
    "length_unit": "mm",
    "speed_unit": "rpm"
  },
  "expected_outputs": {
    "N2": 600,
    "belt_length_L": 2473.738898,
    "speed_ratio": 2
  },
  "working": "N2 = N1D1/D2 = 1200 × 100 / 200 = 600 rpm. Speed ratio = N1/N2 = 1200/600 = 2. Belt length L = 2C + π(D1+D2)/2 + (D2−D1)²/(4C) = 2×1000 + π(100+200)/2 + (200−100)²/(4×1000) = 2000 + 150π + 10000/4000 = 2000 + 471.238898 + 2.5 = 2473.738898 mm."
}
````

## Related workflows

[Motor & Drivetrain Benchbelts](<https://guthlabs.ai/docs/instrument-workflows/motor-drive/>)

## Sources and evidence

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

- `VERIFIED_LEDGER.json · VERIFIED_CLEAN`

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

- `BOUNDARY_HAZARD_CATALOG.json`