Source: https://guthlabs.ai/docs/instruments/banked-curve-centripetal-force-calculator/mechanism/

instrument mechanism / verified-clean

# Banked Curve / Centripetal Force Calculator mechanism

The inspectable method record for Banked Curve / Centripetal Force Calculator, kept separate from implementation and qualification.

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

## Model scope

NEEDS_REVIEW because the specification does not define g, angle units, friction coefficient semantics, or the output mode, and it claims required-friction computation without supplying a required-friction formula. The empty honest_label should be replaced with an explicit scope statement covering the idealized banked-curve assumptions and the denominator/domain restrictions.

- The frictionless relation tan(theta)=v^2/(g r) is standard for a vehicle on a banked curve with no friction, with theta measured from the horizontal and r>0.

- The supplied friction formula is the standard maximum-speed expression only under specific assumptions: mu is the static tire-road friction coefficient, friction acts down the bank at maximum speed, and 1-mu*tan(theta)>0. It is not a general friction formula.

- The stated capability includes computing required friction, but no formula for required friction is supplied. For example, the friction requirement must be solved from the radial and vertical force equations, and its direction changes between low-speed and high-speed cases.

- The gravitational acceleration g is omitted from the inputs and formula specification; a fixed value must be declared, such as g=9.80665 m/s^2 or g=9.81 m/s^2.

- The output selection is ambiguous: the specification says required theta or v_max, while the computes field also claims required speed and friction.

## Units and conventions

- Use SI units: v in m/s, r in m, and g in m/s^2.

- Assume g=9.81 m/s^2 for the worked vectors.

- theta must be explicitly defined as an angle from the horizontal; test-vector angles are in degrees and must be converted or handled consistently by the implementation.

- mu is dimensionless and represents a static coefficient of friction.

- The frictionless formula and the supplied friction formula assume an idealized circular banked curve with no aerodynamic forces, rolling resistance, or grade effects.

## Inspectable vector

One of 4 source-bound review vectors:

````
{
  "inputs": {
    "mode": "frictionless_required_speed",
    "r_m": 100,
    "theta_deg": 30,
    "mu": 0
  },
  "expected_outputs": {
    "v_required_m_per_s": 23.8
  },
  "working": "tan(30 degrees)=0.577350. v=sqrt(g*r*tan(theta))=sqrt(9.81*100*0.577350)=sqrt(566.540)=23.80 m/s."
}
````

## Failure boundary

**BREAK_CLAIMED** · SELF_FLAGGED

The formula has an exact singularity when mu*tan(theta)=1, where the speed result is undefined and must be rejected. The instrument is also vulnerable to a degree-versus-radian angle interpretation error unless the angle unit is explicit.

## Other records

[01**Overview**](<https://guthlabs.ai/docs/instruments/banked-curve-centripetal-force-calculator/>)[03**Implementation**](<https://guthlabs.ai/docs/instruments/banked-curve-centripetal-force-calculator/implementation/>)[04**Qualification**](<https://guthlabs.ai/docs/instruments/banked-curve-centripetal-force-calculator/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`