Source: https://guthlabs.ai/docs/instruments/optimal-launch-angle-finder/implementation/

instrument implementation / implementation-contract

# Optimal Launch Angle Finder implementation

A source-bound implementation contract for Optimal Launch Angle Finder; deployment and executable qualification remain separate.

Status: **VERIFIED_CLEAN**Lifecycle: **implementation-contract**

## Binding contract

This record describes what an executable surface must bind and validate. It does not claim that a public calculator, package, or production route is deployed.

**Record owner**: Guth Instruments

**Lifecycle**: verified-clean

**Evidence ID**: t2-023

**Effect**: Computation or source lookup only

## Input and validation requirements

The height h0=-v0^2/(2g) makes sqrt(v0^2+2gh0)=0, so the angle formula divides by zero and the expected result is undefined. The instrument should reject this input.

## Required corrections

No binding erratum is attached to this unique-name record. Implementers must still preserve the declared units, domain, and failure behavior.

## Inspectable interface fixture

The sample below is evidence for interface and validation tests, not a production implementation.

````
{
  "inputs": {
    "v0": 20,
    "g": 9.81,
    "h0": 0,
    "units": "SI"
  },
  "expected_outputs": {
    "optimal_angle_deg": 45,
    "resulting_range_m": 40.7747
  },
  "working": "θ=atan(20/√(20²+2×9.81×0))=atan(20/20)=atan(1)=45°. R_max=(20/9.81)×√(20²+0)=(20/9.81)×20=400/9.81=40.7747 m."
}
````

## Other records

[01**Overview**](<https://guthlabs.ai/docs/instruments/optimal-launch-angle-finder/>)[02**Mechanism**](<https://guthlabs.ai/docs/instruments/optimal-launch-angle-finder/mechanism/>)[04**Qualification**](<https://guthlabs.ai/docs/instruments/optimal-launch-angle-finder/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-tranche2/tranche2-results.json`