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COLREG - CPA / TCPA Calculator

Closest Point of Approach (CPA) and Time to CPA from own and target ship course/speed/range/bearing - Rule 7 risk of collision.

COLREGRule 7CPATCPA
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Formula, assumptions, limits

V⃗rel=V⃗target−V⃗own\vec{V}_{rel} = \vec{V}_{target} - \vec{V}_{own}

CPA=R⋅sin⁡(θrel)CPA = R \cdot \sin(\theta_{rel})

TCPA=R⋅cos⁡(θrel)/∣Vrel∣TCPA = R \cdot \cos(\theta_{rel}) / |V_{rel}|

Vector resolution of own and target velocity gives relative velocity. CPA is the perpendicular distance from own ship’s relative track to target current position. TCPA is the time until the perpendicular foot is reached. Per COLREG Rule 7, risk of collision is determined by, among others, an unchanging compass bearing of an approaching vessel. CPA below 1.5 nm at moderate ranges typically indicates risk; CPA below 0.5 nm typically requires action; TCPA under 6 minutes indicates urgency.

Symbol legend

SymbolMeaningUnitSource

Relative velocity vectorkncomputed Range to targetnmradar/AIS Relative bearing of target wrt relative motion directiondegcomputed

In short

Closest Point of Approach and Time to CPA per COLREG Rule 7 risk of collision.

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