Closest Point of Approach distance and time from own-ship and target course+speed. The core radar plotting relationship for COLREG compliance.
Formula
$$ \text{CPA} = |r_0 + v_\text{rel} \cdot t_\text{CPA}|, \quad t_\text{CPA} = -\frac{r_0 \cdot v_\text{rel}}{|v_\text{rel}|^2} $$
Symbol legend
| Symbol | Meaning | Unit | Source |
|---|---|---|---|
| $r_0$ | Current relative position vector | nm | derived |
| $v_\text{rel}$ | Relative velocity = target − own | kn | course/speed |
| $CPA$ | Closest Point of Approach distance | nm | result |
| $TCPA$ | Time to CPA | min | result |
Sources
- IMO Resolution A.823(19) - ARPA performance.
- COLREGS Rules 7–8.