What do CPA and TCPA mean?

CPA (closest point of approach) is the smallest distance another vessel will come to if both keep their course and speed. TCPA is the time of that closest approach.

Why doesn't the radar show the other vessel's true course?

Because your own ship moves between observations too. The line joining two echoes only shows the relative motion. The true course and speed follow from the vector triangle of own track and relative track.

What is the difference between north up and head up?

North up orients the radar picture to north, so you read true radar bearings. Head up puts your own heading at the top, so you read relative bearings that must be converted to true bearings with your heading.

Coastal navigation

Radar plotting – how close will the other vessel come?

Two radar observations are enough to answer the key questions: how close will the other vessel come (CPA), when (TCPA), and what are its real course and speed? NauticTools2 works the radar plot out exactly and draws it – right up to avoiding action.

North up / head up
CPA / TCPA
Relative motion
Vector triangle
Second vessel
Avoiding action

Radar plotting in the Windows version of NauticTools2 with radar plot, relative track and CPA — Radar plotting in the Windows version: enter two observations – radar plot with relative track, CPA and vector triangle.

What does radar plotting tell you?

On the radar screen your own ship always sits in the centre. When an echo moves from one observation to the next, that is not its true motion but the relative motion – the other vessel's motion relative to yours. Extend the line through the two echoes and you see how the vessel will pass.

CPA – closest point of approach: the shortest distance to the relative track, the perpendicular from the centre.
TCPA – the time at which that point is reached.
Course and speed of B – the other vessel's true course and speed from the vector triangle.

The two echoes of B and their extension (relative track). The perpendicular from the centre is the CPA. Own track plus relative track gives the true track of B.

When do you need it?

Collision avoidance in restricted visibility: Under Rule 19 of the COLREGs you must determine in fog whether a close-quarters situation is developing – which is exactly what the CPA tells you.
Judging the other vessel: Is it on a reciprocal course, overtaking, crossing? The vector triangle shows its true course.
Planning avoiding action: Which course or speed gives a safe passing distance?
Spotting stationary objects: If the echo's true speed comes out as 0 kn, it is stationary – a buoy, a vessel at anchor or an island.

Working

true track of B = own track + relative track

Plot the observations
Bearing and range of both observations; with head up, first convert relative bearings to true with your heading.
Relative motion
Direction and length from the 1st to the 2nd observation give the relative course; length divided by time gives the relative speed.
CPA and TCPA
The perpendicular from the centre to the relative track gives the CPA. The distance to its foot divided by the relative speed gives the time to CPA.
Vector triangle
Lay off your own track for the observation interval to the 1st observation. From its start to the 2nd observation runs the true track of B – its direction is B's course, its length over time B's speed.

Worked example

You steer 000° true at 6 kn, radar north up. At 10:00 vessel B bears 045° true, 8.0 nm. At 10:12 B bears 047°, 6.0 nm. How close will B come, when, and what are B's course and speed?

Relative: course 219°, speed 10.1 kn
CPA: 0.8 nm at 10:47, bearing 129°
True: course 254°, speed 6.6 kn
Own track: B crosses at 10:54, 1.3 nm astern

At 0.8 nm, B enters the close-quarters zone. In restricted visibility, Rule 19 requires early action:

At 10:18 you want to alter course so that B passes at 2 nm. What course do you steer?

B at 10:18: 5.0 nm bearing 049°
New course: 070° (70° to starboard), CPA 2.0 nm at 10:40
Alternative: on course 000° the speed would have to drop to 0.2 kn – practically stopping

Things to watch out for

Use the first and last observation: With more than two observations, the widest interval gives the most accurate result.
Course and speed must stay the same: The plot only holds while both vessels keep course and speed. Further observations confirm this – or show that the other vessel has altered.
Through the water or over the ground: Using your course and speed through the water gives the other vessel's course through the water – the right reference for collision avoidance.
Drawn versus calculated: NauticTools2 works the plot exactly. A hand-drawn solution will differ by a few tenths of a mile, degrees or minutes – down to drawing accuracy.

How it works in NauticTools2

Choose the radar display
North up (true bearings) or head up (relative bearings). The radar plot is oriented accordingly – just like the exam sheet.
Own ship
True course and speed through the water.
Observations
Time, bearing and range for both observations – times can be typed as 1537. A second vessel C has its own block.
Avoiding action
Optionally from a given time: course for a required CPA (starboard under Rule 19, port if needed), speed for a required CPA, or a given manoeuvre. Everything appears in magenta in the plot.

Printable calculation record

Radar plotting can be printed as a record or saved as a PDF too – with inputs, the plotting diagram and all results from CPA and TCPA to the other vessel's course and speed.

Calculation record of radar plotting with observations, plotting diagram and results such as CPA and TCPA — The printed record of a radar plot with two observations, North up.

View the example record as PDF ›

Frequently asked questions

How do I recognise a risk of collision?

If the bearing stays steady while the range decreases, the relative track runs through the centre – the CPA is zero. Even a small CPA means a close-quarters situation.

What do the arrows in the plot mean?

Following the German standard DIN 13312: single arrow = own motion, double arrow = true motion of the other vessel, arrow in a circle = relative motion.

Can I plot two vessels at once?

Yes. The second vessel C gets its own colour and result block. For avoiding action, NauticTools2 also shows which CPA results for the other vessel.

Related tools

Bearing Conversion – convert relative radar bearings into true bearings
Limiting Course – course sector of a vessel from its lights
Distance, Speed and Time – six-minute rule and speed from fixes

NauticTools2 is free and runs on Windows 10 and 11. An Android version is in preparation.

Get it from the Microsoft Store

Radar plotting – how close will the other vessel come?

What does radar plotting tell you?

When do you need it?

Working

Plot the observations

Relative motion

CPA and TCPA

Vector triangle

Worked example

Things to watch out for

How it works in NauticTools2

Choose the radar display

Own ship

Observations

Avoiding action