Maneuvering Board — Radar Plotting Trainer & Solver
Plot two radar observations of up to five targets and solve each one's true course & speed, CPA and TCPA — then test a course-change manoeuvre. Switch to Trainer to be graded, or Generator for random exercises.
Which mode do I need?
- Solver — you have real (or exam) radar observations and want the answer: enter them, press Compute & plot, read off true course, speed, CPA and TCPA for every contact.
- Trainer — you want to practise: the tool invents a problem, you plot it yourself (on paper or in your head) and type your answers; it grades you and can reveal the true solution.
- Generator — you teach: create seed-reproducible exercises and print student worksheets plus a separate instructor answer key.
How to read the board
- You are the centre dot. The compass rose shows true bearings; the rings are equal steps of range out to the Range NM you set.
- Green arrow from the centre — your own motion vector (course steered, length = distance run in one interval).
- Two dots per target — the plotted positions: open circle = observation 1, filled dot = observation 2. The dashed line through them, extended, is the relative-motion line (RML): how the contact tracks across your radar screen.
- Blue arrow at the target — its true course and speed (what the ship is actually doing through the water). Shown in Solver mode, or after Reveal in Trainer mode.
- Small dot on the RML with a dotted line from the centre — the CPA point: where the contact passes closest to you, labelled with the distance.
- Faint red dashed circle around the centre — your safety ring (Safety NM): any relative-motion line cutting inside it means that contact will pass closer than you accept.
- Red target — its CPA is inside your safety distance; green targets pass clear.
Own ship & plot
What these fields mean
- Course ° — your own true course, 0–359° from true north (compass course corrected for variation/deviation).
- Speed kt — own speed in knots over the interval.
- Interval min — minutes between the two radar observations. 6 minutes is the classic choice: it is exactly 0.1 hour, so distance run × 10 = speed in knots.
- Range NM — the plotting radius of the board (how far the outer ring reaches). Display only — it does not affect the maths.
- Safety NM — your minimum acceptable passing distance. Any contact predicted to pass closer (CPA < safety) is flagged red as dangerous.
Targets — two radar observations
What Brg 1 / Dist 1 / Brg 2 / Dist 2 mean
Each row (T1–T5) is one radar contact. You observe the same contact twice, separated by the plot interval, and enter both readings:
- Brg 1 — the contact's true bearing at the first observation (time 0), in degrees 0–359 from true north. On the radar: put the EBL on the contact and correct to true if your display reads relative.
- Dist 1 — the range to the contact at the same first observation, in nautical miles (radar VRM ring).
- Brg 2 — the true bearing of the same contact at the second observation, exactly one interval later.
- Dist 2 — the range at that second observation.
The two positions define the contact's relative-motion line — everything else (true course, speed, CPA, TCPA) is derived from it. Watch for the classic warning sign: bearing steady while range closes (e.g. 240°/10 NM → 240°/8 NM) means constant bearing, decreasing range — risk of collision (COLREG Rule 7).
| Brg 1 | Dist 1 | Brg 2 | Dist 2 |
|---|
Bearing in ° true, distance in NM. Observation 2 is one interval later.
Manoeuvre to evaluate (optional)
What these fields mean
- Course Δ ° — the planned course alteration: positive = turn to starboard, negative = to port (e.g. +30 means "come 30° to starboard").
- T(man) min — the moment you put the helm over, in minutes after the first observation. E.g. interval 6 and T(man) 12 = two intervals after your first plot.
- T(return) min — your planned time to be back on the original course (for reference on the plot). The solution independently reports the earliest time each target's geometry allows a safe return.
The tool re-runs the relative-motion problem for the altered course and reports CPA′ / TCPA′ — the new closest approach for every contact — so you can check a manoeuvre clears all targets, not just the one you are worried about.
Solution
How to read the results
- Course / Speed — the contact's true course (°) and speed (kt), recovered from the vector triangle. This is what the other ship is actually doing — compare it with what you see visually or on AIS.
- CPA — closest point of approach: the minimum distance (NM) at which the contact will pass if nobody changes course or speed.
- TCPA — time to CPA in minutes, counted from the second observation ("now"). Negative would mean the closest point is already past.
- CPA′ / TCPA′ — the same two numbers after your planned manoeuvre (only shown when one is entered). This is the number that tells you whether the alteration actually works.
- Red row — CPA inside your safety distance: this contact needs action (or a bigger alteration).
What a maneuvering board does
A maneuvering board (radar plotting sheet) turns two timed radar observations of a contact into its true course and speed, and tells you how close it will pass (CPA) and when (TCPA). You plot the target's position at two times, draw the relative-motion line (RML) between them, and resolve the vector triangle: the target's true motion equals its relative motion plus your own motion over the interval. It is the manual skill behind what ARPA does automatically — and it is still examined for Yachtmaster and deck-officer certificates.
How to plot a contact — step by step
- First observation: at time 0, note the contact's true bearing and range and mark the position on the board.
- Second observation: after a fixed interval (6 minutes is convenient — one tenth of an hour), mark the new bearing and range.
- Draw the RML: the line from mark 1 through mark 2, extended past your own position, is the relative-motion line. The perpendicular from own ship to this line is the CPA; the run remaining along it, divided by relative speed, gives the TCPA.
- Resolve the triangle: add your own motion vector for the interval to the relative-motion vector — the resultant is the contact's true course and speed.
- Steady bearing? If the bearing barely changes while the range closes, the RML passes through your position — constant bearing, decreasing range means risk of collision (COLREG Rule 7).
Evaluating a manoeuvre
Before altering course you can test the result here: enter a course change and the time you'd apply it, and the tool re-plots the relative-motion line for the manoeuvred track, giving the new CPA′ and TCPA′ and the earliest time you could safely resume your original course. This mirrors the classic exam question: "will a 20° alteration to starboard at minute 12 give you a safe passing distance on all contacts?"
For instructors
The Generator mode produces classroom-ready exercise sets: choose the number of targets and worksheets, print (or save as PDF) one blank plotting sheet per student with the given own-ship data and radar observations, and keep the single answer-key page — true course, speed, CPA and TCPA for every exercise — for yourself. Exercises are seed-based: hand out the same seed and every student gets the identical problem; reuse it next term and the answers stay valid.
Frequently asked questions
What is a maneuvering board?
A polar plotting diagram — compass rose plus range rings — used to solve the relative-motion problem from radar observations: a contact's true course and speed, its CPA and TCPA.
How do you calculate CPA and TCPA from two radar observations?
Plot both positions, draw the relative-motion line through them, drop a perpendicular from own ship (that distance is the CPA), and divide the remaining run along the line by the relative speed (that time is the TCPA). Adding your own motion vector to the relative vector recovers the target's true course and speed.
What CPA is considered safe?
There is no universal figure — it depends on visibility, traffic, sea room and how your vessel handles. Many skippers use 1–2 NM in open water, more in restricted visibility. Set your own safety distance above and the tool flags anything closing inside it.
Do I still need plotting if I have AIS or ARPA?
Yes. Not every target transmits AIS, ARPA vectors need time to settle after a course change, and electronics fail. Plotting is how you sanity-check the machine — and it remains examinable knowledge.
Can instructors print exercises with an answer key?
Yes — see For instructors above: any number of watermarked worksheets plus one combined answer-key page, printable or saved as PDF.
This tool is for training and exam practice. Always cross-check against your vessel's ARPA/ECDIS and a proper lookout — COLREG Rule 5 and Rule 7 still apply.
Related: practise the same collision-avoidance decisions live on the ARPA · AIS · COLREG Bridge Simulator, or test your rules knowledge in the free Colreg Game.