Maneuvering board: CPA, TCPA and the trial maneuver

An online maneuvering board for radar plotting. Enter your own course and speed and two or three plots of a target — bearing, range, time — and get the target's true course and speed, the closest point of approach, the time to it, the aspect and where she will cross your course. The board draws the plots, the line of relative motion and the speed triangle itself, and the trial maneuver shows what the CPA becomes after an alteration.

How to solve one

Enter your course and speed

And two plots of the target: time in minutes, bearing, range.

Read the solution

The target's course and speed, the CPA with its bound, the time to it, the aspect.

Check the maneuver

Switch on the trial maneuver and see which alteration gives the passing distance you want.

Take two plots and see the whole speed triangle

own course plots relative motion CPA point

Own course, °

Own speed, kn

Target plots

minbearingrange

speed triangle: er your vector, rm relative, em the target's true vector

Trial maneuver

The trial maneuver is computed from the target's TRUE motion: she is assumed to carry on as before. The Rules do not allow relying on her maneuver — the give-way vessel must achieve a safe passing by her own action.

Exercises

The plots are built from a course and speed chosen in advance, so the answer is exact. Solve it on the board and check yourself.

Difficulty

Target course, °

Target speed, kn

A teaching board and an arithmetic check, not a substitute for ARPA and not a basis for a maneuver. The decision to pass is made on the ship's own equipment and on lookout; manual plotting remains a required skill precisely because automation can be wrong, lose a target, or be switched off.

Features

The speed triangle is visible, not implied

The point of the exercise is to see how the own vector and the relative vector add. Here they are drawn in knots as a separate diagram — er, rm, em — so a sign error shows on the drawing rather than surfacing later as a wrong answer.

Every figure carries its error bound

Plots are taken to a tenth of a mile and a tenth of a degree, and the solution rests on their difference. The bound is computed by perturbing the plots directly, not by a rule of thumb, and the CPA reads "1.5 ± 0.3 miles". No tool we know of does this.

It says when it should not be trusted

With a short interval or a slow target the solution is ill-conditioned: measured, the CPA uncertainty is 4.65 miles on a two-minute interval against 0.29 on a twelve-minute one. In those cases a warning appears instead of a tidy number.

Trial maneuver and course selection

Change your course or speed and the CPA is recomputed from the target's TRUE motion, not from the old relative vector. Plus a search for the course that gives the passing distance you want — showing both solutions, to starboard and to port, because the choice between them is made by the Rules, not by the number.

The bearing that does not change

The primary sign of danger is noticed before any calculation: the bearing steady while the range falls. The board tests for it separately and says so plainly, because the conclusion from it is drawn at once.

Exercises with a known answer

The generator builds the plots from a course and speed chosen in advance, so the answer is exact and can be checked. Doing it the other way round — scattering plots at random — produces problems with forty-knot bulk carriers.

What you can do

Find a target's true course and speed from two plots
Get CPA and TCPA with an honest error bound
See the speed triangle and the line of relative motion
Test a maneuver before putting the wheel over
Find the course for a required passing distance, both ways
Work exercises with the answer checked

Why the target's true course comes from addition, not subtraction

Because relative motion is the difference of two true motions, so to get back to the target's true motion the difference has to be ADDED to your own. In board notation: er is your vector, rm the relative one, em the target's true vector, and em = er + rm. The sign here is what people get wrong most often, and the error does not look like an error: you get a plausible course, just not the right one. The giveaway is the aspect — with the sign reversed, a target closing on you comes out as one opening. That is exactly why the triangle is drawn here: on a diagram a reversed sign is obvious, in a column of numbers it is not.

Frequently asked questions

Why should the interval between plots be six minutes?

It is usually explained by the arithmetic: in six minutes a ship covers a tenth of its speed in miles. The real reason is different — over a short interval the target moves too little relative to you compared with the precision of the readings. Measured: on a two-minute interval the CPA uncertainty reaches 4.65 miles, on six minutes 0.34, on twelve 0.29. The six-minute rule is about letting the displacement grow well beyond the reading error.

Why does it sometimes warn even on a long interval?

Because what matters is the displacement, not the interval. If the target is on nearly your course at nearly your speed, the relative speed is small and even twelve minutes give a tiny displacement. Worse, with a slow target the error in the relative vector enters her true course amplified: a 4.5-knot target while you make ten doubles it. The six-minute rule is necessary, not sufficient.

What does "the bearing is not changing" mean?

That the target is on a collision course. If the bearing stays constant while the range falls, you and she are on converging courses leading to the same point. It is the fastest sign of danger there is, and it needs neither a board nor a calculation — two bearings are enough.

Does the trial maneuver allow for the target altering too?

No, and it should not. A trial maneuver answers "what happens if I do this and she carries on as before". Assuming a maneuver on her part means relying on her action, which the Rules do not permit: the give-way vessel must achieve a safe passing by her own action.

Why are two courses offered?

Because the required passing distance is usually achieved by altering either way, and the choice is not made by the size of the CPA. Rule 8 requires an alteration large enough to be readily apparent and made in ample time, Rule 17 forbids the give-way vessel altering to port for a vessel on her own port side in a crossing, and in a narrow channel the choice is limited by the channel itself. The tool shows the options; it does not prescribe the maneuver.

Can this replace ARPA?

No. It is a teaching board and an arithmetic check: manual plotting remains a required skill precisely because ARPA can be wrong, lose a target, or be switched off. The decision to pass is made on the ship's own equipment and on lookout, not on a page in a browser.

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Who is this tool for?

⚓ Sailors and yacht crews

Published 01 Sep 2026 Updated 06 Sep 2026 Author: The Supreme