The one number a beat depends on
A layline is the line from which the mark is laid in a single board: get to it, change tack, and you fetch. Where it sits depends on exactly one thing about your boat — how close to the wind you actually sail. Call it the splay: the angle off the true wind that your boat makes best progress at.
Everything on the navigation plot inherits from that angle. Get it wrong by three degrees and the corner moves; get it wrong by ten and the plot is drawing somebody else’s boat. So Race Control is specific about where the number came from, and says so on screen.
1 Where the angle comes from
| Rung | What it is |
|---|---|
| tuning table | Your own target wind angle, read off the boat’s tuning sheet and interpolated at the live wind speed. Measured on this boat — the best answer there is. |
| polar | The angle that maximises progress toward the wind across your polar. Modelled rather than measured, but defined at every wind speed the polar covers. |
| fallback | A fixed pair — 37° off the wind upwind, 30° off dead downwind — used when nothing better exists. A guess, and badged as one. |
Rung one: your own sheet
A tuning sheet is a table of wind speeds against settings, and one of its columns is the target wind angle. At a wind speed between two rows, the value is interpolated between them:
Read as a sentence: halfway between the two rows of the sheet, so halfway between the two angles.
The reading rules are the tuning sheet’s own, and they are covered in targets and interpolation: between rows it interpolates, past the ends it clamps rather than extrapolating, and a cell containing a word rather than a number yields no number at all. That last one matters here. A crew who wrote Max in a speed column has stated a setting, not a speed, and a layline may not be computed from it — the chain drops to the next rung instead of coercing the word.
Rung two: the polar’s own optimum
Without a usable sheet, the platform asks the polar directly. Progress made good toward the wind is the boat speed at an angle times the cosine of that angle, and the best angle is wherever that product peaks:
Read as a sentence: point too high and you go slowly; bear away too far and you sail extra distance — the layline is the angle where those two stop trading evenly.
The sweep runs in half-degree steps, which is fine enough that the answer is not quantised to the polar’s own five- or ten-degree bins and cheap enough to redo every time a telemetry frame arrives.
The sweep is confined to the polar’s own range of angles, and that bound is load-bearing rather than tidy. A polar lookup clamps to the nearest bin outside its grid, so sweeping from 0° across a polar whose first row is 40° would see a constant boat speed with the cosine climbing toward 1 — and would confidently report a layline of 0°, which is to say that the boat sails straight into the wind.
Rung three, and the plausibility gate
The chain never comes back empty: the fixed pair always answers. That is a deliberate exception to the rule that the rest of the platform follows — an absent number is shown as an em dash rather than guessed — and the badge is what pays for it. A navigator can see immediately that the corner on the plot is drawn from a class default rather than from their own sheet.
A rung only wins if its answer is plausible: an upwind splay has to land between 0° and 90°, a downwind one between 90° and 180°. A sheet with a blank angle cell, or a polar that never reaches upwind angles at all, drops through to the next rung rather than putting a nonsense number under a confident badge.
The two fallback numbers are quoted in different frames on purpose. The upwind one is 37° off the wind, which is already a wind angle. The downwind one is habitually said as “30° off dead downwind”, which is a wind angle of 150° — and it is stored that way, because the other two rungs speak wind angles and a chain whose rungs disagreed about units would be a silent tactical error rather than a loud one.
2 From an angle to a pair of lines
A splay is a magnitude; the tack is which side of the wind you take it on. So one angle gives two courses:
Read as a sentence: the two courses that sail your best angle, one either side of the wind.
Each layline is kept with two bearings rather than one: the course a boat sails to reach the mark, which is the number to compare your heading against, and its reciprocal, which is the direction the line is drawn from the mark outward toward the water the fleet is still in. They differ by 180° and mixing them up draws every layline backwards, so both are named rather than one being derived at the point of painting.
Which splay a mark takes is decided by the mark, not by the boat: the weather mark is approached upwind, a gate mark downwind. Two of the five marks the plot can carry have no laylines at all. The offset is rounded seconds after the weather mark on whatever angle the rounding leaves you on. The safety mark sits a few metres in front of the weather mark, so its laylines would be the weather mark’s own drawn a boat length away — two pairs of near-identical rays over the busiest corner of the plot, which is clutter rather than information.
3 Board times: how long on this one?
The question a navigator asks on a beat is not “when do we get there”. It is how long do we hold this board — two minutes on this one and five on the other, and the mark is laid.
That is the same construction the routed time-to-line tier solves, aimed at a point — a mark — instead of at a line. It is deliberately the same code rather than a second copy of it, so the two tabs can never disagree about how this boat sails.
Two identities do almost all the work, and they are worth knowing because they explain what a board plan is actually made of. Sail two legs at plus and minus the same angle to the wind, and:
Read as a sentence: the total distance depends only on how far upwind the mark is; the split between the two boards depends only on how far to the side it is.
The first line is the one that surprises people. However the two boards are split, and wherever the change of tack falls, the total is the same — the cross-wind halves of the two legs cancel while the along-wind halves add. It is why a beat is not made shorter by tacking cleverly, and why the only thing the geometry can tell you is when, not whether.
The worked example
Take a mark 1000 metres upwind and 300 metres to one side, a splay of 40°, and a boat that does 6.0 knots at that angle:
Read as a sentence: two and five, in the shape a navigator says it.
The headline is the first number, and it is seconds left on the board you are on rather than seconds in total. Which board that is comes from your course over ground — the same reading the routed tier uses to decide which tack you are on. Put the same boat on the other tack at the same spot and the plan comes back in the other order: 4:47 of port left instead of 2:16 of starboard. The total is identical to the last digit, because of the first identity above.
Three shapes of answer
| Shape | What the geometry found |
|---|---|
| two boards | The mark is inside the cone the two laylines span. Hold this one, change, and it is laid. The answer the feature exists for. |
| fetching | The mark is laid from here on the board you are already on. No maneuver at all, and no “time left on this board” — this board goes all the way. |
| change now | The mark is laid the instant you change onto the other board. The current board is done, so its time left is zero. That is an exact reading, not a rounding. |
No separate reachability test decides between them: a mark outside the cone solves with a negative leg length — it would need the boat to sail backwards — and that failure is the signal to try the single-board shapes.
A single-board plan is also flagged overstood when the mark can be fetched at an angle freer than the layline, meaning distance has already been given away. The threshold is half a degree, which is the resolution the layline itself is known to — the polar sweep steps in half degrees and a tuning sheet carries whole ones. Finer than that, the word “overstood” would be reporting arithmetic rather than sailing: at a mile, half a degree is sixteen metres.
4 Which mark the plan is aimed at
The point of sail picks the mark, not the order the marks were laid on the plot. A boat beating is going to the weather mark; a boat reaching or running is going to the gate. The dividing line is a wind angle of 90°, the same rule the targets tab uses to choose between its upwind and downwind tables, so the two cannot disagree about which half of the course a crew is sailing.
Three marks are candidates and two never are. The offset and the safety mark are rounding fixes rather than destinations — a safety mark is always the nearer buoy on a beat, and counting a crew down to a mark they are meant to pass would answer a question nobody asked.
A gate is two marks, so both plans are computed and the shorter wins, badged with which one it is. And when the two come out equal — a gate square to the wind, where each mark costs the identical time — the tie is left standing rather than broken:
Mechanically that is one word: the comparison requires a strict improvement, so an exact tie keeps whichever mark comes first in the plot’s own order and stays there rather than swapping every frame.
A gate’s left and right marks are named looking upwind from the start line, and they keep those names all the way round the course. A boat running back down to the gate is facing the other way, so a label defined per leg would reverse its meaning halfway round — at precisely the moment nobody has time to work out which mark the tablet means.
5 Where the speed comes from
Every board needs a speed to turn its distance into seconds, and there are two sources with a deliberate order:
- The polar, which is modelled but defined at every angle — and is the same lookup the routed time-to-line tier makes, so one boat gets one speed for one angle on both tabs.
- Your own target speed from the tuning sheet — measured on this boat, and admissible only for a board sailed at that sheet’s own target angle.
That restriction is the reason. A row of a tuning sheet says “at this wind speed, sail this angle at this speed”. The speed belongs to the angle. Timing a reach at 70° with the upwind target speed would be a number nobody measured wearing a measured boat’s name.
The consequence is stated rather than hidden: a boat with tuning sheets and no polar gets its beats and its runs, and cannot time a fetch. The card shows an em dash and names what is missing.
What this does not know
- An estimated mark is a radio call, not a position. The weather mark arrives as a bearing and a distance from the middle of the line and is plotted on a flat-earth approximation, so it can be a hundred metres out. Laylines drawn to it inherit that error exactly. The plot draws an estimate hollow and a mark fixed at a rounding solid, because the difference between them is the difference between advice and a line you can bet a lap on.
- It is a plan, not a projection. Every board is timed at its own angle from now. A boat currently cracked off at 70° with a 40° layline is being told how long the board lasts once it comes back up to the layline angle — the present course decides which tack you are on and nothing else. The two answers differ by exactly the distance the crew is choosing not to sail.
- The maneuver cost is a flat number you set. One figure for a tack and one for a gybe, charged whole. Nothing here models a bad tack, a wipe-out or the two lengths you lose to a boat on your hip.
- The wind is assumed to hold. The plan is solved against the wind direction and speed of this instant. A beat is minutes long and the breeze is not; a shift resolves the plan again, and the numbers move.
- A badged fallback is still a guess. When the chain reaches the fixed pair, the corner on the plot is a class default for some boat rather than a measurement of yours. Upload a polar or a tuning sheet and the badge changes with the number.
The worked figures above are arithmetic on a stated geometry — a mark a round 1000 metres upwind, a splay of 40°, a speed chosen so the sums can be checked with a calculator. They are what the formulas produce, not a record of a beat anybody sailed.