What the terms mean

Angle of attack

Angle of attack is the angle between the flow actually arriving and the chord, the straight line from luff to leech. It is not the sheet setting. The sheet fixes where the sail sits relative to the boat; the angle of attack depends on where the wind is coming from at that point on that sail.

Four things move it with the sheet untouched. Heel tips the sail out of the plane the flow lies in. Leeway changes the direction the boat is travelling, so it changes the wind the sail meets. The other sail's upwash or downwash turns the flow before it arrives. The gradient gives every height its own apparent wind, which is why the head can stall while the foot still drives. Underwater the definition holds too: leeway is the daggerboard's angle of attack.

Apparent wind

Apparent wind is the wind the boat actually meets: the true wind combined with the boat's own motion through it. Drawn as a triangle, one side is the true wind, one side is the boat's speed reversed, and the third side is what the sails, the telltales and the crew feel.

Changing either input turns that third side. More true wind swings the apparent wind aft and strengthens it, except deep downwind with the boat running away from the wind nearly as quickly as the wind itself, where more true wind stops meaning more apparent wind. More boat speed always swings it forward, but it strengthens the apparent wind only while the apparent wind is ahead of the beam: square to the boat, extra speed adds nothing to the strength, and further aft than that it takes strength away. Upwind the apparent wind is always well forward, so there speed and strength rise together. A boat stopped in the water feels the true wind exactly, in its true direction.

That is why a gust arrives twice on a 49er: first as a jump in strength with the angle opening aft, then, as the boat accelerates, as a second rise with the angle closing forward.

Association is not causation

An association is a pattern across a set of boats: those that did more of one thing also recorded more of another. It describes how the numbers moved together in that fleet. It does not state what happens to one boat that changes its own behaviour.

The reason is that nobody intervened. The same pattern comes out of several arrangements of cause. The first quantity may drive the second; the second may drive the first, since a boat already leading manoeuvres more in covering; or a third quantity, wind band or boat speed, may drive both while the two have no connection. The data cannot separate them, because each boat chose its own values.

A fleet-wide association is useful for deciding what to test, and the test is the crew's own controlled comparison, one variable with the sides swapped.

Attachment and stall

Flow over a sail or a foil does one of two things. It either follows the surface all the way to the trailing edge, which is attached flow, or it breaks away and leaves a churning wake behind. Lift is made only in the first case.

As the angle between the flow and the surface rises, the air on the low-pressure side has to slow more steeply toward the trailing edge. Past a point it cannot, and it detaches, from the back forward. Stall is therefore a threshold rather than a slope: the last degree costs far more than the previous several, and recovery needs the angle brought well back, not returned to where it broke.

Drag stays high while lift collapses, which is why a stalled mainsail is heavy on the sheet and gives no acceleration.

Attention as a limited resource

Attention is a budget spent in the moment, and the two routes to a decision draw on it very differently. Recognising a condition that has already been named and answered is close to free. Constructing an argument, working out what a reading means and what follows from it, is slow and crowds out everything else, including the sheet and the tiller.

The budget also shrinks under load, so a decision that was comfortable in training takes longer and goes wrong more often in the last minute of a start.

The cost shows in whatever spends attention without adding information: a datum called twice by two people, a word that has to be interpreted before it can be acted on, a rule with no threshold in it, which leaves the evidence to be weighed from scratch each time.

Bedding-in versus permanent stretch

A new wire, its swage and its pins have small gaps and a lay that closes up the first time real load passes through them. That settling is bedding-in: it happens once, it does not return when the load comes off, and after it the assembly is in the state it will work in. Permanent elongation is different. The wire is being carried past what it recovers from, a little more on each loading cycle, so its length keeps growing.

The distinction shows on the gauge. A reading taken before the rig has been loaded and released once is reading the gaps rather than the tension. A reading that drops once and then holds across days at an untouched turnbuckle is bedding-in; one that keeps drifting is elongation or a terminal that has not seated; the terminal is checked first, and a wire whose length keeps growing is replaced rather than adjusted.

Bending stiffness

Bending stiffness is how hard something is to bend sideways, which is a different question from how hard it is to stretch. It depends on the material and, very strongly, on how far the material sits from the middle of the section.

That distance is what makes the diameter matter so much. Doubling the thickness of a round bar gives four times the area to stretch and sixteen times the resistance to bending, because the extra metal is added at the outside where bending loads it hardest. A tension gauge is caught by exactly that: it pushes a wire sideways and the wire resists partly through the tension in it, which is the same whatever the diameter, and partly through its own bending, which rises as the fourth power of the diameter.

A stranded wire sits somewhere between two extremes. If the strands lock against each other when the wire is bent it behaves like a solid bar; if they slip past each other it behaves like a bundle of thin ones, which is far easier to bend. Where in between a given rope falls is not usually published.

Bias and scatter

Errors come in two kinds. A bias is an offset that lands the same way every time: every gauge reading high by the same amount, every forecast left of the wind that arrived. Scatter is spread with no preferred direction.

Repeating a measurement averages scatter down, because the misses fall on both sides and cancel. Repeating it does nothing to a bias, since every repetition carries the same offset, and the mean of a hundred readings is as wrong as the first. The fixes differ: a bias is found by comparing many readings against a reference, then subtracted, while scatter is reduced only by taking more readings or by removing whatever makes the process noisy. Reading the rig gauge at a different height on the wire each time produces scatter; a gauge that disagrees with another gauge produces bias.

Binning

Binning sorts logged samples into groups that share a condition, wind band and sea state, so that a number from one group is compared only with numbers from the same group. Without it an average speed is largely a record of which conditions the crew sailed most.

The width of a bin is a choice with a cost either way. A wide bin holds plenty of samples but mixes conditions the boat is sailed differently in, so the average describes no real state. A narrow bin is clean but thinly populated, and a bin holding a handful of samples will show whatever the last session happened to do. Bin edges are fixed before the samples are sorted, because an edge moved to suit a result is a result manufactured, and each target in the matrix carries its sample count.

Centres of effort and resistance

Force spread over a whole surface can be replaced, for working out what it does, by a single force at one point, chosen so that the total force and the total turning effect are unchanged. The sail plan has such a point, its centre of effort; the daggerboard, rudder and immersed hull together have a centre of lateral resistance; the crew's bodies have a centre of mass.

Each point moves when its distribution moves. Raking the mast aft carries the rig's force aft, raising the board carries the underwater force aft, and a sailor sliding out along the wire carries the crew's mass outboard. What matters is where two of them sit relative to each other: with the rig's point behind the foils' point, the bow is pushed up toward the wind and the tiller holds the difference.

Chord, camber, draft, entry, leech

Take a horizontal slice through a sail at one height. The straight line from luff to leech is the chord. The cloth bows away from it, and the greatest gap between the two is the depth; camber is that depth divided by the chord, so it is quoted as a percentage.

Draft position is where along the chord the deepest point sits, again as a percentage of chord and not of cloth. The cloth is always longer than the line it spans, so pacing the sail gives a wrong answer. Entry is how sharply the forward part turns the flow; exit angle is the direction the flow leaves the leech in, a bearing rather than a shape.

The top batten lies near the chord at its height, so its angle to the boom reads as exit direction at the head.

Cloud wind signatures

A cumulus is the visible top of a column of rising air. The air going up has to be replaced, so near the water the wind is drawn in toward the cloud from every side. Ahead of an approaching cloud that inflow opposes the wind already blowing and pressure falls away; beneath it the surface flow is going up rather than along; past it the inflow runs with the wind and pressure returns stronger. The inflow curves from both sides, so the bend is opposite on the cloud's two flanks.

Once the cloud rains, falling drops drag cold air down with them. That downdraft strikes the water and spreads outward as new wind, and its spreading edge runs ahead of the rain shaft, so the shift and the pressure reach the boat while the trampoline is still dry.

Comparing quantities in different units

Ranking two advantages requires both to be expressed in one unit. Per cent of wind speed, degrees of shift, boat lengths of lane and seconds of manoeuvre are four kinds of number, and nothing orders them until each is converted into what it is worth on the course, metres toward the mark or seconds.

Each conversion has its own arithmetic. Extra wind becomes metres through the speed it adds multiplied by the time the boat holds it; a shift becomes metres through the lateral separation it acts on; a tack becomes metres through its logged loss.

Those conversions carry conditions, so the ordering they produce is local. Change the wind band or the separation and the same three quantities can rank differently. A priority order is the output of the arithmetic rather than a rule about sailing.

Confidence and calibration

A confidence is a number attached to a claim: how likely the claim is to be right, stated before the outcome is known. It is part of the claim, not a description of how certain the crew feels.

Calibration is whether those numbers are honest. A crew is calibrated when the calls it gives seven chances in ten come true about seven times in ten, and those given nine chances in ten about nine times in ten. A single call proves nothing: one given seven chances in ten that fails is exactly what the number predicted some of the time. Only a long run of calls, sorted by the confidence attached, shows whether the scale means anything.

That is why the pre-race model carries a written confidence and the debrief compares it with the outcome.

Confirmation bias and naming the test first

Confirmation bias is not a decision to ignore evidence. It is the ordinary way a belief reads ambiguous evidence: whatever arrives is read in the light of what is already held, so almost everything counts in favour.

It survives because most observations on a racecourse can be read either way. A header on the favoured side is called an oscillation that will return; the same header on the other side is called a persistent shift. With both readings available the model is never contradicted, and a model that cannot be contradicted has not been tested.

The remedy is to fix the reading before the evidence arrives. Ashore, the crew writes down what would mean the plan is wrong, what it has to look like and how long it has to last. A plan with no such signal is a preference.

Controlled comparison

A controlled comparison is a test built so that only one thing differs between the two runs being compared.

The difficulty is that two boats never sail in the same water. Wind speed, wave angle and the wind's own cycle all differ across a few lengths, and any of them can produce a gap larger than the setting being tested. Changing one variable at a time removes the confusion between two changes; reversing the boats' positions removes the confusion between the change and the place. An effect belonging to the boat travels with the boat when the sides are swapped, while an effect belonging to the water stays where it was.

So a line-up is sailed, the gain logged, the sides swapped and the run repeated. A gain that reverses on the swap was a difference in the wind.

Convergence

Convergence is what happens where two streams of air moving in different directions run into each other. The air cannot pile up at the surface, so along the seam the flow is squeezed and lifts; through that band the surface wind is stronger and its direction is a blend of the two.

The cause is usually the shore. Friction turns the surface wind more over land than over water, so air that has crossed a coastline arrives at a different angle from air that has been over water throughout, and the two meet in a band the geography holds in place.

It is a pressure feature, not a shift. It shows as a strip of darker water that keeps its position while gusts travel through it, and it is routed into, not tacked on, because it will not swing back.

Correcting a layline for current

A layline drawn from the wind alone is the line the boat would sail if the water stood still. What reaches the mark is the sum of two motions: the boat through the water, and the water over the ground.

Draw the boat's motion through the water as one arrow and add the current as a second arrow from its tip. The line from the first tail to the second head is the track over the ground, and the layline is the one whose track passes through the mark. Current setting toward the windward mark carries the boat up, so the true layline lies short of the wind-only one and a boat tacking on wind alone overstands.

At a gate the sign reverses between the marks: a set carrying the boat toward one carries it away from the other.

Correlation

Two quantities are correlated when they move together across a set of observations in a consistent way, either rising and falling together or one rising as the other falls. The strength of that pattern is itself the finding: it says the two are tied to something common, not which one drives the other, and not that either causes the other at all.

The absence of a correlation is a separate finding, and it does not mean the quantity is unimportant. Two things can each matter greatly and still show no pattern together, because one is being actively cancelled, because a third quantity moves both, or because neither varied enough in the sample.

On a well-sailed 49er the heel trace and the rudder trace do not move together, since heel is answered with bodies and sheets rather than with the tiller. That absence is evidence the correction is working, not evidence that heel costs nothing.

Cross-track error

Cross-track error is a distance measured sideways from a reference line, and two different quantities go under the name. The class and the event trackers publish the extra distance sailed upwind away from the middle of the course. The crew logs instead the boat's signed lateral distance from the straight line between the marks, one side negative and the other positive. The two are not interchangeable, so the log states which is meant.

A leg produces a series of those values, and one figure for the leg is either the largest excursion or their mean; the first says how far out the boat went, the second how long it stayed out. Either way the number records a decision to take a side, not how well the boat was sailed, so it is read beside the plan and the shift log.

Derived quantities

A derived quantity is not measured; it is calculated from quantities that were. A satellite logger measures position against time: from a run of positions it gets speed and course over the ground, and it carries no instrument that touches the air or the water. Its true wind is therefore worked back from the boat's own motion, on assumptions about how the boat sails, and every error in position, in those assumptions and in the current running underneath is carried into the answer.

The same applies to VMG, distance to line and time to burn, each computed from the same track. The crew's head-to-wind compass bearing is a direct reading of something the logger can only infer, so the derived figure is checked against it before it is used, and the disagreement is noted rather than averaged away.

Directional (yaw) stability

Directional stability is the tendency to hold a heading after a disturbance, and it comes from lateral area both forward and aft of the point the hull turns about.

If the bow swings, the whole boat is momentarily moving slightly sideways, so the board and the rudder each meet the water at a new angle and each makes side force. The rudder's force acts far aft of the turning point and its moment pushes the stern back into line. A longer separation between the foils gives a longer arm and a stronger restoring moment; a shorter one makes the boat agile and nervous.

On the 49er the foils cannot be moved, so the crew changes the immersed lateral area instead. Weight aft settles the boat; a raised board cuts area forward and lets the stern slide.

Distribution and tails

A distribution is the whole list of results an option can produce, together with how often each one happens. The average is one summary of it, how widely the results scatter is a second, and the tails are the rare results at the two ends.

Summarising an option by its average alone throws away what a series most needs to know, because two options can share an average and differ completely in shape. One returns a middling result almost every time; the other returns a good result usually and an occasional disaster. Which is preferable depends on whether the disaster can be discarded.

Each spot on the start line has its own shape. The favoured pin has the best average and the heaviest bad tail; the boat end has a lower average and a thin one.

Downwind load

Upwind the boat sails into the wind and its own speed adds to what the sails feel. Downwind it sails away from the wind, and whether its speed adds or subtracts depends on where the apparent wind already sits.

The apparent wind is the true wind with the boat's motion taken off it, and more speed always swings it forward. Whether more speed also strengthens it turns on which side of the beam it is on. Abaft the beam, which is the slow deep case, more speed takes strength off: a boat stopped in a gybe feels the whole of the true wind and the same boat planing feels much less. Forward of the beam, which is where a skiff sits once it is going, more speed puts strength back and the boat builds its own wind. The turn between the two comes when the boat's speed straight downwind matches the true wind. Because aerodynamic force rises with the square of that wind, the load follows the apparent wind and not the true one: at a given speed, bearing away squarer always takes apparent wind off the sail and heading up puts it back, and the heaviest loads come with the apparent wind built up rather than with the boat stopped.

Sheet load is the instrument. Rising load with rising speed is the boat working; rising load with the boat slowing is the start of the wipe-out.

Equilibrium: two balances at once

A boat at steady speed and steady heel is not a boat with no forces on it. It is a boat whose forces cancel, and they cancel in two separate accounts that must both balance at the same time.

The first is force along the course: drive from the sails equals the resistance of hull and foils. Excess drive is not stored, it accelerates the boat, and the boat accelerates until the added resistance has consumed it. The second is turning effect about the fore-and-aft axis: the heeling moment of the rig equals the righting moment of the crew on its lever. Heel is the free variable there, and it moves until the two moments match.

That is why a gust is answered first by the boat lying over, before either sailor has moved.

Expected value

Expected value is what a choice is worth on average if it were made many times: each possible outcome multiplied by the chance of it happening, then added together.

Its use is that it puts rare large outcomes and common small ones into one currency. A move that works four times in five can still be the wrong move if the fifth outcome is a capsize, a disqualification or a protest hearing, because that one outcome is large enough to outweigh four small gains. It works the other way too: a gain has to be scaled by how often it actually arrives, not by how good it looks when it does.

The marginal cross is the standard case. The length it gains when it works is weighed against the certain cost of a turn and the small chance of damage.

Fatigue and cyclic loading

A part can fail at a load it has carried many times before. That is fatigue: damage that accumulates with the number of load cycles at stresses well below what would break the part in a single pull; the larger the cycle the more damage it does, but no single one of them need be near the breaking load.

Each cycle does a little local damage and nothing repairs it in between. The damage concentrates wherever the material is forced to flex in one small place, which on a wire is at the termination, where the strands are clamped and cannot share the bending. A crack starts there, grows on every tack and every gust, and the strands still intact carry the load until they cannot.

So a shroud gives no warning through rig tension or helm feel, and the inspection looks at the swage mouths rather than the wire between them.

Fleet minima and fleet averages

A tracked fleet yields several kinds of summary number, and they answer different questions. A minimum is one end of a distribution, the single best value any boat reached in that sample, produced by whichever boat had the position, the nerve and the luck. An average is the middle of a distribution, with about as many boats worse as better.

Both discard the spread, which is where the information a crew can act on sits. Neither is a specification. A fleet minimum is not a standard to be matched, because no boat held it race after race, and an average advantage is not a quantity any single boat received.

Such figures are useful as a scale. They give the order of magnitude at this level of racing, against which the crew's own logged gaps and times can be read.

Froude number and hull regimes

Froude number is a speed written as a ratio rather than in knots: the boat's speed set against the speed of the waves a hull of that length makes. Having no units, it puts hulls of different sizes on one scale.

It matters because the physics changes at thresholds in that ratio, not gradually. At low values the hull sits inside its own wave system and buoyancy carries the weight. As the ratio rises that wave lengthens until it is as long as the hull, and going faster means climbing it, which is where wave resistance dominates. Higher again, flow under the bottom carries part of the weight, the hull lifts and wetted area falls.

A 49er crosses both thresholds in ordinary racing wind, which is why the fastest fore-and-aft trim moves aft with speed rather than staying put.

Gradient wind and surface backing

Well above the surface the wind blows along the lines of equal pressure rather than straight from high to low, because the earth's rotation deflects moving air and that deflection balances the pressure force. This is the gradient wind, what a forecast gives.

Near the surface, friction slows the air. A slower stream is deflected less, so the balance breaks and the air swings partly across the isobars toward the low pressure. The surface wind is therefore weaker than the gradient wind and rotated from it, anticlockwise, or backed, in the northern hemisphere and the other way in the southern, because the deflection reverses between them. The rougher the surface the larger the effect, so the turning is greater over land than over water, and the crew's head-to-wind bearings are expected to sit off the forecast direction by that amount.

Ground and water

A satellite logger measures where the boat is on the earth, so every speed and course it reports is motion relative to the sea bed. The water the boat sails in is itself moving.

Motion through the water and the current add together to give the motion over the ground, so each logged number is a sum of what the crew did and what the tide did, with nothing in the file to separate them. The compass shows where the boat points through the water and the track shows where it went over the ground; the angle between the two is leeway plus the current's set, taken together.

The same trim sailed on opposite sides of a tidal course logs different speeds, and the difference reads as a trim gain unless the current is recorded with the run.

Gust and lull statistics

The gust and lull figures here are statistics of wind speed at a point. They say how far the wind varies about its own mean and how often, as proportions of that mean, so the same percentage is a small change in light air and a large one at the top of the range. They describe time, not the geography of the course.

The mechanism is mixing. Faster air from higher up is brought down in parcels, each arriving as a patch of stronger wind travelling with the flow; between the patches the surface wind is slower.

Two things follow. The figures are averages of a spread, not a clock, so a crew counting seconds to the next gust will be wrong regularly. And settings are chosen for the distribution: powered enough for the lull, controllable in the gust.

Halyards: hoist, luff tension and the mark

A halyard pulls the head of a sail up against its tack, so it sets two things at once: how high the head sits, and the tension in the luff between the two ends. On the jib that tension is a shape control in its own right, separate from the rig tension that straightens the wire behind it. Slack, the luff scallops and the draft sits aft; tensioned, cloth is drawn forward, the draft comes forward with it, and the entry keeps its round as sheet load tries to drag the deepest point aft.

Because a halyard is a rope, what it sets drifts. It stretches, and it wears where it turns, so the same hauling gives a slightly different hoist and a slightly different luff tension as a season goes on. That is why the thing a crew records is a mark on the rope rather than a feel in the hand.

Headstay sag and jib fullness

The jib's luff is a wire under tension, and how straight it is decides how deep the sail flies.

The tension does not come from the forestay's own adjuster. The cap shrouds run aft of the mast, so tightening them pulls the top of the mast aft, and the mast then leans back against the headstay and tightens it. Tension applied behind the spar appears in the wire in front of it, with the mast as the strut. Bend in the mast brings the hounds nearer the deck and softens the headstay again.

A sagging headstay bows to leeward, so the luff sits off the straight line between its ends. That adds depth forward and rounds the entry, which is power and a wider groove in light air, and the first thing taken back as the wind builds.

Heel angle as a measured band

Heel angle is the angle between the mast and vertical, signed so that leeward is one way and windward the other. Written with a plus and a minus, it describes a band either side of upright, not a setting to steer to.

That matters because a band is a statement about excursions. The target is zero; the figures say how far either way the boat may stray before the loss is being paid. A boat sitting steadily at the edge has not met it, and a boat that averages upright by swinging equally both ways has not met it either, because the cost is paid at each excursion and does not cancel.

Read that way it belongs to the heel sensor and the video. The trace shows how long the boat was outside the band, and when; memory cannot.

Hold, explosive effort, endurance, recovery

The boat asks three different things of the body, and they are trained separately because they do not convert into one another.

A sustained loaded hold is the trapeze: harness load carried through the trunk to the feet for the length of a leg, while the body moves in and out along the lever. A repeated explosive effort is the manoeuvre, full-speed movement from wire to cockpit to wire, many times in a race. Endurance is neither; it is holding the quality of both, and of the decisions, through the last race of a long day.

Load by itself produces none of the three. Load creates the demand and the adaptation happens afterwards, in the rest. The measurable version is the loss through a manoeuvre in the last race of a day set against the first in the same wind band and sea state.

How a sail can push to windward

A sail makes its force at right angles to its own surface. While every part of the sail still faces to leeward, every part of its force has a leeward component, and easing only makes it smaller. Once part of the sail rotates far enough that its surface faces the other way, the force it makes points the other way too: a genuine pull to windward, not a smaller pull to leeward.

The upper leech gets there first, being free to rotate when sheet load comes off. An undersheeted gennaker opens its leech, the head falls to leeward, and the rotated upper sail pulls the rig to windward on a long lever above the heel axis. With both sailors already out, nothing is left to answer it, and the response is to head up and sheet on.

How structures lose strength

Structures lose strength in distinct ways, each with its own mark. Corrosion is chemical attack, fastest where two different metals sit together in salt water, because the pair behaves as a cell and the less noble one is eaten; the sign is a stain or powder at the joint. Fretting is two parts rubbing through a small movement under load, polishing then wearing the mating faces; the signs are a black streak and an oval hole. Creep is a part taking a permanent set under a continuous load, so a gauge reading drifts between days with nothing adjusted.

Cracks grow with each load cycle from wherever stress concentrates, a fastener hole or a swage mouth, and a hairline is the warning. Ranking follows mechanism: a stain is a finding, a crack at a terminal is the next failure.

How the chine and forward V make force

A hull does not need to be a foil to make force. Any surface that changes the direction of the water running past it gets a force back, equal and opposite to that change.

The forward chine is a hard edge along the topsides. Water climbing the bow meets that edge and is turned down and out rather than up the side. Turning water down means pushing it down, so the water pushes the hull up by as much, and the spray that would have come aboard goes outboard. The lift and the dryness are one effect, not two.

The forward V works on arrival rather than deflection. A flat panel meets the water all at once; a V enters as a wedge, so the wetted width spreads along the section and the impact arrives over a longer time.

How waves grow

A sea state is set by three inputs: wind strength, duration, and fetch, the distance of open water it has blown across. The wind feeds energy into the surface gradually, so the sea keeps building after the wind has stopped rising and keeps running after it has dropped; waves lag the wind at both ends. When the sea holds all the energy that wind can give it, more duration and fetch add nothing and it is fully developed.

Swell is wave energy that has left the area where it was made. It sorts itself into long, regular crests, arriving with a period and direction owing nothing to the wind at the boat. Wind waves run with the breeze in short crests the boat meets many times a minute, while swell runs through them from elsewhere and is steered as terrain.

Hull resistance components

Resistance is a sum of separately caused parts. Friction is water shearing along the wetted skin, so it follows wetted area and dominates while the boat is slow. Wave resistance is energy left in the waves the hull makes, and it climbs steeply as the hull nears the speed at which its own wave is as long as itself. Form drag is the pressure difference between the hull's front and back, largest when flow separates behind an immersed transom. Induced drag is the price of the side force the foils make.

Residuary resistance is what remains once friction is subtracted. Drag area restates resistance as an equivalent area so two trims compare directly. Weight forward in light air cuts wetted area and friction; the same weight at planing speed buries the bow and pays in wave and form drag instead.

Induced drag and aspect ratio

Induced drag is the drag a foil produces purely by making lift. It cannot be faired or polished away, because it is the price of the lift itself.

A foil lifts by carrying higher pressure on one face than on the other, and at the tip the water escapes around the end from the high side to the low, rolling away astern as a vortex. That escaping flow is energy left behind, and it grows faster than the load causing it, roughly with the square of it. A long, narrow foil has little tip for its area, so it leaks less for each unit of side force.

Raising the daggerboard shortens the span, which removes area and that slenderness together: less wetted surface, but every remaining part of the blade works harder for the grip it still has to make.

Ladder rungs

Ladder rungs are lines drawn across the course at right angles to the wind. Progress upwind is progress up the rungs, so the boat on the higher rung is ahead however far apart the two boats are sideways. The distance between two boats measured along a rung, across the wind, is their lateral separation, or leverage.

When the wind shifts, the rungs rotate. Two boats level on the old rungs are no longer level on the new ones, and the gap that opens is proportional to both quantities: twice the shift opens twice the gap, and twice the separation opens twice the gap again. Between two boats on the same line it opens nothing.

So crossing and tacking on a rival's hip freezes the position, and splitting to opposite sides prices every wind change heavily in both directions.

Lag, overshoot and settling

A correction has three parts: a measured error, something that acts on it, and a delay between the two. With a short delay the input arrives while the error is still there and cancels it. With a long delay the state has moved on, so the input is too large for the state it lands in, and the boat is carried through the target and out the other side. The overshoot then needs its own correction.

Play in the rudder stock, tiller and extension joint is a delay of exactly that kind, a dead band in which the tiller moves and the blade does not, so the helm's input arrives late and is then overcorrected. Settling time is separate: the boat is at its new state only when speed, apparent wind, leeway and heel have all stopped moving.

Leech load becomes rudder load

The vang pulls the boom down, so an eased mainsheet lets the boom swing out without letting the leech rise. Upwind that is the point; in a bear-away it is the problem.

With the leech held shut, the upper mainsail keeps its angle to the wind as the boat turns away, so it keeps making force, high in the rig and, with the boom out, well outboard of the centreline. A force that far off the hull's line of resistance is a turning moment: it heels the boat and pulls the bow back toward the wind. Only the rudder can hold the bow down, at a large angle, where its drag is highest. With the vang released first, the leech twists open as the sheet goes, the top of the sail unloads, and the turn takes a small helm.

Leeway

Leeway is the angle between where the boat points and where it is actually travelling through the water, and it is what makes the daggerboard work.

The board is a symmetrical foil. With the water running straight along its chord it produces no side force whatever. Held at a small angle to the flow it turns the water sideways and receives an equal push the other way, and that push is what reacts the sail's lateral force. Leeway is an input bought deliberately, not a leak. Two things follow: the force grows with speed, so the angle needed falls as the boat goes faster, and a boat with no way on has no grip at any angle.

It shows in the wake, whose windward edge leaves the hull at a wider angle than its leeward edge.

Lift and drag

The air pushes and pulls on every part of a sail, and all of it adds up to one force in one direction. Lift and drag are not two forces; they are that single force written in two parts, the part square to the apparent wind and the part along it. Which is which depends only on where the apparent wind is pointing.

That is why lift is not the same thing as drive. Close-hauled the apparent wind is well forward, so the lift vector points mostly across the boat and is mainly heeling and side force, with a small share driving. The further aft the apparent wind lies, the more of that same lift points along the course and the more of it is drive. Downwind under gennaker a skiff holds its apparent wind well forward of the true wind, and how far forward decides how the one force divides between driving the boat and loading the daggerboard.

Line bias as a distance

Line bias is the head start one end of the line holds because the line is not square to the wind.

Draw the rungs, the lines square to the wind: one end of the line sits on a higher rung than the other. That height difference is the line's length multiplied by the sine of the angle between the line and square. For small angles the sine is nearly proportional to the angle, so the gain scales in both terms: twice the bias is twice the distance, and so is the same bias on twice the line. So a modest bias on a long line can be worth more than a large one on a short line: what has to be compared is length times bias, never the bias alone.

The sign comes from the head-to-wind bearing taken in the middle: sighting along the line, the favoured end lies further forward of the beam.

Load path

A load path is the route a force takes from where it enters the boat to where it is reacted. A force cannot stop halfway. It is handed from part to part until something holds it, so every member in between carries the whole of it.

What changes along the path is not the size of the force but the area carrying it. Where the load runs through a wire's full section or a wide patch of laminate, the material is lightly stressed. Where it necks down into a pin, a swage or two fasteners, the same force is concentrated into a small area, and the stress rises in the same proportion as the area falls.

A sailor's weight on the trapeze runs wire, hounds, shroud, shroud plate, hull, which is why failures appear at terminals and fastenings rather than in the middle of a wire.

Luff curve

The mainsail's luff is not cut straight. It is cut with a convex curve, extra cloth along the leading edge, and that surplus is what the spar's bend takes up.

Match the two and the sail takes the shape it was designed to have. Bend the mast further than the cloth allows and the extra bend comes out of the middle of the sail, which flattens, opens the leech and drags the draft aft. Past that limit the sail has no more cloth to give and the surplus shows as diagonal creases running from the clew toward the luff.

A bent mast is also shorter from heel to hounds than a straight one, so bend slackens the whole rig, the forestay included.

Mainsheet and vang: which one moves what

The boom has two positions to set, and there are two controls because one will not set them. How far out the boom sits fixes the angle the lower sail presents to the wind; how far down it is held fixes leech tension and so twist. The mainsheet moves both together, in a proportion that shifts as the boom travels: near the centreline its pull is mostly downward, and outboard it is mostly sideways. The vang moves the second alone.

That division is why the vang's state has to be named whenever the sheet is discussed. With the vang loaded the boom cannot rise, so easing the sheet lowers the angle at every height and leaves the twist where the vang put it; with the vang slack the same ease opens the leech from the head, so the sheet is setting twist instead. Upwind at full power the vang is loaded, and a gust is answered in angle.

They work on different clocks and run out in different places. The sheet answers the gust cycle; the vang is set for a leg, so a gust taken on the vang is a shape change that cannot be undone in time. The sheet runs out at the leech, where the top batten hooks to windward and the boat heels and slows together, and the vang earlier and at the spar, where the bend it makes passes the sail's luff curve.

Manoeuvre loss

The cost of a tack or a gybe is not the time it takes. It is the ground not made toward the mark while the boat was turning and recovering, measured against a ghost boat that carried straight on at the VMG held before the turn.

At every instant through the manoeuvre the real boat's VMG is lower than the ghost's, and the loss is the accumulation of those shortfalls, the gap between the two tracks. Because it accumulates, a fast turn with a slow exit can cost more than a slower turn that carries its speed, which a stopwatch on the turn does not show.

The window therefore needs a closing rule. It opens when the helm goes down and closes when VMG has returned to its pre-manoeuvre value, which puts the acceleration inside the manoeuvre's cost.

Minimum weight, correctors and absorbed water

The class sets a floor for what the hull may weigh, not a target. A hull built under it is brought up with corrector weights fixed where the rules allow, so the boat leaving measurement sits at the minimum rather than below it.

Two things follow. A hull at the minimum has no margin: grams saved by fitting a lighter block come straight back as lead, so the saving buys nothing but a change in where the mass sits. And weight gained cannot be given back, because there is no corrector left to remove. Water soaked into the laminate through a loose fitting, and the resin and cloth of a repair, both push the boat above the floor and stay there.

So the hull is kept dry and unrepaired between measurements, and a weeping fitting is urgent rather than cosmetic.

Model grid resolution

A forecast model divides the atmosphere into a grid of boxes and carries one value for each quantity in each box. The resolution quoted for a model is the width of one box.

Everything inside a box is a single averaged number. A headland, a shoreline bend or a gust band smaller than a box is not smoothed away; there is no variable in which it could exist. A feature must span several boxes before the model can develop it, so the working limit is coarser than the figure quoted. A fine-grid model resolves what a coarse one cannot, which is why sea breezes appear in fine ones first.

The division of labour follows: the forecast gives the regime, the gradient direction and the timing of a change; the local bend and the pressure across one racecourse come from looking.

Modulus

Modulus is how hard a material is to stretch, and it belongs to the material rather than to the part. Steel has one number, aluminium another, and it does not change with how thick the piece is or how long it is.

The stiffness of an actual part is that number multiplied by how much cross-section it has and divided by how long it is. So two wires of the same steel have the same modulus and different stiffnesses, because the thicker one has more metal across it and the longer one has more length to share the stretch along. Thickening a wire cannot change its modulus; it changes only the area the modulus is working on.

The number is quoted as a force divided by an area, so many thousands of newtons for each square millimetre of section. Compacting a wire rope raises the figure quoted for it because the rolling packs the strands together and leaves less air in the section, not because the steel has changed.

Moment

A moment is a turning effect: a force multiplied by its perpendicular distance from the point the boat turns about. Twice the distance gives twice the moment; a force acting through the pivot gives none.

Position therefore matters more than mass. Hull weight sits near the centreline and does almost nothing to hold the boat up, while the same kilograms on the wire work through a long arm and become righting moment. Sail force acts high in the rig and heels through a lever of its own, so lift high on the sail costs more heel per unit of drive than lift low down.

The lever is read as harness load: a straight body perpendicular to the mast hangs its whole weight on the wire, and bending at the waist moves the mass inboard so the load goes soft.

Momentum and the rig in a turn

Mass in motion keeps going in the direction it was going, and the amount of motion stored is its momentum, mass multiplied by speed. Entry speed into a manoeuvre is momentum bought in advance, and it carries the boat through the part of a tack where the sails give nothing.

Turning spends it. To follow a curve, every part of the boat has to be pulled sideways, and the pull needed grows with the square of speed and falls as the radius opens out. The rig's mass sits high above the water, so that sideways pull acts on a long lever and the boat feels it as heel, outward from the turn.

A boat that enters a leeward-mark rounding not already flat therefore heels further as it turns up, and the tighter and faster that turn, the more it heels.

Motor learning

A movement learned by repetition is stored as a pattern, and what is stored is the version actually performed, not the version intended.

Three things follow. Repetition strengthens whatever is repeated, so repetitions made while tired or rushed train the tired, rushed version, and the drill ends when quality falls rather than when the count is reached. A skill binds to the cue it was practised against, so a gybe rehearsed at a moment of the crew's choosing is partly a different skill from one forced by the gate, and its timing is learned again against the new trigger. A technique under change also passes through a phase worse than the one it replaces, because the old pattern is still the quicker one.

A change therefore needs sessions after it, inside the block, not in the week before an event.

Moving the centre of effort

The whole sail plan's force can be replaced, for working out what it does, by one force at one point, its centre of effort. Where that point sits matters in two directions. Fore and aft it decides helm, since a force acting behind the point the hull and foils resist through turns the bow towards the wind and the tiller holds the difference. Up and down the span it decides how much heel is paid for each unit of drive, because force made high acts through a longer rolling lever than the same force made low.

Trim moves it. Luff tension carries the draft forward, so the mainsail's force moves forward and the helm lightens; rake aft carries the whole plan aft and creates weather helm. Easing the jib and holding the main shifts the balance aft, and easing the main and holding the jib shifts it forward. Twist moves it down the span, because opening the head takes load off the top. A hard outhaul moves it up, because the depth it removes was depth low in the sail. Heel moves it sideways, out of line with the resistance, and two opposed forces on different lines turn the boat on their own.

Option value

An option is the ability to make a choice later, and it carries value even when it is never exercised, because information keeps arriving while the choice stays open.

The wind will shift again before the mark. A boat with a tack still available can use that shift; a boat that has run to a layline or a corner holds a position rather than a choice, and later evidence cannot be acted on. Committing converts the option into whatever it bought, and the conversion runs one way.

The same arithmetic prices the discard, the last tack before the layline and the gate call. Each exists once, is worth most while evidence is still coming in, and is worth nothing once spent, so the question before an irreversible move is what it costs to hold the choice open a little longer.

Oscillating and persistent shifts

An oscillation is a direction swinging either side of a mean that stays put, so every header is followed by a lift. A persistent shift is the mean itself moving, and the wind that arrives does not come back.

The causes differ. The swing comes from mixing in unstable air, faster air arriving from above at a slightly different angle, which reverses itself. The trend comes from a mechanism with its own timetable, a front, a sea breeze building, a shoreline bend, and it runs one way while that lasts.

The test is the extremes on each tack. If the lifted heading returns to the same figure, the mean is holding; if both tacks' extremes walk the same way round the compass, the lift on one tack getting better and the header on the other getting deeper, the mean is walking. Most days carry both, a swing added to a drift, and the drift sets the side.

Overfitting

A rule built from a single day will match that day exactly, because it was made out of it. Any set of observations carries both the pattern and the accidents of that occasion, and a rule detailed enough to reproduce every accident has absorbed the accidents too. It then fails on the next day, when the accidents are different. The more conditions a rule names, the fewer occasions it can apply to and the fewer there are to test it against.

So a venue rule is written as a mechanism with named inputs rather than as an outcome. That the left paid on a given date is a record of one race; that the left pays when the gradient is offshore and the sea breeze fills is a rule, and only a second day with the same inputs confirms it.

Period and amplitude

An oscillation is described by two numbers. The period is the time for one complete cycle, from an extreme back through the mean to the other extreme and home again. The amplitude is the size of the departure from the mean, measured one way only.

Two things follow. Half of each cycle lies on either side of the mean, so the lifted and headed tacks each occupy about half a period, and the cycles in a leg are its duration divided by the period, each cycle offering a shift in each direction. The total swing from one extreme to the other is twice the amplitude, so a quoted amplitude means a change of direction twice that size.

Both numbers come from the pre-start log: the mean lies between the extremes on the two tacks, and one period is the time from an extreme back to the same extreme.

Permitted electronics

The class rule lists what may be carried aboard, and anything not on the list is off it. Some items are permitted outright but bounded by function: a compass is allowed, and allowed only to show a heading, remember a heading and keep time. Others are permitted conditionally: tracking equipment is aboard only where the class, the notice of race or the sailing instructions say it may be.

A device is therefore classified by what it does rather than by what it is called. A logger that displays VMG, distance to line and time to burn has functions no compass may have, so it cannot be carried as a compass; it is tracking equipment or it is prohibited, and which of the two depends on the event documents rather than on the boat.

Pressure in the flow

Where air speeds up its pressure falls, and where it slows its pressure rises. A sail makes force from that difference: flow runs faster over the leeward side, pressure drops, and the higher pressure to windward pushes the cloth toward it.

Air that has been accelerated cannot stay accelerated. It has to return to the pressure of the air it rejoins, slowing again as it runs aft. Slowing against a rising pressure is the hard part for any flow: the layer nearest the surface carries the least momentum, and if the pressure rise is steep enough over a short enough distance that layer stops and the flow lifts off. A gentle recovery stays attached; an abrupt one separates.

The gennaker holds its shape from the same difference, which is why a stable sail on a light sheet is no contradiction.

Prior and update

A prior is what the crew believes before it has looked: the expected direction, the expected side, the chance that the sea breeze arrives. Its job is to set how much new evidence is needed to move the belief, so a firmly held prior demands several consistent observations and a weak one is turned by the first clear sighting.

Each new observation is then combined with what was believed before, and the prior's share of the blend falls as observations accumulate, because the observations are many and the prior is one.

On the water the forecast is the prior, for direction, trend and the probability of a sea breeze. Head-to-wind bearings logged at intervals through the sequence are the updates, and by the last of them the forecast carries little weight. An observation that contradicts it wins on the water.

Projection

Projection is where the gennaker is flying and which way it faces, not how much cloth it has, which never changes. Rotated out from behind the mainsail, luff to windward and forward, it is in air the rig has not already spoiled.

It matters because a sail in the mainsail's wake is working in slow, disturbed air whatever its shape. Rotated clear, the whole span meets the flow at once, the luff has clean air to stay attached in, and the leech has somewhere to exit to.

Both ends of the range show themselves at the head. Sheeted too hard, the sail is pulled back in behind the mainsail and the top of it stops working first. Eased too far, the leech rotates up and the head falls away to leeward: the cloth is all still there and the projection at the head is gone.

Purchase and friction

Purchase is the number of line parts sharing a load: four parts each carry a quarter of it, so the hand pulls a quarter of the force through four times the length. Friction is what is lost at every sheave, fairlead and cleat entry, and it does not divide: each part drags its own sheave, so adding purchase adds friction as it reduces the hand load.

On the ease, friction decides whether anything moves at all, because the load left in the line must beat the friction of the whole system, and purchase has already made that load small. A high-purchase control can therefore hold where it is put.

Uncleated at the dock, every control must run out under its own load, and the vang must be adjustable one-handed from the wire by either sailor.

Rake and helm balance

Rake is how far the top of the mast sits aft of its heel. It lives in the standing rigging, so it is set ashore or between races and cannot be moved on a leg. What it moves is the whole sail plan at once: tilt the plan aft and the point its force acts through goes aft with it, while the hull and foils go on resisting through a point that has not moved.

A force behind the point that resists it turns the boat towards the wind, so raking the mast aft creates weather helm, and taking rake out removes it. A small amount of helm is wanted, because a rudder carrying a little lift is making side force rather than only dragging. Past that the rudder is held at an angle for the whole leg, which is drag that returns nothing.

The reading is taken with the boat flat, because heel makes weather helm of its own and will either hide a rake fault or invent one.

Rate times time: accumulating a gain

A gain in metres is not a speed. It is a speed difference multiplied by the time that difference lasts, so a small advantage held for minutes beats a large one held for seconds.

That makes the end of the advantage part of the sum. Routing to a band of pressure is worth the VMG difference between the two pressures multiplied by the seconds spent in the better one before the band moves on or the fleet reaches it, set against the extra distance sailed to get there.

The same arithmetic prices adverse current: the loss is the current against the boat multiplied by the minutes spent in it, which is why the crew takes its medicine early, where the current is weaker.

Reading a logged trace

A trace is one measured quantity drawn against time, and its shape is the finding. A value that slides steadily in one direction across a leg says something different from the same value arriving in a single step: the drift points at a condition that is changing, the step at an event that happened. A flat trace with small ripples around it is a boat in a steady state, whatever its average.

When two traces share one clock, the order in which they move is information. Heel moving before rudder says the water or the gust arrived first; rudder moving before heel says the helm did. That reading exists only if the records are aligned, so video, audio and logger are put on a common clock before anything is read from them, and every written entry carries its time.

Regression coefficient

A regression takes many races, each with a finishing time and a set of measured skill values, and finds the one set of multipliers that comes closest to reproducing those times.

A coefficient is one of those multipliers. It states how much race time changes for a one-unit change in that skill while the others are held still, so it carries units: time per knot of VMG, or time per metre behind the line. The sign gives the direction, and a negative coefficient means that more of the skill shortens the race.

Two coefficients are therefore not comparable as bare numbers, because the units beneath them differ. The useful comparison converts each into the same currency: what a change the crew could actually make is worth in seconds.

Repeatable measurement

A measurement is a comparison against a reference, and the number by itself does not carry the reference. Four things have to be fixed and written down before a logged value can be reproduced: the unit, the method, the zero it is counted from, and the instrument.

A rig-tension gauge shows a position on its own scale rather than a force, so two gauges disagree, and the same gauge reads differently at a different height on the wire, over tape, or before the terminals have seated. A count of turnbuckle turns is a change from a starting point, not a tension at all.

Marks on vang, cunningham and sheets are the same kind of quantity. They hold only while the line and the blocks are the ones they were set against; a new sheet resets every mark on it.

Resolving a force

Any single force can be described as two forces at right angles to each other, chosen for convenience, which add back to the original. Nothing is created or lost in the split; it is a way of asking how much of the force is doing the job in hand.

The share along a chosen direction depends only on the angle between the force and that direction. Pointed nearly along it, the force gives nearly all of itself. Turned toward the perpendicular, the useful share falls away and the wasted share grows, while the total stays the same size.

The sail force resolved into the boat's axes gives a small part along the centreline that drives and a large part across it that heels and pushes sideways. Steering higher turns the same force further across the boat.

Rig tension, the forestay and sag

The shrouds that reach the hounds are made off at chainplates set aft of the mast, so their tension arrives as compression down the spar and as tension in the forestay ahead of it. The sources do not share one set of names for the three wires a side, so this book names them by where they run. One setting therefore does two jobs. It decides how straight the jib luff flies, and, through spreader sweep and stiffness, it decides how much bend the vang, sheet and cunningham can find in the spar at all.

Both jobs point the same way as the wind builds. A slack rig lets the forestay bow to leeward, and forestay sag makes the jib fuller and rounder in the entry; a tight rig straightens the wire and the jib flies flatter and finer. Tension is taken progressively tighter as the wind rises, to flatten the mainsail, and not every wire on the boat is taken the same way.

A gauge reading is not a tension. It pushes the wire sideways and reads how far it moves, and the conversion into kilograms printed on it assumes a wire construction this boat does not use, so it is not valid for any wire on the boat. What it gives reliably is repeatability, which is all this check needs, so the reference is the crew's own logged reading on their own gauge, not a published table.

Rudder angle as drag

A rudder makes side force only by meeting the water at an angle, and all of it is paid for in drag. That holds whether it is turning the boat or holding it against something else.

The second case is the expensive one. If the sail plan wants to turn the boat to windward and the tiller is held to stop it, the two side forces cancel and the boat goes straight. Nothing has been achieved, and both are still dragging; the bill is their sum, not their difference. The drag grows with the angle the blade is held at, and again with speed, because force on a foil rises with the square of its speed through the water.

The tiller reads it: deliberate inputs are large, brief and return to the centreline, corrective ones small and constant.

Sails age with loaded hours

A sail is a shape held by fibres under tension. Every hour under load stretches those fibres slightly further than they recover, and the stretch is not even: it concentrates where the load is highest, so the draft creeps aft, the entry rounds and the leech loses its designed exit. The change is one way, and it accumulates with hours under load rather than with calendar age.

That matters because the class allows one mainsail, one jib and one gennaker per event unless something is lost or damaged beyond repair. The sail chosen for the first race is the sail for the final day, so the choice weighs speed in the expected wind band against how much of the shape will survive the week.

Training sails therefore carry the hours, and the event set is kept for the event.

Sample rate

A logger does not record motion continuously. It takes a position fix on a fixed rhythm, and the sample rate is the number of fixes each second.

Between fixes nothing exists. A manoeuvre lasting a few seconds is described by a handful of points at a low rate, so the depth of its speed dip can be smoothed away; a faster rate resolves entry, turn and recovery separately. The rate also changes quantities computed from it: distance sailed is the sum of straight lines between consecutive fixes, so a fast rate follows the curve of a turn and reports more distance while a slow rate cuts the corner and reports less.

Two sessions logged at different rates cannot be compared for distance or manoeuvre loss, which is why the rate is fixed for a season and written in the file.

Sample size

Sample size is the number of independent observations standing behind a number.

Every observation carries the quantity being measured plus variation that carries no information. Averaging several lets that variation partly cancel while the quantity adds, so the estimate settles as the count rises, but it settles slowly: about four times as many observations are needed to halve the remaining uncertainty. How much something varies is harder still, because it has to be estimated from the scatter itself and needs far more data than the average does.

One boat on the far side heading up may be pinching for a lane; several boats doing it together is a shift. In the same way one line-up is a reading, and a target stays provisional until adding another session no longer moves it.

Scales with

When one quantity is said to scale with another, the claim is arithmetic: multiply the second and the first multiplies by the same factor. Double the closing speed and the margin needed doubles. In direct proportion unless a power is named, so a quantity that rises with the square of speed quadruples when the speed doubles.

Scaling is what lets a number measured once be carried to conditions it was not measured in: a margin established in one wind band is rescaled for the others rather than learned again.

The crossing margin is the example aboard. It is the distance at which the outcome stops depending on the other boat's reaction, and it scales with closing speed, while sea state and how well the other boat is sailed change the multiplier rather than being multiplied, so the logged figure for one band is a base to multiply rather than a number for all conditions.

Scanning distance and lead time

Scanning distance is how far up the course the crew looks for the next change; lead time is how many seconds that look buys. The two are joined by the speed at which the feature travels. A gust band moves down the course at roughly the speed of the air carrying it, so the warning in seconds is the scanning distance divided by that speed, and the same distance buys fewer seconds as the wind rises.

The boat's own motion is the second term. Upwind the boat closes on the band as well, so the warning is shorter than the wind speed alone suggests; downwind it runs away from the band and the same sighting gives far longer. The useful scan is therefore set by what must be done with the information before the band arrives.

Sea breeze

A sea breeze is a local circulation driven by the sun heating land faster than water. Air over the land warms and rises, surface pressure there falls a little, and air flows in off the water to replace it.

The engine is the temperature difference, so anything that removes it removes the breeze: thick cloud shades the land, and a strong gradient wind mixes the heated air away before it can rise. Because the circulation is shallow and local, it fills over the water first and pushes toward the shore as a small front, with different wind either side of a visible line.

Once it is running, the earth's rotation deflects the moving air steadily to one side, so the direction walks one way through the afternoon rather than swinging about a mean.

Shoaling and refraction

A wave stirs the water well below its own crest. Where the sea bed rises into that moving layer, it drags on the wave and slows it. The number of crests arriving each minute cannot change, so a slower wave has to be a shorter one, and the same energy in less length is a taller crest and a steeper face. Past a limiting steepness it breaks.

Crests also turn. The part of a crest reaching shallow water first slows while the rest keeps going, so the line swivels until it lies more nearly along the depth contours, and the crests bend to face the shore. No wavelength need be measured: shorter, steeper, closer-spaced waves in the same wind at one end of the course are the sign, and so are crests aligned with the shoreline rather than the breeze.

Shock and impact loading

The same load applied gently and delivered as a blow are not the same event for the part. A load arriving in a fraction of a second is taken by a structure with no time to deflect and share it, so the peak force reaches many times the steady value.

The reason is that stopping a moving mass takes force, and the force is the momentum divided by the time taken to remove it. A short stop means a large force. A loosened fastener gives the load a short run before it arrives, so a steady pull becomes a hammer blow on every cycle and the hole elongates a little more each time.

Spreading works the same way in reverse: a body landing along its whole length delivers the same momentum over a longer time and a wider area.

Springs in series

Two springs one behind the other carry the same force and their stretches add. That is what being in series means, and a rig is full of it: a load path runs through the wire, the fittings, the spar and the hull, and every part of it gives a little under the same load.

The consequence is that the softest part governs. Stretch adds, so the total give is dominated by whoever gives most, and stiffening something that was already stiff changes the total hardly at all. Making one member a third stiffer improves the whole path by a third only if that member owns the whole of the give; if it owns half, the path gains about a seventh.

It also means a single measured deflection cannot say where the give came from. Two rigs that take up the same number of turns may be sharing that take-up quite differently between wire and spar, and nothing measured at the turnbuckle distinguishes them.

Stiffness

Stiffness is how much load a part needs for a given deflection. A stiff part bends little and a soft one bends more, and the number belongs to the part itself, fixed by its material, its cross-section and its length. Tension is a force applied to something; stiffness is how that something answers.

Because stiffness belongs to the part, it decides the shape taken under load rather than the load. Two battens pulled to the same pocket tension take different curves if their stiffness differs, and two rigs at the same gauge reading bend differently if their spreaders differ. Changing tension moves a part along its own curve; changing stiffness changes the curve.

The boat's own motion changes the flow

The apparent wind at a point on the rig is built from the true wind and the motion of that point, not the motion of the boat as a whole. When the hull only translates, every point moves alike; when it rotates, they do not.

A pitching boat turns about an axis somewhere near the middle of its length. A point far from that axis sweeps a longer arc in the same time, so it moves faster. The masthead is furthest from that axis, so it has the largest velocity of its own through the air, and the apparent wind there swings through a much wider angle than the wind at the boom.

The same holds underwater. Roll gives the daggerboard's tip a sideways velocity of its own, which adds to or subtracts from the angle leeway is providing.

The cunningham: draft and bend

The cunningham pulls the tack of the mainsail down against a head held at the top of the mast, so what it sets is tension along the luff. That tension draws cloth towards the leading edge and the deepest point of each section travels with it. The cloth ahead of the draft becomes rounder, the cloth behind it flattens, and the exit opens, so less of the sail's load is carried aft.

On this boat the same pull bends the spar as well, because tack and head are forced towards each other and the mast takes the compression. The two effects are linked. Bend on its own drags the draft aft, so the more the mast is bent the more luff tension is needed to hold the draft where the sail was cut to carry it, and a bent mast under a slack luff is flat where the sail should be full.

The limit is the luff curve the sail was cut with. While bend stays inside it the loaded cloth still restrains the spar; past it the surplus stands up as diagonal wrinkles from the clew towards the luff, and depth then follows the gusts rather than the crew's hand. At the light end the limit runs the other way: tension pulled on before the mast has bent carries the draft ahead of its designed place and leaves a sail that points without driving.

The discard

A series score is the sum of the race scores with the worst one removed, and that removal is what makes the scoring non-linear.

The discard is an option that can be spent once. While it is unspent, the bad end of a risky race is partly free, because the worst result will be thrown away; the moment it is used, the next poor race costs the better of the two scores, because the worse of them is the one discarded and tolerance for risk falls with it. Other provisions bend the relation further, such as a cap on the gap carried into a final day, or a race whose points count more heavily and cannot be discarded.

The working numbers each morning are therefore the points to the boats immediately ahead and behind, the races remaining, and whether the discard is still in hand.

The groove

The groove is the span of headings over which the sails keep working. Inside it the flow stays attached and small steering errors cost almost nothing; outside it the jib luffs or the leeward flow separates.

Its width is set at the leading edge. A rounded entry meets the flow over a range of angles without asking it to turn a sharp corner, so several degrees of wander are tolerated. A fine, straight entry serves one angle well and breaks down quickly either side of it, which is why it points higher and demands better steering. Forestay sag rounds the entry, so rig tension is a groove control.

In chop the boat's pitching swings the apparent wind at the luff, a steering error the helm did not make, and the wider groove is what absorbs it.

The hull's own wave system

A moving hull makes its own waves: a crest at the bow, a trough behind it, and further crests down the hull. The spacing between those crests is set by speed alone, and it grows roughly with the square of speed, so the second crest walks aft as the boat accelerates. At low speed the hull spans several of its own wave lengths; as speed rises the wave grows longer than the hull.

That makes the station of the second crest along the hull a speed reading, and fore-and-aft trim a wave problem rather than only a wetted-area one. Through the transition the crew moves aft so the bow wave does not build over the forward sections, and video from astern shows the wave forming at the same station in every wind band.

The moving water

Current is the whole body of water moving over the ground, and the boat sails in the water, not on the ground. Everything the sails and foils do is referred to the water; the marks, the shore and the line are fixed to the ground.

A current running across the course carries every boat in it equally, so it cannot favour one boat over another in the same water. What it does is move the marks relative to the water, changing the geometry: the laylines, the line bias and the time each leg takes. It adds nothing to the flow over the foils, which is why pointing to put the current on the lee bow gains nothing.

The compass separates them. A bearing that changes with the heading unchanged is current; a heading that changes with trim unchanged is wind.

The outhaul: foot depth and the lower leech

The outhaul pulls the clew out along the boom, so it stretches the foot between two fixed points and takes the curve out of the lowest sections. The effect fades with height, because the boom holds only the bottom of the sail. It is the flattening step applied to the part of the mainsail the mast cannot reach, and it leaves the head to the sheet and the vang.

Easing has a second effect at the back of the sail. A shorter distance from tack to clew lets the lower sections bag, and a deeper section turns its after part further to windward, so the lower leech closes and holds more load; pulling the clew out straightens that part and opens the leech again. Foot depth and lower-leech tension therefore move together, and neither can be changed alone.

The polar and the envelope

A polar is the boat's target speed and target angle for each wind strength, upwind and downwind. It states what the boat should be doing, not what it has been doing.

It is therefore built as an envelope rather than an average. Within one wind band the log holds a wide spread of speeds, most below the boat's best because of waves, traffic, trim lag and manoeuvres. The mean of that spread describes ordinary sailing; the target is the upper edge, the speed the boat sustained with its settings right.

The method has a weakness to guard. A high sample from a gust binned wrongly, from current, or from a position error sits on that edge too, so the envelope creeps upward on noise alone. A target counts as settled only when adding another session stops moving it.

The slot is not a nozzle

The gap between jib leech and mainsail is often described as a nozzle that squeezes the air and speeds it over the mainsail's leeward side. That picture is wrong, and trim rules read from it come out backwards.

What the two sails do is bend the flow around each other. The mainsail turns the air before it reaches the jib, so the jib meets the flow at a larger angle than its sheeting suggests and carries more than its share. The jib turns the air the other way at the mainsail's luff, reducing the angle there, so the main can be sheeted closer than it could alone without its forward section stalling. The slot is where that exchange happens.

So a narrow slot does not mean fast air. It means the main backwinding, the flow reporting the angle is wrong.

The speed loop

Once the boat is moving, its own speed is a large part of the wind the sails feel, and that closes a circle. More speed brings the apparent wind forward, and while it is forward of the beam more speed strengthens it too, so more drive follows, and more drive gives more speed.

The output of each step is the input to the next, so changes do not stay the size they started. A gust converted into speed keeps paying after the gust has gone, and a check that costs speed keeps costing, because the wind the sails have to work with has fallen too. The circle turns both ways with equal willingness.

It also has to be started. A stopped boat feels only the true wind, lighter and further aft, so a start needs a hole with room to build speed before the gun.

The square law

Force from air or water does not grow in proportion to speed but with the square of it.

Two things rise together as the flow speeds up. More mass arrives at the sail or foil each second, in proportion to speed, and each parcel is turned through the same angle at that higher speed, so each delivers more force. The two effects multiply. Half as much flow again therefore carries more than twice the force, and double the flow carries four times.

On the boat this is the gennaker sheet: a modest rise in apparent wind speed is a large rise in load, which is why load is managed through the apparent wind, not by holding harder. The foils follow the same law with boat speed, so a fast boat needs less leeway for the side force it must make.

The three sources of power

Upwind power has three separable sources. Angle of attack is how hard the whole sail is set against the wind, moved with the sheeting angle. Depth is the curve carried in the sail, set by mast bend and outhaul. Twist is how far the upper sail is let off relative to the lower, set by vang and sheet.

Each raises force and each charges a different price. Depth adds drive cheaply until the flow can no longer follow the curve. Angle adds drive and side force together, so it is paid for in drag and heel. Twist acts at the top, where a unit of force works through the longest lever and heels most for the drive it gives.

Because the prices differ, the three are removed in an order set by cost, and the order depends on how long the crew has. Against a rising mean wind it is flatten, then twist, then angle, with shroud tension between races: flattening removes heeling moment without giving up any part of the sail, twist gives away the top, which is the cheapest part to lose, and angle gives away the whole sail a little. Against a single gust only the sheet is fast enough, so it is ease, then helm, then re-sheet as the boat accelerates, and the shape controls are left alone because a gust is over before a shape change can be undone.

The vang: bend, leech and twist

The mainsheet pulls the boom down and inboard together; the vang pulls it down only. With the vang loaded the boom cannot rise, so easing the sheet swings the boom outboard while the leech stays shut: the angle of attack falls and the sail sheds power. With the vang slack the same ease lets the boom lift, the leech opens from the head and the foot deepens, so the lower sail powers up even as the top unloads. Upwind that is why the vang stays loaded and a gust is answered with sheet.

Vang load reaches the mast as compression through the boom. Past the point where the bend it produces matches the sail's built-in luff curve, further vang bends the spar instead of tensioning the leech, so it flattens rather than twists. The mark calibrated ashore is where that point sits.

The VMG curve

Velocity made good is the part of the boat's speed counted along the true wind line, toward the wind upwind and away from it downwind. Plotted against the angle sailed, it forms a hump with a rounded top.

Near the top the curve is nearly flat, because turning away from the best angle gains speed at nearly the rate it loses depth, and the two cancel. A degree or two off is close to free. Further out the terms stop cancelling and the loss grows quickly, so a mode held too long is expensive in a way a small steering error never is.

The two sides do not cost the same. Downwind the low side is the steeper one, because depth taken before speed removes the apparent wind that was making the speed; the symptom is a gennaker whose apparent wind falls aft and a speed trace sagging with it.

Threshold and persistence

A threshold is the size a reading must exceed before it counts, and a hold time is how long it must last. Together they separate a signal from the variation around it.

The wind pulses in both strength and direction on a short cycle, and each pulse bends the apparent wind so that the boat heads up or bears away without the true direction having moved at all. A reading taken inside one pulse is as likely to be the pulse as a shift. Requiring the reading to be larger than the usual wobble, and to outlast the wobble's own period, removes most of the false calls at the cost of the first part of every real shift.

Where one of those two errors costs more than the other, the threshold moves toward the cheaper mistake.

Time to line and time to burn

Time to line is the distance to the line divided by the part of the boat's speed pointing at it. Time to burn is the seconds remaining to the gun minus the time to line, and so the delay the boat can still afford.

The division uses the speed the boat has at that instant, so the number answers only when the boat would arrive if nothing changed. A boat creeping in a hold shows a long time to line and a generous burn; the moment it bears away and accelerates, the real arrival time collapses and the burn with it. The number is therefore least reliable during exactly the acceleration it is used to manage.

The answer is to count the burn at two speeds, the creep and the full run, with the transition set from logged runs.

Transom drag and the wake

At low speed, weight aft sinks the transom and the water cannot close behind it: the stream separates at the transom edge instead of flowing off cleanly, and the boat tows a broad patch of churned water.

That patch is the drag rather than a symptom of it. The energy stirred into that water came from the sails, so the wider and more turbulent the wake, the more the boat is paying. At planing speed the picture reverses: the flow leaves the transom cleanly and an immersed transom costs little, which is why weight goes aft when the boat is fast and forward when it is slow.

The standard is a transom that leaves a clean wake with no turbulence behind it; moving aft in a tack, when the boat is slowest, is how that brake gets applied by accident.

Turning an angle into a distance

An angle is not a distance until it is multiplied by a length. Draw the right-angled triangle: the length is one side, and the sine of the angle is the fraction of that length which appears as separation across it. Going the other way, a separation measured along a slanted course is that separation divided by the cosine of the slant, since the slanted path is the longer one.

For small angles the separation grows in step with the angle, so twice the angle gives twice the distance, and the same angle over twice the length also gives twice the distance.

On the water a line bias becomes a distance only when multiplied by the line's length, so length times bias is the comparison and never the bias alone, and a few degrees of heading error held for minutes puts the boat lanes away from its intended lane.

Twist and spanwise lift

Span is the sail's dimension from foot to head; chord is the distance from luff to leech at any height. Twist is the difference between the angle the chord makes with the boat's centreline low down and at the top.

It matters because lift can be moved along the span without the total changing. Force made high and force made low drive the boat equally, but the high force acts through a much longer lever about the axis the hull rolls on, so it costs more heeling moment for the same drive. Opening the top lowers the angle there and shifts load down the span, buying drive at the same heel.

Twist is also the only answer to a wind stronger and further aft aloft than at deck level, since one sheet setting cannot suit both ends of the sail.

Upwash and downwash

A sail does not wait for the air to reach it. Carrying a pressure difference across itself, it bends the flow for some distance ahead of its luff and leaves it bent behind the leech. The bend in front is upwash, which swings the oncoming air toward it; the bend behind is downwash, which swings it away.

That is why the two sails cannot be trimmed separately. The mainsail's upwash reaches forward past the jib, so the jib meets the air at a larger angle than its sheeting suggests and carries more load; the jib's downwash arrives at the mainsail luff at a smaller angle, so the main can be sheeted harder before its front section breaks down. The field reaches other boats too, and a boat bow-forward and to leeward sits in it, reading a lift with more pressure.

Variance and risk

Two plans can share an average result and still be entirely different things. The average says where the outcomes sit; the variance says how widely they scatter either side of it. A flyer and a run of small consolidating gains can be worth the same expected number of places while only one produces the occasional win and the occasional disaster.

They are separate quantities, so a decision is judged on both, and which governs depends on the score. A boat that must gain has no use for a narrow spread, because the middle of its distribution is not good enough; a boat protecting a position wants the spread narrow and will pay mean for it.

Lateral separation is the variance control on the water, since two boats on the same line finish in the order they hold.

VMG as a projection

VMG is the boat's speed counted only in one direction: the part of its velocity that lies along the true wind line. It is the speed multiplied by the cosine of the angle between the boat's track and the direction being made good, toward the wind upwind and away from it downwind, so it falls away as that angle opens.

Because it is a product of two quantities pulling against each other, the faster boat can be the one losing ground: sailing lower downwind gains angle and usually costs speed, and which way the product moved is not readable from boat speed alone. Two boats side by side can have the lower, slower one showing the higher figure. Upwind the projection is taken toward the wind and downwind away from it, so the two are separate quantities measured along one line in opposite senses, and are never compared with each other.

Wave period and phase speed

A wave train has three measurements. The period is the time between successive crests passing a fixed point, the wavelength is the distance between those crests, and the phase speed is the speed at which the crest shape travels. Only the shape travels: the water beneath rises, moves forward under the crest, falls and moves back, so a floating object is lifted and set down rather than carried along.

Where the water is deep enough that the wave cannot feel the bottom, phase speed depends on period alone and rises in proportion to it, so a long swell outruns short chop by a wide margin. Period is the quantity the crew can actually take: seconds counted as crests pass a fixed object, a moored mark or the boat lying still, since a boat under way meets the crests at a different rate, averaged over several waves, since individual waves differ and one interval is not the period.

Weather helm

A boat holding a straight course has no net turning moment about its vertical axis: the sail plan, the foils and the hull's immersed shape must cancel between them. The rudder supplies whatever is left over, so the angle held on the tiller is a measurement of the imbalance rather than a fault of the helm.

Weather helm is the boat wanting to turn toward the wind, with the tiller held to windward, the blade angled to leeward and its lift acting to windward, to stop it; lee helm is the opposite, and slower, because the rudder's lift then opposes the daggerboard's. A small weather helm is wanted, since the blade is then a lifting foil working alongside the board and giving the helm something to read. Beyond that it is a brake.

The target quoted for moderate conditions is an angle of the blade, not a quantity of leeway.

Weighting evidence

A weight is the share an observation is given when several are combined. Attach a number to each input, multiply each observation by its number, add the products and divide by the total of the numbers: the answer sits nearer the inputs carrying the larger weights. A weight of zero discards the input; equal weights average them.

Weights are how observations of different kinds are made comparable, since pressure seen on the water, a compass trend and a coach's report cannot be added as they stand. The weight stands for how far the source is trusted and how relevant it is to the question, so the same observation carries different weights for different decisions: the compass weighs most for the next tack, the fleet most for the side.

An observation offered without a weight cannot enter the sum.

What a study can and cannot say

A study is a set of observations gathered under particular conditions, and what it can support is bounded by those conditions. Every study has a range: which boats were tracked, which wind speeds and sea states occurred, how many races were recorded. A conclusion drawn from it holds inside that range and says nothing reliable outside it, because the data never met the conditions it is being asked about.

The sample bounds the claim a second way. A finding built on few races is a weak estimate even inside its range, and one drawn from another class is a different boat, rig and crew weight.

So a tracking study whose wind range stops below the band in which the 49er is depowered says nothing about that band, and the crew's own logged losses there remain the only evidence.

What bending the mast does to the sail

The mast is the mainsail's leading edge, so bending it moves that edge. Pushed forward in the middle, the luff travels away from the leech and the distance the cloth has to span at mid-height grows, while the cloth itself does not. The surplus curve is pulled out: the sail flattens, the exit opens and the deepest point slides aft. Straightening the spar returns all three.

Bend is not one number. Each control bends a different part of the spar: the vang compresses the lower mast through the boom, the mainsheet loads the topmast through the leech, luff tension works on the section between them, and shroud tension and spreader sweep decide how much bend any of them can find. The mix therefore sets where the depth is taken from, foot, middle or head, and two rigs at the same total bend can fly different shapes.

Two limits show themselves. Fore and aft, bend past the sail's own luff curve leaves nothing more to take out, and the surplus appears as diagonal wrinkles running from the clew towards the luff. Sideways, a mast that bends to leeward in the middle loses drive and does it unequally, so the check is a sighting up the track on each tack: a mainsail that flattens more on one tack is a stay or spreader fault rather than a trimming one.

Why a high body feeds a roll

Damping is whatever removes energy from an oscillation, so each swing is smaller than the last and the motion dies away. Without it a disturbance keeps going or grows. What body position changes most directly is the other half of the problem: whether the roll is being fed at all.

A body on the wire is a mass on a lever whose length changes as the boat rolls. A mass carried high, above the axis the hull heels about, swings outboard as the boat rolls to windward and inboard as it rolls to leeward, so its moment grows in the direction the boat has already started and feeds the roll. A mass low, near that axis, keeps almost the same lever through small roll angles and adds nothing to the swing, which leaves whatever damping the hull and foils supply to do its work unopposed.

The evidence is harness load. Low and straight, the weight on the wire stays constant through a roll; high and bent, it loads and unloads each swing.

Why heel costs

The sails and the foils both make forces that act square to something. The sail's lift is perpendicular to the apparent wind; the daggerboard's lift is perpendicular to the water flow and to the board's span, so it tilts when the board tilts.

When the boat heels, each force tilts with the surface it belongs to. Part of the board's side force then points upward instead of sideways against the rig, and part of the sail's side force presses the hull down instead of pushing it sideways. Neither force has changed size, but less of each points where it is wanted, so the boat makes more leeway for the same grip; and the drive falls too, because heel lowers the angle at which the sail meets the flow. Heel also shortens the board's working depth, which raises the drag of the side force remaining.

The signature is heel with no speed: the boat leans, the helm loads up, and height and speed fall together.

Why heel turns the boat

A heeled 49er turns without the tiller, for two reasons at once. The first is the shape in the water. Upright, the immersed hull is symmetric about the centreline and the water passes each side alike. Heeled, it is not: more of the volume sits to leeward while the windward side lifts clear, so the water's pressure on that lopsided shape pushes the bow toward the high side.

The second is the rig. Heel carries the sail plan's centre of effort sideways, out of line with the point through which hull and foils resist it. Two opposed forces on different lines make a couple, and the couple turns the boat. Leeward heel turns the bow up and loads the tiller; windward heel turns it down, so the boat runs downwind with the windward chine in and the rudder straight.

Why oversheeting slows the boat

Sheeting harder raises the angle at which the sail meets the flow. Up to a point that raises the force. Past it the flow can no longer follow the leeward side, it detaches, lift collapses and drag stays high.

On the gennaker, drive is lift. With the apparent wind near the beam the drive comes from the force acting across the flow, so once that has gone the sail is left making mostly a force along the flow, which is resistance. Pulling further is not trimming a working sail, it is operating a brake. The sail stays full, the sheet stays heavy in the hand, and the boat slows.

That is its use in survival conditions: the boat is slowed on purpose so that it does not meet the back of the next wave faster than the bow can survive.

Wind against current

When the water is moving against the wind, the waves keep their own speed through the water but are carried backwards over the ground. Crests are therefore brought closer together: the same energy is packed into a shorter wavelength, so the crest rises, the face steepens, and a steep short wave breaks sooner than a long one. Current running with the wind stretches the train instead, and the same sea lies smoother.

Only the part of the current that lies along the wind counts, so a flow crossing the wind at an angle produces part of the effect and one square to it almost none. The effect is strongest where the flow is strongest, in the deep channel, off a headland and at the peak of the tide, and a band of steeper chop across the course marks that water.

Wind bands and the binding constraint

A wind band is not a range of knots. It is a stretch of wind over which the same quantity is the one in short supply, and it ends when a different shortage takes over.

Three things can run out. In light air sail force is scarce and righting moment is plentiful, so everything is spent on making power. Higher up the two match, righting moment becomes the fixed quantity, and the question is how sail force divides between drive and side force. Higher again, sail force exceeds what the crew can hold and control margin is what is short.

A crossover is the wind at which that answer changes, which is why a heavier crew crosses later. The first one is visible from the coach boat: both sailors straight, low and fully extended, and the boat still heeling.

Wind gradient

Air rubbing along the water surface is slowed by it, and that braking is passed upward through the layer above, so wind speed increases with height. The boat's speed does not: masthead and boom travel together at one speed.

Apparent wind at any height is the true wind there combined with that boat speed, and because the wind near the deck is the weaker of the two, the same boat speed swings it further forward than it swings the stronger wind aloft. The apparent wind at the head is therefore both stronger and wider than the one at the foot, and twist exists to match the sail to that difference.

This runs against the feel of accelerating: extra speed narrows the angle at every height, and the head still keeps the wider angle. A top batten hooked and stalling while the foot still drives is that difference untrimmed.

Wind shadow

A sail takes energy out of the air passing it and leaves behind a region that is slower, turbulent and bent. That region is the wind shadow, and a boat inside it is slow for a reason trim cannot fix.

It travels away in the direction the wind was going relative to the boat that made it, which is the apparent wind, not the true wind and not the heading. On a 49er close-hauled the apparent wind sits well forward, so the shadow lies almost straight astern and slightly to leeward, further aft than a slower boat's; downwind the apparent wind is near the beam, so the shadow lies a little abaft the leeward beam instead. Ahead of the sails the flow bends the other way, which is why a boat close to leeward and forward gets a lift and more pressure instead.

In light air the shadow reaches further, because the disturbance takes longer to mix out.