True Wind and Apparent Wind: The Vector the Ship Actually Feels

The weather service reports one wind. The plating feels another. Between the two sits a vector addition simple enough to do in the head, which is exactly why it is the step in wind correction that gets botched most often, not the regression, not the geometry, but the two lines of trigonometry that decide which wind goes into them. Everything downstream is applied to whatever vector comes out of here, and nothing downstream complains if it is wrong.

The ship makes its own wind

Two velocities are in play and they belong to different frames. True wind is the motion of the air over the sea surface: what a moored buoy measures, what a forecast model outputs. What the hull feels is the motion of the air relative to the ship, which is the true wind with the ship's own velocity taken out of it. Sailors call the result apparent wind; trials and monitoring work calls it relative wind. Same vector.

Its first consequence is the one the calm-air baseline already establishes: a ship at 15 knots on a windless day meets a 15-knot headwind, because relative to a hull moving north at 15 knots, still air is moving south at 15 knots. That is not weather. It is arithmetic about frames of reference, and it holds on the calmest day of the year.

Resolve the addition into ship-fixed components and the whole operation fits in four lines. Measure wind angles from the bow: 0 degrees dead ahead, 90 abeam, 180 dead astern.

athwartships component = V_true × sin(true angle) fore-and-aft component = V_true × cos(true angle) + V_ship

apparent speed = square root of (athwartships² + fore-and-aft²) apparent angle = arctangent of (athwartships ÷ fore-and-aft)

V_true is the true wind speed and V_ship the ship's speed over the ground. The athwartships component is the part of the air's motion crossing the hull; the fore-and-aft component is the part running along it, counted positive when it arrives from ahead. The apparent angle emerges measured from the bow, on the same convention as the true angle went in.

One rule completes the last line. A plain arctangent only returns angles between minus 90 and plus 90 degrees, so when the fore-and-aft component comes out negative, which happens when a true wind from abaft the beam carries more speed along the ship's axis than the ship herself makes, the apparent wind is arriving from abaft the beam and the arctangent has landed in the wrong quadrant: add 180 degrees to it. A true wind of 20 knots from 150 degrees, met by a ship making 14 knots, has components of 10 knots athwartships and minus 3.3 knots fore and aft; the arctangent gives minus 71.6 degrees, and the rule puts the apparent wind at 108.4 degrees off the bow. The two-argument arctangent, atan2, which the course workbook uses, applies the rule by itself, and the ITTC trials procedure writes it as two cases. Code the four lines without it and every apparent wind from abaft the beam lands forward of it, where the coefficient usually has the opposite sign, and nothing downstream complains.

One feature of those lines carries most of the practical weight: the ship's speed enters the fore-and-aft term only, and only with a plus sign. It never touches the athwartships component.

Why the apparent wind always swings forward

Because the ship's speed only ever lengthens the fore-and-aft component, the arctangent's denominator grows while its numerator stands still, and the apparent angle is therefore always forward of the true angle. A 16-knot true wind 70 degrees off the bow, met by a ship making 12 knots, arrives as 23 knots only 41 degrees off the bow. Put the same true wind exactly abeam and it arrives at 20 knots, 53 degrees off the bow. The wind the bridge team calls a beam wind is, aerodynamically, a bow-quartering wind, and the faster the ship, the further forward it swings.

Two cases sit outside the rule, and both are instructive. A wind exactly dead ahead stays dead ahead; it only gets faster. A wind exactly dead astern is a discontinuity: while the true wind is stronger than the ship it stays a following wind and weakens, but once the ship outruns it the fore-and-aft component changes sign and the apparent wind arrives from ahead. Take a ship making 14 knots with a true wind of 10 knots reported from dead astern, 180 degrees off the bow: the fore-and-aft components are minus 10 from the wind and plus 14 from the ship, the athwartships component is zero, and she feels 4 knots of apparent wind on the bow. Exactly at equality the apparent wind is zero: the only condition in which a moving ship carries no aerodynamic force at all.

Reported from, not towards

Meteorology names a wind by the direction it comes from. "Wind 270 at 20" is air moving from the west towards the east. Waves in the standard marine products follow the wind's convention, but ocean currents, drift and some native wave-model outputs use the opposite one and are named by where they go to. Both conventions are correct; both appear in the feeds a performance system consumes; and converting between them is a single line, adding 180 degrees and wrapping at 360. Because a current is named by the direction it flows towards, the mirror image of the wind convention, our Currents and Water Properties course takes the resulting sign trap apart in full, and this lesson needs only the wind half of it.

That line is where wind corrections go wrong, and it is worth being blunt about why. A reversed convention does not raise an exception, produce a negative speed, or fall outside a range check. It produces a triangle that closes perfectly on the wrong side of the ship: a head wind becomes a following wind, the coefficient is taken from the wrong side of the beam, where, as later lessons show, it frequently has the opposite sign, and every corrected power figure in the dataset shifts in one consistent direction. The output looks like performance. It is a sign error wearing a plausible number.

Two cheap defences catch it. First, the inequality from the previous section: the apparent angle must never sit aft of the true angle, so any record where it does carries a convention or a heading error. Second, compare a sample of computed apparent winds against the ship's own anemometer; the instrument has troubles of its own, but it is never 180 degrees wrong. While checking, refer the angle to the ship's heading rather than her course over ground, with leeway and set the two differ by a few degrees, and it is the direction the hull points, not the track it makes good, that the air meets.

Three things, and one subtraction

The force this course computes is decided by exactly three quantities. How much wind: the apparent speed, entering through the dynamic pressure, which is why it enters squared. How much ship: the above-water geometry: projected areas, superstructure height, where the wind area's centroid sits. At what angle: the apparent angle, through a coefficient that varies with it in a way no intuition predicts, and whose regression form comes from Fujiwara, Ueno and Ikeda (2005), Journal of the Japan Society of Naval Architects and Ocean Engineers.

There is also a fourth operation, which is not a force but a removal. The still-air headwind this lesson began with is already inside the calm-water speed-power baseline, measured into it on trial day. Leave it in and it gets charged twice. The word added in "added wind resistance" is that subtraction, and the next lessons take the three quantities and the subtraction in that order.