1What this screen answers

You give five things - vessel type, length, beam, draught, working speed - and press Calculate. The module takes the waves, wind and current for your position and the chosen hour, works out for 36 headings how the vessel sits, and colours each heading green, amber or red. Anything you did not fill in is estimated from the vessel type table and labelled as estimated.

There is no threshold at the front door: the module answers on five fields. What it will not do is hide how much of that answer it made up itself - that is what the confidence score is for, and every field you add replaces an estimate with a fact.

2Two chains under one polar

There are two ways the work can stop, and they have nothing to do with each other.

• CHAIN A - MOTIONS. Does the vessel roll, pitch and heave too much to work? This is about the PEOPLE and the EQUIPMENT: a multibeam that stops measuring, a crane that can no longer be operated, a deck you can no longer stand on.
• CHAIN B - STATION KEEPING. Can the vessel hold position and heading at all? This is about the SHIP: enough thrust against wind, current and wave drift.

Per heading the polar takes the WORSE of the two. A vessel that lies perfectly still but drifts off is no use to you, and neither is one that holds position perfectly while nobody can work.

ratio = max(chain A, chain B)

  < 0.8      green   workable
  0.8 - 1.0  amber   marginal
  > 1.0      red     not workable

Every sector also carries its LIMITER: which quantity closed it down - roll, pitch, heave, acceleration, Hs, or thrust in sway, surge or yaw. That is the most useful number on the screen, because it is the one you can act on: a different heading, a different working point, or waiting for the swell to turn rather than for the wind to drop.

3From five fields to a whole ship

Whatever you leave empty is filled in from the vessel type table. Your input always wins, and the module remembers per field which of the two it used.

That one exception for the roll period is deliberate. If GM and the roll factor are both estimates from the same table, a computed roll period would contradict the roll period column of that same table - that is not an estimate any more, it is noise. So: real GM, compute the period from it; estimated GM, take the period straight from the table.

4Chain A - the motions

The frequency response functions are the closed-form expressions of Jensen, Mansour and Olsen (2004). The model replaces the vessel by a homogeneously loaded BOX of L x B x T with B = B0 x Cb, so that the mass is right. Heave and pitch are solved decoupled; for roll the model is two prismatic beams in line, because a single box does not capture roll at all.

From response to a number on the screen, in four steps:

• WAVE SPECTRUM. JONSWAP with gamma = 3.3, rescaled so that the variance on the computational grid is exactly (Hs/4)^2 - without that rescaling a few percent of the energy disappears into the truncated tail and everything comes out too low.
• DIRECTIONAL SPREADING. cos^2, zero beyond 90 degrees from the main direction, in nine steps.
• PER HEADING. For every frequency and direction: the response, squared, times the spectral density. Summed that is the variance m0. The grid runs 0.10 to 2.20 rad/s in 72 steps - fine enough for the roll resonance of a container ship and wide enough for a workboat.
• SIGNIFICANT AMPLITUDE = 2 x sqrt(m0). At the working point heave, pitch and roll add in quadrature, because they are independent in this decoupled model.

vertical^2  = heave^2 + (x . pitch)^2 + (y . roll)^2
acceleration = omega_e^2 . vertical

If the encounter period at the spectral peak falls within 15 percent of the natural roll period, the sector gets a RESONANCE MARK - the white arc in the polar. That is not an extra limit but a warning that this is where the model is at its most sensitive.

5Chain B - station keeping

THE WIND SPEED. The wind formulas below belong to a one-minute mean wind (IMCA M 140); a weather model gives the hourly mean. Station keeping therefore uses the GUSTS from the wind model, and when a model has no gusts the mean times 1.15. The Workability tab shows the mean, the gust and which of the two was used. Together with the 1.25 dynamic factor this is on the strict side. The same wind speed gives the wind heel on the Waves card (see WIND HEEL).

WIND HEEL. A steady side wind heels the ship, and the waves roll it about that heel. The Waves card therefore adds the heel to the roll before it is compared with the roll limit: wind force abeam (the gust, on the lateral area) times the lever from the centre of that area to half the draught, over displacement x g x GM - the set-up of the IMO weather criterion. The height of the centre is the field Wind area centroid height, otherwise your side view, otherwise (freeboard + 4) / 2.

UNDERWATER AREA. The current force abeam and the current yaw moment use the field Underwater lateral area when it is filled in (a keel or skeg adds to it), and Lpp x T otherwise.

ALL TOGETHER. Under the cards one line gives wind, current and wave drift at the same time, per heading. It is never lower than the worst driver alone: wind and current from opposite sides cancel in the sum, but a gust drops away while the current stays, so that cancelling is not counted on.

A STATIC force balance: mean wind, current and wave drift against the available thrust, over all 360 degrees - the method of IMCA M 140 and DNV-ST-0111. The thrusters are ALLOCATED PER HEADING: a linear programme looks for the largest multiple of the environmental load that the units can still hold together, each within its own direction (a tunnel only athwartships, a main propeller only fore and aft, an azimuth any way) and its own capacity, with every moment about the centre of gravity. The utilisation is one over that multiple. Unlike a sum per axis, an azimuth cannot push fully sideways and fully forward at the same time here.

THE WIND AREA comes from your own side view when a drawing is chosen: the area above the waterline under the upper outline of the drawing, and its centre gives the wind moment. Open structures count as solid, so the area is on the high side. The front area comes from the side and top view together. Without a drawing both are estimated from the freeboard. Wave drift is summed per sea component, each with its own height, period and direction.

wind     Fx = 1/2 rho_air V^2 . 0.423 cos(a) . A_frontal
         Fy = 1/2 rho_air V^2 . 0.800 sin(a) . A_lateral
         N  = 1/2 rho_air V^2 . -0.143 sin(2a) . A_lat . Lpp
current  reference areas B x T along, Lpp x T abeam
drift    F = (1/16) rho g Hs^2 L R
all environmental forces x 1.25 (DNV-ST-0111)

Thrust per kW is IMCA M 140: tunnel 0.145 kN/kW, azimuth ahead and main propeller 0.171, azimuth with reversed pitch and gill jet 0.105. After the worst case single failure what remains is DP1 100 percent, DP2 and DP3 50 percent - the IMCA default, overridable in step 4.

Watch outChain B is SKIPPED, with the reason on screen, when there are no thrusters entered. Then the polar is coloured on motions only and the Wind and Current cards stay empty - they are chain B and nothing else. Above zero working speed the numbers do appear, but with the caveat that a static balance at speed is a load figure and not a capability figure.

6The calculation point

The Waves card judges the motions at ONE point: the working point on the 2D tab. It is a calculation point, not necessarily a place where work is done - it is simply where heave, vertical acceleration and transverse acceleration are worked out and held against your limits.

Watch outNo working point entered: the calculation point is the CENTRE OF GRAVITY. Only heave counts there and the transverse acceleration has no lever arm, so every result comes out at its mildest. The Workability tab names the point it used under "What it calculated with".

7The top view, and the two sets of axes

The 2D tab draws the ship you entered, seen from above, and it is where the geometry goes: the centre of gravity, the working point, and every thruster with its type and its power. Click the hull to place something, then correct the numbers - they are what counts, the click is only a way to get near.

You give positions the way a general arrangement gives them, and not the way the formulas want them.

y   along the ship, 0 = stern, y = Lpp at the stem
x   across the ship, 0 = centreline, + = starboard

the model then works with arms about the CoG:
    arm_x = y - y_cog     + = forward of the CoG
    arm_y = x - x_cog     + = starboard of the CoG

Watch outWatch the swap: the model's LENGTHWISE arm comes out of your y and its TRANSVERSE arm out of your x. That looks wrong and it is not - it is the difference between where a thing sits and how long its lever is. The conversion happens in one place in the code, so it cannot be reinvented differently somewhere else.

What the transverse position buys is not cosmetic. Two main propellers either side of the centreline hold a heading by running one ahead and one astern - the classic push/pull - and that is a real yaw moment of thrust times the distance off the centreline. Until a unit could be placed across the ship the model had no way to know about it and put it at zero. An azimuth unit was short-changed the other way: it can point its thrust anywhere, so the largest moment it can make is its thrust times its WHOLE distance from the centre of gravity, not just the lengthwise part of it.

The centre of gravity does the same work for the environment. The wind and current yaw coefficients of IMCA M 140 are referred to amidships, while the thruster arms are referred to the centre of gravity - two different pivots in the same fraction. The moment is now moved to the centre of gravity before the comparison is made. With the CoG 8 m aft of amidships and 600 kN of beam force on the hull, that is 4800 kNm that used to sit nowhere.

The outline itself is a drawing and not a lines plan, and it claims only what is true: it is Lpp long, B wide, and the area it encloses is EXACTLY the waterplane area Awp that chain A uses for the heave stiffness. The shape is solved from Cwp rather than drawn by hand, so a fuller hull on the screen means a fuller hull in the sum. At a common Cwp of 0.78 that construction gives a parabolic forebody - the waterline of a Wigley hull - which is why the two shape constants have the values they have.

Everything the geometry implies is listed under the drawing before any weather is fetched: per unit its thrust in kN, its two lever arms and the largest yaw moment it can make, and underneath the totals the ship can put into surge, sway and yaw after the worst case single failure. That is the table to watch while moving a unit around, and it needs no forecast at all.

Watch outThose totals are an upper bound per axis, not a thrust allocation. An azimuth unit is counted in full in surge, in sway AND in yaw, and in reality it cannot do all three at once. That is the Level 1 simplification of DNV-ST-0111 and IMCA M 140 - a sum per axis rather than a solved allocation per heading - so the capability is optimistic and the utilisation ratio in the polar is a lower bound.

8Height, and the acceleration you feel sideways

The vertical motion at a point does not contain its HEIGHT. That is not an opinion, it is the formula: the vertical acceleration at a point is heave plus the pitch and roll lever arms, and the height does not appear in it. So for as long as this module only judged vertical motion, there was nothing to ask a z coordinate for.

The TRANSVERSE acceleration is a different matter, and it is the one that decides whether a deck can be stood on. Two sources give it the same way - Journee & Massie eq. 8.59 and DNV Rules for Ships Pt.3 Ch.1 Sec.4 B701:

at = sqrt( ay^2 + (g sin(phi) + ary)^2 )

  g sin(phi)   the slope of a tilted deck, felt as a
               sideways push
  ary          the swing of the lever arm above the
               ROLL AXIS

WHERE THE ROLL AXIS SITS. With CoG z filled in (KG from the stability booklet, entered from the deck) the ship rolls about its centre of gravity - the usual assumption of linear seakeeping theory - and the roll axis is at KG. Without it, DNV Sec.4 B403 puts the axis at the smaller of D/4 + T/2 and D/2 above the baseline. Either way the lever arm is the height of the calculation point above that axis. The 2D tab says which of the two is used.

Watch outThe two terms ADD, they do not cancel. With phi = phi_a cos(wt) the roll acceleration is -w^2 phi_a cos(wt), so -zb phi'' + g phi comes out as (g + zb w^2) phi_a cos(wt). A point above the roll axis gets both the slope and the swing, in phase. At 6 degrees of roll the gravity term alone is already 0.105 g - close to the NORDFORSK limit of 0.12 g RMS before a single metre of arm is added.

What is NOT in it: sway and yaw. This model has no sway and no yaw response - the closed-form theory does not give them - so the figure is the ROLL-DRIVEN part of the transverse acceleration. DNV has that as the larger of the two terms, but it is not the whole of it, and the limit on the Limits tab says so.

Below the roll axis the two terms work against each other, and at a height of -g/w^2 they cancel completely. That is real, and it is the reason a sensitive instrument goes low and near the centreline rather than up on a deckhouse.

The height of a thruster does not enter the force balance at all - that balance has three degrees of freedom and none of them is vertical. What it does tell you is how deep the unit sits. Submergence is the draught minus the height, and a unit close to the surface draws air; a ventilating tunnel thruster loses more than half its thrust while it does. The module SAYS so and does not subtract anything, because a real ventilation criterion needs the propeller diameter and the wave elevation at the unit, and it has neither.

9The hull outline and your own drawing

The 2D tab has two orthographic windows, top view and side view, where a click resolves to exactly one number. Without a drawing they show the outline of the standard hull, stretched to your Lpp and beam. Upload your own top and side view as DXF and the windows draw THAT instead: nothing is built from it, it is only placed in ship coordinates - aligned to the aftmost and lowest line of the drawing, with a correction for where the transom and the baseline really are.

The hull is drawn as a generic OFFSHORE SUPPORT VESSEL, not as a lines plan of your ship: of any given ship this module knows a few dimensions and two coefficients, not a body plan. What it looks like is what a PSV of this size looks like:

• a long parallel midbody with a near-rectangular midship section - flat bottom, small bilge radius, vertical sides
• a wide, full transom with the bottom RISING towards it (a pram stern): that is where azimuth thrusters hang, under a flat, slightly sloping bottom
• a flat keel far forward and a STRAIGHT rise of the bottom aft from about 0.3 Lpp, as on the general arrangements of the Damen PSV 3300 and the Ulstein PX121
• round U-sections forward (no V), a rounded forefoot without a bulb, a near-vertical stem that leans slightly forward above the waterline, and FLARE that only starts high up towards the deck
• a flat main deck over the full length and no superstructure

It carries one claim, checked by the self-test: the section AT THE WATERLINE is exactly the plan outline, so the area it encloses is exactly Awp. The length of the parallel midbody is solved from Cwp to get there - a fuller hull gets a longer one. The volume below the waterline is MEASURED and shown next to the view, not forced; for a PSV it comes out a few per cent under Cb x Lpp x B x T.

An azimuth, a Voith Schneider or a main propeller hangs BELOW the hull, so for those the check is whether the unit sits under the bottom rather than beside it. Every other unit has to be inside the skin at its own height.

A unit that falls outside the hull AT ITS OWN HEIGHT is ringed in red and named in the table. That case is invisible on a plan view: at the waterline the unit sits inside the outline, and ten metres lower the hull has curved in past it.

Two waterlines can be drawn, and two centres of gravity: the loading condition you are computing, and the other one. The second set is REFERENCE ONLY - nothing in the calculation touches it. What it answers is the question one waterline cannot: a bow tunnel with nine metres of water over it when loaded may have two when light, and that is the trip on which it ventilates.

10Significant or RMS - the factor two that bites

This is the pitfall of the whole module. The output is the SIGNIFICANT amplitude, 2 x sqrt(m0). The NORDFORSK / Karppinen table the default values come from states its figures as RMS, sqrt(m0). Significant is therefore twice RMS.

The SeaData defaults - roll 3 degrees, acceleration 0.10 g - are numerically equal to the NORDFORSK figures for intellectual work, but those are RMS. Read as significant amplitudes our defaults are therefore TWICE AS STRICT as NORDFORSK. That is not wrong, but it has to be a choice, which is why the Limits tab offers all three:

All values are significant amplitudes; the NORDFORSK rows are the published RMS values multiplied by two. Survey and bridge work belongs on the middle row, deck and crane work on the bottom one.

11The three plots, three views each

One polar tells you THAT it is tight. Three tell you WHAT is doing it - and that is the difference between waiting for the swell to drop and waiting for the wind to drop.

Each card has three views. POLAR answers which heading - heading is cyclic, so a circle is the honest shape for it. BARS answers how much exactly, because comparing two headings by eye on a circle never quite works. TABLE is not a fallback: it is the guarantee that every number is reachable in text, for a screen reader, for a report, and for anyone whose colour vision the palette cannot serve.

Watch outThe Wind and Current cards carry no motion component at all. A green Wind card does not mean you can work in that wind; it means the wind alone will not push you off position. Read the three cards together: a heading is only workable when it is green on all of them.

12Where the weather comes from

The browser fetches the wave, wind and current data for your position, walks the model ranking per quantity and takes the first source that has data - exactly the same ranking the SeaWave, SeaWind and SeaCurrent tabs use. The table "What it calculated with" names the winning model per quantity.

That is deliberate. If the server fetched the same data by a second route, screen and calculation could drift apart without anyone noticing. As it stands, the number you see on your screen is the number it computed with. Which sources those are, and under which licence, is on the Data sources page at /bronvermelding.

• DIRECTIONS. Wind and waves carry coming-from; a current curve carries going-to. 180 degrees is added before the current enters the calculation - without that the current force points exactly the wrong way.
• TIMESTAMPS. The curves do not all start at the same hour, so matching is done on timestamp and never on index.
• PARTITIONS. Wind sea and swell are computed as two separate peaks as soon as the source gives a PERIOD per partition (a peak period, or a mean period Tm01 that is converted with the shape of the spectrum itself). The model sources on the platform today give the partition heights but not their periods, so for now the spectrum is usually one peak - and a low swell across the heading is then under-represented.
• SWAN COMES FIRST. For "now" the waves come from the SWAN run at your position whenever there is one: its Hs, peak period and peak direction, and also the SHAPE of the sea - the peakedness Qp becomes the JONSWAP gamma, the directional spread DSPR becomes the width of the spreading. With no run yet, or a run older than 30 minutes, Calculate starts a fresh one (about 30 seconds). The model only takes over when SWAN cannot give an answer: a forecast hour (SWAN is a snapshot of now), a position outside the SWAN coverage, a very sheltered or shallow spot (Hs under 5 cm or less than 2 m of water), or no result within 60 seconds. The Workability tab always says which of the two was used, and when it is the model, why SWAN was not. The water depth from SWAN is shown, not used: the motion theory here is deep water.

THE SHAPE PER COMPONENT, without SWAN: gamma from DNV-RP-C205 3.5.5.5 (5 for a steep sea, 1 for a long one, from Tp / sqrt(Hs)); spreading cos^2 for wind sea (31.5 degrees) and a narrow swell with the spread of Mitsuyasu cos^2s(theta/2) at s = 25 (Goda), 15.9 degrees. The Workability tab lists gamma and spread per component under "What it calculated with".

13The confidence score

Three parts, 100 together.

• VESSEL DATA, 50. Points per filled field, weighted by how sensitive the answer is to it: GM or roll period 15, roll damping 10, working point 8, Cb or displacement 5, thrusters 5, kxx/kyy 4, freeboard 3. Step 1 alone scores zero.
• ENVIRONMENT, 30. A full 2D spectrum scores highest, a model forecast with wind sea and swell separated in the middle, and a total Hs and Tp alone the least. From +6 hours a point comes off per hour, with 5 as the floor.
• VALIDITY OF THE THEORY, 20. Hs below Lpp/25 scores full, up to Lpp/20 scores half with a warning, above that zero with the note that it is outside the linear range.

The number matters less than the line beneath it. "Improve by adding" names the three missing fields that gain the most, and that is the part you can act on. Below 40 the result is an indication, not a prediction.

14Where not to trust it

Watch outTHE ROLL DAMPING IS THE WEAK SPOT. At roll resonance the wave damping practically vanishes, so the viscous damping decides the answer on its own - and a factor 2 in damping is a factor 2 in roll angle. The absolute roll level is not proven either: it sits roughly 2.7 times above a quasi-static cross-check, and the source paper itself reports that the method over-predicts roll. For a workability call that errs the right way - it says do not work sooner rather than later - but expect the polar to be stricter than reality near resonance.

• Linear theory; unreliable above Hs of about Lpp/20.
• No parametric roll, no slamming, no green water - the freeboard is the only way either enters at all.
• Station keeping is static: mean forces, no dynamic DP control, no thruster interaction or ventilation, no forbidden zones. The worst case failure lowers every unit by the same percentage instead of removing a specific one.
• The current coefficients and the wave drift reflection factor are rules of thumb without a free source.
• In following seas the encounter frequency can approach zero; it is clipped at 0.05 rad/s.
• Monohulls only. The theory is closed-form strip theory, and for the hull forms listed on the Vessel tab it would produce a number with no meaning.

If a result looks wrong, work through this order: is the limiter roll and is there a resonance mark - then a different heading helps more than waiting. Is GM estimated - then the roll period is a table value and can be seconds off. Is the strict preset still selected for deck work. Does station keeping say skipped. And finally: what does the score say.

15Sources

Every number in this module comes from one of these, or it is a rule of thumb - and the Status column says which. Where a source could not be obtained that is written down as well, because a figure nobody could check is worth knowing about before you plan a day around it.

Motions - chain A

Station keeping - chain B

The top view and the thruster layout

Height, the roll axis and the transverse acceleration

Thruster types

Vessel types and hull forms

Environment