1.  PURPOSE

Demonstrates compliance of a habitable sailing multihull with ISO 12217-2 §6.18 and Annex F: that, when inverted, the buoyant volume exceeds mLDC/950 and that the craft floats with the (upright) design waterline less than 10° from horizontal (§6.18.2). It also locates the inverted waterline and the clearance of the governing escape hatch / downflooding point.

2.  COORDINATE SYSTEM

Upright craft. Longitudinal x measured from the AFT end, positive forward. Vertical z measured from the BASELINE (underside of keel), positive up. The transverse direction is not modelled — the calculation is a 2-D (x–z) hydrostatic problem.

3.  HOW TO USE

a) Enter water density, the ISO divisor (950), and the loaded condition: mLDC and LCG

b) Enter the governing escape hatch / downflooding point as an upright (x, z) coordinate.

c) Fill the buoyant-volume table. For each item give its longitudinal extent (x aft, x fwd), its vertical extent (z low, z high), and its volume by ANY of three methods: weight ÷ density, area × thickness (mm), or a direct volume. Whatever you enter, the governing volume is taken as the MINIMUM of the methods supplied; blank methods are ignored. Densities are pre-filled with typical values but are editable.

d) Optionally set the two SOLVER SETTINGS (top-right of Calc): “Slices per element” (named range SlicesPerElement, default 20 — higher is more accurate but slower; 5 minimum, 50–100 for high accuracy) and “Max trim search [deg]” (named range MaxTrimDeg, default 60 — the largest trim the solver will search).

e) Read the verdict on the Results sheet and the detailed figures on Calc. Excess habitable / trapped-air volume must NOT be entered — §6.18 allows no trapped-air credit.

Note: the file must be opened in a spreadsheet application that recalculates formulas (Excel or LibreOffice).

4.  CALCULATION METHOD

Reserve buoyancy: total buoyant volume V_B = Σ(governing item volumes) is compared with the ISO requirement mLDC / divisor (950). The margin and PASS/FAIL follow.

Distributed-slice hydrostatics: every buoyant item is automatically divided into SlicesPerElement equal longitudinal slices (hidden Expanded sheet). Each slice is immersed by ITS OWN local waterline zWL = a + b·x_slice, with the immersed fraction of its z_low–z_high band clipped between 0 and 1. The submerged volume is Σ(slice volume × immersed fraction) and the LCB is Σ(submerged slice volume × x_slice) ÷ Σ(submerged slice volume). Because immersion now varies along each item, the LCB migrates correctly with trim (the buoyancy-wedge effect). The slice volumes always sum to the parent item volume and their weighted x equals the item centroid.

Inverted equilibrium: the craft is inverted and the floating waterline is a tilted plane z = a + b·x (a = sinkage, b = slope → trim). A nested bisection solves it: (i) an inner loop sets a so the submerged volume equals mLDC ÷ ρ_water; (ii) an outer loop sets b so LCB = LCG. Before the outer loop the residual R = LCB − LCG is tested at a series of trim limits scaling up to MaxTrimDeg; the smallest limit that produces a sign change is used to bracket the root, so the search auto-expands and does not rely on a fixed trim range. If the level condition already balances, the trim is zero. If no balance exists within MaxTrimDeg (e.g. low reserve buoyancy with a large LCG offset, so the LCB physically cannot reach the LCG), the closest attainable trim is shown and flagged “NOT balanced”, with the achievable LCB reported for guidance.

Outputs: trim angle = atan(b), checked against the 10° limit; the waterline position reported as its upright z at the aft and the bow; and the hatch clearance, the perpendicular (vertical) distance of the hatch point above the inverted waterline (positive = dry, negative = downflooding).

5.  MODELLING ASSUMPTIONS TO KEEP IN MIND

• Each item’s volume is treated as uniformly distributed between its z_low and z_high (gradual immersion).

• The problem is 2-D; transverse buoyancy distribution and transverse stability are NOT assessed.

• Each item is integrated as SlicesPerElement longitudinal slices (default 20). This resolves the buoyancy wedge so the LCB migrates with trim. Accuracy improves with more slices (5 min, 20 typical, 50–100 high accuracy); recalculation time increases roughly in proportion. Very steep trims need more slices for the same accuracy.

• Longitudinal balance requires enough reserve buoyancy and fore-aft spread for the LCB to reach the LCG. With very low reserve or buoyancy concentrated near midship, no trim can balance a large LCG offset; the sheet then reports the closest attainable trim, flags “NOT balanced”, and states the achievable LCB.

• The equilibrium uses the real water density (ρ_water), whereas the reserve-buoyancy compliance line uses the ISO mLDC/950 criterion — two distinct figures, both reported.

• No trapped-air buoyancy is credited (per §6.18); only structure, dedicated flotation, fixed-tank gross volume, sealed non-habitable compartments and Annex G air containers should be entered.

• The profile drawing is INDICATIVE only — a schematic catamaran silhouette scaled to Loa and overall height, not the true hull form. The baseline, waterline, trim and hatch point are quantitatively correct; the hull outline is illustrative.

• If the buoyancy happens to be perfectly symmetric fore-and-aft with the LCG exactly amidships, the trim is mathematically indeterminate (any angle balances). Real, asymmetric data gives a unique result.

• VCG is recorded but not used: only the longitudinal balance (LCB = LCG) is solved. The vertical stability of the inverted attitude is outside the scope of this sheet.

6.  WHY THESE SPECIFIC REQUIREMENTS EXIST

The 10° trim limit (§6.18.2) exists because, per the ISO working group, an inverted multihull should not heel more than 10° from horizontal so the crew are able to walk across the bridgedeck platform to reach the liferaft(s) stowed there — a greater trim was judged to compromise this.

The escape-hatch clearance exists so the crew are not required to pass entirely underwater to escape: the means of escape should not be submerged when the craft is inverted, even though part of the opening may still lie below the waterline. This sheet reports the clearance of the hatch point you enter, not the full opening shape.

7.  HOW THE SOLVER WORKS, STEP BY STEP

The Solver sheet (which you never need to edit) finds the boat’s floating attitude when inverted in three steps — the same three steps are boxed and captioned directly on that sheet, in case you want to look:

Step 1 — find a starting range: the solver tests several candidate trim angles between 0° and MaxTrimDeg, in both directions, and checks a residual (how far the boat’s centre of buoyancy, LCB, is from its centre of gravity, LCG) at each. It looks for two angles where the residual switches sign — meaning the true balance point lies between them.

Step 2 — refine by bisection: starting from that bracket, the solver repeatedly halves the range (up to 24 times) until the trim angle where LCB = LCG is pinned down to within about one-thousandth of a percent.

Step 3 — report the result: the last row of the Step 2 table gives the sinkage (a) and trim slope (b) at equilibrium. These become “final b”, “final a”, “final submerged volume” and “final LCB” near the top of the Solver sheet, which in turn drive every result on Calc and Results.

You may see “VB,submerged(a,b)” and “LCB(a,b)” used on the Solver sheet or in supporting documents. This just means “the submerged volume / LCB you get if you test the boat at this particular sinkage (a) and trim slope (b)” — both are recalculated at every trial value during the search, not fixed numbers.

Each buoyant item is cut into many thin slices (hidden Expanded sheet); each slice is checked individually against the waterline at its own position, then all slices are added together to get the total submerged volume and the centre of buoyancy. This slice-by-slice approach is what lets the centre of buoyancy shift correctly as the boat trims — checking only the middle of each item would miss this effect.

8.  OPTIONAL: OVERRIDING AN ITEM’S LCB FROM 3D SOFTWARE

By default, each item’s longitudinal centre of buoyancy (LCB) is taken as the midpoint of its x aft and x fwd extent, and its buoyancy is distributed evenly along that length when checking immersion (see §6). For an item that is fully submerged at every trim angle expected to be assessed, this straight-line approximation can differ from the true volumetric centroid if the item’s actual shape is not uniform along its length.

If a more accurate LCB for such an item is available — for example, computed from a 3D model in dedicated hydrostatics software — it may be entered directly in the LCB override column (column R) of the item table. When a value is entered there, it is used as that item’s buoyancy position instead of the calculated midpoint, for both the reported LCB and the equilibrium (trim/sinkage) calculation.

Leave the LCB override blank for any item that may be only partially submerged at some trim angles within the assessed range: overriding replaces that item’s distributed, trim-dependent immersion (the buoyancy-wedge effect described in §6) with a single fixed point, which is only accurate while the item stays fully submerged. Used on the wrong item, this can make the trim calculation less accurate, not more.