Angle of Vanishing Stability

What is Angle of Vanishing Stability?
The Angle of Vanishing Stability represents a fundamental measure of the boat's ability to recover quickly from the impact of a breaking wave.
The Angle of Vanishing Stability figures strongly in the certification requirements for safety regulations for offshore racing yachts and the international safety standards for production yachts.

How to calculate Angle of Vanishing Stability?
Formulas used to estimate the Angle of Vanishing Stability. The formulas are reproduced from the UK Maritime and Coastguard Agency (MCA)[1] Rules for Sailing Yachts.

formula for Angle of Vanishing Stability
Angle of Vanishing Stability (AVS)

formula for Stability Value
Screening Stability Value (SSV)

The displaced volume depends on the weight of the displaced water, i.e. the density of the water. Seawater (1025 kg/m3) is more dense than fresh water (1000 kg/m3).

Seawater: displaced volume = Total Weight / (1025 kg/m3)

Fresh water: displaced volume = Total Weight / (1000 kg/m3)

AVSdegAngle of Vanishing Stability
BeammGreatest beam measured, excluding rubbing strips
BRnoneBallast Ratio. (Keel Weight / Total Weight)
DCBmDraft of Canoe Body. Maximum draft at the 1/8 of the full beam from the centerline in way of the transverse section of greatest beam.
DVm3Displaced Volume
SSVnoneScreening Stability Value
Total WeightkgTotal weight of the boat

Note: Many authors use - incorrectly - the hull draft (HD) as in the formula in stead of DCB. DCB is always less than HD. HD is only equal to DCB if the boat has a flat bottom, which never happens. If the hull shape is round, using the HD will introduce a 6-10% error. If the bottom has V-shape then the error may be considerable larger; dependent of the V-shape/deadrise of course.

Note: The formula is only an approximation based on the actual results of inclining tests and calculations on a number of typical sailing yachts. The calculated estimate may over/under estimate up to 10-15 degrees in certain cases. But - as Adlard Coles writes[2] - "Nevertheless it offers a good guide."

0-80This indicates a boat suitable for calm water only.
80-100This indicates a boat for inland water only.
100-120This indicates a boat for offshore sailing.
120-140Boats with this angle will usually be left floating upside down once capsized.
140-+Boats with this angle will usually right themselves
110 degrees for near shore racers and 120 degrees for ocean racers are generally accepted standards.

Other capsize indicators
There are some better indicators of a vessel’s likelihood of capsize.
STIX: The EU developed its own stability index called STIX[3], a series of formulas which considered a wide range of factors and provides a reasonable sense of how a boat might perform in extreme conditions. Unfortunately meaningful results require a lot more information than most folks have access to for any specific design.

[Ref 1]: Maritime and Coastguard Agency (MCA)
[Ref 2]: K. Adlard Coles and Peter Bruce (eds.) Adlard Coles’ Heavy Weather Sailing, 6th edition, International Marine/Ragged Mountain Press; 6 edition (2008), ISBN-13: 978-0071592901
[Ref 3]: ISO 12217-2