An overview of Yacht Stability Metrics

This is a very brief overview, for a longer, readable exposition in a chapter or so, see (Bruce, 2016), for the full works covering the state of knowledge in the mid 1990s see (Marchaj, 1996).

WIP: Currently being updated to better cover the Achilles range of yachts.

There are a number of measures of stability and suitability for offshore boats, all must be treated with caution, some were devised years ago, most notably after the 1979 Fastnet disaster, and do not work as well with more modern designs, more recent ones appear to sometimes award high categories to boats that many feel don’t deserve them, and occasionally the other way around. One such is a legal requirement in Europe, the Recreational Craft Directive (RCD) category, and designers are still gaming the system to get better grades and a competitive advantage for the boat commercially or whilst racing.

Several factors come into the calculations, two important ones are measures of stability, the Angle of Vanishing Stability (The GZ Curve) and the STIX (STability IndeX) value derived from it, neither of which are easy to calculate or measure. So over time various other measures have been developed, some of which are explained below.

Despite their limitations they are a starting point, but common sense needs to be applied and before giving them too much weight, especially over small differences, a lot of research needs to be done rather than blindly relying on any of them.

The GZ (Righting Lever) curve

G is the centre of gravity of the boat, GZ is the righting lever – the horizontal distance between the centre of gravity and the centre of buoyancy (which changes with the angle of heel) at a given angle of heel.

In 1979 this was the standard model for stability, the graph below shows the righting lever for a reasonably high performance ½ tonner (a competitive design in 76 but not in 78, such was the rate of change at the time) and a Contessa 32 an example of which was the only class 5 boat to complete the 79 Fastnet.

Ignoring wave action and some other factors (the biggest being the impact of sails in the water), the boats will right themselves from angles with a positive GZ, the more the better. When the value turn negative a boat will continue to roll to a stable inverted position and will only right themselves if something – the waves – rolls them back to a positive value..

Angle of Vanishing Stability (AVS)

The point at which the value goes negative is known as the Angle of Vanishing Stability (AVS) or the limit of positive stability.

Hydrostatic stability, 1/2 tonner Grimalkin vs Contessa 32. Data source: (Wolfson Unit, University of Southampton, 1979) in (RYA & RORC, 1979). The increase in the Contessa’s righting moment at 60 degrees is the result of the coach roof entering the water providing additional buoyancy.

As can be seen there are some very significant differences between the two plots, Grimalkin will invert at about 115 degrees and will then need a big push from a wave to recover. The Contessa will recover from about 160 degrees and if she does invert will only need a small push to recover.

The design of Grimalkin, a Nicholson ½ tonner, has been described as “extreme” (Larsson & Eliasson, 2007) but was considered “typical” [of ½ ton racing yachts] by her internationally respected  designer, Ron Holland and was certainly less extreme than some of the boats at the top of the fleet in 78 and 79 such as Waverider, Green Dragon and Smokey Bear. She was abandoned with the loss of 2 crew in the 79 Fastnet race after at least 5 knock downs and a complete inversion.

Righting Moment

However, mapping stability using the Righting Lever (GZ) ignores the effect of displacement, the next graph shows the curves for the same boats but mapping the Righting moment (GZ x the weight applied) against heel rather than just the righting lever.

Hydrostatic stability expressed as a righting moment rather than leaver.
Data source: 
(Marchaj, 1996)

The area under the positive part of the curve is proportionately greater for the Contessa than for the ½ tonner, showing that the heavier boat provides the greater stability. Interestingly studies have found that increased freeboard does not increase the propensity to be knocked down but does tend to slow recovery, flush decks also do not help in this but a sturdy large coach roof increases buoyancy at very large angles of heel.

You may be lucky and be able to find the AVS or even a curve for a specific boat but it is unlikely for older ones, and to calculate it you need a full table of offsets for the hull and a computer model.

CCA Capsize Screening Formula (CSF).

After the Fastnet Disaster the Cruising Club of America’s technical committee looked at stability in severe conditions making extensive use of original research and data from the UK’s Southampton University and the report on the race (RYA & RORC, 1979) and its underlying data.

One output was a formula giving an indication of resistance to capsize and inversion caused by waves, it is somewhat controversial as it relies on empirical data from the Fastnet race and does not take account of placement of ballast or the shape of the hull.

It therefore needs to be treated with some caution, especially with modern lightweight designs with deep, high aspect bulb keels, movable ballast (not allowed in the 70s, apart from crew) and those that rely heavily on form stability generated by a wide beam carried well aft. It is more likely to be of use comparing displacement boats from the 60’s through the 80’s.

CSF = Beam / ((Displacement/64.2)1/3) in feet and pounds.

A result of 2 or less is regarded as “safe” offshore, the “cut off” point is based on the analysis of Fastnet experience, principally the number of knock downs per boat compared to their beam and displacement for which they had a good sample of contemporary boats with the large number of boats suffering knock downs, detailed in Table 3 of the RORC report. 

For boats designed in the 60, 70s and at least the early 80’s this appears to be the most reliable of the quick and easy to derive measures of stability. See the table below for the number for Achilles yachts.

The “Comfort Ratio”

Was devised by Ted Brewer as a measure of acceptability of a yacht for cruising, it was about how comfortable a boat is likely to be in the conditions it is likely to face, but indirectly there is some correlation with stability. 

Comfort Ratio = Displacement / (0.65 x (0.7 LWL + 0.3 LOA) * Beam 1.333)

Measurements in Pounds and feet. The, again somewhat arbitrary, bands indicate the likely suitability for cruising:

Ratio

Most likely

< 20

a lightweight, uncomfortable racing boat.

20 - 30

a coastal cruiser.

30 - 40

a moderate blue water cruising boat.

40 - 50

a heavy blue water boat.

Of the boats described below only the long keel “Twister” (40.5) and “Honey Bee” (40) scrape into the Heavy Blue Water band with the long keel Vancouver 27 coming out at 32. Many struggle to even reach a score of 25 and the Achilles 24 only rates a measly 14. Achilles and most Jester sailors need to be hardy folk going offshore!

STIX

The STIX calculation takes the Righting Moment and the principal dimensions of the boat and massages them with a number of factors to calculate a Stability Index to give an assessment of seaworthiness. Like all measures it is not perfect and, again, designers will try to game the system so the number will generally be beneficial for modern boats. 

As will be seen from the following it is not easy to calculate even if you have the Righting Moment or  Angle of Vanishing Stability (AVS). Many of the factors requires a lot of maths and data to calculate, they are named here to give a “feel” but not defined, for more details see (Larsson & Eliasson, 2007) or try some internet searches.

STIX = (7 + 2.25 x LBS) x FDL x FBD x FKR x FIR x FDS x FWM x FDF)0.5 + δ

 δ  = 5 if, when the boat is fully loaded with water, it has reserve buoyancy and has a positive righting arm at 90 degrees of heel. Otherwise it is zero.

STIX factors:

LBS = Base Length Factor, a weighted average of the LOA and LWL, it favours yachts with LWL close to LOA (new ones) and penalises those with long static overhangs (old ones including the A9m, A840 etc). LWL will usually increase with speed and for boats with overhangs with heel angle but this is not allowed for.

FDL = Displacement Length Factor, penalises light displacement for a given length, limited to the range 0.75 – 1.25.

FBD = Beam Displacement Factor, penalises a wide beamed light boat (which is likely to be stable inverted and more easily knocked down by a wave) and a very narrow beam “plan on edge” type. Based on research after the Fastnet (Wolfson Unit, University of Southampton, 1979) and more.

FKR = Knockdown Recovery Factor, an attempt to recognise the boats ability to spill water from the sails after a knock down. If the Angle of Vanishing Stability is < 90 it is set to 0.5 the minimum value and you get an awful STIX number.

FIR – Inversion Recovery Factor, the ability to recover from an inversion, the Angle of Vanishing Stability (AVS) is the most important component. An 8 ton yacht needs an AVS of 1200 to get an FIR of 1.

FDS = Dynamic Stability Factor, proportional to the area under the Righting Moment curve with some modification, mainly to allow for down flooding.

FWM – Wind Moment Factor, penalises boats with a down flooding angle of less than 900 if they can’t withstand a wind of 17 m/sec under full sail.

FDF – Down Flooding Factor, represents the risk of water going down an opening in the hull, calculated at design displacement and loaded. If a hatch is offset then it is calculated with the boat healing towards it.

The STIX number is used to calculate the RCD category along with some additional factors, for example category A & B boats must have a quick draining cockpit and a down flooding angle of > 900.

RCD Category

An RCD rating Is mandatory for all boats (with exemptions for canoes, surfboards etc.) sold new in Europe over 2.4 metres in length. Note that the RCD requirement may be applicable to some major conversions of older boats..

For the majority of Jester Sailors it will be of limited use as it did not come into force until 1998[5] and their boats are typically older and clearly no Achilles will have one. There are four categories associated with the conditions they are designed to meet:

Category

Min STIX

Wind Force

Wave Height

Likely use

A

32

> F8

> 4

Oceanic, needs to be self sufficient.

B

23

=< F8

=< 4

Offshore

C

14

=< F6

=< 2

Coastal waters, large lakes & estuaries.

D

5

=< F4

=< .3 / .5

Sheltered coastal, small bays and lakes.

As mentioned above older designs, if the have one, tend to fare badly, particularly those with long static overhangs, and a few modern ones suspiciously well.

Displacement / Length Ratio

This is largely a measure of potential speed, but a low number will also imply a lively and potentially an uncomfortable motion in a seaway. A boat with a low number is likely to be slowed more when stores, crew, fuel etc are added than one with a high number.

Displacement (Long Tons) / (0.01 x LWL (ft))3

Displacement / Length Ratio bands.

Ratio

Classification

> 350

Ultraheavy

275 - 350

Heavy

200 - 275

Moderate

100 - 200

Light

< 100

Ultralight

Comparing some older boats

Remember that small differences are likely to be immaterial which is why broad bands are allocated when putting words to the values as shown above. Data is from sailboatdata.com, it varies somewhat from that in (Marchaj, 1996) but matches my calculations for my A9m and is used for consistency as Marchaj only gives a few examples at this size.

Comparing the Displacement / Length, Capsize Screening Formula and the Comfort Ratio metrics for sample boats (all are fin keeled versions) including the three most numerous Achilles types. 

Design

Example

Design Year

Disp / Length

CSF

CR High more comfort

Twister 28

Tourbillon

1964

448

1.50

40.5

Sadler 29

 

1981

308

1.89

25.8

Achilles 24

 

1968

156

2.06

14.2

Achilles 840

 

 

172

2.04

18.0

Achilles 9m

Sancerre.

1975

190

1.88

21.7

Nicolson ½ Tonner (30ft)

Grimalkin, Silver Jubilee

1977

175

2.27

15.7

Contention 30

Buccaneer[1]

1977

187

2.30

15.5

Hustler 32

Smokey Bear[2]

1978

191

2.39

15.1

Moody 31

 

1983

271

1.95

24.8

Contessa 32

Assent[3]

1972

307

1.80

27.7

UFO 34

Black Arrow

1973

205

2.03

21.8

S&S 34

Slip Stream, Morning Cloud I

1968

290

1.93

24.3

The relative values for the Capsize Screening Factor and Comfort ratio, although in a narrow band, are pretty much in line with my expectation and / or experience.

The Displacement / Length ratio however does not, at least in terms of speed, the UFO 34 and Achilles 9m seem to be classified as faster than comparable boats than I would expect having sailed both significant distances shorthanded and in the case of the UFO raced fully crewed in a world championship. 

In particular the Achilles 9m is nowhere near as fast as the Hustler 32, Smokey Bear was placed 2nd in the 78 ½ ton world championships and "Indulgence" another Hustler was 6th. An Achilles would not have had a chance of even  qualifying for the racing.

Notes:

[1] "Buccaneer" was Brian and Pam Saffrey-Cooper’s Peterson designed ½ tonner before "Green Dragon" and from my experience sailing on both, was less extreme than the latter.
[2] Smokey Bear, was not quite a standard boat so displacement and therefore the ratios shown here may be a bit off.
[3] Assent was the only class V boat to complete the 1979 Fastnet.

Sources:

Bruce, P., 2016. Heavy Weather Sailing. 7th ed. London: Adlard Coles Nautical.

Larsson, L. & Eliasson, R. E., 2007. Principles of Yacht Design. 3rd ed. London: Adlard coles Nautical.

Marchaj, C., 1996. Seaworthiness: The Forgotten Factor. Revised ed. London: Adlard Coles Nautical.

RYA & RORC, 1979. 1979 Fastnet Race Inquiry, s.l.: s.n. (available free on-line)

Rousamaniere J. (editor) 1986, Desirable and undesirable Characteristics of Offshore Yachts by the technical committee of the CCofA, W.W. Norton & co.

Wolfson Unit, University of Southampton, 1979. Stability Conditions on Contessa 32 & 1976 Half Tonner for the RYA, s.l.: s.n.


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