Page 2: hull formulas relating to stability. |
RP (Roll Period) = 1 timed complete roll of boat, by trial or: RP = 60 / roll # , by trial (60 seconds divided by the number of rolls in 1 minute) or: 6.28 x [ (disp ^1.744 / 35.5) / {82.43 x LWL x (0.82 x BOA) ^3} ] ^0.5 The latter method derives the figure by calculation from other measurements and not by trial in practice. The expression (0.82 x BOA) is used if BWL is not known, i.e. it calculates the waterline beam as being 82% of the overall beam. RP is the time in seconds for one complete 'roll' of the boat due to wave motion, i.e. the port beam of the boat fully depressed, through fully elevated, back to fully depressed. Named T by some users (presumably for Time). There are several ways to calculate this by averaging the time for a number of rolls of the boat, which can be induced at the dockside by hauling on a shroud rhythmically until full rolls are developed – and then letting go and measuring the roll time, since it will be constant even with decreasing roll size (in theory, frequency is independent from amplitude). A good method is to time 10 rolls and divide by 10. Since the rolls may well flatten out before sufficient numbers have been counted, timing a run of several should compensate for small variations where the boat has to be helped along. This is a comfort and stability indicator. A figure of over 4 (seconds) is considered desirable for comfort; a shorter roll period is uncomfortable, leading to higher acceleration. This translates as acceleration applied to the crew: over a certain level they are more likely to become sick, and at a higher level will become exhausted. The roll period is proportional to the ultimate stability of the boat. The heavier, bigger and longer the vessel, the longer the roll period – ships have a very long period and don't often get rolled by a wave... A shorter RP may show a beamy, light, boat. This would have more initial stability (with a harder, sharper motion), but less ultimate stability. It is initially stiffer, but ultimately more vulnerable. Therefore a longer roll period indicates a more stable vessel, which is in direct contradiction to the natural inference that a short period = a stiff boat = a more stable boat – this is not so. Note that some commentators have got their knickers in a twist over this (by describing a boat with a short RP as stiff or a boat with a long RP as tender). A boat which is 'stiff' in this respect reaches its AVS (angle of vanishing stability, or vanishing angle) much faster and more easily, and then goes over. As an example a small, light, very beamy boat will show the shortest roll period; and is the easiest capsized by a breaking wave. A stiff boat has both a long RP and has reasonable initial stability, i.e. is not tender. The RP is not directly related to tenderness, the opposite of stiffness: but a boat with an extended RP is unlikely to be tender. If you have trouble visualising this, consider a ship: it doesn't move when you step onto it, and has a very long RP (of 10 seconds plus). A high initial stability combined with a short RP may be a valuable attribute in a dinghy – but not in a cruiser. A nicely-designed medium-size cruiser might have high initial stability combined with a long RP. A big, heavy cruiser is likely to have both. If you try this out on various boats, you will find that the effort involved varies considerably. Boats with a long RP are very hard to get moving, and take a lot of effort to induce any kind of movement; two or more people are needed to get any cyclical movement at all. Boats with a short RP are moved easily by one person, and soon develop a quick, short movement. The roll period directly affects comfort, and in fact is strongly related to the results given by Ted Brewer's Comfort Factor qv – there is a direct and linear relationship despite the Comfort Factor being calculated rather than measured by trial. Again this shows that bigger is better – hardly a revelation. The roll period has the following relationships with other factors: Comfort Factor: very closely related – a direct linear relationship Acceleration: very closely related (inverse relationship) Capsize Risk: closely related (CR is the SNAME / USYRU figure) LOA: related Some average roll period examples for cruising sailing boats are: 26-footer = 2 30-footer = 2.5 35-footer = 3 40-footer = 3.5 45-footer = 4 60-footer = 5 100-footer = 7 150-footer = 10 The term average here means just that: boats vary widely above and below the figure. For instance at 32 feet of boat length, some will measure RP 1.5, some RP 4.5. The smallest boat likely to have a RP of 4 is a heavy 30-footer. ---------------------------------------------------------------------------------------------------------- Rig weight v. stability An interesting concept for pondering. It is normally stated that a heavy rig will affect the boat's stability adversely; but consider the fact that a boat with no rig will be less stable than one with identical dimensions but with a full rig. This is because the rig weight, being at a distance from the CG, acts as a lever arm to increase the roll moment of inertia. A heavier rig will increase the RMI and therefore initial stability without much effect on displacement; but ultimate stability is eventually compromised. Motorboaters and commercial fishermen have been known to ask if a sailboat's rig has to be removed in storm conditions; not being sailors in the wind-and-sail sense they don't realise that a small sailing vessel is a whole lot more stable than a small motor vessel. You can sail round the world in a 20-footer, but it wouldn't be fun in a 20-foot motorboat. Logically, at a given length motor vessels start to become more stable than sailing vessels; perhaps at around the 100-foot mark, when a motor vessel's displacement begins to give sufficient stability to equal the big roll inertias given by the large weight suspended below a sailboat, and the long lever arm above it. You might consider the fact that an infinitely tall rig would give a sailboat an infinite resistance to capsize; the infinitely heavy keel needed to support it might give problems though. A one-mile high rig would still be nearly vertical when a big wave has gone past – assuming there wasn't any wind... Apparently the old-timers used to haul an anchor up the mast, if the ship was rolling hard in a sea; this is said to have slowed it down. ---------------------------------------------------------------------------------------------------------- AVS – Vanishing Angle, or Angle of Vanishing Stability The angle of heel at which a boat capsizes. This has steadily reduced over recent years, at least in small to medium cruising sailboats. The benchmark for stability in medium-size sailboats is the Contessa 32, with an AVS variously reported between 151 and 157 degrees. There are a few boats that can better it, but not many. This figure is closely related to a boat's (static) stability – though it isn't the be-all and end-all of it as there are several other factors involved in practice. The two smallest boats to survive and finish the devastating Fastnet '79 race (in which 15 died, 17 in total in sailboats in that area) were a Contessa 32 and a Sadler 32, which is a modification of the same design. Now, lightweight A-Ocean rated CE marked European production boats are coming out with an AVS of 110° or so. Bear in mind that anything added to the boat will reduce that, since it will nearly always be placed above the CG. Radars, genoa furlers, and so on will all decrease the AVS. It is also probable that the measurements were taken without in-mast furlers, which will give a real hit on the AVS. Therefore two or three years down the line you could expect to see an AVS in practice of less than 100°. How about that? Probably more than anything else, this goes to show that the Euro RCD (Recreational Craft Directive) and CE marking were introduced as a result of pressure by mass-market producers to help elimininate competition, rather than for the 'safety reasons' that have been ludicrously quoted. Obviously, 'ocean' rated boats have never been so dangerous. There have been several cases just in the UK where medium to large models of these A-rated boats have capsized, sometimes staying inverted. One famous case which resulted in loss of life (crew were lost overboard and later recovered dead) involved a fairly large late-model Euro-boat rolled mast to waterline whilst still within a harbour on a rough day – they decided not to put to sea after that. AVS can be measured by three methods: 1. by partial measurement aboard the boat, then by calculation; 2. by calculation using various proprietary formulas; or 3. by careening to the point of capsize. 1. Method 1 is probably the most realistic, and involves swinging a known weight out on the boom a known distance from the boat's centre, and measuring the heel angle resulting. By calculation this gives an approximation of the boat's AVS (and an approximation only, since many other factors influence the final result). 2. By calculation only, using the displacement, length, beam, and so on. This gives a 'near-enough' figure for most purposes. It cannot possibly give a true figure since it takes no account of individual boat characteristics such as deckhouse shape and volume, real-life CG, added inventory, and so on. 3. By careening to capsize – hauling over by a crane – and this is the only truly accurate method. It has lately been used for some round the world raceboats, which had started to suffer an unacceptable number of capsizes. Raceboat owners, with their stripped-out shell boats, are no doubt the only people who would stand for it anyway. ---------------------------------------------------------------------------------------------------------- CF (Comfort Factor) = D / [ .65 x (0.7 x LWL + 0.3 x LOA) x B ^1.33 ] where: D = displacement LWL = waterline length LOA = length overall B= beam A measure introduced by Ted Brewer to show a boat's liveability offshore. It favours bigger boats, unsurprisingly, but in the smaller sizes heavier displacement, narrower beam, and some overhang gives improvements. These all slow down a boat's movement in a seaway. It is related to ultimate stability (but not initial stability), and very closely related to the roll period. Although RP and CF are measured in completely different ways (RP normally by trial, CF by calculation), the results are directly comparable and in fact the graph for one could be mistaken for the other. A figure of around 35 seems to be coming into the comfort zone, with raceboats showing 20 or less, and Colin Archers showing 50-plus. CFs for average boats rise steeply from 20 through 40 feet boat length, in a curve that levels out toward the 100-foot mark. Seaworthy 30-footers show a CF of about 25 or better, with lightweights of that length down below 10. The Comfort Factor has the following relationships with other factors: Roll Period: very closely related Acceleration: very closely related (inverse relationship) LOA: related This is an empirical factor, that is, derived from remote data and not tested by scientific method; though presumably an accelerometer could be employed (though Roll Acceleration in G-force is derived separately, and has separate implications; although once again CF proves closely related). Reportedly released and employed 'tongue-in-cheek' by its inventor, it is nevertheless widely quoted – and quite rightly, otherwise the voice of the 'build-it-light-and-wide-and-sod-the-risk' boys gets to be too loud. ---------------------------------------------------------------------------------------------------------- CR (Capsize Risk) = BOA / [ (Disp / (0.9 x 64) ] ^0.333 Beam is compared to displacement. A measurement developed by the USRYU and SNAME after the '79 Fastnet. Values less than 2 are supposed good, the lower the better (1 is a minimum); boats with values over 2 are not considered suitable for ocean races. Wide beam and light weight are penalised; heavier boats (therefore bigger) are favoured. The researchers concluded that static stability was less important than dynamic stability, which depended on other factors. Beam and displacement were considered more important in determining whether a wave would capsize a boat. Nevertheless, considering the actual results of the race, particularly the Contessa 32 finishing (and ahead of larger boats), static stability must play a part; some of the boats capsized must have had better CR numbers than the Contessa's 1.77. Of course, it is much easier to calculate the CR figure than static stability. Most modern offshore raceboats or 'sledges' would not be deemed safe by this method. ---------------------------------------------------------------------------------------------------------- Hull stability formulae There are several of these formulas in use, used by different authorities and governing bodies. I calculated one through for my boat, and found it to have an AVS of 151 degrees. While this would be an attractive result, and make it nearly as stable as a Contessa 32, I feel it may be a little optimistic – perhaps by as much as 20 degrees. One might think it best to take the results given by such methods with a pinch of salt, and consider two facts: 1. This result gives the best possible interpretation, and takes no account of a real-world CG height – which cannot be as optimistic as that assumed. 2. It can only possibly apply to a brand-new boat just out of the mould. The figure will degrade every time an accessory is added or a tin of food brought aboard. Because such formulas cannot be relied upon, and are therefore not safe, none are included here. Any stability calculation must involve some sort of practical test. ---------------------------------------------------------------------------------------------------------- ^ TOP ^ |
Marine Formulae #2 |