By the numbers... Help!!

[qwerty]

I received these numbers for a design I am considering because I was told to ask for them, not that I knew any better. I am a pretty good sailor, but the numbers mean nothing to me. Can someone interpret them for me?

(It's a 36' aluminum cruiser, though not sure that's important.)

Max RM: 5050 kg.m @ 48,5°
STIX: 32,8 in minimum sailing conditions, 32,1 in load condition
AVS: 119 °in minimum sailing conditions, 114°in load condition

Any help much appreciated.

[Raggi_Thor]

I only know RM, Rightening Moment.
Max RM = 5000kgm means that if the mast top is 10 meters from the center of flotation at that angle of heel (48,5°) you can hang 500kg in it (the mast top) and it will balance.

Many spar makers ask for RM30, rightening moment at 30°.

[Eric Sponberg]

Originally Posted by qwerty

I received these numbers for a design I am considering because I was told to ask for them, not that I knew any better. I am a pretty good sailor, but the numbers mean nothing to me. Can someone interpret them for me?

(It's a 36' aluminum cruiser, though not sure that's important.)

Max RM: 5050 kg.m @ 48,5°
STIX: 32,8 in minimum sailing conditions, 32,1 in load condition
AVS: 119 °in minimum sailing conditions, 114°in load condition

Any help much appreciated.

Qwerty,

"Max RM" means that the Maximum Righting Moment is 5,050 Kg-meters at a heel angle of 48.5°. As you may be aware in the principles of stability, when a boat is sitting upright in still water, the center of gravity (CG) is in line with the center of buoyancy (CB). As the boat heels, the CB shifts to the low side, and the line of force of buoyancy through the CB is parallel to and separated from the force of gravity through the CG by a certain distance, called the righting arm, or GZ in naval architectural terms. The product of GZ x displacement (the boat's weight) is called the Righting Moment, RM. As the boat starts to heel, the distance GZ gets longer, up to a point, and then it starts getting shorter again as the boat continues to heel. At the heel angle where the GZ and righting moment are the greatest is, obviously, the Max RM. Max RM varies from boat to boat, and is a function of hull shape and the location of the CB and CG.

As the boat continues to heel and GZ gets shorter, it finally reaches zero again, and then it goes negative, again to a certain minimum, and finally returns to zero when the boat is exactly upside down, 180° of heel. The point where GZ goes zero is called the AVS, or Angle of Vanishing Stability, sometimes also called the Range of Stability. In your case, this angle is 119° in the lightweight condition, and 114° in the full load condition. This is typical for most designs. Some racing designs smaller AVS, and some offshore cruising designs have larger AVS. In practical terms, if your boat did reach the AVS, it would continue to roll over upside down. As long as the heel angle never reaches the AVS, it will always return upright.

Finally, international standards for stability (ISO 12217) have been passed, and one measure of this is the STIX number, which stands for STability IndeX. There is another thread here on this forum that has been discussing STIX extensively recently. STIX number comes from a long formula with input numbers from the shape of the hull, CG, CB, and the like. Generally, the higher the number, the more stable the boat, and the further offshore it may safely venture, from protected waters inshore to the open ocean. The ranges of STIX are, according to ISO standard 12217:

Up to 5, Category D (waves up to 0.5 M, steady wind Beaufort Force 4)
Up to 14, Category C (waves up to 2.0 M, steady wind Beaufort Force 6)
Up to 23, Category B, (waves up to 4.0 M, steady wind Beaufort Force 8)
Up to 32, Catefory A, (waves up to 7.0 M, steady wind Beaufort Force 10)

That should clear things up for you.

Eric

[qwerty]

Eric,
Thanks for the time and thorough response. I guess I should have simplified, asking: "So would you go to sea in this thing?"

I have no idea what the figures are for my current boat, a Vancouver 27, and was quite happy not knowing them. I have never rolled it, but am confident if it rolled it would continue rolling.

I take it the STIX number and AVS are acceptable for a boat for extended voyages. Is the Max RM acceptable? Given that it varies from boat to boat, does that mean it is not related so much to safety, but rather to tendency and behavior -- just as initial tenderness is something that people might hate, but as far as I know is not really related to safety?

Again, much appreciated.

cheers

[Raggi_Thor]

Thanks Eric, very informative (as usual :-).

Qwerty, you have a STIX of 32.8. That qualifies for category A which means off shore capability if other requirements are met, like the quality of hatches etc.

[Eric Sponberg]

Thanks Raggi Thor.

Qwerty, You don't mention the weight of the boat, but for 36', I would hazzard a guess that it is somewhere around 4500 to 5500 Kg. (10,000 - 12,000 lbs). Typically, a sailboat will have the maximum righting arm occur between 40° and 60° of heel. If the boat is too beamy, this angle will be near to or less than 40°, and if it is too narrow, it will near to or more than 60°. Yours is pretty much in the middle, which says that it is a boat of average proportions. The other numbers being reasonable and according to the standard, it should be OK.

The Max RM varies from boat to boat because it is directly related to displacement. So two boats of the same length but different weights will have different righting moments. Neither may be bad, and there is no "minimum righting moment" that you could say was unsafe. The Max RM is just one of many numbers that are used for analysis, and actually, it has everything to do with safety and it must be used in conjunction with other numbers.

For example, lets take our two boats, A & B, and Boat A has 50% more Max RM than Boat B, and its AVS is 120°. Boat B with the lower Max RM has an AVS that is 160°. Which boat is safer? You can't tell just on the max RM. In the overall scheme of things, Boat B would probably be safer because it can roll to 160° and return upright, whereas Boat A will continue to roll over at just 120°.

The area under the positive side of the righting moment curve (plot of RM vs Heel Angle) compared to the area under the negative side of the curve is also an indication of safety. The larger the positive area over the negative area, the safer the boat. Boat A may have a ratio of 2/1, whereas Boat B may have a ratio of 5/1. And generally, the higher the AVS, to more favorable is this area ratio (large positive area, small negative area). In practical terms, the areas under the righting moment curves are an indication of how much energy it takes to roll a boat over (positive area) versus how much energy it takes to roll it back upright again (negative area). Generally, for an ocean-going boat, you'd like to have a large positive area and a small negative area.

If you have further interest in this topic, I highly recommend reading C.A. Marchaj's (pronounced MAR-ki) book, "Seaworthiness, the Forgotten Factor". It explains this whole subject of stability and safety quite thoroughly.

Eric

[Tad]

It should be doubly noted that, if the above numbers are "as designed", rather than "as built", they are utterly meaningless.

Few designers/builders/marketers are beyond "optimistic fudging" at the development stage. Unless a specific boat (in ready for sea condition) has been inclined for actual VCG and had floatation measured for actual displacement, and then had the numbers re-run, they mean nothing.

The STIX figure in particular requires numerous inputs including stability information (which requires a corrected VCG and disp.). Any case where the boat is only a hair above a major division (Cat A or B) would be very suspect.

Tad

[qwerty]

Eric,

Another helpful response. Thanks for the education, but I will skip the written test and keep an eye out for the book.

The boat was suggested by another forumite in response to my query about a Ted Brewer design. It seems heavy for a 36-footer, especially given that it is aluminum. It's 7,200kg (15,900#) with 2,525kg (5,700#) ballast and 3.8-metre (12.5') beam.

One reason that I wondered if the numbers could tell me about tendencies is that it seems quite flat-bottomed (multi-chine, twin keel) and I also wondered how it would behave generally on different points of sail. It appears to be a case of apples and oranges, but thanks to folks like you I'm learning things despite myself.

cheers

[qwerty]

Tad,
Noted, but I'm not sure what the answer it. Is it a case of false advertising or is it simply impossible for a designer to know how a boat will behave until it is off the paper?

I know a few of these have been built, and now a yard has taken up building on a one-off basis, though I have no idea if designers are obligated to verify or even if they can if they are not production boats.

Does this design qualify as being "only a hair" above a major division?

cheers

PS: Thought I recognized your name from the Christensen site. Just now visited your site. Nice. If we ever meet up in the White Hart waiting for a ferry, I'll buy you a beer.

[Tad]

qwerty,

Not false advertising but perhaps optimistic. Before a boat is built and launched nobody (no matter what they say) knows what it weighs ready for sea, or where the VCG will end up. The main reason for this is that designers have no control over what builders and owners add to the boat. Things like hard dodgers with heavy fixed glass, huge "roll bars" with dozens of massive antennas, davits and monster dinghies with big outboards, life rafts on the cabin top, mast steps, 3 furling headsails, etc...etc. All this adds weight which is often good for stability at low angles, but it also raises the VCG which is bad at high angles.

I just measured the floatation on a steel Bruce Roberts 43', original displacement is supposed to be 30,000 pounds. Well the builder and the owner lengthened the boat a few feet, raised the freeboard 8", and added this and that. She's now floating at about 42,000 pounds and is a long way from finished!

The chance that the designer will ever be able to verify his calculations is small to none. Thing is that would cost big money, the designer must travel to the boat, or the builder must report changes accurately and then make accurate measurements for something that he cares little about or doesn’t see much value in. In Ted Brewer's case (or Bruce Roberts) he is selling stock plans for a few hundred dollars.

In the case of a boat for retail sale in Canada, I submit stability information to Transport Canada and they either accept it or question it. If it's about what they expect it gets approved and there is no verification (though such a process may exist) in my experience. I do expect my calculations to be questioned in court should a problem ever arise (cross those fingers).

I would say that if the Cat A limit is 32 and the boat lands at 32.1, that's cutting it pretty close!!

Tad

[CT 249]

Designers who work with IRC or IMS boats must have a pretty good idea, surely? In some areas, all IRC boats are physically weighed with load cells (not integral Travelift or crane load cells). IMS boats had "wanded" hulls which was a pretty accurate way of ascertaining displacement, I think. In each case, I think measurements are to the nearest kilogramme and (especially in the case of IMS) are often scrutinised very closely by owners, programme managers and competitors. Measurers even check to make sure that halyards haven't been soaked to increase weight, plumb tanks, check bilges etc.

[Raggi_Thor]

regarding weight/displacement,
The LYS table (Lidingö Yardstick, a scandinavian handicap system) is quite interesting.
I remember J80 was adverticed weighing 1200-1300kg, but according to the LYS measuremenst its 1500kg.
Just one example.