# Ultimate Righting Moment

Discussion in 'Stability' started by pha7env, May 21, 2012.

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### pha7envJunior Member

I understand what a righting moment is, but do not know GM plays into it(directly, indirectly, inversely, ect), and what righting moment would a very stable , trawler or motor sailor have. (ultimately and realistically).

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### SleepyOldDogJunior Member

Suggest you take a look at the book "Seaworthiness - The Forgotten Factor" by C. A. Marchaj.
good luck

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pha7........

If you know that RM is equal to Displacement * GZ, you can grasp that movement of either G or M will affect stability directly.....see the diagram below. Note that righting arm is GZ. Raising M or lowering G will increase the length of GZ and increase stability. Lowering M or raising G will do the opposite.

Your question is not really answerable with the information given. RM for a production fiberglass trawler with flying bridge could be half that of an outside ballasted motorsailer. What size of vessel? And RM at what angle? One degree, max?

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### erik818Senior Member

I use the Nordic Boat Standard as a guide. The Nordic Boat Standard for boats shorter than 15 m, issue 1990, was agreed upon between the relevant authorities in the five Nordic countries. My guess is that newer standards, classification societies and other national standards have similar requirements on stability. I´ll check the appropriate standard when I have the need.

The standard sais that for a decked leisure boat, the righting arm at 30 degrees roll angle (GZ30) for any load condition shall be minimum 0.2 m. The GZ curve shall have the maximum at a larger tilt than 25 degrees and shall be positive for any tilt up to minimum 40 degrees.

You really need to read a standard to get all the details. The issue I have of the Nordic Boat Standard is in Swedish so I assume it would be more practical for you to get hold of a standard in a language you would rather read.

Erik

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### jehardimanSenior Member

Righting moment (GZ*displacement) and GM are not really related though they are often spoken of togther. It is important to realize that in actuality, for a free floating vessel not towing, moored, or sailing, CG and BG are always in a vertical line. GZ is an measure of the moment required to heel the vessel to a given angle assuming the CG does not change and only exists when the vessel is acted on by an outside effect. Therefore, what makes up the stability of a vessel is of two parts, the ability to resist motion when and load is applied, and the ability to accomidate that load in a stable configuration

GM is a measure of the instant stability, i.e. the effect of the inertia of the waterplane to resist immediate rolling and does not provide any righting moment on its own. Positive GM is required for the vessel to be stable, negative GM means that the vessel will heel to some angle where GM= 0 (i.e. the vessel will loll). Higher positive GM means the vessel "feels" stiffer, lower negative GM means the vessel heels faster.

GZ on the other hand, is a measure of the actual stability; i.e. the righting moment and the ability to resist overturning. GM is constantly changing as the vessel heels, GZ is fixed for a given displacement and heel angle. Note that when staticly floating upright, GZ = 0 as long as GM>=0. If GM<0, then the vessel will roll until GM=0.

Here is the classic example.
The vessel is floating perfectly upright and you are standing on Centerline (CL). GM>0 and GZ=0 because CG and BG are in vertical line due to gravity. You step athwartships to the rail. You have now moved the CG off CL while the BG is still on CL creating a moment couple that rolls the vessel towards the side you moved to. GM controls how fast the vessel heels and it will heel to an angle where BG and CG are once again in a vertical line. If GM is positive at this point, then roll stops, if GM is negative then roll continues until GM>0, which may never occur until the vessel rolls past 90 degrees (i.e. a capsize). So if you stood on the rail of a rowboat it would eventually capsize, but you can quickly step on it and then step to the center and it resists overturning.

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### pha7envJunior Member

amazingly, and somehow, i do understand that. I am trying this info into something i can actually make effective while looking at a boat at dock or even in an add. A way to figure length, displacement, width, roll in seconds= yes this boat warrants investigation, or no it is not stable it rights to fast to ride decent, or too slow to be stable. I realize it is not that simple, but i have to have something to go by to tell my wife it might or might not work when she says "ooh, i like that one" or "lets drive 100 miles and spend a day and look at this one"! I neither have the luxury nor the technical skills to do a architectural work up on a used boat. Any "ammunition" in my arsenal to keep my family safe is always appreciated!

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### DCockeySenior Member

GM is the slope of the GZ vs heel angle curve (with heel angle expressed in radians) at zero heel for a vessel with a transversely symmetric hull and CG on the centerplane.

Added: GM is also the slope of the GZ vs heel angle curve at zero heel angle for non-transversely symmetric hulls and transversely symmetric hulls with the CG not on the centerplane, provided the metacenter is appropriately defined, and zero heel angle is defined as the static equilibrium heel angle without any external moments.

Last edited: May 25, 2012
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### pha7envJunior Member

i think i understand all the terms. That being said, it seems that, there is no simple calculation that will tell if a boat is going to come back from a knockdown or a roll, and that, when i get to that point, it will be best to pay someone that has more skills and experience that i do to help me figure it out. I do not mind that as much as i mind submitting to the fact that i understand the calculations, but not how to effectively put them together. But then y'all probably could not calculate, off the top of your head , how to build a onsite waste disposal system for 172 homes in Octibee Clay, with a water table at 42 inches. To bad, sometimes we learn to do things that we do not love to get by and when we retire there is this massive block of useless information clogging your brain. I appreciate your patience and the fact that you work to help me understand rather than telling me that it is over my head (for now)!

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### jehardimanSenior Member

There are relatively simple calculations that will show the cabability of a vessel to right from a knock down/capsize if you have all the design and construction details. And there are vessels that are designed to always right, like Coast Guard motor surfboats. But this is not a A=B+C equation that can be passed on a forum because it depends on so many little things. And some things can never be totally accounted for, like wave profile, water or deck, etc.

I think the harder issue is getting a understanding on how much other stuff you sacrifice for self righting capability. For a given cost, boats are zero sum games; you can't have it all unless you are willing to spend without limit to get everything you want. Do you want a trawler that is self righting... always?... or is 90 degrees enough... or 60... or 45. For complete self righting are you comfortable with non-opening ports, sealed buoyancy tanks, dry sumps, and hp air systems... and the associated costs.

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### pha7envJunior Member

not sure what i will end up with. My quest to learn is driven by the desire to know and understand what can be at what physical and monetary cost. Then comes the "if this then that" struggle for me in deciding what is necessary and what is not. What comfort and convenience is needed and what stability designs we feel necessary. Meanwhile we will be cruising in a lesser boat in safer waters, looking, learning, and thinking. Then it will boil down to build, refit or buy and the money on hand. I just received a couple of the books suggested and will be studying. I would guess, as of now, I would probably trade the buoyancy tanks for dogged, watertight doors compartmentalizing the stern bunk area, the aft lazerette or quarters and the engine room, all with lower portholes. Weather tight deck house with 1/2 glass. As for the rest, i am yet to discover. I have no idea what the answer will be about the self righting angle, which is the main reason that i asked this question. i was hoping to be able to figure the hull issues. I have a decent grip on what it takes to keep water out of the places necessary for so as to keep the boat afloat. Now i need to know what it takes, hull design wise, to make it come back from the big wave(or the stupid captain). By the way, what would the hp air be for and please explain what you are talking about when you say Dry Sump? I am only familiar with dry sump in reference to engine/trans oiling systems. thanks!

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