How to know if a design's righting moment is enough?

Hello all!

When designing a monohull sailboat, how do you know the design has a sufficient righting moment?

lets say we have a sail of 100 square feet, and the horizontal center of effort of that sail is 10 feet from the center of gravity of that boat. at 25 mph, the wind will exert 2.5 pound of force per square feet of sail so 250 lb for the whole sail. if you multiply by the lever the mast create, 10 ft, you get 2500 lb-ft of torque.

should the boat have a righting moment of 2500 lb-ft to be able to withstand this sort of wind on a beam reach?

as the boat heels, the force on the sail will decrease, but is there a general rule to how much righting moment a sailboat needs?

 

There was (in 2005) a couple of formulas for the minimum righting moment in one of the Australian Standards (that I no longer have).

It was:
Mr=1.5*B*(225*n+Dwt) (Nm)
where:
B was the overall beam (m)
n was the maximum number of persons on board
Dwt was the displacement weight (kg).

And:
As<Mr/128
where:
As was the sail area (m^2)

Also sail area is typically estimated using:
As=k*Dvol^0.667 (m^2)
where:
k is between 15 and 22
Dvol is the displacement volume (m^3)

You can estimate the Displace volume using:
Dvol=Pc*LWL*BWL*DWL (m^3)
where Pc (the Prismatic coefficient varies between 0.5 to 0.8, but for a sailboat the optimum is 0.63.

Anyway, hope this helps AlanX

 

@AlanX and MR is minimm righting moment? im surprised its not dependant on the sail area.

 

The first equation based on displacement and beam (plus people hanging on the beam).
The second is based on sail areas (which is just a factor).
The above are simple rules or checks from the Australian Standards (circa 2005).

If you want to calculate the actual moment then you need wind speed, sail area, keel and sail centroids. (If you want to get carried away, the drag coefficient of the sail would be even better.)
If you want to calculate the actual righting moment then you need to map the righting moment verses heel. (Yeah, I did that too.)

This is how I used them (to check the mast Z) way back then:


Regards Alan

 

I found another one for estimating the righting moment that looks like something I did:

Form Righting Moment = 90%*9.81*BWL*Dwt/6
Form Righting Moment = DEGREES(ATAN(2*DWL/BWL))/90%​

It was obviously based on centre of buoyancy for the mid-section of a flat bottom unballasted sharpie.

Here are my calcs for a sharpie based on maximum heel moment (done to 5 degree heel increments) and 16.4m^2 sail area with a 12.5kt/hr wind speed (way too low!).
Clearly I had problems with freeboard and did not meet the required righting moment from the standards:


Yeah, I build the boat and capsized on the first outing. Had to add ballast.

Regards AlanX

 

Define 'sufficient'...?

You can't really ascertain this without knowing the waterplane 2nd moment of inertia and location of the centre of buoyancy relative to the KG.
A simplified explanation of what you're trying to understand is noted HERE.

 

It is not the same to speak of the righting moment, which depends to a great extent on the shapes of the boat, than of the heeling moment, which depends on the external forces applied to the boat. It would be useful to clarify what the various formulas mean.

Righting moment cannot depend on sail area.

 

@AlanX thanks a lot! I was confused about what Mr and As stood for in your first post.

As I understand it, the first formula is the righting moment that come from the hull shape the displacement + the number of people who can use their weight to try to right the ship. I still find it a big weird to use that formula instead of taking the maximum righting moment you get by calculating the righting moment for different heel angle, as I'm trying to calculate this for a keeled sailboat where the form stability is half the story.

What I find more interesting is "required righting moment" = sail area ( in m^2 ?) * 128. which is dependent on the sail area which makes a lot of sense, although not as precise as I'd imagine something like that to be since it doesn't take into account the length of the mast(s), and maybe a couple other things that I think should matter.

for the design I'm looking for it would be about 10*128, and since its a really small boat that is in the ballpark of the righting moment it would already have.

@Ad Hoc Hi! What I meant by sufficient is what a naval engineer would consider sufficient. if you know the conditions in which the boat should perform well, how do you go about finding a 'sufficient' value for the righting moment.

I looked at your post and well It definitely underline that it's not a simple matter. On the other hand it's true that a boat wouldn't necessarily sail well at the heel angle it has its maximum righting moment and it's something that I would like to take into account. But my question remains... I guess MR=AS*128 is simplistic, but what would be a more precise formula, if you know what conditions the boat should perform well in? I'd imagine it would take the sail area into account, the beam, the draft, the maximum wave height and possibly other things... is there such a formula or it's just impossible to approximate the necessary righting moment in a single equation?

 

Simple answer - no!
There are far too many variables, to reduce it down to a - one liner - equation.

 

As the boat heels, the heeling force is reduced. The calculation at zero heel only takes into consideration initial stability. The maximum stability for a keel boat is usually close to 90 degrees of heel, at which angle the force on the sails is negligible. Flooding angle is often the driving constraint, since floating is the most important safety aspect of any boat.

 

@Ad Hoc if you had to figure it out for a design, how would you do it?

 

A sail area of 100 square feet implies a small boat, and the weight and location of the crew would be a major factor in determining the heel angle. In some small sail boats the crew hikes out over the water or is on a "trapeze" entirely over the water. So without knowing the type of boat and how it will be sailed any discussion of stability is meaningless.

In small sailboats the G part of KG is highly dependent on the crew weight location and usually is not on the centerplane of the boat. In some boats with the crew hiking out or on a trapeze the horizontal distance from the center of buoyancy to the CG of the crew can be the dominant portion of the righting moment.

General comment - criteria and calculations used for larger boats may have limited applicability for small boats, depending on where the crew is located while sailing. International Canoes are an extreme example. International 10 Sq Metre Sailing Canoe Home Page https://intcanoe.org/en/index.php

 

@DCockey Alright I guess I agree that you would need a bit more info to determine how you would do it. What I'm looking for is for a general keeled sailboat, not a light dinghy.

 

By having the sail plan the boats hydrostatics and the weight & centres of the boat.
Without which it is just speculation...which we can all do, but how close to reality, for what you seek, is it?!

Indeed.

Which is why one line statements about - how do you know if you have enough "righting moment" on a sail boat is not possible, other than the general notes I made in that previous post.
The design itself is just one issue - complex as it can be....not forgetting that the sea conditions you wish to sail in, also have a significant influence...again, as noted in that previous post on the K35.

 

Or, build it and see.