How valid is Marchaj area under the stability curve for catamarans?

There are always a few who take the Marchaj stability curves for catamarans and monos as being proof that catamarans are "inherently" more unstable than monos.
The famous equation is RM = Gz * Displacement * gravity
But of course this not valid for proas as the distribution of weight is asymmetrical.
So a more accurate equation is what?
RM = Loss of Displaced volume * gravity * horizontal distance between the centers of mass of the 2 hulls ??

 

Adding hulls and changing weight distribution will change the shape of the RM curve, but not the way you calculate RM.

 

Richard Woods writes about it:
Sailing Catamarans - Stability Part 2 http://www.sailingcatamarans.com/index.php/articles/12-to-be-published-mainly-technical/55-stability-part-2

 

Part 3 talks about dynamic stability. Sailing Catamarans - Stability Part 3 http://www.sailingcatamarans.com/index.php/articles/12-to-be-published-mainly-technical/56-stability-part-3

 

As Gary Brown said that formula and the resulting curve are as valid for multihulls as for monohulls, assuming the calculations are done properly. Some software may not accommodate multi-hulls.

It's valid for proas, and any other floating object, as long as the calculations are done properly. Some software may not accommodate asymmetric vessels.

Richard Woods' articles discuss why they curve shown in Marchaj may not be representative of many catamarans, and how to interpret the curves.

 

Thanks for the replies.
Richard Wood uses the curve but says in Part 2 Sailing Catamarans - Stability Part 2 http://www.sailingcatamarans.com/index.php/articles/12-to-be-published-mainly-technical/55-stability-part-2

emphasis is mine.

Of course, if pressed Richard would have to qualify the statement that the crane must lift directly through the center of something such that the lift imparts zero rotation moment to the boat. I call this lift the finger of God trick. Nit picking?
So, in the real world, how are catamarans overturned? And what lessons can we learn?

Restricting ourselves to wind as the capsizing force, it seems clear that the wind loads the catamaran in a completely non-linear fashion as the hull rotates and of course the dynamic response of the boat must be considered, but how?
Two catamarans have identical stabilities according to Marchaj but in use one has strong weather-helm.
Absent Hurricane Irma level winds, at what wind speed is the weather-helm dynamic unable to bring the wind to zero apparent before the boat capsizes?
Clearly as the wind rises you must reef but this takes time and how much time does the boat provide?
Hulls with flat bottoms and thus small draft react to side loading by slipping. Shouldn't this be considered as a stability parameter?

 

Richard's statement is incorrect. The height of the curve is the moment which must be exerted on the boat for it to heel to the corresponding angle in calm water with the boat at rest, not the load on a crane to lift a hull. Moments on the boat which cause heel can arise from multiple sources including shifting of weights on the boat and wind forces on the sails. The moment due to wind forces on the sails can be estimated.

 

I believe that Richard is right. AFAIK, Marchaj does not explicitly refer to use of a crane but the curve is derived assuming an external force, not a moment developed on the hull.
Now I agree with you as to the sources of moment so the question is "how relevant is the area under the Marchaj curve"? The shapes of the two curves, cat and mono, are interesting but only affirm common sense.

 

Marchaj's curve is Right Moment vs Heel Angle. Righting moment is as I described above, not some sort of vertical force. This is a basic definition in naval architecture.

 

Marchaj calculates Righting Moment = Vertical force (displacement) * offset of CenterOfMass from the axis of (something- is it the center of buoyancy of lee hull?)
You were referring to how, in the real world, the hull becomes inclined.
Marchaj does not assume a crane with a load scale to create the graph but his equation assumes that there are no external moments acting on the hull -- which explains Richard Wood's comment.
That is, Marchaj thinks of the hull inclined at 45 degrees, determines the appropriate offset value, multiplies it by half displacement which yields the righting moment at 45 degrees.
changed 1/2 displacement to displacement -- was thinking of Wharram's heuristic.

 

The standard definition of Righting Moment = Buoyant force (aka "Displacement) x Horizontal distance between center of buoyancy and center of gravity. That's a force multiplied by a distance which is a moment, which is the moment required for the boat to heel at the corresponding angle. The buoyant force is the combined buoyant force of the hulls which for the boat to be in vertical equilibrium equals the weight of the boat. The center of buoyancy is the combined center for all submerged portions of the boat.

 

Indeed.

Also noted in a slightly more detailed explanation here.

 

Ad Hoc, welcome.
Does the Marchaj curve take into consideration the increase in draft of the lee hull?
umm, strike that, looks like the changes in draft are unimportant.

 

Have you ever done a stability calculation?

 

There was never any need.
This arose from an argument on catamaran stability in another forum and the usual criticism was heard that "catamarans are dangerously unstable, they keep capsizing"
There is no denying that once inverted they stay that way.
But it appears that most capsizes are due to operator error, i.e. failure to reef or head up.
Questions were asked about the modern trend for greater freeboard and bigger deckhouses. These should raise the height of CoM and thus reduce the peak stability.
Some posters stated that the extra weight was sure to increase stability and quoted the Marchaj curve as evidence, but no one was able to argue the point definitely.