Is calculating stability for a catamaran really this easy?

Discussion in 'Boat Design' started by dustman, Dec 6, 2022.

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dustmanSenior Member

Let's say I have a catamaran with 12' beam that weighs 1200lbs, has a CE above the waterline of 15', with 160ft2 of sail area, at 40mph wind speed.

I take 1/2 the beam and multiply that by the total weight. 6x1200=7200

I take the height of the CE above the waterline and multiply that by the wind pressure on the sails. 15x640=9600

In this situation I would capsize.

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You have omitted the most important part... the hull!!

The shape of the hull and spacing of the hulls plays a major role in this.....without which, you can't "estimate" the effect.

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dustmanSenior Member

You are talking about the distance of the pivot point from the centerline, as opposed to the overall beam?

I'm taking your answer to be "yes, but..."

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No!
Im referring to he inertia of the waterplane area, it is this, that influences the restoring force/moment.

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dustmanSenior Member

So I'm talking about static stability with one hull barely out of the water. I'm not sure how, on a catamaran, the shape of the hulls would affect static stability except for determining the angle of heel at which maximum righting moment occurs.

Forgive my ignorance... Are you talking about a dynamic situation where some kind of roll momentum has been imparted? Can you give me a quick example of how the shape and spacing would affect the stability? By inertia of the waterplane area I'm assuming you mean it's buoyancy, or the rate at which it would pick up buoyancy as it is immersed?

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In referring to this is an older thread, but very pertinent to your question.
Look at the GZ curve, which determines the stability, noted HERE.
Trust this helps to clarify?

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waikikinSenior Member

The spacing of the hulls is important, though one simplified model wants max righting moment greater than 5 degrees heel.
There was a USCG simple model that used the half beam between the hull centrelines as assuming most sailing cats have skinny cylinder "like" forms.
If cat's weigh nothing they blow over, if they are very wide the CE goes up^ quickly when they heel.. there's many factors at play.. even lumps in the water called waves... there's more than one way to flip
Jeff.
New stability requirements for catamarans https://www.boatdesign.net/threads/new-stability-requirements-for-catamarans.13962/
Catamaran Stability | Luxury Catamaran Long Island, New York https://www.aeroyacht.com/catamaran-learning-center-2/catamaran-stability/
https://www.catamaranfreedom.com/why-catamarans-capsize-a-scientific-explanation-for-beginners/

8. Joined: Jun 2019
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dustmanSenior Member

We are both talking about static stability, correct?

My understanding is that a catamaran has zero righting moment while completely flat, the righting moment rises quickly as it heels until one hull comes out of the water, at which point maximum righting moment occurs, from then on the righting moment falls at a rate determined by the righting arm, weight, and center of gravity. I can only see hull shape on a catamaran having a significant influence on where the tipping point is and a minor influence on the rate of the curve, and it may have a small influence on the angle of heel at which that maxima occurs. I don't see how it would have any influence on the magnitude of the maximum righting moment.

I don't really understand what you mean by hull spacing, to me that is the same as the beam between the centerlines of the hulls, which is the number I am referring to when calculating righting moment in my initial post.

I'm sorry, it didn't add any further clarification. I'm simply trying to confirm that my understanding of how to calculate static stability is correct, then from there I can try to quantify the other factors like wave action, wind gusts, etc to try and settle on an appropriate sail size.

On the Wharram website the Catamaran Stability article basically lays out the same method of calculation I stated in my original post, and says to multiply the righting moment by .6 for a safety factor to account for wind gusts, etc. They call the resulting number the dynamic stability.

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waikikinSenior Member

Hi Dustman, that's a critical measurement as there's a very distinct difference between beam overall and the distance between hull centrelines that wasn't clearly defined in your original post though most of the cat's with heavy fat hulls are very unlikely to "blow over".. on the other hand some skinny hulled very lightweight cats with greater hull to hull centreline beam most certainly will in quite mild conditions.
Best be keeping up side up
Jeff.

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DCockeySenior Member

All hulls have "zero righting moment" when at zero heel, assuming symmetric shape and CG is on the centerplane. Nothing special about catamarans.

To what extent the shape of the hulls of a catamaran can be neglected in stability calculations depends on the beam of the hulls, the spacing between hulls. The larger the spacing between hulls is compared to the beam of the hulls the less significant the shape of the hulls will be, everything else being equal. For a Wharram type vessel neglecting the effects of the shapes of the hulls on right moment may be a reasonable assumption. For power cats with spacing between hulls a few hull beams or less than the effects of the shapes of the hulls may be significant.

11. Joined: Oct 2008
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Ok, let's say you are standing, and standing up right. Your feet are close together, side by side.
If i give you a rope, a thick rope, that you hold in both hands. I then stand to your side, not in front of behind you, but exactly on your side, to the left or right, makes no difference.

I then pull the rope....what happens?
You struggle to hold and stay up right...and if i increase the pull(force) you will eventually fall over.

If you now spread your feet, so they are say - shoulder width apart - and perform the same action...what happens?
You are able to resist the same force that previously pulled you over. You remain upright.

The further apart you place you feet from each other, the greater the load(force) you are able to withstand and remain upright.

Replace your feet with the demihull of the catamaran (hull spacing), and the rope being pulled with the wind on the sails.
That is it in a nutshell.

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