Catamaran Wave Interference

Sorry, i keep forgetting I am sometimes talking technical terms to a non naval architect.

GM = metacentric height. It is the distance from the CoG to the metacentre (KM). So in picture view you have this:


M being the location of the metacentre and G being the CoG. Or in naval arch language, KM and KG.
If you subtract the KG from the KM = GM.

The righting moment of any vessel is = restoring moment = heeling moment (or any disturbance off centre)
heeling moment (or righting moment depending how you are understanding this) in this sense is anything which disturbs the equilibrium of the vessel from its natural upright condition.
Restoring moment is the value of GM x Displacement.

So if a gust of wind came along and heeled the vessel to say an angle of 10 degrees, the restoring moment must be equal or greater than the heel created by the wind. Otherwise she'll keep rotating and possibly capsize if the heeling moment always exceeds the restoring moment.

If you place your feet together and stand up, if someone were to push you at say shoulder height with a force F...and this force F makes you fall over. But if you now stand with your feet apart...lets say more than shoulder breadth apart and the same force F is applied, you wont fall over. You're stable. The distance apart of your feet creates a "resistance" to this motion.
So the distance apart of your feet dictates how stable you will be.

If you now image your feet are now the hulls...the same occurs.

The closer together your feet, or in this case the hulls, the easier it will be to roll the boat through any given angle.

If you move the hulls farther apart, it gets more and more difficult, for the same applied force, F, to roll the boat.

Does this make sense?

If so, the location of M, or KM, is dictated by the waterplane area, WPA and the distance apart - it is the second moment of area. So, just like an I-Beam, the farther apart the flanges the stiffer the beam. This is exactly the same.

Now, the location of M, or KM, is dictated by this 2nd moment of area, or Inertia. So the farther apart the hulls, the higher the location of KM.
And since the KG remains relatively unchanged, (other than additional hull bridge structure) the GM is increasing each time the hulls move apart. - Just think, the farther apart your feet the more stable you are = higher GM. The feet being G and M, in this sense.

Make sense?

So, the boat is now more stable. It is much harder to roll the boat.

BUT, the downside is that because it is harder to move the boat in roll, as soon as a wave or wind or boat attempt to heel the boat, the restoring force of the vessel is very very high, so it moves back to equilibrium much quicker and what is called "snaps" back. It is a short motion = higher accelerations.

This is why riding on a catamaran the motions are short and sharp compared to a monohull which has a lower GM and less snappy and benign motion by comparison.

Make sense now?

 

My estimated gmt is -0.430 M,
bmt is 0.120 M

Also a semi-d powercat; so not much heeling. Of course, not none.

 

Something is not right there.
For a cat you shouldn't have a negative GM and your BMt is too low.
How did you arrive at those numbers?

 

These are from Richard. I am guessing he has a homemade program that has some input error. He probably didn't notice it or think it would bother me. And it didn't for 24 months.

Do be kind to Richard; Dorian took his boat, most likely, on Abaco. He doesn't know yet because people are the current worry; not property.

 

Perhaps we could calculate the numbers from other things in the hydrostatics.

 

I have a lot of sympathy for those caught up in Dorian.
Last year typhoon Jebi destroyed my test tank and I lost my car too.
Hey ho - such is life...at least we survived.

Yup...please do.
Do you have a set of hydros on the dwl (design waterline)..??

 

I am also getting a negative GM (scratching my head). I tried Benford's method and Tupper's method and both came out negative. Although the formulas differ a bit, both came out negative. My KB is 52% of Draught and my KG is high because of top loading. The hull is too narrow to be usable. It is a tri so all the hulls are narrow.

 

Not a tri. A cat.

Too narrow to be usable? Sorry. You mean in the modeling?

 

Mine is a tri. All three hulls are narrow. All persons on deck hence high CG nearly at base of the deck. It is supposed to be just a little above waterline but because of top loading, it went up.

 

FG- To find BM, you have to find I first. I is the transverse moment of inertia of the ships waterplane. The formula infers that a wide beam provides stability of the boat. Cats and tri have narrow beams, monos have wide beams. Looking forward for AH to explain the quirkiness of this formula.

 

Can do. But I need the data requested.

 

I probably need to remove these once you grab the numbers. They are proprietary..although also kind of advertising done right..

 

I did modify the beams a tad.

The actual beam of each hull is perhaps a bit narrower.

The actual centerlines are 12' 6".

This was done for convenience and maximizing spaces.

 

Is this for one single hull?