Using Simulation Motion, has anyone simulated or investigated design parameters in boat dynamics? Specifically, a buddy of mine is interested in determining "...at what roll angle the boat will sustain and still be self-righting unless taking-on water...". Apparently some design variables called "meta-center", "center of bouyancy" and CG come into play, here. I have not done any of this type of analysis, so any suggestions for software to use for an application like this is appreciated. This buddy of mine does not want to model fluid flow or gas/liquid interfaces - he's just interested in somehow using rigid bodies, springs, masses and dampers such as what Simulation Motion offers. Thanks for any suggestions.

I think Ian is assuming you have a model of the hull.

"he's just interested in somehow using rigid bodies, springs, masses and dampers"

While the hull is a rigid body, the hole in the water is not, and it is the hole that provides the restoring force.

Naval architects don't use mechanical analogs for boat stability so it is probably a lost cause, but that should not stop you trying. You never know what you will learn.

Here are some some scant recollections from studying fluid statics. Locate centre of bouyncy and centre of gravity. SW would be useful for both. Determine moment due to side load. If COG is high it is harder for the boat to right itself. If you have a big heavy keel and the COG is low then the boat may be self righting. Set up a moment equation to determine the limiting values.

Hi Anthony:

There is specific software for solving your question.

Anyway, here you have a brief theoretical background, the whole thing could become really complex.

Ships transversal stability can be divided in two types: Weights stability (CG possition), and Shape stability (CB Center of buoyancy)

Lets take as transversal reference plane, the midship plane and for vertical distances, the Base line, K.

CG is assumed to remain constant, lying on the midship plane, in normal conditions.

CB, moves with heeling angle, becouse the submerged body shape changes. For any heeling angle -> Buoyancy=Weight(Archimedes).

Buoyancy vector is applied at the moving CB, while weight is applied to the fixed CG, creating a forces couple.

If the hull is correctly designed, buoyancy vector will cut the midship plane at a point OVER the CG. That point is the Metacenter (M), and the distance, from CG to M, the Metacentric height, or GM. GM is not constant, hence its value is only an approximation of stability for little heeling angles, normally below 10º.

The really important parameter is the minimum distance from Buoyancy vector to CG, that changes with heeling, named GZ.

This value returns the lever arm lenght of the forces couple. Being Force=Buoyancy=constant, distance changes, is what minds.

By computing GZ for given angle increments, the transversal static stability curve is obtained. This curve is then compared with the suitable Rules for the ship and navigating conditions.

By step integration of GZ curve, and by plotting each partial integral for each angle, the Dynamic Transversal Stability curve is obtained, that must also fullfill the Rules.

The geometry and relations are self explanatory from the attached drawing.

Weights Stability: The closer CG to K, the higher stability values.

Shape Stability: The bigger the transversal translation of CB, the higher stability values.

Dont hersitate to ask more if needed.

Regards

Hi Tony,

I did something on this many years ago, and the challenge is really understanding the buoyancy variation with the position & orientation of the boat.

If there is a known variation of bouyancy force (location and magnitude) with roll angle, it is easy to represent using a force and moment. That is a big if though.

One thing I would try, is using 3-D contact to approximate the buoyancy force. The way 3-D contact works is it is a function of penetration. in other words it relies on the interfering volume and applying a reaction force at the center of the interfering volume based on the distance to the nearest free surface. So for example, let's say the volume of the hull below the waterline puts a center of volume at 200mm below the surface. The contact force is a function of this depth times the stiffness which would just be density of water times gravity.

This will ignore any rotational resistance you may have with the hull rolling, but should make an interesting simulation. I don't have time at the minute to give it a go, but let me know if this helps.

Cheers,

Ian