Metacentric Height

Hi everyone,

My group is working on designing a boat on wheels and we are trying to calculate metacentric height of this boat. I was wondering if someone has done these calculations before, and would like to help us. if there is any online sites which could help us in detemining this height, that would be geatly apreciated. Also the fators that affect it would be awesome.

thanks much

Biomechanist.

 

For simple intial stability purposes (say, up to 5 or 10 degrees) you can use BM = It / Nabla where:
BM = distance from centre of buoyancy to Metacentre
It = the transverse inertia of the waterplane (2nd moment of area)
Nabla = the displaced volume of the hull.
Keep the units consistent.

Centre of buoyancy is simply the volumetric centre of the hull below water, and if you have a centre of gravity calculated, you can find GM very easily by subtraction or addition.

Steve

 

Bm

BM (centre of buoyancy to metacentric ht) calculations are relatively straightforward for rectangles as described in the posting above... unfortunately most boats aren't rectangles... If you've got any drawings of what you're workin' on I'd be happy to have a look for you... I'd prefer iges surface files, but whatever you've got'd be helpful...

Cheers,

Dave

p.s. you said it was a boat on wheels... it does go into the water right?
(Not just a parade float or something like that...). From my understanding and limited experience with these vessels is that stability's often tricky... (tend to be unstable at times)

 

Fortunately, though, the above formula works for ANY shape of boat, so it doesn't matter.

Steve

 

Obtaining Metacentric Height, GM

Salvors use a quick formula that I have found fairly accurate for determining the transverse moment of inertia of the boats waterplane. It is I = (C x C x BWL x BWL x BWL x LWL) /12. Where is C is the waterplane coefficient which is calculated as follows C = waterplane area / (BWL x LWL). The metacentric radius is BM = I / V where V is the displaced volume. The metacentric height is calculated as follows GM = metacentric radius + vertical center of buoyancy - vertical center of gravity. See the following article for more details http://hawaii-marine.com/templates/stability_article.htm. This approximate method involves using hull form geometry and weights and moments data. Usually more accurate calculations involving numerical integration procedures and accurate weights and moments data are utilized. These methods apply to boats that are not yet constructed. Two other methods are available for boats that already exists. First an approximate method involves conducting a "roll experiment." Second a accurate method for determining GM on existing vessel is a "inclining experiment."
Note: All this is based on the assumption that your boat with wheels is in the water floating. If it is on land, it is a whole different story.

 

As long as you know the shape of the waterplane (which you should if you're designing it) you can either use a CAD package to give you a 2nd moment of area (Rhino will do it) or if it is a simple function, by an analytic method. Or if it is not a simple shape, then numerically. For details see "Ship Hydrostatics and Stability" by Adrian Biran.

Tim B.

 

hateto be the party crusher (as I am lately) but, as only daveb picked it up, I have to say it: the post is a joke. Who has ever seen a boat on wheels? with wheels... yeah...ok. but not ON. amphibious vessels do not count, "biomechanic" would have specified it.

and april is way off...