Help with LCG LCF and LCB!!

Hi guys,I'm studying about stability metters,I realized that I have a bit of confusion in my head when speaking of LCG LCB and LCF.
LCG : long. centre of gravity.
LCB : " " buoyancy
LCF : " " of Floatation

My textbook says LCB is the centre of the hull (translating from italian)
principles of yacht design says it' the centre of the volume of displaced water...is this the same thing??
LCF is the long. centre of the water plane area.
LCG is the long centre of gravity....
How do I get the CG of a bare hull ? from what I get CG equals the sum of all component's static moments (calculated from sect.0) divided by total weight.
Then...how do these C. relate with each other? how do they move when the hull is heeled?
Thanks for your help!
fede

 

LCB = Longitudinal Center of Boyancy = The centroid of the underwater volume of the boat expressed as a longitudinal location. Unless otherwise specified LCB is usually understood to be the centroid when the boat is floating on its datum waterline (DWL) with zero trim.

LCG = Longitudinal Center of Gravity. A boat will trim until the trimmed LCB is directly below (or above, but in any case vertically in column with) the LCG. If you know a vessel's MT1 (moment to trim an inch, or, in Europe, a cm) you can use the distance between the datum LCB and the actual LCG, times the displacement, to make a first approximation of trim.

LCF = Longitudinal Center of Flotation = center of the waterplane. When you are considering the addition of new weight (cargo) and you want to calculate its effect without having to recalculate the LCG of the whole vessel, use the distance from the LCF to the CG of the added cargo.

I've focused on trim because the L stands for longitudinal. When discussing stability you're using some of the same concepts, but you're interested primarily in vertical & transverse location.

Hope that helps. I understand more definitions can be found on Ted Brewer's website.

 

Thanks Stephen!

 

But I'm still struggling trying to figure out what's the formula/s to calculate a hull CG when the weight is given (let's say 5 tons) and when there's nothing more than the hull itself involved,no engines,no upperstructures...etc.

 

It's related to calculating wetted surface....you have to find the center of each hull surface area of like scantling, calculate the weight and center of structural floors & keel, deck, and transom, then sum the moments. There's more than one method and I'm a bit rusty in this area, but it seems to me taking a girth at each station would be a starting point. A hull design program that calculates hydrostatics is helpful if you have a handle on what to look at. Some guesswork is often involved, but you should learn to use the tools at your disposal to make informed guesses.

Sorry not to be more specific. If you keep in mind that it's related to calculating wetted surface you should be able to find a satisfactory answer somewhere.

 

numerical integration

Hi,

I think that the best way to do this sort of thing is to use numerical integration to find immersed volumes and moments of volumes. It's tricky to sort all this out for a given hull and given displacement as it's a bit of an iterative process that lends itself to the use of a computer...

A good description of what's involved can be found at:

http://www.usna.edu/NAOE/courses/en200/ch02.pdf

Good luck with it all,

Cheers,

Dave

 

Are you talking about calculating how much the hull weighs or how much it displaces at a given waterline?

 

Buy this book:
principi di funzionamento di una imbarcazione a vela

Fabio Fossati, Giorgio Diana

Shonenfeld & Ziegler

Mirco

 

I'm talking about figuring out how much a boat displaces at a given waterline (ie from a drawing) and where it displaces it (important in figuring out LCB)

have you come across a simpler/better way of doin' it by hand?

I'm suspicious that there aren't any...

Cheers,

Dave

p.s. you should be able to track down an excel spreadsheet somewhere on the web that's all set up to do this stuff... all you need to do is throw in the offsets (a fair bit of work....)

 

the thing here is that I've plenty of books (including the one I'm studying on for the course i'm attending) ,I know perfectly how to calculate Volume,Lcb Lcf AWL VCB r R and God knows what else but I still can't figure out how to calculate the center of gravity of a hull when the weight is given,I'm also learning the use of maxsurf but it seems that it does not calculate lcg (or vcg or tcg),in the calculations it gives you lcb and lcf no lcg.
I'm shure i'm missing something obvious...

 

Aliright then... LCG=LCB, otherwise there would be an unbalanced moment and the ship would trim... It's often assumed that the cg is along the centreline (a good thing as hulls are symmetrical and vessel would heel otherwise, but should check this using wt. estimate), and the VCG also needs to be determined by wt. estimate. Could set one as a goal based on desired GM and try and 'achieve' it by being careful where stuff goes...

How's that sound?

Cheers,

Dave

 

Fine!
So let's say that if a hull is not trimmed the LCB = the LCG...correct?
When the hull trims there is a variation of immersed volume shape and LCB goes somwhere else.
LCG remains where it was before (which is where LCB was when the hull was upright).
Correct???
So...Lcg is ok, TCG = centreline.
VCG is still a little fuzzy...let's say I have a vessel that has a 20 tons displacement and for which I know all the geometric elements (AWL LCB LCF.... )
How do I get VCG?

 

It might be well to say out loud what was tacit in the last reply. You can not calculate the center of gravity of a hull from the shape; you have to sum the pieces from the scantlings, etc. Only if you assume a complete, correctly designed boat can you assume that the CoG will be at the fore/aft place marked on the drawings for the CoB.

 

I agree... the only way to do it is to weigh everything, noting its cg and figure out the total cg...

This is why inclining experiments are done... to verify designers estimated VCGs, or perhaps I should say to find the VCG (during an inclining expt the regulatory bodies don't care what the designer thought the VCG would be...)

 

If you want to find the center of garvity of a hull that weighs, say 5 tons, and it is made up of a single material, and a single thickness, then the CG is the geometric center of the hull, you can use the hull surface calculation to find this. In real life you will need to find the centers,weights,and moments of all areas of different scantling as mentioned above.