# Calculating Center of Gravity, multipliers?

Discussion in 'Stability' started by mcm, Mar 26, 2010.

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### mcmSenior Member

To calculate the center of gravity i must multiply the weight of every 3 foot ( 1 meter ) section of hull material and equipment according to how far forward or aft of the center of buoyancy it is.

What are the multipliers?

What is the multiplier at 3 foot ( 1 meter ), 6 foot, 9 foot, 12 foot, ext. ext... from the center of buoyancy?

Also,,,

To calculate the center buoyancy it's suggested that one should balance on the edge of a pencil a paper cut-out profile of the hull below the waterline.

But a profile cut-out doesn't factor in the increased buoyancy aft due to the fatter buttocks lines aft than forward that one can clearly measure on a section drawing but not on a side elevation profile drawing.

Do i thus have to use multipliers to more accurately calculate the center of buoyancy just as i do to calculate the center of gravity?

And if so, what are the buoyancy multipliers for each 3 foot further forward or aft of amidships?

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### jehardimanSenior Member

Using a trapizodial rule (what you implied) is not the best method to use.

First, you need to seperate the continious weights (shell, deck, longitudinals) from the descrete weights (frames, pipes, tankage, pumps,etc).

The continious weights are calculated using Simpsons 1st and 2nd area rules for a single unit of length around some station (usualy Sta. 0, the FP). The descrete weights and thier moments are just summed. The total of the moments is divided by the total of the weights to get the LCG.

the LCB is determined the same way as the continious weights, but using station area as the ordinate.

Normally, Displacement does not equal Weight and LCB does not equal LCG. To correct both of these, ballast is added so that weight= displacement and LCG= LCB. If you are really far out, you may end up with negative ballast (which will require the removal of weight or an increase in draft) or a ballast position that is outside the hull (again weight will need to be shifted or the hull lines adjusted). Normally, it takes several turns through the design spiral before weight, displacement, LCG, and LCB close to a buildable solution.

See this quick overview slide show preliminaly hull design and hyrdostatics concentrating on slides 40-61.
http://www.docstoc.com/docs/16813343/HULL-FORM-AND-GEOMETRY

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### mcmSenior Member

Thanks for the link to the slide show.

How is 'moment' defined?

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### terhohalmeBEng Boat Technology

In this case, moment = weight x distance.

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### mcmSenior Member

Now i see my errors.

I confused the simpson multiplier assigned to each section to determine volume with the levering arm multiplier assigned to each section to determine the center of buoyancy.

Also i confused the profile cut-out balanced on a pencil edge used to locate the center of lateral resistance with the X-Y coordinate grid cut-out balanced on a pencil edge used to locate center of buoyancy.

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### conceptiaNaval Architect

MCM, i think you are confused with center of floatation and center of buoyancy. :?:

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### LyndonJSenior Member

I don't think he's confused its just an older way of finding COB by balancing the plotted x sectional area curve

If you find the centre of the curve of areas that is the COB.
The static waterplane centre is simply the centre of the waterplane cutout,
The CLR is the centre of the profile cutout.

Even some naval architects seem to get confused about waterplane and COB at times. There was a post asking about waterplane centre recently that was answered wrong.

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### conceptiaNaval Architect

ok.. now i understood what he meant..

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