Help a student, stability!

Bit confused here, Stability question;
Trying to calculate BM for a hard chined dinghy/canoe... Now BM=It(or Ixx it seems)/volume of displacement, but how do you find It(Ixx)? I suspect it involves simpmsons and a big table, just at a bit of a loss as to how to do it exactly. Any help would be very welcome!

The most confusing thing is 'Principles of Yacht Design' calls It(Ixx) the transverse moment of inertia, while my notes seem to suggest its the 2nd moment of area of the waterplane. HELP!

'P of Y D' also says theirs a proof fo it but doesn't go into detail would be quite interested to see the proof if anyone has enough time....

Cheers

 

Yup, its a simpsons thing... but not so hard.. to get the moment of inertia set up the table as follows: the first column will have your station numbers, the second the half-breadths of the loadwaterline in feet and decimals of a foot, the 3rd the cube of the half-breadths, the forth simpsons multiplieres (e.g. 1, 4, 2, 4, 2, 4, 2, 4, 2,4, 1), and the fifth you enter the result of multiplying the cubes by the Simpsons multipliers. Total the fith column, multiply by 2, then muliply by one-third the common interval (the distance between stations), and then divide by 3.

Then you need to divide that by the cubic feet of water your boat displaces, and you have the BM... the distance that M is above the CB (when CG is below M, the ship is stable)...

hope this very summary explaination helps...

 

The role of moment of inertia in stability is precisely the same as in a bending beam. Each dA of the integral x2 dA provides a force that is linear with the displacement of the element dA. This results in a measure that is linear units to the fourth power, which is conventionally divided by volume to get a linear unit, BM.

 

Transverse moment of inertia may be found by

1. Multiply half-breadth (at the waterplane) of each section by the Simpson's Multiplier (1,4,2,4,1) to get a "Half-Breadth Product" for each section

2. Sum all the "Half-Breadth Products"

3. Multiply that sum by 1/3, and again by station spacing



Now, to find BM simply divide the moment calculated in step (3) by your submerged volume. Since you are dividing ft^4 by ft^3, your answer will be in feet




Joshua N Straume

 

Interesting, to put it in concise mathematical terms... It = integral y^3 dx. This means that BM = (integral y^3 dx) / Volume

Where are you in the UK?

Tim B.

 

The transverse moment of inertia (refering to an area) is the second moment of area, by the way, two different names for the same thing.

 

Cheers for the help guys, lecturer explained it a couple of days after I had asked on here and got it done, Didn't realise I had got ahead of myself.

Tim b; I'm at southamton for uni at the one that used to be known as the destitute, although I'm back home in essex for a bit. Just been looking at new design Tornado being made, good reminder why to stick at it!

 

Ah, welcome, so am I

Tim B.