Stability Of Floating Bodies

Nov 2019
Hello again

I was hoping someone could help shed some light on understanding an equation for floating bodies.

I am trying to work out the distance between B and M shown in the sketch below:-


I have been given the equation:-

BM = I/V

BM = is the distance from center of buoyancy to the meta center

I = Is the second moment of area

V = Volume of the submerged portion of the body.

I just want to know how to calculate I?

Is I worked out for the entire floating board or is I worked out for just the portion of the body above the water line or is I calculated to the portion of the body below the water line?

I know that I is bd^3/12 but in my example do i use q for b and k for d - how do you know what values to use and what portion of the bosy I relates to?

Can anyone help?

Thank you.