Static stability(Academic problem)

Hello,

I am a master student in Naval Architecture and Ocean Engineering and I am having a hard time in solving this problem. I am Mechanical Engineer and I can't understand it so much. Is quite different from my area. Attached is the problem about static stability. I would appreciate if you can help me. Any advice is welcome.

Thanks

 

Hi diegoperrera

Welcome to the forum.

Well, what is static stability?...it is a measure of how stable the vessel is. How do we determine that?...from the metacentric height and the vertical centre of gravity.

So to find KM....first we need BM, which is simply I/V

I being the inertia of the water plane and V = volume of the vessel. Since no length is given you can calculate the values using the term "L" for the length, and i'm sure you'll find it'll cancel out as you do your sums.

The KB is easy, since it's a box, just half the draft. So YOu can get KM.

As for KG...one assumes the vessel and boxes are homogenous, thus you have the density and also their dimensions, so again assume half their depth. Then a simple moments to get the KG from the keel, K...gives you KG.

Thus you can then establish when the KG rises above the KM, making it statically unstable.

 

Actually, It never loses its static stability....the boxes are 2D and therefore have no mass...very poorly written problem...

 

Ad Hoc is absolutely correct.

Formula К_M = K_B + B_M, where B_M = I/V is explained in http://en.wikipedia.org/wiki/Metacentric_height

In your case I=(B^3)/12 , B is the "breadth of the barge ship".

 

The problem seems to be the typical calculation of limiting KG value but
is incorrectly posed. I agree with Ad Hoc,
What is the static stability?
Whatever it is, stability is not lost but there comes a time when a stability criterion is no longer fulfilled. It should therefore be noted stability criteria barge must meet.
As for the transverse stability, what is necessary calculate is Ix = L * B ^ 3/12 (L is the length and B is the breadth, Ix second moment about the longitudinal axis)

 

Hello AdHoc. Thank you for your answer. The L dimension I can cancel it, you are right. But,I also need to calculate the draft, there is not in the problem. I need it, because I must calculate the displaced volume and also try to find the weight. Because for calculating BM, the V according to the literature is the volume of displacement. Not the volume of the ship.
Don't you agree with me?

 

Calculating V

Yes Diego, you need V. But that is found by calculating weight of the ship and her boxes.

What school is this problem from?

 

Dir cmckesson,

Yes, you are right. But I don't have the weight. And I also don't have the L dimension. So, the displaced volume is the same as the weight?

I am studying in Korea.

 

The displaced volume is ALWAYS the same as the weight

 

The displaced volume weight is ALWAYS the same as the weight.

 

The problem is not well-written, as others have noted.
It is a 2-D problem which uses 3-D density for the calculation of masses, so I believe that the author wanted you to reason on a "per unit of longitudinal length" basis. The objective is clearly not to analyse a realistic stability case, it serves to make you use the correct formulae and get a physically consistent result.
So, I would assume a 1 meter long barge and perform the calculations suggested by Ad Hoc.
Cheers

 

The problem has no solution if you do not know what it means to "lose the static stability".
I, honestly, am not able to decipher that sentence.

 

It is terribly written. It says "the boxes should be attacked". I get images of pirates boarding. On a static system, stacking boxes on the center of the barge will make it sink completely while staying level.

 

I take it that, from the left out information, that this is clearly a meta center problem. No length is given for the ship. And, apparently, no length is given for the blue boxes. So the only way this problem can be workable is to assume the blue boxes are as long as the ship.

That being so, all one has to do is figure out the meta center height of the ship alone, using 1.0 as a constant for its length value.

After that, figure out how much the ship's draft increases, with each box added.

Then calculate how much the ships CG raises, with each box added. This is tricky because the boxes are being stacked on top of one another, so it is probably best to to do your calculation under the assumption that previous boxes are removed and successively taller and heavier boxes take their place.

If you know how to do calculus, you can do this all mathematically. If you don't, you'll have draw a line graph, like the rest of us.

 

sharpii2, all that is fine. Suppose we already have all the data. Could I ask how you calculate when the static stability is lost?.
You can make all the assumptions you want.