Static stability(Academic problem)

Perhaps the following example will help the OP in his quest for truth. It is controlling the stability during the construction of a concrete block on a floating pontoon. As you increase the height of the block, the set goes deeply. Finally you have to enter ballast water in the pontoon tanks for it to sink and the concrete block floats freely .
At no time is "stability lost"
(Block dimensions in mm)

 

I graduate as an NA in four weeks, I'm not in this thread to learn something.

If you were kidding around when you said there were NAs here saying there was no solution that's cool, my bad, it just wasn't apparent in what you'd written - so I looked and found no NAs saying that.

It won't help him, the answer he needed was Ad Hoc's in post #2.

 

Well, strictly speaking, those (like TANSL) who say that there is no solution to the problem as it is described are right. No solution can be found without making some arbitrary assumptions, which might be correct or they might not be. For example, the assumption that the ship's mass is uniformly distributed on the cross-section, hence making it's CoG coincide with the geometric center of the cross-section area. In reality, ballast is used to shift the CoG into a position necessary to ensure a desired stability margin. Another assumption is the uniform longitudinal distribution of the ship and cargo volumes, thus reducing the problem to a 2-D case.
All things which could have been cleared by the author of the exercise with just few more words in the description of the problem. The way it is written, no unambiguous solution can be given. Place the CoG of the ship closer to the keel and you have a different yet perfectly valid result. The professor will have a hard time in explaining why did he accept some of the results and did not accept some others.
Cheers

 

Amazing. Congratulations.

 

Of course. But again, with information on the statement, the problem has no solution.
I know well, as I explain in my previous post, when the data is complete, with a study as I've shown, that at last, after all is to be putting weights higher and higher on a pontoon, stability studies are possible. My experience tells me that if the weights are controlled properly, stability is not lost. (I repeat that we should define what is meant by "losing stability")

 

As long as the Center of Gravity and the Center of Flotation are aligned vertically, there is no loss of stability.

 

No, Gonzo, not exactly. See post #19. In addition to what you say, which is correct, on a ship that is not a submarine, the center of buoyancy must be below the center of gravity. But also, if the distance between them is small, the ship can be very unstable, ie, flip with a very small heeling moment.
And it is not the center of Flotation, but the center of buoyancy.
In addition, the alignment of two points is required to achieve equilibrium, but that does not mean that equilibrium is stable. Again, a light breeze can unbalance.
Correction: any floating device the position of the center of buoyancy and center of gravity must be such that a righting moment is formed.

 

Looks like you have missed a reply or two on the page 2: http://www.boatdesign.net/forums/stability/static-stability-academic-problem-51560-2.html#post707171

 

I posted my variant of the problem ( for density = 1/3 ) in my LiveJournal and got a really interesting comment from "hyperpov": We'll get much more fun when the density is 1/4, i.e. anything from the interval from (3-sqrt(3))/6 to 9/32. http://biglebowsky.livejournal.com/94265.html?thread=1366329#t1366329

Update.
"hyperpov" added some kind of animation for density 1 ... 999 kg/m^3 (999 frames). To watch you will need either move scroll bar or hold PgUp / PgDn
https://www.dropbox.com/s/q5b5z2i2tyl82do/brus1.pdf

 

You are absolutely correct. I have made a mistake.

I transposed each box being worth 0.25 m of ship depth to being worth 0.25 m of ship draft.

My bad.

Actually, each added blue box would increase the ship's draft by only 0.0833 m. So, it would take three boxes to increase the ship's draft, as much as I said one would.

 

HelloCmckesson, how did you find this answer? Did you make any arbitrary assumptions? I couldn't calculate it because I don't have the weight. Do you agree with me?

Thank you again

Diego

 

You have weights per unit length (through densities), but you don't have the length of the ship and containers, and the KG of the ship. So, yes, some arbitrary assumptions are necessary to get the result.

Cheers

 

I'm not cmckesson, but I can answer your question.

Assumptions:

1) The density of barge is uniform.
2) The density of each box is uniform.
3) The length of the box = the length of the barge.
4) Cross section is constant on length.
5) The length of the barge > the width.

 

I actually broke down an did the problem myself.

The first thing I did was assign a length to the ‘barge ship‘.

Next, I assumed the ‘blue boxes’ were as long as the ship.

Using this assignment and this assumption, along with the ’densities’ given in the problem, I came up with a displacement for the barge ship and a weight for the blue boxes.

Here’s what I came up with:

Barge Ship

Length = 6.0 m
Beam = 3.0 m
Draft = 0.333 m
Displ. = 6.0 m^3

Blue Box

Length = 6.0 m
Width = 0.5 m
Depth = 0.25 m
Weight = 1.5 mt

Now that I have the actors in this play, it’s time for the drama to begin.

The first step is to find the inertia of the barge ship.

I hadn’t done this in a long while, so I had to look up the procedure.
1.)
I divided the barge ship in half, lengthwise and drew six stations (seven actual lines).
2.)
Next, I measured the length of each, from the center line to its end, at the side of the ship.

Since the ship is a rectangle in plan form, all of these were the same length, 1.5 m.
3.)
Next I cubed them (1.5 * 1.5 * 1.5) and ended up with 3.375 m^3.
4.)
I then multiplied each by 1/3 the station spacing (0.333m), except for the first and last stations, which I used 1/6 station spacing for (0.166 m)
5.)
I then added these products up to get 6.725 m^4.
Because the barge ship has two halves, I doubled this number to get 13.5 m^4. This is the Inertia of this barge ship, which doesn’t change, because it has vertical sides and a vertical bow and stern.
6.)
Next, I found the Meta Center Radius (MCR) for the barge ship, by dividing its Inertia by its Displacement (13.5 m^4/ 6.0 m^3) to get a MCR of 2.25 m. Now this number does change, as more weight is added to the ship.

Now I need to find the Meta Center Height (MCH). To do this, I need to find the distance between the Center of Buoyancy (CB) and the Center of Gravity (CG).
7.)
Since the ship has rectangular sections that are all alike, the CB is going to be at half the draft of the Barge ship (0.333 m/2) which will be 0.167 m from the bottom. Since the Barge ship is assumed to have uniform density, its CG has to be halfway between the bottom and the deck, or 0.5 m, from the bottom.
8.)
By subtracting The CB from the CG (0.50 - 0.167), I get the distance between the two, which is 0.333 m.
9.)
This, I subtract from the MCR to get the Meta Center Height (MCH) (2.25 m - 0.333 m) to get a MCH of 1.92 m.

Now, each time I add weight to the Barge Ship, four things are going to happen:

a.) the displacement is going to increase,
b.) the draft is going to increase,
c.) the CG is going to change, and
d.) the CB is going to change.

All of these affect the MCH of the Barge Ship, so each time a blue box, or number of blue boxes are added, a new MCR and a new MCH are going to have to be calculated. So steps 6.) through 9.) are going to have to be repeated.

I tried one blue box, two blue boxes, then six blue boxes.

I found that, with six blue boxes, the CG ended up about 5.0 cm above the MCR of the Barge ship. This means the ship is unstable, at this point, and will capsize.

The MCH can never be a negative number, unless some form of dynamic stabilizing is added. Such could be vertical thrusters or lifting fins, if the barge ship is moving through the water.

So. My number of blue boxes is five.

 

For me, "loss of stability" is loss of righting moment.

It is like standing a ruler on its short edge.

It may stand there a moment or two, but will inevitably fall over.