Stability?

[Bill Roosa]

What is important

Good morning Sailingdog

Let me see if I understand you correctly. If we fill both bowls and then place the smaller in the larger the amount of water "displaced" from the larger will be equal to the amount of water (plus the bowl itself of course) in the smaller in both volume and weight.

Well I agree totally. Now riddle me this;
Ross did this in his kitchen with some nesting pots and he found as I'm sure anyone would, that the "displaced" water ran out the bowl and down the sink drain. The bowl did float.

So how does the water that is now down the drain float the bowl? Or to put it in your words "...it is the amount of water that the hemisphere displaces that is important. "

Now I know I'm not the sharpest tool in the shed but I really don't see how water that is not even in the room can possibly contribute to the floating of the bowl. And by analogy how the displaced water from putting a boat in the water can float a boat.

Please explain how it is not the pressure forces of the water but it is the displaced water that causes a boat to float.

Love ya man

 

[sailingdog]

Good morning Sailingdog

Let me see if I understand you correctly. If we fill both bowls and then place the smaller in the larger the amount of water "displaced" from the larger will be equal to the amount of water (plus the bowl itself of course) in the smaller in both volume and weight.

No, actually, I said if you had ballasted the smaller bowl so that it would sink into the larger bowl but still float, the amount of water it displaces from the larger bowl would be equal to the mass of it and its ballast.

Well I agree totally. Now riddle me this;
Ross did this in his kitchen with some nesting pots and he found as I'm sure anyone would, that the "displaced" water ran out the bowl and down the sink drain. The bowl did float.

So how does the water that is now down the drain float the bowl? Or to put it in your words "...it is the amount of water that the hemisphere displaces that is important. "

I never said it was the water that was specifically displaced that was important. I said it was the amount of water that the hemisphere displaces—the actual volume of water that is being occupied by the hemisphere, that would otherwise be water were the hemisphere not present, that was important.

Now I know I'm not the sharpest tool in the shed but I really don't see how water that is not even in the room can possibly contribute to the floating of the bowl. And by analogy how the displaced water from putting a boat in the water can float a boat.

Please explain how it is not the pressure forces of the water but it is the displaced water that causes a boat to float.

Nope, not the sharpest tool... more like a sledgehammer. The water that is displaced, and flowed over the bowl's edge down the drain has nothing to do with floating the boat, after all it is down the drain. However, provided the inner bowl is actually buoyant—less dense than the water overall, and not sitting on the bottom of the larger bowl, the mass of water that poured over the rim of the outer bowl, assuming it was filled to the top to begin with, would equal that of the smaller bowl and its ballast. Because the smaller bowl is less dense than water overall, it floats.

Water pressure has nothing to do with it. It is all based on overall density. If I put the whole thing into a bathymetric chamber and cranked the air pressure up to 3000 psi, the smaller bowl would still float. If it were due to water pressure in the most traditional sense, something would have to change, since the bowl and its ballast has not changed but the water pressure would increase from being under greater atmospheric pressure, would it not?

The only force working on pressing the bowl down into the water is gravity. Once the bowl has displaced a volume of water equivalent to its weight, gravity can no longer pull it any further down into the water. If the bowl were more dense than water, it would eventually sink to the bottom, since it never displaces its own weight in water. If it is the exact same density as the water, it is neutrally buoyant, and its position in the water depends on forces other than gravity.

Love ya man

 

[sailingdog]

If the center of buoyancy is lower than the center of gravity, then the boat is going to have to rely on form stability to keep it upright. Most boats have fairly limited form stability.

In my previous post, #28, I addressed this with regards to sailboats and how they would behave on a sea of mercury. Due to the fact that all commonly used ballast materials are less dense than mercury, all monohulls would effectively be lying on their sides, since the amount of mercury they could displace would leave their center of buoyancy well below their center of gravity. They would not be able to sail.

My boat—a trimaran—being almost wholly reliant on form stability and having three hulls, would leave you guys in the dust, however with so little of the centerboard and rudder in the sea of mercury, steering and leeway would both be major issues.

In fact, most boats would have no form stability due to not sinking deeply enough on their lines into the mercury to have the form stability to remain upright. My boat would, but my boat depends entirely on form stability for its upright position, and most monohulls would be lying on their sides, as lead, concrete and cast iron are all too light to provide a righting moment as ballast on a sea of mercury. The only keel material that would suffice on an ocean of mercury is Osmium—with a density of 1411.49 lbs./cubic foot, most forms of which, IIRC, are either highly toxic or radioactive.

If we go back to the basic idea of a log as a boat.. it is a cylinder and as such, has no top or bottom...and it rolls quite nicely. A log has buoyancy, but no stability. Now, the Polynesian approach was to lash two logs together, making a catamaran of sorts. It now has a usable top and bottom.

The Polynesians quickly realized, that if they spread the logs further apart—increasing the beam of the boat—it would become far more stable. This led to their development of the Proa, outrigger canoe, etc...which they used to conquer a section of the Southern Pacific greater than North America in area.

The main drawback to this is the complexity of engineering the connections between the multiple hulls in such a way they can resist the forces they will be exposed to. The modern epitome of this is BMW Oracle’s new trimaran, with a LOA and beam of 90'. The sucker is a square in its footprint or nearly so.

The best example of how not to do this is David Vann's Tin Can, where he made the akas (or crossbeams) converge to the main hull. This was a really stupid design as it amplified the forces the amas (or outriggers) would have on the main hull attachment points. When I saw his design, I predicted that the akas would fail at the main hull—which they did in 15 knots of wind an 6-8' seas. Mind you, this was a 50' LOA trimaran, and if it had been properly designed, 15 knots of wind and 6-8' seas should have been nothing for it. As a trimaran designer, David Vann is an idiot without a shred of common sense. If you’re using inexpensive materials, your engineering generally has to be better than if you're using high-tech, high-strength materials.

The other approach to making a boat more stable is to add weight to one side, to keep that side down and the other side up. This is the approach the Europeans took. In its most extreme form are the narrow beam deep keel designs that were fairly common years ago. The problem with this can be most easily seen in the recent Texas A&M Cynthia Woods disaster—if the keel falls off, the boat turns turtle.

Of course, there’s the old argument that multihulls have a position of ultimate stability of being upside down, floating on the surface turtled, using the mast as a keel. The counter is that monohulls have a position of ultimate stability of sitting upright, on the ocean floor. YMMV.

Gentlemen,
This is all very well but when are you guys going to stop throwing brickbats (and apologies) at each other and get on to talk about STABILITY?

BTW nobody has yet mentioned that old Greek guy who ran down the street naked and wet yelling "Eureeeka"!
Archimedes knew then what many have yet to appreciate.

 

[Bill Roosa]

ah, yea

Well sailingdog I think we are in agreement about the whole volumes of water displaced thing. We are in agreement about the weights being equal also.

I think we are in agreement that if I add up all the forces and moments on the boat, and the boat is not accelerating, then the forces HAVE to sum to 0.

sailingdog said
"Water pressure has nothing to do with it. It is all based on overall density. If I put the whole thing into a barometric chamber and cranked the air pressure up to 3000 psi, the smaller bowl would still float. If it were due to water pressure in the most traditional sense, something would have to change, since the bowl and its ballast has not changed but the water pressure would increase from being under greater atmospheric pressure, would it not? "

If I put a model boat into a bowl and put the whole thing in a barometric chamber and cranked up the air pressure the boat would continue to float because the air is also pressing down on the boat "dry" surface. Try thinking of the boat as a block of wood also floating in the water. Would not the air press down on it just as hard? How is the wood surface resisting the increased pressure?

So the pressure on everything increases and cancels out.

BTW air and water are not the same in this respect. Gases fill their containers and thin out or compress to do it. Liquids fill their containers (in a gravity field) to the extent they are able being constrained by the volume of liquid introduced.

He also said
"The only force working on pressing the bowl down into the water is gravity. Once the bowl has displaced a volume of water equivalent to its weight, gravity can no longer pull it any further down into the water. If the bowl were more dense than water, it would eventually sink to the bottom, since it never displaces its own weight in water. If it is the exact same density as the water, it is neutrally buoyant, and its position in the water depends on forces other than gravity."

When my boat is on the travel lift for haul-out there are those sling things counteracting the force of the weight of the boat that keep it in the air. If they break, the boat falls to the ground. It accelerates till hitting the ground due to the unopposed (forces don't sum to 0) force of gravity (weight). Then, after the boat stops moving around and people stop yelling, the ground supplies the forces that keep the boat from sinking into the earth. So if weight is the only force that is acting on the boat why don't it start accelerating downward and sink?

I would submit that there is in fact a force acting (in the aggregate) upward to counteract the force of gravity (weight) acting on it when she is in the water. We have in the past called it the buoyant force or the pressure (acting on a surface it is a force) of the water.

I'm curious, you say that if the body is neutrally buoyant it has other forces acting on it. What are those forces?

 

[Bill Roosa]

I got another one

sailingdog
I love ya man, I ain't upset or anything but this is important to understanding stability.


Imagine that I have a lightweight block of wood that would normally float on the water. If I grab it and hold it under water I have to supply a force to keep it there right? If I let go of it it will accelerate till it gets to the surface and then stop so there must be some force accelerating it. Gravity is certainly not acting upward so what is causing the force that I have to counteract with my hand?

 

[sailingdog]

I guess it depends on what you're referring to as water pressure. Yes, the water is exerting a force upwards on the bowl/boat, but it isn't water pressure in the tradtional definition of the term "water pressure". The water pressure at the surface of a liquid is basically zero, since it depends on the height of the water column to exert pressure, which is also zero at that point. I think the term water pressure isn't accurate.

As for the boat not sinking, it has offset the force of gravity by displacing its weight in the volume of water it is now occupying. I won't say that water pressure is holding it up, but buoyancy is... since buoyancy is defined as the upward force caused by an object displacing its mass in a fluid. BTW, I never said there were no other forces working on the bowl/boat. I said that gravity was the only force working to submerge the boat.

As for the neutrally buoyant object... say we take a underwater camera system that is neutrally buoyant and drop it into the water from the deck of a boat. The camera will continue to sink until all the momentum of it dropping into the water has been bled off by friction with the water. At that point it won't sink or rise. If you were to dive into the water and push up on it... it would rise until the momentum you imparted on it was used up or it reached the surface.

 

[Bill Roosa]

Great, a breakthrough

I have to give you that I agree with all your statements. Gravity IS the only force pushing the bowl/boat INTO the water.

So the definition of buoyancy is at question.

I think we will both agree that some force is "buoying" up the boat. I'll use your neutral buoyancy comment to demonstrate. In the attachment there are forces due to pressure on the block. Since the bottom of the block is lower in the water than the top it experiences a greater pressure from the water than the top. It is exactly that difference in pressure that causes a net upward force.

Imagine the block is made of water. If the dimensions of the block are 1'x1'x1' then its weight is 62.4 lb since the specific gravity of water is 62.4 lb/ft^3. If I add up the force on the bottom and subtract it from the top I get:

Net force on the block upward = 62.4(d2-d1)

If I pick any d1 then d2 is one more than that so (d2-d1) is always 1. Hey, the forces on that block are exactly equal to the weight of the water in the block. So there are no net forces and the block does not accelerate. If I displace the water from the block with some magical gas that has no weight then the forces on the block would sum to 62.4 lb.

So the block experiences a force equal to the weight of the water displaced.

But the force is from water pressure not the displaced water.

If the magical gas had a variable weight we could alter its density since the volume is constant. If that density was greater than the surrounding water its weight would be greater also and it would sink, if its density was made less than the surrounding water it would move upward break the surface and float. But the force comes from water pressure.

 

[jibes138]

Water Pressure at the Surface is not zero

If you take an infinitely small slice of water right at the surface and draw a free body diagram of the element then the force pushing down on the element is air pressure from above is 14.7 PSI. The force on the bottom must equal the force on the top or the element would take off like a rocket. So the force pushing up the element is 14.7. since the force pushing up must be water pressure then it is clear that water pressure at the surface is 14.7 PSI or 1 atmosphere. This is why at 33 feet scuba divers are at 2 atmospheres. For the people that say air pressure is negligible think about how heavy the air is. The column of air above the earth is equal to 33 feet of water. Take a 1 square foot container 33 feet tall and see how much it weighs. That's how much the air above you weighs assuming you occupy about 1 square foot of surface space on the earth.
To be honest all this pressure is weighing me down and wearing me out. I much prefer to be in the water where I am weightless and my joints can get some relief.

 

[Jim Kolstoe]

jibes138, the air pressure at sea level is 14.7 psi. Since the water does not exert pressure (force) in an upward direction at the surface, the water pressure is zero. If the water were exerting an upward force at the surface, you would expect it to move upwards from the surface.
You are correct that at 33 feet depth of saltwater you experience 2 atmospheres absolute pressure (3 atm absolute at 66', 4 atm absolute at 99', etc.), but that is the sum of the air pressure and the water pressure.
But that does not generate bouyancy. If you put a container with water and air in a zero-gravity setting, then add a bouyant solid object, it will not float in the water. Does anyone have contacts at NASA? Maybe we can convince them to do a science experiment on this.
Jim Kolstoe, h23 Kara's Boo

 

[Skipper]

The underlying truth

The only thing that keeps my boat afloat is my wallet.

 

[Ross]

Jim, The vapor pressure of water at the surface is 14.7 psi absolute. The water must be in equilibrium with the air. The storm surge during a hurricane is the water moving upward in an area of low atmospheric pressure in responce to higher atmospheric pressure elsewhere on the earth's surface.