Stability?
- Thread starter Roger Long
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Isn't it simply that the boat sinks until it displaces water that weighs the same as the boat and then it stops sinking. So my 12,500# boat displaces that much water. For a boat to float it has to displace more water than it weighs. If the boat weighs more than the water it displaces it sinks. Submarines are like this but they can change their displacement using tanks filled with water or air as desired. I am sure that I must be missing something as my answer comes from High School Physics.
I am with MoonSailor on this one. If your boat weighs more then the water it displaces then it is a sinker or an anchor. If the boat displaces an amount of water equal to its weight and still has some freeboard then it will float. The only disclaimers to this is when a lot of gas gets into the water (thus reducing its specific gravity) and your boat may sink lower into the water. Again, boats in fresh water ride lower then if they were in salt water with the same laden weight.
If your boat happens to pass over a sea mount that is releasing lava and gases you may also ride a bit lower in the water or even sink. There is even postulation that there is trapped CO2 gas in the edge of the continental shelf which when released could reduce the significant gravity of the seawater such that your boat would sink.
That said, one is much more likely to be pooped by wind and waves at the surface then unusual disturbances due to gasses. Look at the US Navy's fleet of aircraft carriers and other craft. They weigh a hell of a lot more then any of our puny boats yet they do manage to cruise the world.
Air pressure keeps them on the surface of the water and gravity is the main component of both air and water pressure. Without gravity we could all fly without an airplane. I saw an airplane drifting down with the ebb tide in the Hudson River a few days ago. It was a pretty amazing sight. It was kept afloat by the air trapped inside it's fuselage and then by tethers which were attached to points on shore. They said the plane weighed 1 million pounds before they loaded it onto the barge. It looked more like a disoriented whale to me as it drifted south towards the Statue of Liberty.
Huck Finn and Tom Sawyer could have made a raft out of empty gas containers but they used wood instead. Displacement craft all rely on pushing enough water aside to achieve equilibrium with the ATMOSPHERE. I guess that air pressure has nothing to do with it.
If your boat happens to pass over a sea mount that is releasing lava and gases you may also ride a bit lower in the water or even sink. There is even postulation that there is trapped CO2 gas in the edge of the continental shelf which when released could reduce the significant gravity of the seawater such that your boat would sink.
That said, one is much more likely to be pooped by wind and waves at the surface then unusual disturbances due to gasses. Look at the US Navy's fleet of aircraft carriers and other craft. They weigh a hell of a lot more then any of our puny boats yet they do manage to cruise the world.
Air pressure keeps them on the surface of the water and gravity is the main component of both air and water pressure. Without gravity we could all fly without an airplane. I saw an airplane drifting down with the ebb tide in the Hudson River a few days ago. It was a pretty amazing sight. It was kept afloat by the air trapped inside it's fuselage and then by tethers which were attached to points on shore. They said the plane weighed 1 million pounds before they loaded it onto the barge. It looked more like a disoriented whale to me as it drifted south towards the Statue of Liberty.
Huck Finn and Tom Sawyer could have made a raft out of empty gas containers but they used wood instead. Displacement craft all rely on pushing enough water aside to achieve equilibrium with the ATMOSPHERE. I guess that air pressure has nothing to do with it.
I don't suppose you'd accept a demon named Maxwell frantically pushing water molecules out the hole you knocked the in hull after a few too many drinks. Well then, how about this: assuming you're in a gravitational field (otherwise everything floats and nothing is trying to sink lower, for lack of a defined "lower" to sink to, making the question irrelevant) the boat weights less than the volume of water it is displacing. If the boat weigths more than the volume of water it displaces, it sinks either until equilibrium is established (weight of water displaced equals weight of boat) with some freeboard remaining or it hits the bottom. But note, neither the water nor the atmosphere float! They've alread sunk as low as they can go. The atmosphere remains on top of the water merely because it does not mass enough per unit volume to push past the water.
All of which suggests that you're being tricky. If you assume gravity, then a boat floats because it weights less than the volume of water its displacing. But without gravity constraining the actions of the water, this would not happen, since the water would be free to displace away from the boat in any direction. Suggesting your ultimate answer is: boats float because of gravity - neatly ignoring the fact that in a non-artifical setting, you won't get a body of water (ice doesn't count) without a gravitational field to hold it in place.
Having spouted off in response to your question, I commend you reread all of these postings, twice. That'll teach you to get bored.
Jim Kolstoe, h23 Kara's Boo.
All of which suggests that you're being tricky. If you assume gravity, then a boat floats because it weights less than the volume of water its displacing. But without gravity constraining the actions of the water, this would not happen, since the water would be free to displace away from the boat in any direction. Suggesting your ultimate answer is: boats float because of gravity - neatly ignoring the fact that in a non-artifical setting, you won't get a body of water (ice doesn't count) without a gravitational field to hold it in place.
Having spouted off in response to your question, I commend you reread all of these postings, twice. That'll teach you to get bored.
Jim Kolstoe, h23 Kara's Boo.
Franklin, my initial thought was enough foam to fill the hole and stop the water from coming in. But I guess that you don't want to make that possible. A really, really big hole. My recollection from scuba classes several eons ago, is that salt water weighs in around 67 lbs per cubic foot. Since you need to displace 18,000 lbs of water to float an 18,000 lbs boat, you need 268.7 cubic feet (18,000lbs /67lbs per cubit foot) of foam displacing water out of the boat, if the foam itself has no weight, to stay at the surface. Floating some part of the boat above the surface requires more.
Jim Kolstoe, h23 Kara's Boo
Jim Kolstoe, h23 Kara's Boo
Sure will. Never in my life, I think, have I seen a simple idea sent a group into such a frantic collective mental spasm. Even back on the Usenet, I don't think I can remember a thread that so much resembles an ant nest with the top knocked off.
Oh, well. The trim strips got steamed. I didn't wander oft, get distracted with other things, and let the flame go out or the steamer run dry.
Thanks all for the amusement.
What is the salinity of the water? 
If you're on the Dead Sea or the Great Salt Lake, it will take considerably less foam to float the boat than if you're on Lake Superior. Assuming that you're on the Atlantic ocean, where the water's density is about 64 lbs. per cubic foot and you're using foam that weighs 4 lbs. per cubic foot, you need 18,000/60 or 300 cubic feet of foam.
BTW, Jim, you're way off on your density of salt water... I hope you don't rely on the 67 lbs. / cubic foot number for any serious buoyancy calculations, cause it is just wrong.
TSMWebb—
As for the idea that buoyancy can exist without gravity, that's also wrong. By definition, buoyancy requires WEIGHT, which is something that only occurs within a gravitational field. Mass is unchanging, but weight depends on the gravitational field the mass is acted upon by.
While things can "float" in zero gravity, there would be no buoyancy, since the boat has the same weight, and density as the water in zero gravity, assuming that the zero gravity is not in vacuum, or the water would boil away and disperse in gaseous form. Don't confuse "floating" with buoyancy. Floating has no condition requiring displacing an object's own mass in the liquid, buoyancy does.
One final point. Most boats would do horribly when sailing on an ocean of mercury, due to the extremely high density of mercury—847.14 lbs./cubic foot.
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 you're on the Dead Sea or the Great Salt Lake, it will take considerably less foam to float the boat than if you're on Lake Superior. Assuming that you're on the Atlantic ocean, where the water's density is about 64 lbs. per cubic foot and you're using foam that weighs 4 lbs. per cubic foot, you need 18,000/60 or 300 cubic feet of foam. BTW, Jim, you're way off on your density of salt water... I hope you don't rely on the 67 lbs. / cubic foot number for any serious buoyancy calculations, cause it is just wrong.
TSMWebb—
As for the idea that buoyancy can exist without gravity, that's also wrong. By definition, buoyancy requires WEIGHT, which is something that only occurs within a gravitational field. Mass is unchanging, but weight depends on the gravitational field the mass is acted upon by.
Without weight, which by definition requires gravity, to force the object down into the seawater, buoyancy can not exist. And yes, an object can only float if it can displace a volume greater than its actual weight in water. In the case of an 18,000 lb. boat, it would require displacing a volume of 281.25 cubic feet, so the boat itself would have to take up a volume greater than 281.25 cubic feet to float, using 64 lbs. per cubic foot as the density of the seawater. If it displaced 281.25 cubic feet, it would not float, but be neutrally buoyant.
While things can "float" in zero gravity, there would be no buoyancy, since the boat has the same weight, and density as the water in zero gravity, assuming that the zero gravity is not in vacuum, or the water would boil away and disperse in gaseous form. Don't confuse "floating" with buoyancy. Floating has no condition requiring displacing an object's own mass in the liquid, buoyancy does.
One final point. Most boats would do horribly when sailing on an ocean of mercury, due to the extremely high density of mercury—847.14 lbs./cubic foot.
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.
First you must determine the collective specific gravity of the boat. Just because it weighs 18000 pounds on land does not mean that when submerged it will weigh 18000 pounds. A 500 pound wooden dinghy with no ballast will float when completey filled with water. An unballasted cat or tri would not require as much flotation as a ballasted mono.
Re: in a word, what makes a boat float is...
Well, gravity also can make a boat sink. Excuse me while I go take a couple of Exedrin.
Well, gravity also can make a boat sink. Excuse me while I go take a couple of Exedrin.
Boyant force
The buoyant force is equal (in magnitude) to the weight of water displaced. That is not how the force is generated however. Just a nice equalivance that we use to help us understand how big a boat is. I would note a boat also displaces a volume of water that is exactly the magnitude of the volume below the waterline. This is why it has a weight equal to the water displaced. You have to replace the forces in the fluid to get the boat to float.
Forgetting that a boat must have greater potential buoyant force to actually float (storms, waves, people getting in etc) it can be said that the force that the pressure of water on the hull acting upward must be equal to the weight of the boat.
Now if we have a flat bottomed barge with rectangular cross section that weighs 10k lb, is 10' wide and 15' long how low will it sink into fresh water?
I could use the weight of water displaced method but that don't help us understand what is going on and is of little use when we can't pull out a formula for the volume of a shape like a boat bottom.
The pressure of the water column anywhere is:
Pw= x * 62.4 Where x is the depth in feet and 62.4 is the specific weight of fresh water. P is the pressure in lb/ft^2 not PSI BTW
I'm going to let x also be the depth the barge sets in the water because I note that it is a horizontal surface and therefore a constant pressure is exerted on its' surface.
I note that there is also pressure on the vertical sides of the barge that are submerged. However the pressure on the vertical sides does not contribute to floating the boat because it acts horizontally. So I can ignore its contribution .
I will ass u me that the barge floats with its' bottom horizontal (gravity rears its head) otherwise I'm teaching calculus here. The pressure needed to "float" the boat is
Pb = weight / (length * width) = 10,000/(10 * 15) = 66.6 lb/ft^2
Now unless the two pressures (and the forces they generate through the mathmatical constructs of center of area and center of gravity and center of buoyancy) are equal the barge will not stop moving. Unless the force generated by the water gets greater with greater x the barge will not float either. If the pressure in the water did not get greater with depth the barge would either a) never reach a pressure sufficiently high and sink or b) float on the surface because the pressure was already sufficient.
So
Pb = Pw
or
66.6 = x * 62.4
resolving for x we get
x = 66.6/62.4 = 1.06 ft. The barge will have a draft of 1.06 ft.
Now the contribution of air pressure to the boats weight is calculated as follows. If I ass u me that the barge is hollow and has super strong hull material the thickness of the hull can be ignored. imagine a surface inside the barge that is the continuation of the waterline of the barge. Clearly the air above this line is exactly like the air on the outside of the barge at the water surface. The air below this surface does have a weight and adds a VERY SLIGHT contribution to the weight of the barge. I don't remember the density of air (because you can ignore it for nautical problems) but it is something like 0.001 lb/ft^3. Lets use that for the example.
The weight of air under the waterline surface is:
Wa = x * L * W * 0.001 = x* 15 * 10 * 0.001 lb = 0.15*x lb per x ft of depth
So each ft of air depth in the boat adds 0.15 lb to the weight. A whopping
1.06* 0.15/10000 = 0.0016% increase to the total weight
If you really want to know more ask me what happens when a 150 lb person boards the barge amidships.
The buoyant force is equal (in magnitude) to the weight of water displaced. That is not how the force is generated however. Just a nice equalivance that we use to help us understand how big a boat is. I would note a boat also displaces a volume of water that is exactly the magnitude of the volume below the waterline. This is why it has a weight equal to the water displaced. You have to replace the forces in the fluid to get the boat to float.
Forgetting that a boat must have greater potential buoyant force to actually float (storms, waves, people getting in etc) it can be said that the force that the pressure of water on the hull acting upward must be equal to the weight of the boat.
Now if we have a flat bottomed barge with rectangular cross section that weighs 10k lb, is 10' wide and 15' long how low will it sink into fresh water?
I could use the weight of water displaced method but that don't help us understand what is going on and is of little use when we can't pull out a formula for the volume of a shape like a boat bottom.
The pressure of the water column anywhere is:
Pw= x * 62.4 Where x is the depth in feet and 62.4 is the specific weight of fresh water. P is the pressure in lb/ft^2 not PSI BTW
I'm going to let x also be the depth the barge sets in the water because I note that it is a horizontal surface and therefore a constant pressure is exerted on its' surface.
I note that there is also pressure on the vertical sides of the barge that are submerged. However the pressure on the vertical sides does not contribute to floating the boat because it acts horizontally. So I can ignore its contribution .
I will ass u me that the barge floats with its' bottom horizontal (gravity rears its head) otherwise I'm teaching calculus here. The pressure needed to "float" the boat is
Pb = weight / (length * width) = 10,000/(10 * 15) = 66.6 lb/ft^2
Now unless the two pressures (and the forces they generate through the mathmatical constructs of center of area and center of gravity and center of buoyancy) are equal the barge will not stop moving. Unless the force generated by the water gets greater with greater x the barge will not float either. If the pressure in the water did not get greater with depth the barge would either a) never reach a pressure sufficiently high and sink or b) float on the surface because the pressure was already sufficient.
So
Pb = Pw
or
66.6 = x * 62.4
resolving for x we get
x = 66.6/62.4 = 1.06 ft. The barge will have a draft of 1.06 ft.
Now the contribution of air pressure to the boats weight is calculated as follows. If I ass u me that the barge is hollow and has super strong hull material the thickness of the hull can be ignored. imagine a surface inside the barge that is the continuation of the waterline of the barge. Clearly the air above this line is exactly like the air on the outside of the barge at the water surface. The air below this surface does have a weight and adds a VERY SLIGHT contribution to the weight of the barge. I don't remember the density of air (because you can ignore it for nautical problems) but it is something like 0.001 lb/ft^3. Lets use that for the example.
The weight of air under the waterline surface is:
Wa = x * L * W * 0.001 = x* 15 * 10 * 0.001 lb = 0.15*x lb per x ft of depth
So each ft of air depth in the boat adds 0.15 lb to the weight. A whopping
1.06* 0.15/10000 = 0.0016% increase to the total weight
If you really want to know more ask me what happens when a 150 lb person boards the barge amidships.
Gravity on the boat makes the boat sink.
Gravity on the water around the boat makes the boat float.
Better ?
Todd
How sure are you that gravity isn't just a thought convienience also ? Some physicist using string theory might call it so.
Just use the appropriate level of abstractions for your intended purpose. Of course if your purpose is to stir up the internet, use an in-appropriate mixture
Now git back to the boat work.
Todd
What is force
Heck Todd we still don't really know what a force is.
Gravity is particularly hard to conceive of as it is force at a great distance. "Normal" electromagnetic forces that keep our feet from sinking into the earth and stop our cars acts over MUCH shorter distances (with any effect that can be measured) and so we think of the two surfaces "touching". They never really touch. The electrons do repel each other and give that appearance however. It is still action at a distance and we don't really understand what means is used to transmit momentum or energy across the gap.
So we constructed 4 forces to explain it.
Perhaps reality is a thought experiment?
But who is doing the thinking?
Heck Todd we still don't really know what a force is.
Gravity is particularly hard to conceive of as it is force at a great distance. "Normal" electromagnetic forces that keep our feet from sinking into the earth and stop our cars acts over MUCH shorter distances (with any effect that can be measured) and so we think of the two surfaces "touching". They never really touch. The electrons do repel each other and give that appearance however. It is still action at a distance and we don't really understand what means is used to transmit momentum or energy across the gap.
So we constructed 4 forces to explain it.
Perhaps reality is a thought experiment?
But who is doing the thinking?
You're missing my point. If you were in a rocket ship in zero gravity accelerating at 1g you would be able to fill a tub with water and float a boat on it. No gravity, but the equivalent buoyancy force you'd have on the surface of the Earth. If you were plunging Earthward in a powered craft and were accelerating faster than 1g you could float stuff upside down... A touch less esoterically, you can use a centrifuge for your experiments. At any rate, it is clear that gravity is not necessary to have buoyancy. What you need is a fluid or fluids and a force or forces that order them by mass. I would not typically make this rather strained argument, but RL's assertion that buoyancy is a make believe force and it is dependent on the real force of gravity and that seeing this will somehow provide particular enlightenment to the question of stability annoys me. First, buoyancy is a real force as is pressure. Second, of all the fundamental forces you need to have buoyancy, gravity is the easiest one to replace with some other force (not some imaginary force, but a real one). Third, I've seen Roger make this argument before and he's yet to get to the stage where he demonstates the usefullness of thinking of buoyancy as an imaginary force in the understaning of stabilty.
Anyway, I've got to go finish installing my new solar panels so I'll leave it there...
--Tom.
Time for a fresh view, although I like the barge example.
The easiest way to approach this problem is to draw a free body diagram. This is a picture of the boat sitting all by itself in space. For equilibrium conditions (meaning the boat is floating on a perfectly still sea with no motion whatsover) the sum of the forces in the vertical direction have to equal zero. The forces pushing the boat downwards (gravity times mass) are equal to the forces pushing the boat upward. So what is the force pushing the boat upward? It is the sum of the water pressure vector components that are acting in a vertical direction. In short water pressure is applied normal to the surface, but for a sailboat the surface is a complex curved shape, so at every point there is a force vector that can be shown as horizontal and vertical components. The sum of the vertical components across the entire hull must equal the sum of the forces pushing the boat down into the water. The deeper the boat goes into the water the greater the pressure and the harder it is to force it even deeper. Free body diagrams are a great help to understand problems like this.
The easiest way to approach this problem is to draw a free body diagram. This is a picture of the boat sitting all by itself in space. For equilibrium conditions (meaning the boat is floating on a perfectly still sea with no motion whatsover) the sum of the forces in the vertical direction have to equal zero. The forces pushing the boat downwards (gravity times mass) are equal to the forces pushing the boat upward. So what is the force pushing the boat upward? It is the sum of the water pressure vector components that are acting in a vertical direction. In short water pressure is applied normal to the surface, but for a sailboat the surface is a complex curved shape, so at every point there is a force vector that can be shown as horizontal and vertical components. The sum of the vertical components across the entire hull must equal the sum of the forces pushing the boat down into the water. The deeper the boat goes into the water the greater the pressure and the harder it is to force it even deeper. Free body diagrams are a great help to understand problems like this.
In defense of Roger
I think what Roger is trying to say is that buoyancy is an abstraction of the electromagnetic force. Pressure is an electromagnetic force. We use the concept of buoyancy so we don't have to look at the electron to electron interaction between the boat and the water.
Comments Roger?
Jibes138
When you introduce the free body diagram you have to make some assumptions about your audience (or educate them).
A free body diagram has lots of weird assumptions about it that make it easy to use. Stuff like you can't bend the object in a free body diagram no matter how much force you apply to any part of it. All its mass is concentrated at an abstraction called the center of mass, all the buoyant forces are concentrated at an abstraction we call the center of buoyancy. They also have the nasty habit of being 2-dimensional which makes them hard to use in boating.
I think what Roger is trying to say is that buoyancy is an abstraction of the electromagnetic force. Pressure is an electromagnetic force. We use the concept of buoyancy so we don't have to look at the electron to electron interaction between the boat and the water.
Comments Roger?
Jibes138
When you introduce the free body diagram you have to make some assumptions about your audience (or educate them).
A free body diagram has lots of weird assumptions about it that make it easy to use. Stuff like you can't bend the object in a free body diagram no matter how much force you apply to any part of it. All its mass is concentrated at an abstraction called the center of mass, all the buoyant forces are concentrated at an abstraction we call the center of buoyancy. They also have the nasty habit of being 2-dimensional which makes them hard to use in boating.
Not much of a physicist, I"m guessing, eh Bill? Einstein provided a wonderful (and actually "intuitive") explanation for Gravity via his theory of General Relativity. Gravity is not a force at all, but rather a bending of the space-time continuum. The popular analogy is a bowling ball on a rubber mat. The rubber bends under the mass of the ball, causing nearby balls to naturally roll towards it. It's not a perfect analogy, but it's a good start. If this stuff piques anyone's interest, btw, I have an excellent book to recommend you read.
As for true forces (like electro-magnetism, the "strong" atomic force, etc), you need to understand String Theory to understand them. And by the way, if anyone tells you he/she understands String theory, he/she is lying through their teeth.
...but I digress...
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