Floating a cruise ship in a bucket of water

[votingmachine]

I would not think it necessary. Prove displacement of water.

But if you really wanted. Build a triangular pool with a known volume. Fill it to the brim. Put a triangular ship (known volume and known weight ... just 8.3 lbs less than the weight of the water in the pool) in and measure the height of the ship and the water displaced. Show the weight of the ship and water displaced is the same. Take out 1 gallon. Measure the height of the ship and the water displaced. Show that the weight of the ship and the water displaced differs by the weight of the 1 gallon of water removed prior to displacement. Take out another gallon and repeat.

When you take out the last gallon, the ship is marginally lower. And your equation for the weight of the ship vs the water displaced (or removed prior to displacement) is suddenly unbalanced.

Personally, the unbalanced equation at the end of the sequence is enough for me. But the reality is that the ship is now lower, and a careful measurement will show that.

You could also go the other direction. Start with a gallon of water in transparent container. Use a large styrofoam bucket as your ship. Keep adding weights and measuring the height of the water around the styrofoam. Again you prove displacement. Your "ship" is always floating on a gallon, with the height based on the weight of the water displaced

The fundamental principle is difficult to show at the extreme case, and easy to show for non-extreme cases. I don't quite understand the reason why the extreme case needs proof, when the principle is established and no one needs a ship in a tank that is form-fitting.

 

[DaveC426913]

When you take out the last gallon, the ship is marginally lower. And your equation for the weight of the ship vs the water displaced (or removed prior to displacement) is suddenly unbalanced.

Marginally being the operative word here.

At the scale of a cruise ship and a bucket of water, that 'marginally' may be measured in microns.

And how do you demonstrate to a skeptic that that counts as floating?

 

[anorlunda]

One way used to remove fouling from a boat hull, without slipping the vessel, is to wrap the hull in a big plastic bag, pump out the water from between the hull and the bag, then pour a bucket of bleach into the gap to kill the fouling organisms.

I think that's a clever way to de-foul. A simpler way, if you can arrange it, is to simply sail into fresh water. The salt water creatures die quickly. When you return to salt water, the fresh water creatures attached will die quickly.

 

[SongDog]

I wondered about this. Yeah, I think it would work.

It will if you do it right. Capacitance can be measured to exquisite sensitivity by counting individual electrons with a SQUID (vide Rod Harris-Lowe).

 

[italicus]

That makes a lot of sense in practice but the accuracy depends on knowing absolutely everything about the structure and contents of the ship. No one would be in a position to challenge your answers but would it matter?
As a matter of interest, does the inclining test result agree well with the calculations that surveyors do? There is a philosophy that tells us to be pessimistic in design ratings and that works well except when a spot of corruption affects construction methods and materials.
It's interesting that most disasters where structures are involved can always be put down to commercial (and even criminal) interests, rather than the good old Engineers and Surveyors. Good regulation is the key.

You can easily understand that it is not possible to know exactly what is the weight and the G coordinates ( referred to an Oxyz ideal reference frame, have a look at my sketch), of every steel plate, every section frame, every engine, motor, pump, compressor, pipe, electrical device, crane, rope, and so on, including furniture, that are assembled together to make a ship, whichever kind of ship : passenger, general cargo, bulk carrier, tanker, even navy ships!
So, concerning commercial ships ( but navy ship too are subject to similar rules), it is compulsory that , at the end of construction ( or almost the end...I cannot enter into details here!) , a ship undergoes an inclining test. This test is simple to describe in line of principle, but not so easy to carry out, believe me! I have directed a lot of tests like this, and it takes first of all an accurate survey of the ship in construction , in order to unload as many unnecessary items as possible, f.i. welding machines that are still on board...and other! The masses that create moments are moved from port to starboard several times, and the relevant angles of inclination are measured, in several ways : a test like that can require a whole day !

The result of the inclining test, imposed by international safety rules ( e.g. , first of all, the rules issued by the IMO = International Maritime Organisation) are sufficiently reliable, to be the basis of all subsequent stability calculations that are to be carried out in every given loading condition : the empty ship weight, and the coordinates of its center of gravity, are the basis for calculations of the ship’s stability future condition of loading, and these conditions are to be in compliance with the international safety rules , first of all SOLAS ( safety of life at sea) rules, which are in a continuous evolution and improvement , since the first London convention , which followed the TITANIC sinking. Nowadays , we are no longer in the conditions of the TITANIC , there are mountains of rules issued by periodical conferences at the IMO. IF you wish , look for its site, to get a simple idea ! You will be astonished against the quantity of rules to be applied in this context ! The shipping industry is a very complicated world , I hope you trust me.

It's interesting that most disasters where structures are involved can always be put down to commercial (and even criminal) interests, rather than the good old Engineers and Surveyors. Good regulation is the key.

Well, dear Sophie, don’t be so extreme! It is out of doubt that disasters at sea occur , but not always for commercial or criminal interests. A ship cannot depart a harbour with more goods on board than allowed by its Load Line marks, that establish the maximum allowed draft (Plimsoll marks, never heard?) : no Port Authority will let she go. Good regulation are there, and of course must be respected. But disasters sometimes occur for unforeseen circumstances, f.e. technical failure, and of course human errors, which are always behind the corner! I have been nominated by italian courts as an expert in some ships disasters, and have learned a great lesson from my experiences : big disasters are often due to a lot of concurrent causes, some of which may be considered not significant , if taken alone ! In any case, the heavy work of surveyors isn’t to be underestimated .

One of the guy, Bob 012345, asked what “reading the drafts” means; Bob, have a look at the attached sketch :

You have to imagine that the still water surface ideally cuts the ship in two parts : only the portion under the surface displaces water, of course. The Archimede’s principle says that the weight of the whole ship ( or a floating body in general) equals the weight of the amount of water displaced, for it is in equilibrium under its weight and hydrostatic buoyancy.
On both sides of a ship, draft marks are welded, fore, middle and aft. The mean draft allows you to enter the ship’s hydrostatic curves, nowadays replaced by computer calculations, which give you the immersed volume, so S = dgV ( d= density of water) , and other geometrical characteristics of the ship. But the final weight and position of G, when the ship is loaded, cannot be read from geometrical characteristics, they depend strictly on the amount of goods loaded , and their position on board.

Excuse me for my bad English.

 

[votingmachine]

Marginally being the operative word here.

At the scale of a cruise ship and a bucket of water, that 'marginally' may be measured in microns.

And how do you demonstrate to a skeptic that that counts as floating?

I wouldn't call it floating either. Since capillary forces matter, it is likely that the force of gravity and buoyancy are exceeded by surface tension effects from the water.

I would actually expect deviation form the buoyancy masses earlier. The normally negligible surface tension force would probably create a measurable deviation as the volume of water becomes small, and the surface area large.

If that is true, then it is not correct to say that a ship with a large surface area can be floated in a very small water volume, with a carefully constructed tank.

I had not spend a lot of time thinking about the boundary conditions of buoyancy. If one wanted to take it to the ridiculous extreme, hypothesize a volume of water spread such that the depth is 1 angstrom. Obviously water molecules no longer fit. At the boundary conditions of a large thing and a very perfectly conforming tank ... it is not possible to prove buoyancy. Surface tension of water would matter.

Take a small barge. 200 ft x 50 ft. Call it 50 meters by 20 meters. So about 1000 square meters. Call it 4 liters of water, so 4 cubic decimeter of water. 4x10^-3 cubic meters. The barge on top of 1 gallon would squash it to a thickness of 4x10^-6 meters, or 1 micrometer.

That is a measurable distance.

But consider if instead you had placed a 1-gallon ball of tortilla dough under the barge. How thin can you squash the dough before it resists and supports the barge? Are you "floating" the barge?

1. The skeptic might be right.
2. It doesn't matter. I'm not invested in proving the boundary conditions of buoyancy in form fitting boundary conditions. I'm quite willing to allow the skeptic his doubt towards the limiting conditions of buoyancy. As long as the skeptic does not deny the basic principles.

 

[hutchphd]

surface tension effects from the water.

The font of all knowledge says the surface Tension of water is 72 mN/m. Gonna need a pretty small Ark for that to matter

 

[DaveC426913]

I wouldn't call it floating either. Since capillary forces matter, it is likely that the force of gravity and buoyancy are exceeded by surface tension effects from the water.

I would actually expect deviation form the buoyancy masses earlier. The normally negligible surface tension force would probably create a measurable deviation as the volume of water becomes small, and the surface area large.

Surface tension is something to consider - although I'm not sure, in the end, if it matters. Just because surface tension applies does not necessarily mean it negates the meaning of floating.

I mean, I can float a pin in a small glass of water that has a noticeable meniscus (surface tension). Though the pin's centre of mass might not be the same height in a larger container, does that disqualify the pin's claim to be floating?

But consider if instead you had placed a 1-gallon ball of tortilla dough under the barge. How thin can you squash the dough before it resists and supports the barge? Are you "floating" the barge?

Tortilla dough is not a liquid.

 

[votingmachine]

The point remains that there is a limit if we took that 1000 square meter flat barge, we had a 1 micrometer depth with the 4 liter volume. So 4 mls would be one 1-thousandth that depth, or 1 nanometer. 0.4 mls gets you to 1 angstrom, smaller than a water molecule. Put 0.4 mls under that barge and it will be higher than the height expected for "floating".

Likewise, a cruise ship that is 300 meters by 50 meters with a depth of 10 meters has 20,000 square meters of surface area in the water. The 4 liter volume spreads to one-twentieth of a micron, 50 nanometers.

Floating has a common meaning of freedom of movement. Not just buoyant suspension. When we constrain the volume to so small an amount that movement is no longer possible ... we may demonstrate buoyancy, but are we demonstrating floating?

Every "ship" will have a surface area below the water. We express buoyancy based on the volume based mass of water, and in theory, that could be demonstrated with the smallest amount of volume of water and a perfect tank. In practice, there are properties of water that matter and the boundary condition will always break down at some point. 1 gallon may well be close to that limit for some surface areas.

 

[anorlunda]

Floating has a common meaning of freedom of movement. Not just buoyant suspension.

Others may disagree with your points because they disagree on the freedom of movement as a requirement.

 

[votingmachine]

Others may disagree with your points because they disagree on the freedom of movement as a requirement.

True. But a puck floating on an air hockey table, is not buoyant. We do somewhat consider the word floating to have a meaning beyond buoyancy. That may not matter to this debate.

EDIT: I've seen cool fountains with a spherical rock "floating" on water pumped from below. Again, this use of the word is not necessarily important, but definitions can cinfuse the issue.

 

[votingmachine]

I am somewhat unwilling to argue with that skeptic. If I have a ship that displaces 1 million gallons, I would only say that it displaces 1 million gallons. I would not make a claim that I could build a 1 million-plus-1 gallon tank and float it.

Sure in theory ... But it is not a thing anyone should TRY to prove. Prove displacement and buoyancy. Those matter. The actual experiment is really difficult. So let the skeptic be skeptical. If he wants to prove people wrong by building a 1-million-plus-1 gallon tank ... go for it.

I would add the surface area component I mentioned matters. 1 million gallons can have many surface areas.

 

[hutchphd]

Is anyone else concerned that we have passed the silliness threshold here? Angels and pinheads come to mind...

 

[DaveC426913]

Sure in theory ... But it is not a thing anyone should TRY to prove. Prove displacement and buoyancy. Those matter.

I'm going to hazard you haven't watched Mythbusters...

 

[votingmachine]

I'm going to hazard you haven't watched Mythbusters...

No ... but then again, I watch about 20 sports games per year on TV and nothing else. So the set of TV shows I haven't seen since Seinfeld is about everything.

I'm still of the opinion that the thing to say is that a particular ship displaces a certain volume. Anyone that wants to make statements for or against conformational tanks is free to do so. The fact is that a ship that displaces 1 million gallons, displaces 1 million gallons. If you want to buy a ship and try to prove some other thing about tanks and boats ... have at it. If you want to say the ship that displaces 1 million gallons DOESN'T displace 1 million gallons ... then we have disagreement.

I guess I hold with a position analogous to a Copenhagen-interpretation. I will say the fact I know (the ship displaces 1 million gallons) and if you want to make an unfounded statement about ships and impractical tanks ... I guess I don't care. Build your impractical tank and run the experiment.

This does seem like an angels-on-the-head-of-a-pin debate.

 

[DaveC426913]

If you want to buy a ship and try to prove some other thing about tanks and boats ... have at it.

That is the whole point of Mythbusters.

There are widely-held myths out there, some true, some false. The purpose of Mythbusters is to definitively confirm or bust them - based on actual experimentation - not theory.

That is the spirit of this thread.

I guess I hold with a position analogous to a Copenhagen-interpretation. I will say the fact I know (the ship displaces 1 million gallons) and if you want to make an unfounded statement about ships and impractical tanks ... I guess I don't care. Build your impractical tank and run the experiment.

Yes. This is where theoreticians pull off the road, and experimentalists put their foot on the gas.

This does seem like an angels-on-the-head-of-a-pin debate.

It isn't though. That's the point. It can be done - it can be confirmed or busted.

Some people find theory to be "good enough" or them, and some people prefer definitiveness.

Notice that you already have introduced some confounding effects (eg. surface tension) that suggest you could theorize till the cows come home but never actually know the answer, thus your confidence that it displaces as much as it displaces is already on thin ice.

 

[hutchphd]

It isn't though. That's the point. It can be done - it can be confirmed or busted.

Except the devil is in the detail. And unless everything (Surface finish on boat and tank, definition of "float",etc) is exactly specified, there will not be a definite result. And so we argue angels on a pin.
There is no doubt that somewhere between an ocean of water and a thimble of water is transition and that value depends upon definitions. No need to build a big ark mold, unless you want to open a museum in Kentucky.

.

I liked mythbusters but I would occasionally be annoyed that at the end of the episode they didn't show why it was silly to do the experiment, because we do know the outcome to near certainty.

 

[DaveC426913]

Except the devil is in the detail. And unless everything (Surface finish on boat and tank, definition of "float",etc) is exactly specified, there will not be a definite result. And so we argue angels on a pin.

Also the point of this. As long as all we're doing is talking, there will not be a definite result. Only experimentation will show - first whether it can be done - and second - what the answer is.

No amount of talking will ever confirm that it can't be done.

Engineering will be the solution to fine-tuning specs.

I liked mythbusters but I would occasionally be annoyed that at the end of the episode they didn't show why it was silly to do the experiment, because we do know the outcome to near certainty.

Well that doesn't apply here. Even people in this thread on a Physics forum can't agree on the outcome of this one.

This is a surprisingly tricky concept, a lot of people believe that it can't be done in principle - often surmising something along the lines of "a 10 tonne boat can float in a minimum of 10 tonnes of water. Any less and it will sink." That is false, of course.

 

[hutchphd]

Well that doesn't apply here. Even people in this thread on a Physics forum can't agree on the outcome of this one.

The fact that some are incorrect does not compel me to build a boat!
You did a good job proscribing the original challenge, but if you can define floating in a reasonable way, and allow stipulations as to support stiffness (and other details) then the answer reguires only application of known Physics. For instance the surface tension of water (which I quoted earlier ) is 72 N per kilometer. That is reason enough to not mention it again
There is no tricky Physics here. Only details and nitpicking. Suppose the boat has a surface (below water) of $100m^2$ then the surface layer made by the bucket of water will be about a tenth of a millimeter thick. So linear thermal expansion per C will be 10 times the clearance.
As a practical matter, the experiment is interesting to contemplate. The result is less so IMHO.

 

[DaveC426913]

As a practical matter, the experiment is interesting to contemplate. The result is less so IMHO.

Science is my thing. My sibs and friends don't intuit engineering, physics and large/small numbers like I do.

They will be skeptical, and nothing will convince them except proof. I like to be the know-it-all.

 

[Baluncore]

They will be skeptical, and nothing will convince them except proof. I like to be the know-it-all.

Then do not educate them.
Be the mystic and a storyteller.
Tell the physics like it is a fairytale.

 

[Charles Link]

With reasonable allowances for a layer of water that is about an inch thick, that experiment could be readily engineered. When that layer gets to be about a millimeter thick, thermal expansion of the boat and/or the tub could start to present difficulties. If you start getting to where the surfaces need to have optical like constraints, that can be very difficult to engineer for sizes that are much bigger than an inch across. In any case, the thread has been very entertaining. Meanwhile, I still think there is a good percentage of the population who would be surprised to find, contrary to Archimedes, (without the qualifier that it is the effective volume displaced), that you can even float a five pound boat with far less than five pounds of water.

 

[votingmachine]

For instance the surface tension of water (which I quoted earlier ) is 72 N per kilometer. That is reason enough to not mention it again

Is there a simple calculation to turn that into energy per area (ergs per square meter)? I have some confusion on tension when it is a surface energy calculation. I recall that when I would drop a cover-slip onto a microscope slide, it would really pull down. Prying it off with a razor blade required a lot of force. I'm not convinced that the surface energy is an insignificant factor. Especially once the thickness is a very thin capillary thickness.

And of course it matters what the boat surface is. A teflon coated boat is different from a hydrophilic coated boat. And the tank coating matters also. And the water purity matters. A trace amount of surfactant changes everything.

 

[italicus]

The Archimede ‘ s law keeps its validity for a ship even in a narrow dock, with a small gap between side and bottom plating, and the corresponding dock walls and bottom. Also when the ship is navigating in open sea, and one ignores resistance to motion, essentially due to viscous forces and other causes, such as shape-resistance and waves-making forces, it is valid.
But , if one considers particular situations, some problems arise. I’ll explain what i’m referring to. Suppose a ship is to be pulled in a narrow canal, where side and bottom gaps are small, compared with the ship’s breadth and draft. A very simple application of the continuity equation tells us that the water speed, around the ship, must increase; one can carefully equilibrate the forces that pull forward (f.i. exerted by tugs) or by ground ropes. But a problem arises at the bottom, because there is shallow water: a simple thought to the Bernoulli theorem tells that the increase in speed is accompanied by a decrease of pressure. So the bottom of the ship can hit the canal’s bottom very hardly , and this, together with pulling, causes a series of indents and severe damages to the bottom plating.
This isn’t a joke, in the past the problem arised a lot of times, and I’ve repaired many ships, damaged that way.

 

[hutchphd]

Prying it off with a razor blade required a lot of force. I'm not convinced that the surface energy is an insignificant factor. Especially once the thickness is a very thin capillary thickness.

That is an interesting point. But remember that 1 atm is 15 PSI. So the cover slip has 5 pounds of force pushing it down as long as there is a water seal (independent of viscosity and surface tension). The details of that seal do depend upon these and geometric factors. Air must invade the interface. This doesn't affect lateral forces, and it does not really affect buoyancy. It greatly affects attempts to lift objects out of a buoyant state until the seal is breached.

 

[DaveC426913]

But a problem arises at the bottom, because there is shallow water: a simple thought to the Bernoulli theorem tells that the increase in speed is accompanied by a decrease of pressure. So the bottom of the ship can hit the canal’s bottom very hardly , and this, together with pulling, causes a series of indents and severe damages to the bottom plating.
This isn’t a joke, in the past the problem arised a lot of times, and I’ve repaired many ships, damaged that way.

Yes, I've heard of this. Ships navigating shallow canals ride lower the faster they move.

 

[hutchphd]

I think this is also why floats on seaplanes have the characteristic "step" halfway down the length to create turbulence so they will not be pulled down. Down is the wrong direction for an airplane...

 

[italicus]

So in the case of ships a good provision is to change the trim , if possible, increasing the aft draft and decreasing the fore one. This can be done moving ballast water towards aft.
Of course, everything is to be done “ cum grano salis” ( salt in your brain!)

 

[Charles Link]

That is an interesting point. But remember that 1 atm is 15 PSI. So the cover slip has 5 pounds of force pushing it down as long as there is a water seal (independent of viscosity and surface tension). The details of that seal do depend upon these and geometric factors. Air must invade the interface. This doesn't affect lateral forces, and it does not really affect buoyancy. It greatly affects attempts to lift objects out of a buoyant state until the seal is breached.

See https://www.physicsforums.com/threa...e-surface-of-water.944587/page-3#post-5977523 post 58 by @haruspex . There will likely, IMO, be some thickness at which the water starts to behave like a water-tight seal, and loses some of its buoyancy properties.

 

[hutchphd]

Suppose I have a rubber duck in the bathtub. Everyone agrees it is floating. Now I spray a very high tensile strength (no surface tension) coating on the water (assume it is very duck-phillic and seals to ducky). Is ducky, by your definition, still floating? How come?

 

[DaveC426913]

There will likely, IMO, be some thickness at which the water starts to behave like a water-tight seal, and loses some of its buoyancy properties.

Certainly, if you tried to lift the ship out of its container, it will definitely resist. (Heck, this happens whenever I try to pull the trash bag out of my kitchen trash bin. It takes, like five minutes to come out!)

But how does it follow that that means it's not floating? Just because you can't lift it from its neutrally buoyant position doesn't mean it's stuck there and not floating. The forces keeping it in place are zero when its stationary, but rise rapidly as you attempt to move it, because water has a very tough time flowing into (or out of) the voided space.

 

[haruspex]

See https://www.physicsforums.com/threa...e-surface-of-water.944587/page-3#post-5977523 post 58 by @haruspex . There will likely, IMO, be some thickness at which the water starts to behave like a water-tight seal, and loses some of its buoyancy properties.

Isn't it just a rate issue? The thinner the layer the greater the force needed to get the water to flow at a given rate. You just need to be patient.

 

[Rene Dekker]

We take a typical cruise ship size, with a length of 202m, width of 28m, and draft of 6.3m (I took the first one from https://www.cruisemapper.com/wiki/753-cruise-ship-sizes-comparison-dimensions-length-weight-draft). Then the surface area of the ship under water is 2 x 6.3 x (202 + 28) + 202 x 28 = 8554 m3 . The volume of a bucket of water we assume to be 20L = 0.02 m3. If we assume the water thickness on all sides of the ship to be the same, then this will give a water layer thickness of 2.3 micrometer. That is, if the bucket follows the shape of the ship to an accuracy of about 1 micrometer, then the ship will be surrounded by water on all sides.

Now, can we call this "floating"? We consider three aspects of that. First of all, afaik, the thickness of a water layer sticking to a steel plate due to adhesion forces, is thicker than 2.3 micrometer. That is, when you remove the bucket, then the water would still cling to the ship on all sides.

Secondly, 2.3 micrometer is less than the diameter of capillary tube. Therefore, the water on the sides of the ship will creep up between the ship and bucket wall, due to capillary forces. That will remove water from the bottom, reducing the thickness of the layer on the bottom. I have not done a calculation on how high the water will go up, and of course that also depends on the shape of the bucket above the "water line".

Thirdly, the cohesion forces of the water would give the thin layer at the bottom extra buoyancy force. I have not done the calculations, but there is a chance that if you remove the walls of the "bucket", but leave its bottom in place, then ship would still "float" on the thin film of water underneath it.

So do we still call this "floating" in the sense that the question asks about? I would say no, but you'll be your own judge.

 

[DaveC426913]

That's a really insightful analysis.

 

[italicus]

We take a typical cruise ship size, with a length of 202m, width of 28m, and draft of 6.3m (I took the first one from https://www.cruisemapper.com/wiki/753-cruise-ship-sizes-comparison-dimensions-length-weight-draft). Then the surface area of the ship under water is 2 x 6.3 x (202 + 28) + 202 x 28 = 8554 m3 . The volume of a bucket of water we assume to be 20L = 0.02 m3. If we assume the water thickness on all sides of the ship to be the same, then this will give a water layer thickness of 2.3 micrometer. That is, if the bucket follows the shape of the ship to an accuracy of about 1 micrometer, then the ship will be surrounded by water on all sides.

First of all, a surface is expressed in $m^2$ and not $m^3$ .
But I haven’t understood your determination of the wetted surface area (WSA) of the hull . There are some empirical formulas, see f.i. this , page 6 :

1 Evaluation of wetted surface area of commercial ships as ...https://repository.si.edu › bitstream › handle › Mil...

there are others indeed.
Anyway , the point isn’t this. Do you think that the external hull surface is as smooth as a mirror? It isn’t. You cannot speak of a water layer of some micrometers, uniformly distributed on the whole wetted surface. Have you ever examined the hull surface from a distance , say, of 20 cm ? The surface is not uniform at that level you are considering.
Moreover, the Archimede’s principle , which we can define really a “law of nature” , is a matter of global hydrostatics, doesn’t take into consideration molecular forces of adhesion and cohesion forces of water. This law can be summarised in the vector equation :

$$\ vec\ P + \ vec\ S = 0 $$

nothing more.