Lewis C. Epstein's "Battleship Floating in a Bathtub"

[greypilgrim]

Hi.

In Epstein's Thinking Physics, there is following problem:

Can a battleship float in a bathtub? Of course, you
have to imagine a very big bathtub or a very small battle-
ship. In either case, there is just a bit of water all around
and under the ship. Specifically, suppose the ship weighs
100 tons (a very small ship) and the water in the tub weighs
100 pounds. Will it float or touch bottom?

a) It will float if there is enough water to go all around it
b) It will touch bottom because the ship’s weight exceeds the water’s weight

The correct answer is a). I'm not sure if I understand his premises correctly, does he really mean a 100 ton battleship smaller than a regular bathtub should float? How would you make sure that "there is just a bit of water all around and under the ship"? A 100 ton battleship smaller than a bathtub wouldn't even float in the ocean, would it?

 

[jbriggs444]

Hi.

In Epstein's Thinking Physics, there is following problem:

Can a battleship float in a bathtub? Of course, you
have to imagine a very big bathtub or a very small battle-
ship. In either case, there is just a bit of water all around
and under the ship. Specifically, suppose the ship weighs
100 tons (a very small ship) and the water in the tub weighs
100 pounds. Will it float or touch bottom?

a) It will float if there is enough water to go all around it
b) It will touch bottom because the ship’s weight exceeds the water’s weight

The correct answer is a). I'm not sure if I understand his premises correctly, does he really mean a 100 ton battleship smaller than a regular bathtub should float? How would you make sure that "there is just a bit of water all around and under the ship"? A 100 ton battleship smaller than a bathtub wouldn't even float in the ocean, would it?

The intended supposition is that the tub is large enough to enclose the battleship, at least up to its normal water line. There will be 100 pounds (1.6 cubic feet or so) of water in a small puddle at the bottom of this "tub".

As the battleship is lowered into the tub, it will squeeze the water to the sides forming a skin-tight layer. Obviously, this means that the bathtub must have been formed to almost exactly match the size and shape of the battleship.

How thick a layer?

If we scale an Iowa class battleship of about 50,000 tons with (very rough guess) 200,000 square feet of wetted surface area down by a factor of 500 (mass/volume/displacement) then we will be talking about a factor of about $500^{2/3} = 63$ in surface area. So 100 tons with about 3000 square feet of wetted surface. [In a bathtub about 100 feet long]

That 1.6 cubic feet of water would then be in a layer with a thickness of about 0.005 inches. About 5 times the thickness of a garbage bag.

 

[DaveC426913]

This is one of the ones I wish Mythbusters had tried, because so many people don't believe it to be true. They stopped production before I had the chance to write it up and submit it.

Probably moot anyway. I think they would have rejected it as too technically problematic to test. I've given some thought to it myself and, I can't see a path to a truly convincing outcome.

Even if our experiment was scaled down to just a 1000lb. block, I still think the tolerances are prohibitive. I think the crux of the problem is to "prove" (i.e. demonstrate irrefutably) that such a block is indeed not touching the walls or floor in a way such that it can be described as actually floating.

Would a skeptic be convinced that a layer of water .004 inches is sufficient to declare that the block is "floating"? If you put more weight on top of the block, would you be able to "sink" it convincingly?

Surface tension would greatly pollute the results of the experiment. Would a few drops of dish soap in the water eliminate the effects of surface tension?

 

[greypilgrim]

But then we must seal the rim of the bathtub to the ship? Otherwise, why wouldn't it just displace the water out of the tub?

There's an illustration in the book where this is clearly not the case:

 

[DaveC426913]

But then we must seal the rim of the bathtub to the ship? Otherwise, why wouldn't it just displace the water out of the tub?

No we do not. Floating is floating.

The bathtub must be big enough to hold the ship's submerged volume plus the 5 or so gallons of water.

There is another way of looking at this experiment.

1. Start with the ship floating in the ocean, free from any bathtubs or other constraints.
2. Add bricks under the ship until you have displaced alost all the water under its keel.
3. Add more bricks next to those one to create a wall up the port side of the ship, really close to its hull.
4. Add bricks all around the hull: bow, starboard and stern until the gap is so small that you can't even slip a piece of paper between the brick and the hull.

You now have an enclosed "harbour" that contains a 100 tonne ship and just a few gallons of water. At no time does the ship stop floating and at no time does the "harbour" overflow its banks.

 

[Baluncore]

It could be demonstrated by floating a cone in a conical tank.
Spin the cone to demonstrate non-contact.

 

[DaveC426913]

It could be demonstrated by floating a cone in a conical tank.
Spin the cone to demonstrate non-contact.

I think, unfortunately, that surface tension will provide so much friction that there will be no discernible distinction between liquid friction and solid friction.

 

[greypilgrim]

I understand that a ship that floats in the ocean will also float in a fitting bathtub, however thin the layer of water. Not the water present matters, but the displaced.

What I don't understand is why a 100-ton-regular-bathtub-sized-ship would float at all (in any body of water) since it needs to displace 100 cube meters of water which is way bigger than a regular bathtub.

 

[DaveC426913]

What I don't understand is why a 100-ton-regular-bathtub-sized-ship would float at all (in any body of water) since it needs to displace 100 cube meters of water which is way bigger than a regular bathtub.

Sorry, I don't know where you got this scenario from but it is not the "floating an ocean liner / battleship in a bucket's-worth of water scenario."

A 100-ton-regular-bathtub-sized-ship would not float under any cicusmtances - bathtub or otherwise. it is too dense.

A real world ship is, by definition and by necessity, less dense than water.

 

[Baluncore]

I think, unfortunately, that surface tension will provide so much friction that there will be no discernible distinction between liquid friction and solid friction.

Then measure the electrical resistance between the conical surfaces.

A real ship actually floats in the thin layer of paint they gave it in dry dock.

 

[greypilgrim]

A 100-ton-regular-bathtub-sized-ship would not float under any cicusmtances - bathtub or otherwise. it is too dense.

A real world ship is, by definition and by necessity, less dense than water.

Then I probably just misunderstood Epstein:

Can a battleship float in a bathtub? Of course, you
have to imagine a very big bathtub or a very small battle-
ship. In either case, there is just a bit of water all around
and under the ship. Specifically, suppose the ship weighs
100 tons (a very small ship) and the water in the tub weighs
100 pounds. Will it float or touch bottom?

The "in either case" made me think the 100 tons supposition also applies to the "very small battleship" and that this meant it fits into a regular bathtub.

 

[DaveC426913]

The "in either case" made me think the 100 tons supposition also applies to the "very small battleship" and that this meant it fits into a regular bathtub.

I disagree. Battleships are typically two orders of magnitude larger.

So 100 tonnes is a small battleship. Or would be - because there are no battleships that tiny. 100 tonnes is not really even big enough to be called a ship; it would merely be a boat.

The point being: I think you're misinterpreting the writer. A "small" 100 tonne battleship is still much larger than any bathtub.

 

[jbriggs444]

Then I probably just misunderstood Epstein:

The "in either case" made me think the 100 tons supposition also applies to the "very small battleship" and that this meant it fits into a regular bathtub.

A 100 ton battleship built to scale would be about 100 feet long, 13 feet wide and 4.5 feet deep to the waterline.

You'll need a big bathtub to fit that ship.

If you want a more realistic scaling factor, you want to scale down each dimension by a factor of 172 or so. So your Iowa class battleship with 860 feet of length, 108 feet of beam and 37 feet of draft massing 50,000 tons will now have 5 feet of length, 7.5 inches of beam and 2.5 inches of draft. It will displace about 20 pounds of water (2.5 gallons).

Not 100 tons.
20 pounds. Firing rounds a bit bigger than an airsoft pellet. Houthi's beware!

You can buy a scale model at 1:300 scale. That one is only 31 inches.

Here is a video of the Mighty Mo (BB-63) at 1:150, 71 inches.

 

[greypilgrim]

Can a battleship float in a bathtub? Of course, you
have to imagine a very big bathtub or a very small battle-
ship.

I can't help but read this as "... or a very small battleship in a regular sized bathtub".

I guess it's just unfortunate that Epstein uses "very small ship" for a very different scale only two sentences later.

 

[sophiecentaur]

A real ship actually floats in the thin layer of paint they gave it in dry dock.

Nice but it's far too sophisticated for anyone who doesn't understand how 'limits' work.

 

[DaveC426913]

Then measure the electrical resistance between the conical surfaces.

That was where I was going too. Some sort of electrical sensor.

But I couldn't find a solution that made a distinction between "this surface is wet" and "this surface is buoyantly and hydrostatically floating at a very small distance from that one".

A real ship actually floats in the thin layer of paint they gave it in dry dock.

Hah! (but paint is a solid, so...)

 

[sophiecentaur]

What are we actually arguing about here? If Archie works for a big bath then why not for a 'just a bit bigger' bath? Does normal Physics - based argument not apply on this thread? IF you want to introduce other forces then you'd have to specify their values.

 

[Vanadium 50]

What I don't understand is why a 100-ton-regular-bathtub-sized-ship would float at all (in any body of water) since it needs to displace 100 cube meters of water which is way bigger than a regular bathtub.

If you change the question, you change the answer.

 

[DaveC426913]

If you change the question, you change the answer.

Greypilgrim has since stated that he interpreted the author's words to include a bathtub-sized-yet-still-100-tonne battleship. So he did not think it was a change from what he thought was the question.

 

[Klystron]

But then we must seal the rim of the bathtub to the ship? Otherwise, why wouldn't it just displace the water out of the tub?

There's an illustration in the book where this is clearly not the case:
View attachment 346785

Apropos the diagram: that is a very odd warship. It seems to fly the Confederate battle flag, has two gun turrets each armed with two cannons. The central bridge also sprouting a turret does not fit the profile of a CSS ironclad designed before 1866, the war ending in 1865. The central housing interferes with port and starboard cannon turret rotation even more than actual dual turret monitors. The tall smokestack would be riddled in a first exchange.

The ship diagram looks like a doodle John Ericsson might have drawn after returning to Sweden but why the CSS flag, ship #38, and what is written on the port signal flag? Conclusion: a cartoon.