Battleship: Newsletter Challenge (11/29/05)

I think an object that is floating displaces it's volume, not it's weight. This however doesn't determine whether an object floats or not. In order to float, the density of an object must be less than water. A boat is made of steel and air such that the average density is less than water, so it floats. I'm not sure if salt water is more or less dense than fresh water, that might make a difference. Also, if the tub overflows from the displaced volume of the boat, then there would be a problem.

It displaces both its weight of water, _and_ its volume-to-the-waterline of water.

The boy's conception is faulty. If the tub is to be able to float the ship, the tub must be able to hold at least the weight of the ship in water. If it is a tight fit in the tub, the water _left_ around the ship may have less weight than the ship - but the integral(rho*g*h*dA) must equal the ship weight (the water pressure acting on the ship hull reacts the ship weight). So, even if there is not enough volume of water left in the tub to fill a thimble, the _height_ of the water must be adequate to float the ship.

And the water that is _not_ in the tub (since the ship is there instead) weighs precisely what the ship weights out of water.

Yes my daughter, if you scale the battleship down to a reasonable size, it will float in the tub. As your brother stated, the displacement of weight is equal to the area of the surface being displaced. The laws of physics does allow for a varience in the fluids used to float the battle ship. There are many constants to look at for your answer to this equation. The content of water mixture is the key. Fresh water is less dense then ocean water. Therefor, you will need a deeper tub to float your battle ship. Due to the fact of the air:hydrogen:water mixture. In salt water, which is the ocean and the general area you will find the battle ship, the density of the ocean water is thicker then fresh water. Most ocean constants are at ~12% to ~17% in the pH factor of salenity, there for it can support more weight then regular fresh water as found in most rivers. However, there are other densities of water areas that are even more densor then the general oceans around the world. Take for instance the Dead Sea, the Caspion Sea, and the Great Salt Lake. These three areas of water contant have a more dense factor then fresh water and the general oceans around the world. The content of the Great Salt Lake is a estounding ~22% more dense then regular fresh water. If a battle ship enters the mouth of a fresh water river, or a delta, say the Nile river in Egypt, or the Mississippi on the Gulf of Mexico, the fresh water mixture at the delta is spreading the density of both the delts. There for, the mouth of the deltas are less dense then out in the ocean. Requiring for the riviers to be dredged, or for better terms, dug deepper to acount for the less dense water surfaces. Which in turn, will be ~ 10% to 15% less dense and the battle ship will displace more water per square foot of weight displacement. There for sinking and raising the water line on the ship. This is a great question to stir the chemistry lab for a demonstration in the school arena. Good question.

"Kids, in this case you are both right. As long as the volume of water left in the tub is greater than or equal to the amount displaced, the ship will float. If the tub is too form fitting, the water will rush out of the tub or over the gunnels and the ship will not float."

In order to float a battleship in a bathtub, the bathtub would have to be a very close fit to the battleship's hull. Since a floating object displaced it's weight in water in this case, the displaced water is gone, spilled over onto the bathroom floor leaving only enough water to fill the void between the hull and the bathtub. The son's argument is invalid. It's theoretically possible to float a battleship with a gallon of water if the bathtub were an extremely close fit.

Sure the ship would float ... if the bathtub was about 1200 feet long, 300 feet wide and 60 feet deep, full of nice warm water (like a bath)and even had a bunch of bubbles floating around, the battleship Missouri would float. It would draw several feet more water (float deeper in the water) because fresh water is less dense than salt water, and warm water is less dense than cold water. The bubbles would not have an adverse effect on the physics involved but would embarass the sailers aboard the ship. Conversely, if the battleship was a true scale model, and just the size to fit in your tub at home, it would still float. (BB-1 class vessels had very thick hull plates to ward off most enemy devices intended to sink them. This would make the scale modeling difficult to do, because of the need to bend some fairly thick steel to achieve the hull scaled thickness.)This is not something to try at home ... unless you can tolerate some spillage, and a few scars on the bathtub!

Two things come to me here... One, where does "100 pounds of water" and "100 tons of ship" come from? These two parts of an "equation" don"t belong here. Why? They are way out of proportion. Doing the math, I've found that a scaled down version of an Iowa Class battleship at a maximum combat displacement of 64000 tons...yes they got that heavy with all of the anti-aircraft armament along with the extra crews to man that stuff... would be about 450lbs. That's 6 ft. long and about maybe 10 inches wide. if you immersed this model into a FULL tub, you would have water coming over the top of the tub untill that relationship equalized...hence, floating battleship model. Think about it, how much does a gallon of water weigh?... And, how much does the average bathtub hold? Bet it'more than 450 lbs worth... Sidebar... As far as I know, American battleships' main armor was NOT the hull, but INSIDE the hull set at a certain angle, and in certain places in order to create what was called an "armored citdel"...This took into consideration the probability of a shot penetrating the hull, but being utterly stopped before hitting any vitals. Also, all American battleships were designed to have no more than a 108 ft, beam because the Panama Canal is 110 ft. wide. So, with all those locks, there are your bathtubs. Warm water(Pacific), cold water (North Atlantic), battleships floated in either...(Forget the Mercury...What was that one?...)

WWII battleships had an armored box in the center of the ship, pretty much starting at the front of the forward turret and ending at the back of the rear turret. The turrets and command center are armored. Theoretically the nose or tail of the ship could be blown off and the ship could continue to fight. The Iowa class has two levels of armored deck and the hull in the center section was armored. The main armored deck was 8 inches thick and the side armor was something like 16 to 18 inches thick at the torpedo belt. The ships were designed to slug it out with other battleships hurling 2200 pound, 16 inch diameter armor piercing explosive projectiles traveling at supersonic speeds. Modern non-nuclear antiship weapons would hardly phase these WWII behemoths.

I believe that the battleship weight must be equal to the displaced volume x the specific weight of the fluid. Therefore, the battleship could be floated in the bathtub if a "heavy" enough fluid was used. Fill your bathtub with mercury and you'll be set.

Or go get Elisha.(2Kings6:6) Normal laws of Physics don't apply.

Besides, your mother would kill me...
So, yes dear, (you congratulate your daughter for thinking of a question that stumps her brother) you're right; either a BIG bathtub, in a half-mile long bathroom...or a small ship with all dimensions scaled down - including the thickness of the hull - would float.
And son, you were right too, until your conclusion. It's not the mass of the water that's left that matters, it's the mass of the water that would have otherwise filled the volume of the space taken up by the ship - up to it's water line - that matters. The 100 pounds of water left would be plenty, assuming a form-fitting tub and a floor that can support that kind of weight.
Oh - and some epsom-salts thrown in for a softer bath might even do something to help reduce that waterline/volume issue... ;)
Sandman ~

Know what your wife is thinking and reply: "Kids, it is not polite to call each other Moron's."

After many weeks of these amazingly adept questions from a couple of precocious brats. I think the only possible answer would be: "Where is the nearest adoption agency so I can drop off these two inquisitive monsters and pick up a couple of quiet, thick kids"

While it's true that a floating object will displace its weight in water, it's not a requirement for floatation. Differential pressure, not water displacement is what's needed to counter the weight of the ship. Pressure x area = force. The volume of water in the tub can be much smaller than the volume normally displaced on the open water. As the ship is lowered into the tub, it will float once the water level comes up to the ship's waterline. You need little more than the volume of water to fill the space between the ship's hull and the vertical walls of the tub. The tighter the fit, the less water that's needed. only be large enough to allow the ship to lower into the

Oops... Drop the "only be large enough to allow the ship to lower into the" at the end.

Mike is right you could float the largest ship in a cup full of water providing you had a close fitting bath. The upward force that floats the ship is dependant on the density and depth of the water. You would need sea water to make it float at the same level but once the water comes up to that level it will still float even though amount of water might be very small.

Hello Mike, I hope you can still get this message. In trying to tell people that it takes very little water to float a battleship, you are the only one to tell it like it is. Those other people just want to talk about it and you and I want to get the job done. van

Now let's see...64,000 tons displacement is 128,000,000 lbs. That corresponds to (128/8) * (10)e6 gallons of water (8 lb/gallon). So as long as that tub has a cross sectional area at least large enough to leave a couple of inches of clearance between the hull and the tub wall, and is at least as tall as the ship's waterline depth, that puppy will float. Total contained volume of the tub will need to be about 18 million gallons to give a little bottom clearance.

Now who was that prophet (around the 17th century) suggesting that someday- metal will float on water? How obsurd!

Although the analysis offered as a solution to the battleship floating in the bathtub is interesting, it is wholly specious. Nice try with the bouyancy force integral, but that would only work in a closed system, and you have ignored atmospheric pressure component. Think of the battleship as a piston or a press in the bathtub: do you really think a 100 ton battleship could not press a significant amount of the supposed 100 gallons out and settle against the bottom of the tub?

I served as a Naval Gunfire Shorefire Spotter ashore in Lebanon (1983-84)with the USS New Jersey as a General Support Ship. I would like to add to the equasion that the scale ship that was described was Not to scale except in outside dimensions. The factor that was not considered was the THICKNESS of the steel that is used. The steel alone on the turrets is roughly 36" thick so the 1/100th scale would make this surface only approx 3/8". When you figure the internal thickness of the ship @ approx 1/2" to 1" thickness scaled down would be about as thick as aluminum foil... Regardless of the exact figures, a scale ship would not displace the 64,000 tons that the actual Missouri Class Battleship displaces... Any Metalurgists wanna give this some computations??

Its the draft of the ship that floats it. A 45,000 ton battleship draws about 40 ft of water. On the bottom area of the vessel you have 20 lbs PSI of hydrostatic pressure pushing up and it will be there on the high seas, drydock, bath tub. I f it is there, it will float. Put a pencil to it