Battleship´s displacement

[Karl Heidenreich]

I´ve been wondering about something curious:
Bismarck´s nominal displacement was of 41,700 tons, and at full load it went up to 50,900 tons.
Hood´s nominal displacement was of 43,144, and at full load it was of 49,136 tons.
So, Hood had greater displacement than Bismarck by herself, including Bismarck´s superior armour. That´s because at full load we measure fuel, amunition, water, etc. etc. The armour is contemplated in the nominal displacement, not at full load.
But displacement is not the same than sheer weight. Displacement is the weight of the water displaced by the ship´s hull. Bismarck displaced 41,700 cubic meters of water and Hood 43,144 cubic meters (around 1 ton per cubic meter). So, where is the weight that can give us the true comparison between the vessels? Because with the displacement other factors like draught, beam, lenght influence the result.
Am I right? Which was Bismarck´s and Hood´s real weight? Is it there a formula to obtain such result?

Regards!

[Tiornu]

Each navy had its own system of calculating displacement. There's no point in trying to be exact in it. Remember, for ships of this size, the paint alone can weigh several tons. It is sometimes said that full load displacement is the only true point of comparison, but in reality there is no such thing as full load--you can always add more. Just ask the Americans, who would sometimes load their battleships with thousands of tons of fuel above the nominal "emergency maximum" displacement for lengthy Pacific operations. Perhaps light displacement is the closest thing to an objective criterion.

[Karl Heidenreich]

What you say about maximun (full load) displacement sound quite right: the only maximun load is the one that doesn´t make the ship capsize. The logical issue is to evaluate the nominal displacement (ship empty) to compare one against the other.
In this order, then, Hood was slightly bigger than Bismarck. And that´s what I don´t understand because draught and beam of Bismarck are bigger than Hood (only in lenght the Hood is longer). If Bismarck was more armoured, how is it that Hood had more displacement?

[marcelo_malara]

Hi Karl:

A ship´s weight equals the weight of the displaced water. That is the Archimede´s principle. If the ship is heavier than the displaced water, she will go on sinking until the displaced water weight equals the ship´s weight. Weight and buoyancy are two oposite forces that must agree.

Your toughts about the displacement of both ships are interesting. The data I collected is:

..................Bismark.........Hood

LOA..............250.5 m........262.12 m
Beam..............36.0 m..........31.7 m
Design disp....45451 t.........41200 t
Draught at "........9.3 m...........8.6 m
Full load.........49406 t.........48360 t
Draught at "......10.2 m.........10.0 m

Hull..............12700 t.............14950 t
Power plant....4400 t...............5300 t
Armament......5500 t...............5200 t
Armour........18700 t..............13550 t
Subtotal.........41300 t ............39000 t
Fuel................4000 t...............1200 t
Design dis......45300 t..............40200 t
Max fuel..........8000 t...............4000 t
Max. displ......49300 t.............44200 t

Hood´s hull and and machinery are heavier. The first seems to come from the fact that she is longer. The second from the fact that Bismarck´s machinery is newer and lighter. The weight so saved (and a little more) went in Bismarck to the protection. I couldn´t find where the figure of the deep load condition of Hood of 49000 t comes from. Succesive refits added up to that weight (including a further 1000 t of fuel in 1931), the figures here are from 1917

[Karl Heidenreich]

Marcelo:

I read something that the RN added 5,000 tons of armour to Hood over her original design. But if that is true then that must happened before 1919 and not around WWII eve.

It´s interesting to see your data because on this same webpage Jose Rico puts Bismark at 50,900 tons full load and Hood at 49,136 tons full load either. Your data clear points that Bismarck, empty, displaces 45,300 tons vs. 41,200 of Hood, which clearly differs of this webpage data: 41,700 tons of Bismarck vs. 43,144 tons of Hood.

Your data points that even empty the Bismarck displaces more than Hood. And that makes sense if we consider all the armour the German BB had.

Best regards!

[Tiornu]

"If Bismarck was more armoured, how is it that Hood had more displacement?"
The weight of armor is no more significant than the weight of anything else on board.
A hull form inolves a lot more than length and beam and draft, just as a the "powerfulness" of a ship is a lot more than any equation can show.
Hood and Bismarck were roughly the same size.

[Tiornu]

This is why I hate statistics so much. They give the appearance of being informative when in fact they may be scheming to deceive you.
Hood's LIGHT displacement was approximately 41,125 tons. Bismarck's was near 39,000 tons. That's not the same thing as design displacement, which in fact might mean different things in different navies.
Note that the figures for Hood in Marcelo's list appear to be for the 1917 design, not for the ship as actually completed.
Let's put out the warning--don't rely on statistics as anything but a most general indicator, unless you have dug deeply enough to know what the really mean and don't mean.

[Karl Heidenreich]

Tiornu, I agree with your remark about statistics. But it´s the only way we have to discuss and stablish similarities and differences.
From where came this data about Bismarck light displacement of 39,000 tons?

[Tiornu]

Yes, you're right. The good thing about statistics is that they can give you a framework for increasing your knowledge.
Bismarck's light displacement is given in G&D (38,892 tons) and K&S (39,931 metric tonnes, which is 39,302 tons). Why the difference? Who knows? That's why stats are best as general indicators or when you can dig into their true meaning.

[RNfanDan]

Bear in mind too, that the German designers used Baltic Sea water densities when calculating displacements. Baltic water has a different specific gravity than many other saltwater bodies.

In other words, the weight of one cubic meter of seawater varies, depending on the body of water from which it is taken. Generally, the greater the salt content, the more bouyant the water. Put either ship in a US Great Lake (freshwater) or Lake Baikal, and they'd probably sink!

[marcelo_malara]

Mathematics and statistics should not be disregarded so lightly. After all, they modelled the modern world and all the technologies we have, so we will go back to the Stone Age if they are put aside.
Ship´s displacement is a very lenghty calculation, they are not just put on a scale. It involves calculating the volume of the submerged part of the ship, which in turn is not a box but a complex shape with curves in all dimensions and not a straight line except for the keel.
Add to this the fact that nominal, full, design...etc displacement means different things in different navies. For example the design displacement for Hood only takes into account 1200 t of fuel, while that for Bismarck takes 4000 t.
If we take the distribution of weight till the subtotal line they are almost equal. Bear in mind that there are many items I disregarded to focus on the major weights.
So my guess is:
-little differences in weights shoud not be taken into account, because of the difficulty of calculating the displacement accurately.
-when comparing different ships you have to know how the displacement is made up (for example the different quantities of fuel mentioned)
-the empty weight of both is very close. The armour of Hood is lighter and had to be disposed on a longer hull, making it thinner yet.

[Ulrich Rudofsky]

Bear in mind too, that the German designers used Baltic Sea water densities when calculating displacements. Baltic water has a different specific gravity than many other saltwater bodies.

That is a very important point. Most German ships and their equipment were tested in the Baltic. The specific gravity for the eastern portion is only 1.003 to 1.005, while the western Baltic is 1.012 to 1.015. The North Sea at the center is ~1.026. These values can vary with the tides and currents and must be checked during each test, acc. to Evers "Kriegsschiffbau". Volume = weight/sp. gr. ........ Archimedes......for a 50000 t ship the difference between the east Baltic and the Atlanic could be as much as 1000 t of displacement. Right? But I think balast may have been added to achieve the proper waterline for speed tests.

[ontheslipway]

for a 50000 t ship the difference between the east Baltic and the Atlanic could be as much as 1000 t of displacement. Right?

Wrong, displacement is the same but the volume differs.

Note that the light displacement is a definition. It may or may not include fuel, foeul in the pipes, food, ammo, cargo, lube oil etc. Differs per nation.

[Ulrich Rudofsky]

Boy, oh boy. I thought displacement is volume . I did flunked physics more than 50 years ago and the repeat was not a very glamorous achiement either.....thanks for the lesson.....

[ontheslipway]

Well, you could be right depending on your definition for ton. Normally a weight, but it can be a volume tonnage as well! (tunnage).