Metacentric Height & GZ


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Oct 28, 2000
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Attention rivet counters--here are a couple or three "doozie" questions: Does anyone have a reference on Titanic's metacentric height at its normal draft? Along the same lines, what was the righting moment? And, how many tons of additional weight did it take to increase Titanic's draft by one inch?

--David G. Brown
 
Jan 5, 2001
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Hi!

I may be able to offer help on one:

And, how many tons of additional weight did it take to increase Titanic's draft by one inch?

I may be on the wrong thing here,
blush.gif
but part of an earlier table shows roughly the displacement difference (figures from Edward Wilding and Thomas Andrews, so pretty accurate).

<table border=1>[tr][td]33 feet 6 inches - - - - 50500 tons [/td][/tr][tr][td]34 feet 0 inches - - - - 51340 tons [/td][/tr][tr][td]34 feet 7 inches - - - - 52310 tons[/td][/tr][/table]

Best regards,

Mark.
 
Oct 28, 2000
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Thanks, Mark. I've seen those numbers, but I was looking for the official "tons per inch" calculations--if they exist. Your numbers can suffice, however.

--David G. Brown
 
Jan 5, 2001
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Hi Dave!

I am sorry I couldn't be more precise -- all we can guestimate of course is that the displacement increases by 1,810 tons when the draft increases by thirteen inches.

Or
1,810/13 inches = 139.2 tons​

I suppose it would vary depending on the exact draft -- I mean, the difference between 21 and 22 feet would be much different to between 37 and 38 feet, due to variations in hull shape, etc.

Best regards,

Mark.
 

Bill Sauder

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Nov 14, 2000
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Dave:

1. How many tons of additional weight did it take to increase Titanic's draft by one inch?

This is commonly referred to "Tons per Inch" or TPI. It varies with draft. The "legal" draft for Titanic (assigned to her by the BOT and confirmed by the Wilding Testimony at the British Inquiry (summarized in ENGINEERING JUNE 14, 1912, p803: Also MERSY REPORT p7
) is:

34'-7" which corresponds to a displacement of 52,310 Long Tons (salt water immersion)

and a deadweight (cargo capacity) of 11,390 Long Tons.


At this draught, the TPI is 144.6 Long Tons

It should be pointed out that because of Olympic's fairly boxy hull, the TPI remains nearly constant at ordinary draughts.


2 What was Titanic's Metacentric Height?

From memory, it was about four feet, departure condition. I saw the number many years ago in an archive in England, but the notes and copies that I made were lost by the airline. The number is quite similar to that for Aquitania (See her Shipbuilder) and fits nicely between Lusitania's 3-0 and Queen Mary's 5-0.

If there are any truly ambitious naval architect students out there, you can calculate it for yourself. At the above displacement (52,310) the Transverse Metacenter is 37.70 feet above the baseline.
The Center of Buoyancy can be calculated from the ship's form taken from hull lines now fairly available.


3 What was the righting moment?


I don't know. I've never seen the figure, but it too can be calculated.


Now my question Dave: What do you want this poo-poo for?

Bill
 
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Bill -- a million thanks.

I've been reading about the design of late 19th and early 20th century passenger ships. Especially those of the 1890 to about 1900 era. There seems to have been a trend to lower the GZ to a rather questionable (by modern standards) amount in order to provide a "more comfortable" ride for passengers. Apparently, people objected to the snap roll of a vessel with a high metacenter...or at least that's what the author of this book is claiming. So, I got curious about Titanic. And, I knew that somebody...somewhere on the ET forum...for some odd reason... has been waiting to provide the answers. Now, I'm not sure where to go with the numbers, but I've warmed up my TI-58 calculator with the marine nav pack and maybe I'll be able to bore myself to sleep tonight punching numbers.

For the idle curiosity of it, the last large ferry I worked had a metacentric height of about 4.5 feet on a length of 64 and beam of 20. We were in the process of ordering stabilizers when the company sold the boat. To calculate the height I actually used the transom (out of the water) as my "drafting board" and worked it out graphically at a 1:1 ratio. That was five years ago and at the moment I'm unable to remember all of the details of how to do it. Have to go back to my reference library.

--David G. Brown
 

Bill Sauder

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Dave writes:

There seems to have been a trend to lower the GZ to a rather questionable
(by modern standards) amount in order to provide a "more comfortable"
ride for passengers.


What book did you get this information out of? I'm not in the least surprised but I'd like to see it documented.

Campania got by with a metacentric height of 2-9. Battleships (W.W.II American) run about 11 feet. This is to provide a dead-level gun platform and ensure the ship never heels over too far. Their small freeboard makes them vulnerable to swamping. Sailing ships are about the same or larger to resist the press of sail.

The stunning example of a ship with a too-small metacentric height is the Imperator in her original configuration. Reducing the height of a passenger ship's metacenter is not necessarily a bad thing ... the vessel will become more comfortable to ride since metacentric height measures how urgently a ship will return to vertical when rolling.

Since passenger liners have very, very high freeboard and fixed weights (unlike cargo ships) there's very little danger of them tipping over. The Queen Mary, for example must heel over 110 degrees before she flips (the righting arm becomes negative) a la the Poseidon.

The disadvantage of those "comfortably low" metacentric heights is that the ships will have a tendency to hang on a roll, assume a heel in a beam wind and, at the end of a voyage, the metacentric height may become negative, causing the ship to "loll" to one side.

As Maxtone Graham points in "The Only Way to Cross," there's hardly a photo of the Imperator's fabulous swimming pool that actually has the waterline match the tile line in the pool.

I assume the Germans had second thoughts and dropped the center of gravity for the Vaterland and Bismarck, since there are no reports of these problems in the later vessels. I would certainly like to know what W.F. Gibbs thought of the stability of Vaterland and the modifications he made for her conversion to Leviathan.

Bill Sauder
 
Oct 28, 2000
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Bill -- you're comments about metacentric height pretty much follow what I have read elsewhere. The book is a 1960s vintage effort by K.C. Barnaby of the Royal Instituion of Naval Architects called "Some Ship Disasters And Their Causes." A few of the thoughts expressed seemed odd, such as deliberately using low metacentric height to improve the comfort of the passengers.

The sort of roll that he is talking about would, from my experience, be quite likely to produce sea sick passengers. A queasy stomach is not much to enjoy.

I have wondered if perhaps lowering the metacenter was not in part motivated by those tall "stovepipe" funnels. A quick roll in a seaway would strain the stays and mountings of those funnels. Sailing warships needed relatively high metacentric heights and were notorious for "rolling out their sticks" as a result. Raising a cannon to the top was one way of increasing the roll and easing the strain on the masts and standing rigging. Interestingly, Barnaby brings this up in his book with regard to the loss of H.M.S. Captain.

The only time I've been on a boat that had the sort of "comfortable roll" resulting from a low metacenter, it was sinking. This was decidedly not a comfortable situation, although we all came through with dry feet.

By the way, the book contains the following dedication: "To the Memory of Two Much Maligned Master Mariners Captain Richard Dawkins R.N. of H.M.S. 'Vanguard' and Captain Stanley Lord of the S.S. 'Californian.'"

--David G. Brown
 

Erik Wood

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Metacentric height and it's associated weight played a very big role in the design of the Voyager of the Seas as well as the Carnvial Destiny series of ships. From mid deck up the ship is made out of a lighter grade of steel that weighs something like a quarter of the normal grade of steel used.

This makes it so ships with high decks are able sustain large waves by keeping the weight of the ship (or the ships center of gravity) less then 20 feet above the water line. The Voyager of the Seas is one of those ships that is like 8 stories tall or something like that. But if her entire superstructure was made of the same steel one 15 foot wave would have rolled her and sank her.

Erik
 

Cal Haines

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I have slightly different numbers than Bill's:

From the appendix of the guide booklet for "Titanic: The Official Story -- April 14-15, 1912", Random House, Inc., 1997. (This is the little box containing facsimile's of 18 documents from the British Public Record Office.)

The appendix is a single page, titled "Particulars of Ships Built by Harland and Wolff - Entries for the Olympic and Titanic". It appears to be two rows from some sort of ledger. I count 81 columns of data. You may find the following interesting:

Load Conditions:
Dft. 34'7"
Disp. 52,310
Tons per Inch 143.8
D.W. 14,030 (400)
D.W. 13,550 (401)
Block Coef. .684
Prism. Coef. .705

Light Conditions:
Dft. 26'4" (400)
Dft. 26'7-1/2" (401)
Tons per Inch 138.8
G.M. .87 (400 only)
Block Coef. .660 (400 only)

(values for Olympic (400) and Titanic (401) are the same, except as indicated)

It's interesting that the table only has a space for G.M. at light conditions--anyone care to hazard a guess as to why?

Cal
 
Aug 10, 2002
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I'm looking for information on Titanic's Cross Curves, Statical Stability Curves, Hydrostatic Data, Curves of Form, Displacements, Light and Loaded. Does anyone know any sources for this information?
Charlie Weeks
 

Erik Wood

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Charlie I have a copy of the Andrew's notebook. I will attempt to get a copy of it off to you.
 
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