Can anyone provide a quantitative solution about the sinking of Titanic


Chung Rex

Member
Dec 25, 2006
50
10
98
I have tried to work out the solution by approximation, but it was difficult to calculate. For example, I have tried to assume there is equilibrium state of the ship when n compartments of Titanic was flooded(n = 1 to 16).

I know that exact solution would be nearly impossible, but I would like to hear any possible rough calculations for sinking of Titanic. However, I failed to find any of the calculations in books related to Titanic.

Thank you.
 
Dec 2, 2000
58,614
694
483
Easley South Carolina
>>However, I failed to find any of the calculations in books related to Titanic.<<

Perhaps that's because they're not relevant in terms of naval architecture so the precious few books which even bother to deal with forensics issues wouldn't even mention them. If you can get a copy, try "Titanic Ships Titanic Disasters" by Garzke and Woodward. Love it or lump it as you will, it presents the mathamatical principles that are relevant.
 
Sep 22, 2003
571
4
111
Coatesville, PA
I Would also recomend reading "Titanic Ships Titanic Disasters" by Garzke and Woodward. I can't say agree w/ them on everything, and in some in some places on the board they've had lots of Criticism. the book itself though is very useful as it explains a bucnh the stuff you asked about in simple terms
 
Dec 2, 2000
58,614
694
483
Easley South Carolina
Some of the history in the Garzke/Woodward book is a bit dodgy in my opinion, and the sourcing for some of the claims attributed to certain people had me scratching my skull, but the principles of naval architecture is pretty solid. As little heard from as that particular quarter is, I would say it's an important book to have in your collection.

One of the big problems in this area of interest is that naval architects and professional mariners spend a lot of time talking at each other rather then with each other. (There's a difference!) In the latter approach, both listen to and learn from each other.
 
Mar 22, 2003
6,134
1,491
383
Chicago, IL, USA
www.titanicology.com
quote:

One of the big problems in this area of interest is that naval architects and professional mariners spend a lot of time talking at each other rather then with each other.

I'm sure you will agree that it is not just naval architects and profession mariners with that problem. You see a lot of that in many professions I'm afraid, especially by those that consider themselves experts rather than students of a subject.

I never saw the Garzke/Woodward book, but there is also the work of Hackett and Bedford that was published and makes for a good reference if you have some of the background already. Like any analysis, the results are only as good as the model that is created based on certain assumptions that have to be made. Also, the validity of the input data and assumptions that are used. Sometimes I find that results that come out of these types of studies become accepted as a reality. Many times stated caveats are simply ignored, or results are not adequately cross checked with other evidence.​
 
Dec 4, 2000
3,242
535
278
Sam-- Your original answer to this question was a bit of a disappointment. You were, of course, correct. However, all you gave us was a taste of the frosting and not the whole cupcake.

I suspect a lot of people are confused by the idea that water coming into the ship was not the cause of the loss of Titanic. Stability is the key to what took place. I know you can expand on what you wrote without producing a treatise on naval architecture. There are those on this board who would welcome an expanded, but simple explanation.

Thanks.

-- David G. Brown
 
Mar 22, 2003
6,134
1,491
383
Chicago, IL, USA
www.titanicology.com
Good suggestion David, but I only had time for the frosting as you put it. If I have more time later today or over the weekend I'll be glad to do as you suggest. If anyone else want's to explain it before I do, please feel free to do so. Of course the complexity in all of this is the added fact that the ship broke in two near the end. That I cannot discuss at this time.
 
Dec 2, 2000
58,614
694
483
Easley South Carolina
>>I'm sure you will agree that it is not just naval architects and profession mariners with that problem.<<

You're right. I do agree with that. In this instance, what's at issue is that two different but related diciplines have pieces of the puzzle which they have the training and experience to understand. The catch is that each might get the idea that it's the whole picture when it's not.

>>I never saw the Garzke/Woodward book, but there is also the work of Hackett and Bedford that was published and makes for a good reference if you have some of the background already.<<

I have both at my disposal. The Garzke/Woodward work is something you'll have to get on the used book networks as it's long out of print, but I think you'll find it useful.

BTW, if anybody wants to get a down and dirty understanding of at least one of the aspects of ship stability that Samuel is talking about, go to; http://www.navweaps.com/index_tech/tech-009.htm
 
Sep 22, 2003
571
4
111
Coatesville, PA
Acutually I think the book is still Available from the Publisher. sname.org Quiite pricey though at $50.00 US. I have never seen this book on a site for used books, It might be now though as I have not looked recently
 
Mar 22, 2003
6,134
1,491
383
Chicago, IL, USA
www.titanicology.com
OK David, I love these challenges you throw at me. As a professional technical instructor I often find it necessary to explain difficult concepts without going into all the technical details or the math, even when teaching technical students. So without a treatise on naval architecture, or GM or GZ curves, here goes.

The example I'll use is small pontoon boat that was built to hold say 9 average people. We then will load the boat above its design capacity by first adding 3 more people, then 3 more again. But we will do this two different ways. The first way is to distribute the added load uniformly across the length of the boat. The second way is to add all the extra people to the bow section of the boat. The picture, yes I need to illustrate it, is shown below.

119211.gif

On the left side is the symmetrical loading. As more and more people are put into the boat, the boat will get deeper into the water displacing more and more water equal to the added weight. Despite the increase in weight and buoyancy, the center of all the buoyant forces (called the center of buoyancy, CB) will remain directly under the center of gravity (CG), the point at which all of the weight of the loaded boat appears to be concentrated at. (It's also the balancing point of the loaded boat.) As long as these two balancing forces remain acting on the same line one above the other, the boat will remain essentially stable.

On the right side of diagram we are loading the same number of extra people all forward of amidships into the bow area. This creates unsymmetrical loading and with it some problems in stability. By putting all the extra people forward, the added weight shifts the center of gravity forward. That means the boat not only has to displace more water a before, but it has to displace more water forward of amidships than aft of amidships in order to balance out the extra weight that was put there. Notice that there is more profile area below the waterline forward of amidships than aft of amidships. The boat will tip as shown until the new center of buoyancy falls directly under the new center of gravity. The total volume of water displaced by the boat on the right side of the diagram is exactly the same as the total volume displaced on the left side of the diagram because the total number of people in the boat is the same. However, the weights are shifted very differently as shown. With only 3 more people added, the boat on the right side is still stable but it is down by the head instead of being level with the waterline as in the case of the boat to the left.

Now suppose we add 3 more people forward. The center of gravity continues to move more forward away from amidships. The boat needs to settle deeper to displace more water to balance out the increased weight. But, as before, it also has to shift its center of buoyancy more forward to fall under the new center of gravity. But in this case an angle is reached where the under water profile area forward is not enough to shift the center of buoyancy far enough to fall under the new center of gravity. When this happens we have two forces acting in opposite directions (buoyance up, weight down) that just don't want to line up one under the other. The upward buoyancy force is to the left of the downward force of the loaded weight of the boat. The result, as shown, is a turning moment which causes the boat to rotate around what's called the center of floatation (CF) with the bow going down, the stern going up, until it achieves the vertical if the hull is strong enough not to break beforehand.

In the case of the Titanic, it was water flood into the ship that added the extra weight. Despite her head getting lower and lower as the night wore on, the ship was relatively stable until near the end when things started to develope a bit more rapidly.

A capsizing, by the way, is the same thing but a rotation in the transverse direction.
 

Tim Foecke

Member
Jul 16, 2003
134
2
111
Sam,

Not to be a pit-nicker, but the ship sank EXACTLY because of how much water came into her. She may have become *unstable* because of *how* the water came in, but if she had been airtight beyond the point of instability, she would have floated stern-up. She sank when the water displaced all the air. Even in your diagram, the sinking is due to more water coming in over the gunwale.

Just the physicist in me. Sorry
 
Mar 22, 2003
6,134
1,491
383
Chicago, IL, USA
www.titanicology.com
Pit-nicking is fine with me. But the point I was making is that in the case of the boat on the left, it doesn't sink but remains afloat in a fairly stable condition. On the right side it sank because it became unstable allowing for a loss of all reserve buoyancy. In the case of the Titanic the same was true. If the same amount of damage could have been spread uniformly across all 16 compartments instead of being confined primarily to the first 5 compartments, the ship would have probably stayed afloat for a number of hours longer. This assumes that a loss of transverse stability doesn't develop beforehand.
 
Dec 4, 2000
3,242
535
278
As both Sam and Dr. Foecke are friends, I feel some guilt from creating the situation that appears to have put them at loggerheads. However, the truth is both are 100% correct. They are really talking about two different--but closely related--topics.

"Sinking" and "stability" are not the same thing. A ship can be quite unstable and float, provided it is watertight. My pontoon boat ferry is a good example. The 'toons are filled with closed-cell foam and are in that sense "unsinkable." But, the vessel can be unstable and capsize as one did in Baltimore harbor a few years ago.

Likewise, a ship can be completely stable and sink. Every submarine accomplishes this on every dive. The vessel becomes heavier than the water it displaces, so sinks, but submarines remain stable in both the transverse and longitudinal directions.

As Dr. Foecke pointed out, normal ships sink when their interior spaces fill with water. (Submarines do not fill in the same sense.) In simple terms, they become heavier than the amount of water they displace. We could sink a ship by filling it with hot lead or feathers, it matters not--just so long as the ship weighs more than the displaced water.

Think of the displaced water as much like the pile of dirt from digging a cellar hole in the ground. In this case, however, the water is not in a pile, but pushed aside in all directions. The cellar hole is the dry area inside the ship suitable for carrying engines, people, and cargo.

Steel sinks. What keeps any ship afloat is the buoyancy created by that "cellar hole" space inside the hull. The space is normally filled with air, but it could be a vacuum and still provide buoyancy. The reason is that buoyancy is really the pressure of the displaced water trying to fill that cellar hole space inside the ship. Water can't get through the steel, so pushes upward on the bottom with a force equal to the weight of the displaced volume.

When you knock a hole in the hull with an iceberg, water rushes in. The amount of buoyancy available to the ship decreases in proportion to the weight of that ingress.

Now to stability. Sam's diagram is loosely based on my pontoon boat ferry upon which we embarked last fall on an expedition to the museum ship SS Willis Boyer. His diagram and explanation of longitudinal buoyancy is exactly correct. And, in point of fact, I am dealing with precisely the problem he outlines in my real boat.

People (other than me as I have achieved the new norm well ahead of schedule) are getting fatter. The Coast Guard will be increasing the per passenger weight from 140 to 185 pounds shortly. That increase will mean we either have to reduce the passenger capacity of our boat, or remove some of the "dead weight" (other than the captain).

Our plans are to reduce the engine size by 136 pounds, remove a 45 pound battery, and take off about 80 pounds of fuel to save weight for passengers. Once those changes are made, we will have to create exactly the longitudinal capsize situation Sam diagramed. We will do this with the real boat in stability tests performed for the Coast Guard. Instead of drowning passengers, however, we will use measured weight sandbags to test the boat's ability to resist a longitudinal capsize. We will move all of the sandbags toward the aft end where the engine, batteries, etc. are located.

In Titanic, the tipping was not done by sandbags, but by loss of buoyancy from incoming water. That loss caused the bow to sink downward. The amount of water inside the ship had not become "fatal" in the sense of overcoming the overall buoyancy of the hull when the ship lost stability.

As Sam points out, on a strictly weight-to-buoyancy relationship Titanic was still OK when the ship began to go unstable. We know it was going unstable for two reasons. First was the lifting of the stern out of the water. And, second (but perhaps of more importance with regard to stability) the ship lost its starboard list, rolled upright, and then continued into what effectively became a death roll to port.

As the ship tipped, the shape the hull presented to the water changed. This is a complicated concept which naval architects sum up with the one word description "waterplane." In simplest terms, the buoyancy was no longer spread over the whole length of the ship. It became concentrated near the "tipping center" around which the hull was rotating longitudinally. In human terms, instead of being well balanced with legs wide-spread, the ship was trying to stand upright on one leg.

As stability was lost the bow tipped downward even more and the internal waterline soon exceeded the height of the w/t bulkheads. That was a minor matter compared to the secondary downflooding that began as hatches, companionways, port holes, and other openings were submerged. Massive ingress occurred with the breakup.

It was this secondary water that erased the ship's buoyancy. The death of Titanic, as Dr. Foecke pointed out, was as inevitable as the sinking of a rowboat when water tumbles over the gunwale. Bits and pieces of what had been Titanic went on their final journey to the ocean bottom.

In the end, loss of stability and loss of buoyancy were like sharks in a feeding frenzy on the carcass of Titanic.

-- David G. Brown
 
Dec 2, 2000
58,614
694
483
Easley South Carolina
Might be interesting to get Sam, and Tim together in the same room the next time The Scotland Road Irregulars gets togther for a face to face meet. Bring Roy Mengot in as well, get them togther with the mariners to work things out and I think the result will be a much better understanding of how the Titanic sank and why she behaved as she did as she went down.

A team like this which collectively understands both the science and the art of shipbuilding, and shiphandling would be tough to beat.
 
Feb 23, 2007
81
1
86
Very interesting guys. All things being equal, water doesn't have anything to do with it per se, other than being the instrument. David hit it on the head by saying the "loss of buoyancy". Whether this is achieved by adding weight in the form of objects or by adding water it makes no difference as long as you defeat buoyancy the object will sink. Not being an expert or reading any of the aforementioned books I can only base this on what I see everyday. since weight has everything to do with displacement it stands to reason that buoyancy is tied in to the weight displacement issue. The way it, {weight}, is distributed along the displacement curve is all that matters as to the way an object will sink or float. This is why the trades of the time thought the Titanic was practically unsinkable. They could not conceive the ship sustaining the type of damage it took. They assumed that the damage that the ship might occur was similar to what was the norm of the day. I.E. head on into the side of a ship or berg, running aground etc. The ship builders conceived of these types of accidents also. The ship would have survived these types of accidents probably, Even with the same amount of water taken in. They designed it to take damage to four compartments even to the point of flooding completely. Which is what Sam illustrates in his diagrams. Which is how the ship actually sunk but it would have sunk by flooding four compartments in a row anywhere along the line. Even with the four middle compartments. Simply by defeating the buoyancy, weight/displacement equation . I know this probably doesn't help much it is just my view which can be completely off line at times. Tom
 
Mar 22, 2003
6,134
1,491
383
Chicago, IL, USA
www.titanicology.com
Yes, there are no loggerheads here. We are all on the same page.

What Dave said about submarines is a good example of something that can sink under control and remain stable. It sinks because they initially add weight by allowing water to fill empty ballast tanks to the point were the loaded weight of the boat is greater than the weight of the water displaced by the sealed hull shape. If the loaded weight remains greater than the displaced water it would sink until it hits bottom. But on a submarine they will blow out some of the water in one of the variable ballast tanks so that the total loaded weight of the boat equals exactly the displaced weight of the water. What they try to achieve is a condition of neutral buoyancy, where the boat weighs exactly the same as the displaced water and has no tendency to rise or sink. (Airships use the same principle.) They then control the boat in three dimensions by being propelled through the water using the planes and rudders.

Hey, for those you who like to play with toys try this. Take one of those plastic 35 mm film containers and place 5 US nickles in it. Seal it with the cap and place it in a basin filled with water. It should just float. Now open the container and start to add a few drops of water at a time, reseal it and see if stays afloat. Keep doing this until it seams that it doesn't want to either float or sink. (If it sinks to bottom you added too many drops of water. Just spill out a few to get it just right. It may take a bit of time to get it exactly right.) When that condition is reached, you achieved neutral buoyancy. Have fun!
 
Feb 7, 2005
331
1
111
Sounds like fun, Sam! I'll have to try it. Thanks, by the way, for the lovely artwork (above) that makes understanding bouyancy and stability easier for nautical slow learners like me! ;-) The visuals, when added to your very clear explanations, really help.

Tom Goldsmith--I know another Tom Goldsmith who lives in Ashland, Ohio. You two must be related, as Tom in Ashland is Titanic survivor Frank Goldsmith's grandson. Nice to see you on the boards!

Denise
 

Similar threads

Similar threads