Could an improvised barrier have been rigged up on Titanic's E deck to slow the flooding?


Could an improvised barrier have been rigged up on Titanic's E deck above the E bulkhead, and would it have delayed the flooding for long enough to save those left on board? I understand Captain Smith was trying to find the Carpenter after he had 'sounded the ship' with Andrews, could this have been what they were thinking of?

The Titanic took on around 10,000 tonnes of water in the first 40 minutes after the iceberg collision; this compares with its displacement of approximately 50,000 tonnes. The net rate of flooding rapidly reduced to around 1000 tonnes/hr as the height of water built up above the breached portions of the hull, and the pumps were put on line. These figures are based on flooding rate estimates from Figure 10: 'Time history of total floodwater' in Stettler & Thomas. However, after that time there was a gradual increase in flowrate, eventually leading to the ship sinking about 2 hours 40 minutes after the collision.

The water must have moved along the two corridors of E deck across the top of bulkheads until it met stairs which led down to F deck giving the water free access to another compartment to flood. This pushed the ship down further, moving the water further along E deck until it met more stairs across another bulkhead and so on. These two corridors were key channels for rapidly flooding lower and aft parts of the ship without having to increase the head of water which otherwise would have slowed it further.

Therefore, perhaps the best place a barrier to stop the flooding propogating down the ship was directly over the E bulkhead on E deck, effectively extending the E bulkhead upwards. I suggest if carpentry tools and any accessible timber from the store had been taken to this spot by 00:25 when the water started reaching this line, perhaps there was have been a good chance of erecting a temporary barrier. This might have provided the extra time needed for a rescue the occupants or even save the ship.

How would this have been implemented in the short time available? I suggest an improvised 2-3 foot high wood panel, possibly made of a door, tables or (if time permitted) cut from timber wedged between the starboard corridor walls, followed by the wider 'Scotland Rd' corridor. Tarpaulin cut from the hold covers could have been used as well, although a perfect seal wouldn't have been necessary. The barriers should then have been supported and buttressed by further strips of wood nailed up the walls and along the floor behind the panel, stopping water flowing along the bottom of the corridors. Starting with a low barrier height and building it up would have allowed workmen or stragglers from the rooms just in front of the barriers who couldn't reach the stairs to D deck. Once this had been completed, some attention could have been given to sealing any doors across the new bulkhead line. In the hours ahead, these doors and walls could have been buttressed as the height of water and pressure increased.

How much time would a barrier blocking off the E deck above the E bulkhead have given the Titanic? The net flooding rate around 1 hour after the collision (~1,000 tonnes/hr) can be compared with how much water the barrier could hold up towards the bow. For a rough estimate of volume, the area from the barrier to the bow is assumed to be a simple triangle with its base at the barrier and apex at the bow. Obviously this underestimates the volume of the ship towards the bow, but this allows for some of the space taken by structures such as furniture and goods. The average height of water is estimated from lines drawn from the centre of turning (from Halpern), through the bottom and top of the barrier towards the stern. This is coloured green in the attached diagram. Since the angles assume ingress of water to the stern of E the ship, rather than being held up this is only a ball point figure. The answer is 3788 cubic metres which gives an extra 3 hours 47 minutes or until 04:12, around the time the Carpathia arrives.

The second way is to assume an asymptotic relationship between water height up the bulkhead and flood rate. This assumes the flooding reduces to zero at some bulkhead height, as would be expected from theory if the extended barriers were completely successful, and this was the only flooding line. The height is determined by curve fitting five points between 11:40 and 0:25 hrs using an asymptotic model between flow and time after impact. Then the flow at later time periods can be estimated. This suggests the flooding would stop after 13,218 tonnes of water had entered the ship, or 2850 tonnes had been held up behind the barriers which takes the water to about 75% of the way up the new barriers. The same type of model can be used to relate the angle of trim to time after impact, from Halpern. This suggests the height of water would stop around the top of such E deck barriers, or the top of the green area.

H&W's naval architect Edward Wilding presented a plan which showed how the Titanic would trim down by the head as individual compartments are flooded. A screen-capture of a gif file from his findings (3) illustrates the height of water which would be reached after the first five compartments have filled, which is approximately what we are trying to determine here. This indicates the water will reach about 15% over the height of bulkhead E or a trim angle of 4.2 degrees. This is the approximately height of E corridor, the same as in the 'angle of trim' calculation above. The sequence also suggests that the front upper compartment probably remained dry until the water level on E deck reached a certain height. So shoring up E deck may have provided enough time to prepare a barrier there as well.

The accuracy of these calculations depend on reading flows, angles and lengths from the graphs and diagrams in the references, since I don't have access to the exact figures. It also ignores any potential increase in flooding rate in boiler rooms 4 and 5 after 00:25 which could overcome the pumps. The rush of water observed between the boilers in boiler room 5 observed later was probably the coal bunker wall fracturing from the head of water built up in that space. This would have merely redistributed the water over that wider area, although the reduced head would increase the flow again. There's also some evidence that the flooding in boiler rooms 4 and 5 was relatively small and the pumps were successful at controlling the flooding here at least for a time. Perhaps these rooms were abandoned due to flooding seeping in from G deck above or trapping the exits, rather than from below? This wouldn't have happened if the E bulkhead had been raised.

References
(1) Figure 10 Flooding and Structural Forensic Analysis of the Sinking of the RMS Titanic J.W. Stettler (M), B.S. Thomas (M)
(2) Page 2 Angles of Trim and Heel (Revised August 2017) Samuel Halpern
(3) FloodingByCompartment
 

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Titanic was taking on the equivalent of the contents of an olympic sized swimming pool every 7.5 minutes.
An Olympic pool has 660,253.09 gallons of water, which
equals about 5,511,556 lbs.
Even at a reduced rate, I don't see how you could stop the weight from pulling the bow down and I'm trying to think of what sort of improvised barrier(s) and who would construct them?
Wouldn't that take officers and crewman away from the boats?
I'm not an architect or an engineer, and I admire the time and thought that you have put into this; obviously a lot!
But given the obstacles-- the biggest being time... I don't see how it could be done. The other obstacles are manpower, while filling the boats, and keeping the passengers from widespread panic.
The last obstacle is the weight of the water-- wouldn't it blow the barrier loose once the pressure built up enough?
It's a tall order-- but an interesting idea.
 
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Thomas Krom

Member
Hello gentlemen,



I personally do not believe that an improvised barrier on E-deck forward could not guarantee a difference in the time it took the Titanic to sink.


If the water stopped at this improved barrier it would mean that more water would be focused in flooding the third class permanent. There were multiple stairwells nearby the third class permanent which led to the third class open space on D-deck and the third class open space was connected to a small stairwell which would flood up the crew areas under the forecastle on C-deck. This stairwell was primarily used by the able seamen to reach their dormitory on E-deck. If it flooded up quicker to D and C-deck forward it would mean that the store rooms above the forepeak tank would have flooded quicker as well. If this didn’t decreased the buoyancy it would have caused a higher angle earlier in the sinking around 1 o’clock. Seen it is presumed that the non-watertight door of boiler room number 5 burst open due the pressure of the 180 tons of water in it which is behind this suggested barrier it would sadly meant that the water would have flooded behind it anyway. The ship sadly wouldn’t be able to stay afloat even with this improvised barrier.



I hope this shares some light on this suggested scenario.





Yours sincerely,



Thomas
 
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Jim Currie

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Could an improvised barrier have been rigged up on Titanic's E deck above the E bulkhead, and would it have delayed the flooding for long enough to save those left on board? I understand Captain Smith was trying to find the Carpenter after he had 'sounded the ship' with Andrews, could this have been what they were thinking of?

The Titanic took on around 10,000 tonnes of water in the first 40 minutes after the iceberg collision; this compares with its displacement of approximately 50,000 tonnes. The net rate of flooding rapidly reduced to around 1000 tonnes/hr as the height of water built up above the breached portions of the hull, and the pumps were put on line. These figures are based on flooding rate estimates from Figure 10: 'Time history of total floodwater' in Stettler & Thomas. However, after that time there was a gradual increase in flowrate, eventually leading to the ship sinking about 2 hours 40 minutes after the collision.

The water must have moved along the two corridors of E deck across the top of bulkheads until it met stairs which led down to F deck giving the water free access to another compartment to flood. This pushed the ship down further, moving the water further along E deck until it met more stairs across another bulkhead and so on. These two corridors were key channels for rapidly flooding lower and aft parts of the ship without having to increase the head of water which otherwise would have slowed it further.

Therefore, perhaps the best place a barrier to stop the flooding propogating down the ship was directly over the E bulkhead on E deck, effectively extending the E bulkhead upwards. I suggest if carpentry tools and any accessible timber from the store had been taken to this spot by 00:25 when the water started reaching this line, perhaps there was have been a good chance of erecting a temporary barrier. This might have provided the extra time needed for a rescue the occupants or even save the ship.

How would this have been implemented in the short time available? I suggest an improvised 2-3 foot high wood panel, possibly made of a door, tables or (if time permitted) cut from timber wedged between the starboard corridor walls, followed by the wider 'Scotland Rd' corridor. Tarpaulin cut from the hold covers could have been used as well, although a perfect seal wouldn't have been necessary. The barriers should then have been supported and buttressed by further strips of wood nailed up the walls and along the floor behind the panel, stopping water flowing along the bottom of the corridors. Starting with a low barrier height and building it up would have allowed workmen or stragglers from the rooms just in front of the barriers who couldn't reach the stairs to D deck. Once this had been completed, some attention could have been given to sealing any doors across the new bulkhead line. In the hours ahead, these doors and walls could have been buttressed as the height of water and pressure increased.

How much time would a barrier blocking off the E deck above the E bulkhead have given the Titanic? The net flooding rate around 1 hour after the collision (~1,000 tonnes/hr) can be compared with how much water the barrier could hold up towards the bow. For a rough estimate of volume, the area from the barrier to the bow is assumed to be a simple triangle with its base at the barrier and apex at the bow. Obviously this underestimates the volume of the ship towards the bow, but this allows for some of the space taken by structures such as furniture and goods. The average height of water is estimated from lines drawn from the centre of turning (from Halpern), through the bottom and top of the barrier towards the stern. This is coloured green in the attached diagram. Since the angles assume ingress of water to the stern of E the ship, rather than being held up this is only a ball point figure. The answer is 3788 cubic metres which gives an extra 3 hours 47 minutes or until 04:12, around the time the Carpathia arrives.

The second way is to assume an asymptotic relationship between water height up the bulkhead and flood rate. This assumes the flooding reduces to zero at some bulkhead height, as would be expected from theory if the extended barriers were completely successful, and this was the only flooding line. The height is determined by curve fitting five points between 11:40 and 0:25 hrs using an asymptotic model between flow and time after impact. Then the flow at later time periods can be estimated. This suggests the flooding would stop after 13,218 tonnes of water had entered the ship, or 2850 tonnes had been held up behind the barriers which takes the water to about 75% of the way up the new barriers. The same type of model can be used to relate the angle of trim to time after impact, from Halpern. This suggests the height of water would stop around the top of such E deck barriers, or the top of the green area.

H&W's naval architect Edward Wilding presented a plan which showed how the Titanic would trim down by the head as individual compartments are flooded. A screen-capture of a gif file from his findings (3) illustrates the height of water which would be reached after the first five compartments have filled, which is approximately what we are trying to determine here. This indicates the water will reach about 15% over the height of bulkhead E or a trim angle of 4.2 degrees. This is the approximately height of E corridor, the same as in the 'angle of trim' calculation above. The sequence also suggests that the front upper compartment probably remained dry until the water level on E deck reached a certain height. So shoring up E deck may have provided enough time to prepare a barrier there as well.

The accuracy of these calculations depend on reading flows, angles and lengths from the graphs and diagrams in the references, since I don't have access to the exact figures. It also ignores any potential increase in flooding rate in boiler rooms 4 and 5 after 00:25 which could overcome the pumps. The rush of water observed between the boilers in boiler room 5 observed later was probably the coal bunker wall fracturing from the head of water built up in that space. This would have merely redistributed the water over that wider area, although the reduced head would increase the flow again. There's also some evidence that the flooding in boiler rooms 4 and 5 was relatively small and the pumps were successful at controlling the flooding here at least for a time. Perhaps these rooms were abandoned due to flooding seeping in from G deck above or trapping the exits, rather than from below? This wouldn't have happened if the E bulkhead had been raised.

References
(1) Figure 10 Flooding and Structural Forensic Analysis of the Sinking of the RMS Titanic J.W. Stettler (M), B.S. Thomas (M)
(2) Page 2 Angles of Trim and Heel (Revised August 2017) Samuel Halpern
(3) FloodingByCompartment
In a word...no!

For such an idea to have any hope of succeeding you require athwartship - side to side continuity of wt integrity/strength above WT Bulkhead C.
A look at the plan shows you this would not be practical given the time. The water would meet your bulkheads, rise, then enter sideways into the compartments and bypass the corridor bulkheads.

A Ship's Carpenter had little carpentry work to do. In fact, one of his main jobs was to maintain a running record of the contents of all the ship's water storage compartments, including bilges and ballast tanks. He normally went around them daily and, using a sounding line, measured the contents and /or ensured they were dry. He would fill in his record book and take it to the Chief Officer every morning. When Smith called for the Carpenter, it was for the latter to sound the tanks and compartments to determine the rate of flooding. Only by consulting th Carpenter's book could they know which compartment was broached.
 
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Always fun to think outside the box and try to "Macgyver" something but like Jim said...No. Not enough time and what materials would have been used to build it? Wall paneling from first class spaces? Given the time they had I just can't come up with something that would hold the water back. But I did like the charts you showed. Cheers.
 
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Incony

Member
a metric tonne of water cannot be compressed, its a cubic metre of water at 4 deg C. so a little over 3ft high.. and a little over 3 ft wide... the idea that one could stop such force with wood, nails and screws, long enough, for even minutes difference, is - i think, impractical ? . it supposes that the opening you are trying to seal, is the only way an increasing amount of water can go... which isn't true, because the internal decks themselves were not water tight, they were never designed to have water in them, so were not watertight... so you plug one hole, and the hydraulic effort of the water is increased through any other opening... think about how a water fountain works,,, if you stop one spray, the others increase.. ie put a hose on a tap , put holes in the hose, stop up its end, and turn on the tap, you might get 2 bar pressure from a water tap.. the holes in the pipe will all make sprays the same height if they are the same size... block one up, and the others increase, because water is non compressible.. and the more down pressure from weight of water, the more any leak below it will increase flow... so one would need to stop up every single hole to stop the flow... and Titanic decks between the watertight doors and plates, were full of holes, there is no certainty that even the plates were watertight even... No one filled the Titanic watertight compartments with water to see where the leaks were... so once you have more water coming in, than you can pump out, thats your lot, if you stop water coming in at the top, the force of the water increases, and so the flow through any holes below increases... either way. the pressure of the flow equalizes
 
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...see how you could stop the weight from pulling the bow down and I'm trying to think of what sort of improvised barrier(s) and who would construct them?
Wouldn't that take officers and crewman away from the boats?
Yes, any weight of water it would pull the bow down, the angle of which it pulls the bow (front) down is shown in the diagrams (see 2nd attachment). You do have to tip the diagram up by 4 degrees so the top of the green area is parallel. The purpose is to ensure the ship doesn't trim down by more than around 4 degrees until help arrives.

The water would meet your bulkheads, rise, then enter sideways into the compartments and bypass the corridor bulkheads.
This is exactly why I said in my OP

"Once this had been completed, some attention could have been given to sealing any doors across the new bulkhead line. In the hours ahead, these doors and walls could have been buttressed as the height of water and pressure increased"

The bulkhead might look something like this attachment. As near as possible to the bulkhead underneath to minimise seepage through the deck below. It would take some time for the water to seep through into these rooms, so these would have secondary priority to the corridors.

Of course, even if the walls & doors weren't buttressed and collapsed, it would still gain time. The experts analysing this sinking often mention the ease of which water would have flowed along these corridors compared to the rooms which took time to fill up, creating air pockets & delaying the sinking

I understand there were two Carpenters, but we don't need joiners just people who have some DIY experience which could cover half of the people standing around doing nothing on deck. My Grandad lived at this time and was a handyman with wood, but not a Carpenter. The rate of work may have been limited to the number of hammers, saws & axes rather than capable people.

There was also a Carpenters shop and store, admittedly both towards the front of the ship, but they were on C deck, so this wouldn't have been flooded until late. The critical path is the bottom of those two corridors. If they could have been secured which might only need a 2ft x 7ft plank of wood & 2'' x 2'' support, it would have given them the time to do more.
 

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Titanic was taking on the equivalent of the contents of an olympic sized swimming pool every 7.5 minutes.
An Olympic pool has 660,253.09 gallons of water, which
equals about 5,511,556 lbs.
Even at a reduced rate, I don't see how you could stop the weight from pulling the bow down and I'm trying to think of what sort of improvised barrier(s) and who would construct them?
Wouldn't that take officers and crewman away from the boats?
I'm not an architect or an engineer, and I admire the time and thought that you have put into this; obviously a lot!
But given the obstacles-- the biggest being time... I don't see how it could be done. The other obstacles are manpower, while filling the boats, and keeping the passengers from widespread panic.
The last obstacle is the weight of the water-- wouldn't it blow the barrier loose once the pressure built up enough?
It's a tall order-- but an interesting idea.

Wooden barriers are used to stop flooding to buildings and I don't think these are even buttressed as I've suggested here which adds considerable strength. The pressure of water depends on the height above the deck, not the volume held behind it.
1624704580237.png

1624704523165.png

 
Just my 2 cents, but the volume of water on Titanic was able to crush a boiler room bulkhead. I don't think a wooden barrier would stand a chance.
Just saying.
 
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Jim Currie

Member
Yes, any weight of water it would pull the bow down, the angle of which it pulls the bow (front) down is shown in the diagrams (see 2nd attachment). You do have to tip the diagram up by 4 degrees so the top of the green area is parallel. The purpose is to ensure the ship doesn't trim down by more than around 4 degrees until help arrives.


This is exactly why I said in my OP

"Once this had been completed, some attention could have been given to sealing any doors across the new bulkhead line. In the hours ahead, these doors and walls could have been buttressed as the height of water and pressure increased"

The bulkhead might look something like this attachment. As near as possible to the bulkhead underneath to minimise seepage through the deck below. It would take some time for the water to seep through into these rooms, so these would have secondary priority to the corridors.

Of course, even if the walls & doors weren't buttressed and collapsed, it would still gain time. The experts analysing this sinking often mention the ease of which water would have flowed along these corridors compared to the rooms which took time to fill up, creating air pockets & delaying the sinking

I understand there were two Carpenters, but we don't need joiners just people who have some DIY experience which could cover half of the people standing around doing nothing on deck. My Grandad lived at this time and was a handyman with wood, but not a Carpenter. The rate of work may have been limited to the number of hammers, saws & axes rather than capable people.

There was also a Carpenters shop and store, admittedly both towards the front of the ship, but they were on C deck, so this wouldn't have been flooded until late. The critical path is the bottom of those two corridors. If they could have been secured which might only need a 2ft x 7ft plank of wood & 2'' x 2'' support, it would have given them the time to do more.
Such a plan would not have the remotest chance of working.
This was 1912. DIY was a dream of the future.

It would not reduce the volume of inflow of sea water and the ship would continue to lose buoyancy. This would, as you point out, cause her to trim more by the by the head, and increase the water pressure in flooded compartments. The water inside the flooded part of the hull would rise quicker but it would not be motionless, there was a a long, low swell in the area, there always is. A few feet burst open the coal bunker doors what do you think it would do for a flimsy wood door and the hatch covers in the cargo hold wells?
Incidentally - what would be used to seal the doors and your barrier? In 1912, the preferred sealant at sea was boiling tar.

As for utilizing those standing around? Now who was going to do the organizing? The Deck Crew including the Carpenter and the Joiner were fully employed with the boats, and the engine room crew were desperately trying to save the day below decks. Of the men passengers - many were foreigners who did not speak English. Many were wealthy business men who hadn't a clue. Then add to that the proportion who thought the ship was unsinkable. Retrospective thinking is a fine thing, but seldom practical.
I served in passenger ships much later than, but like, Titanic, and I can assure you - even then, such an idea would be totally impractical.
 
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On similar lines I have wondered about dropping weighted tarpaulins over the side to partially seal the rips in the hull. Such repairs are a recognised way of keeping a ship afloat. However there simply wouldn't be the time, materials or manpower to achieve any such tasks from a standing start. If they were a rehearsed contingency plan, then possibly, but in the heat of the moment, no chance.
 
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Incony

Member
and any practical work, with materials to hand would have to be carried our from moment of impact, in less than two hours.. in respect, probably less than the first hour after collision, since it was already too late to delay the sinking after that.. since by 1 am, water had reached E deck.., which means that any leaks aft, below that level were filling the ship.., the idea of blocking passageways, does not address the weight of the water acting on any deck below it.., and so the example of the floodwater gate stopping flooding, on the other side of the gate, only works because there is no airspace under the road, and if there are pipes, that are not watertight anywhere, even then water will find those ways in, many folks first notice groundwater flooding when the toilets wont empty on flush, because water has already filled the drains beneath the toilet.. and on the Titanic, imagine how many toilets there were that would need the outlets making watertight.. every toilet becomes an open ended hose... I do understand the Titanic used storm valves, and maybe they were all closed and being new, did not leak -, and staff closed as many possible water ingress places as they could - my reasoning says, that while every effort was made to stop water coming in... escape while still possible, was a greater motivator, and seeing water creeping toward you, the idea of wading through it to close a valve or opening now under several feet of water... was not. :)
 
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Incony

Member
of note... despite the land mass, this drain is below the water level, though not under it yet... such is the effort of the water to equalize pressure, that water is coming out of the drain and running back down the street. any opening however small would be doing the same thing on the Titanic.. This drain cover is heavy and strong enough to support road vehicles, but look how high the water fountains out of its edges and small openings.. if you were given the job of stopping it, with something, what would you need...? put yourself back to 1912... and you are in a passage way, and see this... " oh i would go to the passage way door behind me, find some wood nails and screws, and go down to a boiler room get some hot coals, melt some tar, and seal up the passage way door..... " :) ok, and by the time the water reaches your sealed up door... its already flowing out of every other opening behind it and down to your sealed door.. even bubbling up from between the floor boards because you didnt seal up the wooden walls either side of your door, so its been coming through those too..... its found its way into the air vents as well, and now its running out of those as well... but hey, you closed the portholes... you can watch the fish swimming about now... File:Overflowing drain, Waterside, Evesham - geograph.org.uk - 501267.jpg - Wikimedia Commons
 
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Just my 2 cents, but the volume of water on Titanic was able to crush a boiler room bulkhead. I don't think a wooden barrier would stand a chance.
Just saying.
The boiler room bulkhead collapse theory is very speculative, although not impossible. More likely it was the coal bunker door than the bulkhead which collapsed. The smaller volume in there allowed the water to attain a large height building up pressure. If the thin iron door was already damaged and made brittle by fire, then a collapse would be almost inevitable. The initial rate of ingress was described by a boiler room man as the rate of a fire hose. A modern fire hose would be 30 litres a minute, so this isn't going to be significant. It's possible that late on, water collected against the g deck bulkheads and seeped through into the boiler room coal bunkers.

The quantity of water held behind the barriers is irrelevant to its integrity, it's the height over the improvised barrier which determines the pressure and stresses. This varies between a maximum of 1.5 metres in one of the calculations to 2.5 metres in others, so buttressing would be necessary to reduce the bending stresses and deformation along the new bulkhead if these were to last longer than 30 mins. By buttressing, I mean nailing struts of timber at 45 degrees between the floor and wall, perhaps chopped of at 45 degrees at the ends with an axe. This might have to be supported by further wood to stop sliding. A quick, rough a ready affair, but this would add a lot of strength. Alternately the buttress could be a door on its side covering a whole stretch of wall.

The higher the water goes, the more the flow through the breeches are reduced as the head builds up gradually reducing to zero at the heights. So every inch gains more time. This could be used to carry out more elaborate strengthening of the new bulkhead. Only 10 minutes would be necessary to launch the last two collapsible boats perhaps saving 60 people, but it would around 2 hours for the Carpathia to arrive to save everyone.

Modern B-class non-watertight 'joiner doors' the sort employed in ships today aren't designed for strength, but noise and fire protection. They collapse at at typically 1.5m water depth (last column) without further support. Whether these would be better or worse than Titanic doors I don't know. Interestingly, slider doors, a bit like the bunker doors are easily the weakest.

A study on leakage and collapse of non-watertight ship doors under floodwater pressure​

1624817020877.png
 
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Jim Currie

Member
Hello Peter.
The wt bulkhead collapse theory is 100% nonsense. WT bulkead strength was over-designed.. plates thicker at the base and vertical steel stiffener angles at 2 to 3 ft centers.

The only way to delay the inevitable was to pump out as fast as the water was entering. This was impossible since the pumps could not handle the rate of flooding.
 
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