Hitting the iceberg head-on

[M Torme]

A friend posted this on Facebook and thought it was interesting enough
to post here:

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To be published in my Titanic book, due out next month.

( Based on information contained in http://www.rmstitanicremembered.com/?page_id=282
)



Revisionist calculations argue that the Titanic would have been
shredded from bow to stern; the
main proponent of this is author Daniel Butler, and the calculations
from his website
deserve to be quoted in full:

"Working in SI units, calculating power generated by ship movement and
using the figures I gave above, 55000 tonnes (note, I’m using metric
tonnes, 2200lbs, not long tons, 2240 lbs) and velocity of 22 knots = …
22 x 1850 (metres in a nautical mile) / 3600 (seconds in 1 hour) =
55,000,000Kg x 9.81 (newtons per kg) x 11.3 m per sec = 6096,915,000
watts, or 6096 Mw.

The force generated, assuming a dead stop, would be mass(Kg) x
velocity(m/sec) x 9.81(grav force, newtons/kg)/ 9.81 (Newtons/kg), or
55000000 x 11.3 x 9.81/ 9.81 = 651,500,000 kg.= 651,500 tonnes.

By comparison, a 1 ton car travelling at 60 mph (96 km/hr) would be:
1000 kg x 9.81 (g) x (96 x 1000/3600) = 1000 x 9.81 x 26.6 = 261600
watts, or 261.6 Kw, and the force generated in coming to a dead stop
would be 1000 kg x 26.6 m/sec = 26600 Kg, or 26.6 tonnes.

Quite a difference. Carbon steel has a maximum strength of 56,000 psi
in tension and compression but a maximum shear strength of only 42,000
psi so the steel would have an shear strength of 800 bar (42000/15).
If the steel was 1.875 (from http://www.tpub.com/content/construction/14250/css/14250_14.htm)
a 1 metre length could withstand a shear impact of 800 / 1 x 0.018 =
44444 newtons, = 4530 kg, or 4.53 tonnes."

Since this figure of 44444 Newtons is less than the force generated by
the impact, the Titanic, we are told, would have been ripped apart
from prow to stern. Based on the numbers, this conclusion isn't
correct.

The ensuing discussion will revolve around the units used by the
scientific community (Metres and Newtons),
termed as SI units. Sadly, this is mathematically intensive, but this
treatment has been made as simple as possible.

The first point of contention is that the author of this analysis has
calculated incorrectly. He gives an answer of 651,500,000 kg as the
"force" when it should actually be 621,500,000 Newtons. Not only has
he calculated wrongly, but he mixes up "mass" (kg) with
"force" (Newtons) - a mistake that no scientist would make.

He also implies that the weight of the ship was 55000 tonnes. Her
actual displacement weight, a measure
of the actual weight of the ship, is dependant on how heavily loaded a
ship was at the time, but
a figure of 53147 tonnes is generally accepted. This is about 3% less
than the number Butler quotes, but we
shall use his numbers to allow a fair comparison.

Then we are told that steel has a maximum shear force of 42,000 psi,
and that this is less than highest compression and tension values. But
he has mixed up the forces. Shear forces exist when two opposing sides
of a block
are forced in opposing directions, thus transforming a rectangle into
a parallelogram. With the Titanic
racing head-long into an iceberg, we would actually have a compressive
force acting on the plates; the ship
heading forwards, and the iceberg acting to resist this forward
motion, squeezing the plates, rather than
shearing the two sides parallel to the motion in opposing directions.
The value of "1.875" is presumably the thickness of the hull plate.
Ironically, the web reference that Butler uses next says, "therefore,
when dealing with maximum strength, you should always state the type
of loading," ironic considering the confusion.

The power is also computed wrongly. The force on the ship due to
gravity (that is "the weight"), is not acting
in the same direction as the force driving the ship forward, so it is
incorrect to say that the power is equal
to the weight multipled by the velocity. The weight is given by the
mass times the acceleration due to
gravity (9.81 metres per second per second) and 9.81 is NOT the number
of Newtons per kilogramme; this is the conversion between mass and
weight, which is a force acting straight down towards the centre of
the Earth and not in the direction of the Titanic's motion. In fact,
the whole concept of power is a red herring, and should be ignored.
"Quite a difference" between a car and a huge ocean liner? Of course;
one wonders why this stated,
it is obvious.

Then the equations are used incorrectly. Force is the rate of change
of momentum (which itself is the multiple of mass and velocity), not
just the change of momentum. One needs to know over how long this
change happened.
A perfectly linear decelaration to a perfect stop over, say, 10
seconds, would enable us say that
force is the momentum divided by 10. It isn't quite as simple as this;
with the iceberg tearing through
the hull, resistive force would be applied, hastening the
deceleration. This resistance could be from
steel plates accumulating in front of the 'berg, or from internal
structures within the ship, hastening
the slowing down process. Then Mr.Butler says that the figures assume
"a dead stop." The ship simply wouldn't
(possibly couldn't) stop instantaneously. Incidentally, his "force
generated" implies a duration for this
of 1 second, or change of momentum/1 second. If a dead stop were to
occur immediately, the forces involved
would be so astronomical as to be unimagineable. It would, succinctly
put, be the same as the Titanic running
at full speed into an unyielding object, like a cliff face. The
iceberg, while massive, would be subject to the usual laws of motion,
including the conservation of momentum, and would not be an object
incapable to movement.

The next set of calculations are also used incorrectly. Mr.Butler says
that 42000 psi is the equivalent of 800
bar. He assumes that dividing by 15 converts these numbers from one
set of units to another (the actual
conversion is about 14.7 since this is atmospheric pressure). At any
rate, using 14.7 - or 15 - gives a figure
of about 2800. No doubt Mr.Butler made a typographical mistake here,
as he says "800", or a factor of 3.5 out,
but we must be dubious as this works in his favour.
Next, we come to the coup de grace: calculating the force from the
stress. To do this, one needs
to know the surface area to which the force is applied. For a shear
stress, this area is parallel to
the direction in which the force is applied. This area is actually the
length of the plate multiplied
by its height since this is where the force is applied, and not, as he
implies, edge-on.
Then Mr.Butler mixes up his non-SI and SI units when he says "800 / 1
x 0.018"; 800 (an inaccurate
figure) is non-SI, and the next two, and the answer are in SI. This is
not trivia. As the old adage goes, its
like comparing apples and oranges. In this case, we end up with
bananas.

So, calculating the numbers correctly, we find that 42000 psi is 290
Million Newtons per square metre.
So, now we have the pressure, or the force acting on an area. To find
the force, we multiply
the area on which this pressure is applied - the surface area of the
hull plate. We do NOT, as Mr.Butler
has done, divide the pressure by the area. This leads to a meaningless
number, as pressure is already
force divided by area.

Estimating the area of the hull plate one uses figures gleaned from
"Titanic: The Ship Magnificent";
we use a length of 36 feet (11 metres) and a height of 6 feet (1.8
metres). The maximum force that could
be applied until failure occurs is therefore 290 Million Newtons x 11
x 1.8 = 5700 Million (Mega) Newtons.
Compare that to the 622 Million Newtons that Mr.Butler would tell us
is imparted by the impact. Using these
figures, it is clear that the plates would deform, but not break.



The danger of using Mr.Butler's figures is that he has taken one plate
and extrapolated to form
a conclusion upon which lesser scientific figures have fallen.
In practise trying to prove a failure scenario would need a model that
had an interior spaces containing beams,
columns, bulkheads and corridors would add resistive strength to the
iceberg crushing through the hull,
slowing its progress as it proceeded.
The plates would also buckle.
It is not unlikely the berg would be stopped well before 216 feet
which is a "worst case scenario." We also
do not know exactly how the rivets holding the seams would fare. Would
they pop before a siseable fraction
of compressive damage was reached, or would they only yield at the
last second? And how easily would the
compressive force be transferred from plate to plate? It is not a
simple matter of taking one plate and guessing;
rigourous and intensive computation modelling is necessary.

It should also be noted that the 56,000 and 42,000 psi values no doubt
apply to modern steel, and not the
material used ten decades ago.

Free from any revisionist posturing, we must remember what Edward
Wilding, a naval architect at Harland
and Wolff said regarding the stem-on collision proposal: "...she would
have crumpled up in stopping herself. The momentum of the ship would
have crushed in the bows for 80 or perhaps 100 feet. [The impact would
not be] a shock, it is a pressure that lasts three or four seconds,
five seconds perhaps, and whilst it is a big pressure it is not in the
nature of a sharp blow."

It should be pointed out, in 1879, a ship named the Arizona collided
head-on with an iceberg at a speed of 15 knots, and she survived, with
her bows "broken and twisted." Reportedly, she was left with a hole
"20 feet broad by 30 feet deep."
It may be incorrect to compare the Arizona and the Titanic; the afore
named ship was only of some 5600 tons, but it
is not clear what tonnage this refers to, as ships had gross,
displacement, deadweight etc. tonnage. Interested
readers will find more information on David Gittin's titanicebook.com
website.

Other examples of stove-in bows exist but their numbers do not provide
any meaningful comparison: the Stockholm, after the Andrea Doria
Collision had a huge segment of her bow missing but only her speed
(about 18 knots)
is known at the time of the collision; her gross tonnage of about
12200 tonnes does not allow meaningful comparsion.

While it is clear that Wilding's discussion that the Titanic might
have survived was conjecture, with no
calculations to reinforce his argument, the simple argument is that,
spurious physics aside, we do not know.

[sdavmor]

That was an excellent read. Thank you very much for posting it.
--
Cheers, SDM -- a 21st Century Schizoid Man
Systems Theory project website: http://systemstheory.net
find us on MySpace, GarageBand, Reverb Nation, Last FM, CDBaby
free MP3s of Systems Theory, Mike Dickson & Greg Amov music at
http://mikedickson.org.uk

[paul.l...@googlemail.com]

Here are some more musings on Mr.Butler:

http://www.paullee.com/bandb/butler.php#Nov22011

[Mike DiCenso]

On Nov 2, 9:44 am, "Paul.Lee.1...@gmail.com" <paul.lee.

1...@googlemail.com> wrote:
> Here are some more musings on Mr.Butler:
>
> http://www.paullee.com/bandb/butler.php#Nov22011

Paul, I think just about everyone who's been a poster on this
newsgroup has their own "special" Dan Butler story. ;-)
-Mike