Reaching the Sea Floor

The disaster of the "Titan" submersible, which took tourists on a deep sea dive to view the remains of the Titanic, has, of course, first and foremost, been a tragedy for the families of the five people who lost their lives.

It is hoped that the forthcoming inquiry will provide answers, both to give some closure to the families and also to try and prevent a future accident of the type suffered by the passengers of the "Titan". Without wishing to prejudge the issues for the inquiry, topics are likely to include: (1) design and safety. (2) accountabilty, (3) insurance.

This page, whilst in no way constituting a legal or expert statement, gives my humble understanding of the enormity of the pressures that occur at the bottom of our oceans.

Our Units of Measurement

We shall use metric units for our main calculation. This makes sense, since the official international definition in 1959 defined the weights and measures used in the English-speaking world in terms of the metric systerm of units. Thus,

• Length: 1 yard is exactly 0.9144 metre.
  This is equivalent to "1 inch is exactly 2.5400 centimeters".
• Mass: 1 pound (avoirdupois) is exactly 0.453 592 37 kilogram

Our Givens

Here we can start with two givens. One is a physical property and the other is ultimately made by the formation of our planet. Both, of course, are important for our investigation!

• Density of Water. We assume 1000 Kg/cubic metre, although, at 4°C water has a maximum density of 997 Kg/cubic metre. See, for example: "Engineering Toolbox". A density of 1000 Kg/cubic metre means that a cube of side one metre would, theoretically, hold one metric tonne of water! Heavy!
• Depth of Titanic. We assume 3777 metres (i.e. about 3.8 Km or almost 2.35 miles). See, for example: "Newly released Titan footage". This footage was viewed on BBC News on 19th September 2024; the video it contained was dated 22nd July 2023 and contained a depth marker counting up to 3777 metres below sea level.

There is a further "Given" which we shall mention for completeness, and then conveniently "forget"!

• "Incompressibility of Water". At this point we can actually sneak in another "Given", hopefully without adding undue complexity to the situation. Essentially, we can conveniently regard water as incompressible. This is borne out by the following source: phys.libretexts.org (sections 2.73 and 2.75 as well as Table 2.71 comparing normal and seawater). Also relevant is water-science-school. Both sources suggest that, by regarding water as incompressible, we are likely to underestimate our weight of water by no more than 2%! I think you, the reader, will agree that, in the context of the aim of this our web page, the resulting simplicity in our calculations is a worthy aim!

Mass of Conceptual Vertical Column of Water

The key task is to find the mass of a conceptual column of water above the sea bed. To start with, the simple diagram shown below may be helpful.

• Depth: We have assumed (see above) that the Titanic lies at a depth D of 3777 m.
• Volume of a vertical column, with square cross section A = 1 m², is V=AD = 3777 m³
• Density: We have assumed (see above) water has a density ρ of 1000 Kg / m³.
• Mass of this vertical column is ρ x D x A = 1000 Kg/m³ x 3777 m x 1 m² = 3777000 Kg.

Conclusion So Far: The Mass of this vertical column is 3777 Metric Tonnes sitting on an area of 1 square metre on the sea floor. This gives about 3717 UK Tons (Long Tons), since 1 Metric Tonne is equivalent to 0.984207 UK Tons (Long Tons).

Mass and Weight

According to our present knowledge of Physics, the Four Fundamental Forces in the universe comprise: Gravity, the weak force, electromagnetism, and the strong force.

The force of Gravity allows us to determine the mass of an object. Traditional weighing scales balance the unknown weight of an object on one plate against the known weights of one or more objects on the other plate.

Back to our main subject! The pressure at the base of the column exerted by the weight of the column of water is the weight of the mass of 3777 Metric Tonnes acting on an area of 1 m². This is the answer we want!

Here we can make the following observations.

• We can reference the weight of our column of water to conditions at the surface of the earth including sea level. This so, because the depth D of the sea bed is negligible compared to the average radius of 6,371 km of the almost spherical earth.
• The air pressure at the surface of the earth is important for us as living entities, but the calculation of the water pressure on the sea floor is relative to the surface of the earth including sea level.

We have now spoken not only about the mass of our column of water, but, also, about its weight on one square metre of the sea bed.

Pressure per square inch.

We have used standard metric units to get us this far on our journey to understand the pressure on the sea bed.

Something which is perhaps much closer to our physical being and existence, is the length of the each of the two segments of an adult's thumb. Usually, this length is about one inch for each segment. So, knowing this, let's calculate the pressure per square inch on the sea floor where the wreck of Titanic lies. Remember, from above, 1 inch is exactly 2.5400 centimeters. This means that, for our calculations on this web page, we are effectively staying with metric units! All consistent!

There are 1550.003 square inches per square metre. If the pressure on the sea floor is 3777 Metric Tonnes force per square metre, then, per square inch, this becomes 3777/1550 Metric Tonnes per Square inch, or about:

2.4 Metric Tonnes Force per Square Inch.

According to "My Car Import", mid-size cars in the UK, including sedans and hatchbacks, can weigh between 1,200 kg to 1,600 kg (weight or force). So, our 2.4 Metric Tonnes Force per square inch would be equivalent to balancing two of the lightest cars in this category on one square inch at sea level, if this were logistically possible!! Gadzooks!!

Inquiry Latest.

The inquiry has now reached its conclusion. Here are what appear to be three relevant articles. We can expect more actions to follow.

• "Key Takeaways from the Inquiry".
  BBC, 20 September 2024
• "An 'abomination' of a sub - and the boss convinced Titan was safe"
  BBC, 28 September 2024 @18:17
• "Allegations of greed and recklessness in Titan submersible hearings"
  South Carolina Public Radio, Victoria Hansen, 30 September, 2024 @5:07 PM EDT
• "What's next now that the hearings into the Titan implosion are over?"
  CenLANow, Jameson Moyer, 01 October 2024 @10:08 AM (Central Daylight Time, USA)

As stated above, the inquiry has ended, but it looks as if we can probably expect further actions and consequences beyond the remit of the inquiry.

Attributions & Thanks

The calculations are mine, but the sources for the necessary input data are given in the links. Of these, the following were particularly useful and relevant.

1. "Engineering Toolbox"
2. "BBC - Key Takeaways from Inquiry."
3. phys.libretexts.org
4. water-science-school
5. "My Car Import"

Many Thanks also to all the additional organisations, to which I have made links on this page!

Of course, Many Thanks to you the reader for whom this page was written!