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Life, OBS, a little maths and of course Nigel

Life on board:

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Ian relaxes in a homemade chair – made by Jason (sooo clever).

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Dean is kitted out to deploy an expendable probe. This is Dean’s first voyage and there is a tradition (in the same vein as getting a new worker to purchase a tin of striped paint) of getting  the new person to kit themselves out in full PPE – personal protection equipment (note Dean even has ear defenders on) to deploy the probe. The only PPE you really need for deploying an expendable is standard steeltoed footware required for anyone on deck.

Left: enjoying fresh tuna from the sea. Right: tea break in the sun.

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My view as I read my book earlier today.

Four OBS return from the deep:

Above – an OBS returns to the surface. An acoustic signal triggers an electric current that causes burn wires to sever (above right – a burnt through wire next to a wire that is still complete). This then ‘unlocks’ the OBS from it’s concrete base and the OBS floats to the sea surface.

 

 

Above: the concrete base of an OBS. Matt is holding an acoustic release. The acoustic release is attached to the concrete block along with the rest of the OBS.

 

 

Anna and Christine check that the acoustic releases can ‘hear’ them.  The inside of an OBS with seismometers in watertight compartments.

A completed OBS. Ben, Nuno and Tim  ‘speak’ to the acoustic releases. The release wires  (in a picture above) then burn and the OBS returns to the surface. 

The scientists have checked that the OBS are working as expected and have redeployed the OBS in a position to have a more concentrated survey over the Ocean Core Complex.

Juan’s bit:

Juan has kindly provided the working for Q1 in his ‘Why don’t ships roll over?’ blog.

Answer to Q1 of the Stability question

The key thing here is that you are being asked to work out the centre of gravity of the equipment only.

The problem can be rephrased as “If all the weights acted through a single point, but with the same weight distribution, what distance from the ship’s centreline would that point have be to provide the same moment?”

I used the word “same” so an equals sign must appear somewhere.

=

There we go. Then I said, “all the weights acted through a single point… to provide [a] moment”. Here we go – the old Moment = force x distance. And that single point? That’s the centre of gravity we’re trying to find out. And the weight, of course, is the force we know. So:

Centre of gravity Cg (m) x Total Force (N) = Total Moment (Nm)

From the question, we have a list of masses (in tonnes) and offsets from the ship’s centreline. We can use these to find the total moment by adding all the moments together:

Total moment (Nm) = sum of {all the Force x Distance’s} (Nm)

Remember than 1 tonne = 1000kg ≈ 10,000N, g = 9.81

If you didn’t do the conversion you should get about 93 tonne.m, or if you converted into Newtons, then you should have 930,000Nm.

We have the Total Moment. Now we need to know the Total Force, in this case the total Weight. That’s just the sum of all the weights involved, which will give you 330,000 N, or if you stayed with tonnes then 33 tonnes.

So, altogether, we have two equations:

Total Moment (Nm) = Centre of gravity Cg (m) x Total Force (N)

Total Moment (Nm)  = sum of {all the Force (N) x Distance’s (m)}

As the total moment is the same we can equate the two:

Centre of gravity Cg (m) x Total Force (N) = sum of {all the Force (N) x Distance’s (m)}

We are interested in finding the Centre of Gravity. So make Centre of Gravity the subject of the equation by dividing both sides by the Total Force:

Centre of gravity Cg (m) = sum of {all the Force (N) x Distance’s (m)}/Total Force (N)

And this should leave you with about -3m, or 3m starboard.

For the mathsy people:

The equation:

Centre of gravity Cg (m) x Total Force (N) = sum of {all the Force (N) x Distance’s (m)}

Can be expressed as:

EQ1

Where ‘i’ denotes that that force or distance is related to the i’th mass.

Making the Cg the subject of the equation by dividing both sides by the Total Force gives:

EQ2

As force = mass x acceleration due to gravity, we can substitute this in, and expanding the summation, so the equation reads:

EQ3

The top and bottom contain a common factor of g, the acceleration due to gravity. So this can be cancelled out, leaving:

EQ4

Which, if we rewrite in terms of summations:

EQ5

Or, in words this means that:

“The centre of gravity (in one axis) is equal to the sum of all the items’ mass x distance, divided by the total mass of all the items.”

The convenient thing about that is you don’t need to convert the units of mass from tonnes to kg, or tonnes to Newtons to get forces, as the units of mass and terms gravity eventually cancel out.

Thanks Juan – A 🙂

Nigel:

Yesterday Nigel was under everyone’s feet. Today after his shower he took to hiding under the yellow streamer. He has not come out all day. He had eaten some tuna that Andy caught from the back of  the ship.

 

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Nigel looking at a flying fish that had landed on deck the other day.

Thank you to Will and Dean for new photos of Nigel.

Do have look at Christine’s excellent blog: obsatsea.wordpress.com

Please keep asking questions.

Cheers

Angela 🙂

 

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3 thoughts on “Life, OBS, a little maths and of course Nigel

    1. Sea depth @3000m. Surprised me? Hmmm – being a teacher for 20 years there’s little that shocks me….I suppose some of the scientists shirts are rather surprising….I do think it’s surprising that you can forget you are on a boat. Nigel – No he’s considered a quirky mascot, now I am surprised by how people like him. Me …I feel that that beak and those talons are rather intimidating.

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      1. Sorry pressed send by accident. I am surprised how much people like Nigel. The crew and scientists spoil him completely. He has really become part of the team. Everyone has so many photos of him. As I say, me …that beak is scary.

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