Maths at sea:
Short teacher rant here –
Please don’t tell your children that you were rubbish at maths, can’t do maths, found maths boring, that maths is really hard. This makes a teacher’s work really difficult. The child believes it is OK to give up, they too just can’t do it, at the end of the day it just too hard. I have had intelligent A Level students who have absolutely refused even to try to understand basic numeracy and felt justified that this was acceptable because they have told me they can’t do it. I have had adults tell me they can’t do maths yet they have: ordered the correct amount of fabric and made to measure their beautiful curtains; quoted for building work, ordered the correct amount of materials to complete the job and made a profit; known when they’ve been overcharged at a restaurant. Maths is an everyday part of our lives and just as we can become fitter by going to the gym we can improve our maths skills with practice. My mental arithmetic improved vastly when, many years ago, I worked at Melbourne Cricket Ground, the tills were wooden boxes and I had to serve drinks very quickly between overs – practice. Please do tell your children that everyone can do maths and not to worry if they need to think about concepts – that’s called learning. Teacher rant finished.
Scientists use all sorts of maths in their research – some of it really basic, some rather complex. I’m going to give you an overview of some of the more basic maths.
We know that the Mid Atlantic Ridge is spreading at about 25km every million years. We know this because we can date the rocks through magnetism and coring and correlating these dates to rock on land. (See blog on Magnetism).
To work out the age of the crust at Line R I just needed to know the distance from the spreading ridge. Firstly I measured the distance and put it against the scale. The distance is 100km (you’ll have to take my word on this).
I know that here the ridge spreads at a rate of 25 mm/year, but I want that in km/year. To get that, I divide by the number of mm in a km, (so divide by 1,000,000).
This gives me a figure of 0.000025km/per year.
I know that Line R is 100km away from the ridge axis so I use D/T
100km/0.000025 = 4,000,000 so the seafloor at Line R to the South of the transform fault is about 4 million years old.
The square on the hypotenuse is equal to the sum of the squares on the other two sides.
Do you remember now?
This is used to calculate how long it will take for an Ocean Bottom Seismics to reach the surface.
The OBS (Ocean Bottom Seismics) team ping the OBS to release it from the seabed. It then starts to rise to the surface. The OBS pings back to the James Cook at regular intervals enabling scientists to know the hypotenuse h. The scientists know the distance between them on the James Cook and the where the OBS is expected to surface b. They know that the OBS will rise at 45 metres a minute. All they have to do is work out the distance of a in order to precisely predict the arrival time of the OBS at the surface. This is important as scientists ping the OBS is advance – who wants to sit above the OBS for 90 minutes waiting for it to reach the surface? The James Cook needs to be at the site of the OBS as it surfaces otherwise it can float off in the currents with all the data the scientists need.
So here is a real example that I’ve just calculated for OBS number 66 which is rising to the surface as I type this.
The scientists pinged the OBS and received a ping back in 9.29 seconds. The speed of sound in water is about 1500 meters a second so:
1500 x 9.29 = 13,935.
The ping was to the OBS and back so the result needs to be divided by 2 = 6,967 (we will round that up to 6970 for ease).
So our hypotenuse is 6970 metres in length.
We have the length of b because we know where the ship is and we know where we put the OBS into the sea. That length is 6,100 metres.
We need to square both of these numbers to find out the square of a.
6970 x 6970 = 48,580,900 that is the square of the hypotenuse h.
6100 x 6100 = 37,210,000 that is the square of b.
We know from the very clever Pythagoras that h2 = a2 + b2
So we now have the following equation: 48,580,900 = a2?? + 37,210,000
We can rearrange our equation now to read: a2 = h2 – b2
a2 = 48,580,000 – 37,210,000
or you can write it the other way round if your prefer:
48,580,000 – 37,210,000 = a2
48,580,000 – 37,210,000 = 11,370,900
So now we have the square of a. All we have to do now is find the square root. This used to be done with tables but now we just press the square root button on our calculator.
Hint from Matt: You should take a calculator you are familiar with into exams – if you use your phone on a day to day basis and then borrow a calculator for the exam you can get into difficulties.
Square root of 11,370,900 is 3,372 so the length of a is: 3,372 metres.
We know that the OBS rise at 45 metres per minute: 3,372/45 = 74.9 so the OBS will rise to the surface in 75 minutes or 1 hour and 10 minutes.
This calculation is recalculated every 10 minutes to check the progress of the OBS to the surface.
Air is less dense than water. Sealed 4 glass balls of air are placed on top of the OBS in yellow plastic casing. When the OBS is released from the concrete bottom (by an acoustic release -ping) the glass balls displace the surrounding water and the OBS floats to the surface. Clever.
To finish off Nigel and Bert: