From BBC News:
Swiss Gotthard rail tunnel - an engineering triumph
The world's longest - and deepest - rail tunnel opens in Switzerland on Wednesday [1 June 2016].
The Gotthard rail link has taken 20 years to build, and cost more than $12bn (£8.2bn). It will, the Swiss say, revolutionise Europe's freight transport.
The Alps are sometimes described as Europe's natural trade barriers. From Roman times, the routes across them have been mapped, and fought over.
But the plan was ambitious, costly to the Swiss taxpayers who had agreed to pay for it, and fraught with engineering challenges.
A massive 10m (30ft) diameter tunnel-boring machine could, on a good day, dig out 40m of tunnel a day - a world record.
But now the tunnel is ready, and Europe's leaders, including German Chancellor Angela Merkel, French President Francois Hollande and Italy's Prime Minister Matteo Renzi, are all arriving to take a look.
Twin tunnels running in both directions north-south should transport Europe's freight not only much more safely, but much faster. With no danger of collision, trains will race through the tunnel at speeds of up to 250km/h (155mph).
Where older alpine tunnels corkscrewed their way up through the mountains, the new railway line, from Zurich in the north all the way to Lugano in the south, is completely flat and straight.
What can we work out? (It might be useful to explain that there are two 10-metre diameter tunnels and that four boring machines were used – they met up in the middle.) This is one where the students could come up with their own questions. Here are mine:
- What exchange rate did they use?
- How much of the cost went on salaries? (What assumptions did you make?)
- How much did it cost per year?
- The Swiss people voted in a referendum to pay for the tunnel: look up how many people there are in Switzerland. How much did it cost them each, per year?
- How long is a football field?
- What volume of rock was cut on a good day?
- Give a lower bound for the length of time to drill the tunnel.
- How much freight does a single shipping container hold?
- How many times would the copper cable go along the tunnel?
- How much concrete is there in the Empire State Building?
- My favourite question: how thick is the concrete in the tunnel?
For question 11:
If we assume the tunnel was cut as a circle, diameter 10m and that there is an equal amount of concrete all around (presumably the base should be flat for the trains to run on, so this won't be perfect!) then we have this:
We could use trial and improvement to estimate the thickness of the concrete.
Or we could form and solve a quadratic equation.
Call the thickness of the concrete BC = t.
This gives AC = 5-t
The area of the red annulus is:
Multiply this by the length of the tunnel and this would equal (approximately) the volume of half of the concrete (because there are two tunnels).
Solving this (using the quadratic
formula) gives about 1.3 metres.
Source:
http://www.bbc.co.uk/news/world-europe-36416506
