# The fascinating world of boring tunnels

## That's Maths: Laser-guided machines are today used to drill tunnels from both ends, but how did the ancient Greeks do it?

The Gotthard Base Tunnel opened in June and will be fully operational by December, cutting the journey time from Zurich to Milan by more than an hour. The accuracy of modern tunnel construction is impressive: when the British and French tunnelling teams met in December 1990 under the English Channel, the two shafts were misaligned by less than a metre. Thanks to their skill, a rail trip from London to Brussels now takes less than two hours.

The Channel Tunnel was a magnificent engineering accomplishment. Boring tunnels from both ends makes sense: two teams boring in opposite directions simultaneously can halve the construction time. The one obvious – and essential – requirement is that the two shafts meet accurately in the centre. Modern laser-guided tunnel boring machines make this possible.

#### Geometric principles

Boring tunnels from both ends is nothing new. More than 2,500 years ago, a tunnel of more than a kilometre in length was constructed on the island of Samos in Greece. It was designed to serve as an aqueduct and was the first tunnel to make use of geometric principles. The engineer was Eupalinos, and the tunnel was bored under Mount Kastro to serve the ancient capital of Samos, today called Pythagoreio. The aqueduct was concealed underground to prevent enemies of the tyrant Polycrates from finding and destroying it. It served for more than 1,000 years until it fell into disuse, to be rediscovered around 1883.

Since parallel lines never meet, two shafts may fail to intersect if there is an error in position. To avoid such a catastrophe, Eupalinos arranged for the two straight shafts to zig-zag slightly near the centre point, to ensure a successful juncture even if the cuts were initially misaligned. As it turned out, the construction was so accurate that if the diggers had continued along straight lines they would have made an almost perfect connection.