The gyrotheodolite lets you navigate by the turn of the earth

Illustration for article titled The gyrotheodolite lets you navigate by the turn of the earth

One of the wonderful things about science is that it often accomplishes things that you didn't even think were possible in the service of doing things you would never think to do in the first place. A great example of this is the gyrotheodolite, an instrument that lets you navigate underground, by using the rotation of the earth to pick out direction.


The Chunnel, which connects England to mainland Europe by way of an underground tunnel deep enough to scoop under the English Channel, was completed in 1994. It's over thirty miles long, and since trains rush through it every day, it can't have any sudden turns. It was constructed by crews on both sides of the Channel, each digging away in hopes of meeting at the same spot in the middle. To everyone's great pleasure, they did meet, and no extra digging had to be done.

One great feat, of course, was figuring out which way to dig. Calculating the most perfectly straight route from one distance to another is tough enough on the surface of the earth. There are trees, hills, and other barriers to contend with, but it is possible to use landmarks to navigate, or to build towers large enough to get direct sightlines. Finding your way beneath the earth, when even the slightest miscalculation can, over fifteen miles from each side, result in catastrophe, is even harder.


Above Ground Theodolites

A theodolite is a surveying tool used to measure very precise angles over long distances. The first one was not a terribly complicated piece of machinery. It was a telescope that sat on a tripod, with a very sensitive dial which measured how far the telescope was turned. To give its user a standardized reference for direction, it used a compass to measure how many degrees off north a person turned it. The person looked through the telescope to find the place they were going to, then measured on the dial (which was so carefully graduated that it had to be looked at through a magnifying glass) which angle they needed to go.

Modern theodolites are basically the same set-up, but use a lot more modern technology. Infrared lasers measure distance. The angles are displayed on laptops instead of a dial. And a global positioning system is used instead of a humble compass. Still, the technology is sight-based, even if the machine does the seeing for the user. What happens when no sight is available?

Nothing but the Earth

Dive below ground, and everything the theodolite can even potentially use is taken away. It's hard to get GPS technology to work through hundreds of yards of solid earth. Navigating by the stars is out. A compass is unreliable, since mineral deposits in the ground will throw it off. No one even has the advantage of sightlines. All there is to see is dirt. How in the world is it possible to find a way through it?

Illustration for article titled The gyrotheodolite lets you navigate by the turn of the earth

Below the ground, there is only one constant - you are definitely still on earth. And the earth moves. This was proved by Leon Foucault, using his famous pendulum. He helped everyone out again when he came up with a similar theory about a gyroscope. Foucault mounted a gyroscope on two rings, one that allowed the gyroscope to freely swivel vertically, and the other which allowed it to freely move horizontally. When spun quickly, it seemed to swing out of true, but Foucault knew that this was due to the world turning underneath it, not the wobbling of the gyroscope, which, since it could move freely, tried to maintain its position in space as the ground turned under it.


What if it couldn't? If the gyroscope were restricted in its movement, it could be used as something else. If the ring that allowed the horizontal movement of the gyroscope were weighted, it would apply force to the gyroscope. But this force wouldn't be noticeable at once. Only when the world turned would the gyroscope 'feel' the force of gravity on the ring that let it turn horizontally. When a rotating object feels an unbalanced force at one end, in this case the force of gravity pulling it horizontally towards the earth, it will respond by moving at right angles to that force. This move will pull the gyroscope around vertically, until the axis it is rotating around is parallel to the north-south axis of the earth. It has become a compass. What's more, it has become a compass that points true north, not magnetic north.

By using this reading of magnetic north, and by releasing the gyroscope from its tethers and measuring its precession throughout the day, a gyrotheodolite is able to measure the exact position of true north. And so, without stars, or magnets, or the ability to see where they're going, people are able to make their way through the center of the planet. They just have to be careful not to hit water or magma.


Via Electronics Bus, The Franklin Institute, and download information here at Scribd.

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I guess these guys just eyeballed it: