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Figure Out Where You Are With Nothing But a Watch and Protractor –

Figure Out Where You Are With Nothing But a Watch and Protractor - 1

In a recent episode of MacGyver, Angus (yes, that’s his first name) finds his location in the desert using only a string, a protractor, and a watch. Is this actually possible? Basically, yes. (At least that’s what I told the show-runners as the technical consultant for the show.)

But you can do this, too. So now, for your super basic introduction to navigating the world. And don’t worry—this won’t be a full blown semester course on navigation, it’s just the basics.


If you want to find out where you are on Earth, you need some type of coordinate system. Humans like to use longitude and latitude. You need to understand these in order to actually navigate. Both longitude and latitude can be thought of as circles (but not actual circles). Let me start with a basketball as an example. It already has some lines on it, so I just need to add some extra to make it look like this.

The lines that are already on the basketball are like lines of longitude. They all cross through the top (North pole) and bottom (South pole) of the basketball. This means that all these lines of longitude form circles that have the same radius—the radius of the Earth. Longitude is basically a way of breaking the sphere into 360 degrees. However, we don’t measure longitude all the way to 360°. Instead we have 0 to 180° East and 0 to 180° West. The 0° value is in Greenwich, England, and as you move West you would be increasing in longitude West.

OK, but how do you measure longitude? This is where a clock comes in handy. Yes, a clock. To understand this measurement, you need to know two things: The Earth is spherical (mostly spherical, offer not valid in all US States) and the Earth rotates so that it appears the sun travels around the whole sky every 24 hours (again, not exactly true, but close enough).

Now suppose you are in Greenwich (where longitude is 0°). At some time during the day, the sun will be at its highest position in the sky (which will not be directly overhead). We can call this 12:00 noon. If you are in Greenwich, you can set your clock to the sun. Now your clock also says 12:00 noon. Next, you travel westward all the way to New Orleans (since it’s close to where I live). You repeat the same experiment by waiting until the sun is at the highest point. But wait. Your clock doesn’t say 12:00 noon, it says 6:00 AM since it’s still set on Greenwich time. Since the Earth is spherical, the sun is at its highest point in Greenwich, but maybe it hasn’t even risen in New Orleans.

In fact, if you know the difference in time between Greenwich noon (what your clock says) and local noon (when the sun is at the highest point), you can find your longitude. This time difference is essentially your longitude. You just need to convert from hours to degrees (which I will skip). But notice how important it is to have a clock to determine your longitude. Really, there is no way around it—that’s why the Longitude Act of 1714 was so important. It established a prize for the development of an accurate and portable clock. OK, technically the prize was for a method to determine longitude—but really, a clock of some type is the only practical solution (unless you have GPS).

But wait! What if you want to navigate at night when you can’t see the sun? Yes, this method can still work. However, you need to know something extra. If you know the time a star rises (or the moon, or a planet) with respect to the time it would rise in Greenwich then you are all set. It’s the same idea as using the sun at noon. Of course. the problem with this method is that most people don’t memorize the rise-times of different celestial objects.

Measuring Lattitude

The lines of latitude also make circles around the Earth. However, they don’t all pass through the same points like the longitude values do. Instead, these are circles that are all parallel to the equator. If you look at my basketball above, the horizontal lines would be lines of latitude. Yes, I had to draw this on the ball.

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Latitude is also measured in degrees but it starts at the equator which would be zero degrees latitude. As you move away from the equator (North or South), you increase your latitude degree such that New Orleans would be about 30°N. If you go to Sydney, Australia, you would have a latitude of 33.8°S since it is 33.8° below the equator.

OK, but how do you determine your latitude? This one is pretty straight forward—especially if you are in the Northern hemisphere. In short, you just need to measure the angular height of the North Star (Polaris) above the horizon. This works because the North Star is almost directly in line with the Earth’s axis of rotation. So, if you were at the North pole (and hopefully on ice), the North Star would be directly overhead with an angle of 90° above the horizon. If you traveled to the equator, the North Star would be exactly on the horizon and you would be at 0° latitude.

What about the Southern hemisphere? Yeah, that’s a small problem. Unlike the Northern hemisphere there isn’t a star right on the axis of rotation. Instead you just have to approximate the location of the celestial South pole by looking at other constellations.

Finally, how do you get this angular height of the North Star? That’s where the protractor comes in play. Here’s what you do. Take a string with a weight to act as a plumb bob. Now hold the protractor upside down and aim the straight part towards the North Star. Boom. That’s it. The plumb bob will hang at the angle reading for your latitude. Now you aren’t lost.

Note that with my DIY sextant (and most others), the string would point to a value on the protractor that is not the angle above the horizon. Actually, you would have to take your angle measurement and subtract from 90° to get your latitude. Also, there is a straw on top of my protractor to assist with the aiming—and it looks cool.

Of course both of these methods work, but the key is precision. For latitude, just a 1° difference in measurement means a distance of 69.1 miles or 60 nautical miles. In fact, the nautical mile is defined by the size of 1 minute of a latitude (where there are 60 minutes in 1 degree). This means that the better your angle measurement, the better you will know your actual location. Sure, a protractor works, but a sextant does this even better. A sextant is essentially just a much better protractor.

That’s it. That’s the basics of finding out where you are on Earth. But there are many other cool and fun details; if you want to learn more, I can recommend this nice online course from Vanderbilt University—AstroNavigation (it’s free).

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