by David Colarusso - August 13th, 2008
For those of you interested in such things, “Yes” I will be finishing the relativity series. It’s just that the animation will take a little time, and I’ve had other priorities. Until then, however, enjoy this latest Explainer.
Now you can find out where you are even if you don’t have GPS. Learn how to find south along with your latitude and longitude using only a few household items. I should note, that in using the home-made quadrant cited, the precision of your findings will be rather low. Don’t worry, you’ll be within a few hundred miles. ;)
The Tabletop Explainer
(Honda Pilot DIY Contest Entry)
How to Navigate by the Sun
Today if you want to know where you are, chances are you’ll use one of these, but we’re going to go ahead and focus on using the materials here and the sun to figure out due south, your latitude, and your longitude.
Our measurements of time are based on the apparent motion of the Sun, the stars, and the moon. Which means a lot of information is packed into your watch.
Take for instance the idea of noon. Before standardized time zones, noon was simply the time of day when the sun crossed an imaginary line connecting due north and due south, called a meridian.
Let’s look down on the earth from the north pole. Here in Somerville, noon occurs when the Sun is due south. In Beijing it’s the same thing.
Anyhow, at local noon in the northern hemisphere, the sun is due south, at midnight, it’s half a world away.
We could make a clock with an hour hand that went around once every 24 hours, but most hour hands go around twice a day. This means the hour hand moves half as fast as the sun appears to.
Meaning if you take your watch and point the hour hand at the sun, halfway between the hour hand and noon is due south. In the southern hemisphere it’s due north.
So the next time you need to find south, just take your watch hold it parallel to the ground, point your hour hand at the sun, and halfway between the hour hand and noon is due south. Now that’s if you’re in the northern hemisphere. Keep in mind, your watch doesn’t run local time. So if daylight savings time is in effect, you’ll have to subtract an hour, and thanks to standardized time zones, you’ll be off by a few minuets. Plus there’s the fact that the geometry of the situation means that things will be less precise around sunrise and sunset, but you get the idea.
Now how does something like this [points to sextant] help us find out where we are. Well this is a sextant, and it’s really just a super-protractor.
You look at one object, like the horizon, through the sighting scope and a half mirrored piece of glass lets you line up the reflected image of some other object like the sun, the sextant telling you the angle between the two. [fade to table of materials]
You can make a similar device called a quadrant from these materials here. It’s basically a protractor that we are going to affix a straw to as a sight and a string too, to help us find the vertical. You can print these plans out from the URL you’ll see here.
A quadrant lets you measure the angle between the horizon and an object, in this case, the sun. So do not look through the sight. Instead, place an object behind the quadrant, and look for the shadow cast by the straw. When the shadow’s a circle, you’ve got the sun lined up.
Two numbers can describe every place on earth: latitude and longitude. These are measured in degrees from two imaginary lines, the prime meridian, and the equator.
All points at a certain longitude are the same amount of degrees east or west of the prime meridian, and all points at a certain latitude are the same number of degrees north or south of the equator.
We know from working with our watch that at noon here in Somerville, the sun is due south. That is, it falls on an imaginary line connecting north and south’a meridian. So let’s look at the noon-time sun.
Keep in mind, the sun is really far away. So anyone pointing at the sun will point in the same direction.
Knowing this, if the sun were directly above the equator, we could find our latitude by simply finding the angle between the sun and overhead.
That is, 90 degrees minus whatever our quadrant reads.
Unfortunately, the sun doesn’t stay directly over the equator. The earth has a tilt in its axis. So over the year the sun moves above or below the equator by roughly 23 degrees.
This is called declination, and we simply add or subtract it from our measurements.
Sailors used to produce books listing the sun’s declination for every minuet in the year, but today you can find this on the web
We know local noon is when the sun crosses the local meridian, and probably noticed that a meridian is also a line of longitude. So if you know when noon happened you already know you longitude.
All we have to do is convert our time to GMT, the local time at zero longitude. Every minuet the sun covers a quarter of a degree. So if your noon took place 5 hours and 4 minuets after noon GMT your longitude is 76 degrees west.
3 hours before GMT, 45 degrees east.
Of course, we had to find local noon first.
To do that, plot the mid-day measurements from your quadrant against your watch time. They’ll make a curve and the top of the curve is local noon.
I’m David Colarusso for the Tabletop Explainer.