How to Estimate Hours Left Until Sunset

Do you know that math can help you survive? I’m not talking about jobs, money, and feeding yourself—I mean the lost in the wilderness, life depends on it kind of surviving. How does this work? Keep on reading The Math Dude to find out.

Jason Marshall, PhD,
June 4, 2016
Episode #234

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Aventure ManHave you ever watched the show Survivorman? Or any of the numerous other shows of that ilk? I must admit I went through a phase a few years ago that involved a fair bit of survival expert program binging. Not only were the shows entertaining, but I learned a few things that could come in handy someday.

As it turns out, one of the things I was enlightened to learn involves a lovely combination of math and astronomy (my favorite, exquisitely delicious pairing.)

What could it be? And how can math help you escape a wilderness disaster and survive? Those are exactly the questions we’ll be answering today.>

Math to the Rescue?

Here’s the scenario: You're hiking in the remote wilderness with a friend, when one of you gets sick. High fever and fatigue has slowed your walking down to a snail's pace, and it’s becoming increasingly clear that you and your friend are not going to make it back to camp before the sun sets and the temperature drops.

What do you do? You shake yourself awake from that awful dream, get off the couch, turn of the TV, stop watching so many episodes of Survivorman, and go climb into bed.

Unless, of course, you really are actually stuck in the woods. In which case, I’d say its about time to pull a little math out of your bag of tricks.

In particular, it’s time to use some simple math to figure out exactly how much time you have left to build a shelter and a fire before the sun sets. So it's time to get to work.

Angular Sizes

Did you know that sometimes it makes sense to measure the size of something in degrees? As in, an angle? If you read the Math Dude episode on angular size, you certainly did know this.

In that episode, we learned that angular size is often the best way to compare the apparent sizes of things like the full moon and the sun—which, as luck and cosmic coincidence conspired to have it, turn out to be similar in angular extent. And thus, as a result, cool phenomena like eclipses are actually cool phenomena, and not just things people dream about.

Angular size is often the best way to compare the apparent sizes of things.

As a reminder, we can think of angular size like this: Let’s say you want to measure the angular size of a tree in the distance. Begin by imagining you’ve drawn two lines that extend from you to each side of the tree. Since these two lines both start at you, they must intersect and form an angle.

This angle between the lines is the angular size of the object—which can be measured in radians, or degrees, or any other unit by which angles can be measured that strikes your fancy.

In a nutshell, angular size tells you how big an object—in this case a tree—appears in terms of its angular extent, from wherever you’re looking at it.


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