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
Listen
How to Estimate Hours Left Until Sunset
Have 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.
How to Estimate 1º, 5º, 10º, and 25º Angles
It turns out there are some pretty handy methods for estimating angles using only (as you may have guessed) your hand.
For all of these estimates, the trick is to hold your hand out at arms length, and compare the extent of the object whose angular size you’re measuring with the extent of some particular portions of your phalanges and/or paws.
Here are your angular options:
- The width of your pinky finger with your hand held at arms length spans an angle of about 1º
- The width of your index, middle, and ring fingers all held together, with your hand held at arms length, spans an angle of about 5º
- The width of the back of your fist (with your thumb kind of tucked in) as seen with your arm held all the way out spans an angle of about 10º
- The angular span between the tip of your pinky finger and thumb when held apart (making kind of a “hang loose” sign) at arms length is about 25º
And believe it or not, these angle measuring tricks are all you need to figure out how much time you have left to build that potentially life-saving fire and shelter before the sun sets for the night.
How to Estimate the Time Until Sunset
The trick is to know that for every approximately 10º that the sun still sits above the horizon where it will set, you have roughly 1 hour of daylight left. You can see that this must be true by making a series of 10º measurements across the sky using the back of your fist.
If you start at one horizon and follow a path across the sky to the opposite horizon, you’ll need about 12 fist-widths. And since there are about 12 hours in a day on average (fewer in winter, more in summer), each of these 10º fist spans must be about 1 hour of daylight.
And that’s all there is to it…at least, for the part where you figure out how much daylight is left before the sun sets. Just use any of the methods we talked about to estimate the angular distance between the location where the sun currently is, and the point along the horizon where it will set, and convert this angle into the number of remaining hours.
As for the part where you build a fire and a fort ,and save you and your friend from a wilderness disaster, you’ll have to watch a few more Survivorman episodes to figure that out.
Wrap Up
Okay, that’s all the potentially life saving math we have time for today.
For more fun with math, please check out my book, The Math Dude’s Quick and Dirty Guide to Algebra. And remember to become a fan of The Math Dude on Facebook, where you’ll find lots of great math posted throughout the week. If you’re on Twitter, please follow me there, too.
Until next time, this is Jason Marshall with The Math Dude’s Quick and Dirty Tips to Make Math Easier. Thanks for reading, math fans!
Adventure man image courtesy of Shutterstock.
Betterment LLC is an SEC Registered Investment Advisor. Brokerage services are offered by Betterment Securities, an SEC registered broker-dealer and member FINRA/SIPC. Investments are not FDIC Insured. No Bank Guarantee. May Lose Value. Investing in securities involves risks, and there is always the potential of losing money when you invest in securities. Before investing, consider your investment objectives and Betterment’s charges and expenses. Not an offer, solicitation of an offer, or advice to buy or sell securities in jurisdictions where Betterment and Betterment Securities are not registered.
About the Author
Jason Marshall is the author of The Math Dude’s Quick and Dirty Guide to Algebra. He provides clear explanations of math terms and principles, and his simple tricks for solving basic algebra problems will have even the most math-phobic person looking forward to working out whatever math problem comes their way.