Did you know that you can get an estimate of distances and elevations conveniently using nothing more than your eyes and your hands? It’s really quite amazing and useful; hikers, hunters, and preppers really need to learn these skills.
Ol’ Remus at the Woodpile Report (www.woodpilereport.com) recently recommended a book by Tristan Gooley entitled The Lost Art of Reading Nature’s Signs: outdoor clues to find your way, predict the weather, locate water, track animals and other forgotten skills.
It sounded downright intriguing, so I’ve been reading it on my Kindle and enjoying it quite a bit. The first Appendix had the following useful distance and angle approximations (not original with Gooley) that might turn out to be really useful for those of us who can’t afford a decent laser rangefinder (or whose “decent laser rangefinder” has become a “decent paperweight” for one reason or another).
DISTANCE
Before the invention of sub-nanosecond timing circuits and compact lasers, there were native tribes-people in Europe and the Americas who used body-proportion estimation to determine sizes and distances. They observed that the apparent distance our extended fingertip will “jump”, when viewed first with one eye and then the other against a background of an object or distance to be measured, is approximately one tenth the distance we are from the object in question. The further away you are, the more the apparent jump. This jumping is called “parallax” and is a consequence of having two eyes with a little distance between them.
Based on the geometric postulate that “corresponding sides of similar triangles are proportional” you can use parallax to calculate the distance between two distant objects, if you know how far away you are from them. (You are three miles from town and see two tall buildings; if your finger jumps exactly from one to the other building, they must be about 1,600’ apart: 3 miles divided by 10.)
Or, if you know the distance between two objects, you can work out how far you are from them. (You see a church that you know is 0.6 miles from the edge of a lake. If your finger jumps exactly from one to the other, then you must be approximately 6 miles away. Fractional or multiple jumps are fractional/multiples of the distance. In this example, if your finger jumped past the lake edge and the parallax jump was 1½ times the visible distance between church and lake, you would know you were nine miles away.)
This will also work if you know the approximate size of an object (the distance from one side to the other). How long is the barn you can see? How long is a typical pickup truck? How tall are the telephone poles in your area? Door heights are pretty standard, and how tall is a standard “floor” of a building? If you know A, you can calculate B and vice versa. This technique works vertically as well as horizontally; you just view the object with your head on its side (finger sideways too)!
If you want to refine this method, mark out a greater test distance of say 50 feet and have a friend with a tape measure determine your exact “jump”. (Eye separation and arm length vary.)
Here’s some more information that is not from the book: Another explanation of why this works can be found online. Also, see this reference.
Here’s a powerful example of the “corresponding sides of similar triangles are proportional” postulate. (I always wanted to use the word “postulate” in an SB article!). However, you’ll need some room to walk! This is an example of determining the width of a river, but you could use it to tell the distance to anything, really.
Find an object across the river (your target object, which in this illustration we will label as tree “T”), and stand facing it on the other bank. Mark point K with a pile of something or a red handkerchief or IR chemlight.
Now, squarely face the tree, hold your left arm (in this example) straight out to your side and pick a point M that is 90° from K-T that you can walk toward. (Want to make your measurements more accurate? Use your compass, like this nice one I’m recommending, to make sure you’ve made a 90° turn. Count your paces.
When you’re about halfway to M, stop and make another marker at L. (If you get to L and “shoot an azimuth” to T and it’s 45°, then K-L (the distance you just walked) is equal to K-T, and you can just stop there! Why don’t we use this property of 45° every time? Because if K-T is really far, you’ll have to walk that far as well.
Let’s say you walk 10 yards from K-L. Now keep walking to M, and count paces again. Let’s say L-M was five yards. Once at M, turn your back to the river and point your left arm again, so it points to both L and K, which you can see because you left nice markers there.
Now, when you walk forward you will be (roughly) walking at a 90° angle to K-L-M. Pick a point that’s directly in front of you, and walk towards it. Keep looking back toward the marker at L until it lines up with T (the tree) on the opposite bank. Keep track of your paces.
Let’s say M-N was 20 yards. The ratio of the distance between K and L and the distance between L and M is equal to the ratio of the distance from K to T and M to N. Gaaaa! That sounds so complicated, but it’s not! Don’t panic. Just write it out and do the simple math. (Here’s Mr. Barns, the nice math teacher, doing it for his students, beginning at the 8:14 mark: ) You just need three numbers and your “unknown” value K-T:
Cross-multiply, 10×20 and divide by 5 = 40. The river is 40 yards wide. (Remember when you were in high school and you thought to yourself, “I will never, ever need to use algebra or geometry for anything!” Well, looks like you were wrong.)
All you do is face the target, make two turns, drop three markers, and count your paces. It’s easy peasy. You can do this! You could have calculated the width of the river in the time it takes you to walk 35 paces. (There are several ways to do it, but I think this is the simplest.) You just need to know what to do. Doing it isn’t so hard!
Don’t like the idea of counting strides across the countryside in full view of your target? Pre-measure a length of paracord with high-visibility endpoints and midpoint and you can “measure” the baseline K-L-M at a crawl. Play out paracord for M-N and measure it later when you’re safely out of sight again. We didn’t even break out the trigonometric tables or a calculator!
Using a related principle, here are a couple of web pages that describe how to estimate distances based on angular width, with a known object height. Be sure to look at the business card you can print out and carry that will let you quickly estimate distances to objects of known size. It’s very cool!
ANGLES (covered by Gooley)
You can also use your body proportions to roughly determine angles. That might come in handy when describing the location of a hard-to-see object relative to a known object. (“He’s in the bushes 15° to the left of the biggest pine tree…”) Here’s how that’s done:
Holding your hand at arm’s length and closing one eye, the outer joint of your index finger is about one degree across. The width of your first three fingers (Boy Scout salute) = 5 degrees. The width of your fist (with thumb on top) is about 10 degrees across, and a wide open hand span is about 20 degrees (depending on how flexible your hand is!).
You can use this rough approximation technique to gauge your latitude or to estimate how much longer until sunset, etc. Hint: It has been demonstrated and estimated that each finger-width between the sun and the horizon is about 15 minutes until sunset.
FOOTNOTE
In mid-March, G.P. sent SurvivalBlog the a brief article and video, which I think is worth mentioning here again. This is John McPhee’s method to estimate how far away a person is, using only your naked eyes. The article says, “100 meters – recognize a face, see what they look like. 200 meters – No face, cannot distinguish facial features. 300 meters – No hands, soldier can distinguish what the enemy is doing, but cannot make out individual fingers or the entire hand. 400 meters – The head cannot be distinguished, in fact it looks like they don’t have one at all. 500 meters – Cannot see individual legs, especially the light between their legs, an enemy is moving, but he is moving as a whole, without legs to the soldier’s eye. 600 meters – Humans look like little triangles in shape. He says, ‘A fat little triangle’.”
In the video, John is saying “yards”, but whoever summarized the article (cited above) wrote it as “meters”. The difference between the two doesn’t really become an issue until about 400 meters. (400 meters equals 437 yards, 500 meters equals 546 yards, and 600 meters equals 656 yards.) Really, given the large-ish margin for error inherent in this method, the 10% error of yards vs meters isn’t going to make a whole lot of difference. If you need precision, buy a laser rangefinder. Yes, there are other quick, effective, and convenient ways to measure distances and sizes (like measuring shadows), but this will get you started. There are quick rules for shooting up a mountainside or down into a valley. There are easy-to-calculate shortcuts to determining how fast the wind is blowing and how it will affect your bullet. Isn’t mathematics fun? And there’s so much more in The Lost Art, I hope you take the time to read it!
Now, I’m going to condense all this, print it really small, and paste it into my pocket-sized All-Weather Rite in the Rain fieldbook for future reference! (Note: either print it with a laserprinter or print it with your ink-jet printer and then photocopy it. Laser printed text won’t run and smear if it gets wet!)
Trust God. Be prepared. We can do both.