Estimating distance is important in daily life, hiking, and survival situations. It helps you to maintain your sense of direction, calculate distance and height, and estimate travel time while hiking relative to your pace.
Estimating distance by using only your finger is based on this known fact about human anatomy: Your arm is about ten times longer than the distance between your eyes.
The distance between your eyes is about 2” apart and the distance from your eye to your extended finger is about 20” apart. How can this be useful for estimating distance?
Scenario: You are standing on a hill and want to estimate the approximate distance to where the foot trail disappears into a thicket of blueberry bushes. There is a nearby red barn, which you estimate is about 100 feet wide.
To calculate the distance:
- Hold your right arm out directly in front of you, elbow straight, thumb upright.
- Align your thumb with one eye closed so that it covers (or aligns) the distant object. Point marked X in the drawing.
- Do not move your head, arm or thumb, but switch eyes, so that your open eye is now closed and the other eye is open. Observe closely where the object now appears with the other open eye. Your thumb should appear to have moved to some other point: no longer in front of the object. This new point is marked as Y in the drawing.
- Estimate this displacement XY, by equating it to the estimated size of something you are familiar with (height of tree, building width, length of a car, power line poles, distance between nearby objects). In this case, the distant barn is estimated to be 100′ wide. It appears 5 barn widths could fit this displacement, or 500 feet. Now multiply that figure by 10 (the ratio of the length of your arm to the distance between your eyes), and you get the distance between you and the thicket of blueberry bushes — 5000 feet away(about 1 mile).
Why it works:
When you hold out your thumb and view it with one eye open, then with the other eye open, your finger seems to shift relative to the object background. This makes it appear that the object has “moved” from side. This phenomenon is known as parallax. The parallax of a distant object is the angle between its directions of view from the two ends of a baseline.
To accurately measure the distance to a far-away object, it has to be viewed from at least two points. The baseline is the line connecting those points. You can then use simple trigonometry to estimate the distance. In the illustration, notice the thumb forms the tip of two identical proportional triangles. The base of the first triangle is the distance between the eyes (about 1/10 of the distance of the thumb and the eyes). The same ratio holds for the second triangle, between the thumb and two distant points it covers, when viewed from either eye.
Even though humans vary in height, the proportion of our anatomy is similar. The angle of the line between our eyes (XY) to the thumb is about 6 degrees, a ratio of 1:10. The smaller triangle XYZ has same portion as the larger triangle XYZ; If the distance YZ to thumb is 10 times distance XY between the eyes, the distance XZ to the far object is also 10 times distance XY.
Why parallax exists
Humans, like other animals, have two eyes located in different positions on the head, to present different views simultaneously. This feature allows the eye to gain depth perception and estimate distances. Not all animals function in this manner. Some animals use motion parallax, in which they move their head to gain different viewpoints. For example, most birds (whose eyes do not have overlapping fields of view and thus cannot see depth) have eyes on the sides of their heads, making their vision mostly monocular. Pigeons make use of motion parallax by bobbing their heads up and down to see depth. Owls, on the other hand have binocular vision. Their eyes are spaced apart similar to humans. The barred owl pictured below is a frequent visitor in our backyard.