Rangefinding Without Instruments

Rangefinding Without Instruments

Figuring out how far away something is without instruments has long been an interest of mine. I'm always impressed how people using just their eyes can make confident statements such as, "Oh, that's 250 yards away." How? The human eyes and brain can't use parallax beyond a few dozen feet to determine distances.

So I started measuring the angular diameter of various common body parts. My right index fingernail, at a distance of 24 inches (the length of my extended car) subtends 60 minutes of arc--far too coarse to measure the distance of anything except mountains except at very close distances. Turning my index finger to the side, it still subtends 50 minutes of arc. (Worse, it isn't a consistent thickness.)

What about a ballpoint pen? The barrel (not the end, where the ball is) is .090"--and this seems to be pretty typical for every pen that I have measured. (No surprise, if you need interchangeability.) At the length of my extended right arm, that's 13 minutes of arc. With this, I find that it is slightly wider the front door of a neighbor's house. Entrance doors are typically 36" wide, so the barrel of the pen is covering approximately a 45" wide angle.

45" / 13 minutes of arc x 100 yards (since 1 moa equals 1 inch at 100 yards) = 346 yards--which is about right for the distance to his front door. Obviously, the precision is probably only +- 10%, because of the uncertainty of matching the pen barrel to the width of his door--but it does give a reasonably accurate measure of range.

UPDATE: I had a reader ask how to calculate the angle that an object covers. It's pretty simple:

W = width of the object
D = distance from your eye to the object
A = angle in degrees

A = 57.296 * W / D

The magic number 57.296 is the number of degrees in a radian. Make sure that W and D are in the same units (inches, centimeters, meters, light-years). The angle A will be in degrees, so multiply by 60 to get minutes of arc. Example: The Moon is approximately 238,500 miles away. It is 2160 miles in diameter. Do the math; it comes to 0.52 degrees, or 31 minutes of arc. The Sun is approximately 93,000,000 miles away; it is 865,000 miles in diameter, or just under 32 minutes of arc. This is why a total solar eclipse is so awesome; the Moon is almost an exact fit for the Sun.