Measuring with your hand

Your outstretched hand is a protractor, your arm a ruler, your eyes a rangefinder. Nobody can take them from you.

UNDERSTAND

It all rests on two ideas. First: the same angle covers a bigger object the farther away it is. Know the angle, from your hand, and one of the two sizes, the height or the distance, and you get the other. Second: similar triangles. A stick held at arm's length makes a 45 degree triangle with your arm; the tree and the distance to its foot make the same triangle, only bigger. The visor does the same thing: it keeps the angle when you turn your head.

The thumb jump is parallax: your two eyes see your thumb from two points about six and a half centimeters apart, and your arm is roughly ten times longer than that gap. So the jump you see in the distance is ten times smaller than the distance itself.

Sound travels about 340 meters per second, one kilometer in three seconds, while the light of the flash reaches you instantly. The gap between the two is the time sound takes to travel.

The sun moves fifteen degrees per hour across the sky, but it doesn't drop straight down: at mid-latitudes it loses eight to ten degrees of height per hour late in the day, roughly the width of four fingers. Hence the rule of a quarter of an hour per finger, and hence its error far north, where the sun slides down at an even shallower angle.

ACT

Angles: your hand at arm's length

Stretch your arm out fully, hand facing you. At that distance, whatever your size (tall people have bigger hands, but also longer arms):

• your little finger covers about 1 degree;
• three fingers together (index, middle, ring) about 5 degrees;
• your closed fist about 10 degrees;
• your hand spread wide, thumb to little finger, 20 to 25 degrees.

Check it once: from the horizon to the point straight above your head is 90 degrees, nine fists.

How long until dark

Stretch your arm, rest the bottom of your hand on the horizon, and count fingers up to the bottom of the sun. Each finger is worth about a quarter of an hour at mid-latitudes. Four fingers: roughly an hour of daylight. Add twenty minutes or so of usable twilight. It's an estimate: be generous, especially in the mountains, where the horizon is higher.

How far away something is: the thumb jump

1. Arm outstretched, thumb up, close your left eye and put your thumb on the object.
2. Without moving, close your right eye and open your left. Your thumb seems to jump sideways.
3. Estimate the length of that jump in the landscape, at the object: the width of a car, a house, a tree.
4. Multiply by ten. Your thumb jumps the width of a car, about four meters: the object is about forty meters away.

The height of a tree, a wall, an antenna

1. Take a stick. Hold it upright at arm's length so that the part sticking out above your fist is as long as the distance from your fist to your eye.
2. Walk forward or back until the stick exactly covers the object: your fist on its base, the tip of the stick on its top.
3. The distance between you and the base of the object equals its height. Count your steps.

The width of a river without crossing it

1. Standing on the bank, lower the visor of a cap, or the edge of your flat hand on your forehead, until it exactly touches the far bank.
2. Without moving your head or the visor, turn a quarter turn toward flat ground on your side.
3. Spot the point on the ground the edge of the visor now touches. The distance to that point is the width of the river. Walk there counting your steps.

How far away a thunderstorm is

Count the seconds between the flash and the thunder and divide by three: that's the distance in kilometers (divide by five for miles). Under ten seconds, the storm is less than three kilometers away: take shelter, and wait thirty minutes after the last thunder before going back out.

ADAPT

You have no stick. For a height, use shadows: measure your shadow and the object's shadow in steps. Object height = your height × (object's shadow ÷ your shadow).

You have a map. Distances counted in steps and angles taken with your hand are enough to place yourself on it: see Lire une carte.

You need to hold a heading. Your hand also offsets a sighting: one fist to the right of the sun is ten degrees. Finding and keeping north: Finding your way without instruments.

At night. The Pole Star sits above the horizon at a height equal to your latitude: in Paris, a little under five fists. Reading a sky that's building up to a storm: Reading tomorrow's weather in the sky.