Navigation and the sky

Northern hemisphere — Polaris.

1. Find the Plough (Big Dipper): seven bright stars shaped like a ladle, which circles the pole all night and is visible all year from most northern latitudes.
2. The two stars forming the outer edge of the ladle's bowl — Merak and Dubhe — are the Pointers.
3. Follow the line from Merak through Dubhe about five times their separation. The moderately bright star there, alone in a dim patch of sky, is Polaris.
4. Drop a vertical line from Polaris to the horizon. That point is true north, to within a degree.

If the Plough is below the horizon, Cassiopeia — a bright W on the opposite side of Polaris — gives the same pole.

Southern hemisphere — the Southern Cross.

1. Find Crux, the Southern Cross: four bright stars in a kite shape. Beside it lie two very bright stars, the Pointers (Alpha and Beta Centauri), which distinguish the true Cross from the fainter 'false cross' nearby.
2. Extend the long axis of the Cross, from its top star through its foot, about 4.5 times the length of the Cross.
3. Draw the line bisecting the Pointers at right angles. Where the two lines meet is close to the south celestial pole — an empty patch of sky.
4. Drop vertically to the horizon for true south.

Anywhere: Orion's Belt. The top star of the belt, Mintaka, lies almost exactly on the celestial equator — it rises due east and sets due west from every latitude on Earth.

The quick shadow method — 15 minutes, a few degrees.

1. Push a straight stick vertically into flat ground.
2. Mark the tip of its shadow with a stone.
3. Wait 15–20 minutes and mark the tip again.
4. The line from the first mark to the second runs roughly west to east. The sun moves east to west, so the shadow moves west to east. A line at right angles is north–south.

It is least accurate early and late in the day and at high latitudes, and best within a few hours of noon.

The equal-shadow method — a few hours, about a degree. Shown in the figure above.

1. In the morning, mark the shadow tip and draw a circle round the stick through that mark, using a cord tied to the stick.
2. As the day goes on the shadow shortens, then lengthens again. Mark where the afternoon shadow tip touches the circle.
3. The midpoint between the two marks, and the stick, define true north–south. The morning mark is west; the afternoon mark is east.

Local noon is the moment of the shortest shadow of the day. At that moment, outside the tropics, the shadow points true north in the northern hemisphere and true south in the southern. In the tropics the noon sun can be on either side of overhead depending on the season, so shadows can point either way.

By Polaris. In the northern hemisphere, the altitude of Polaris above the horizon equals your latitude, to within about a degree. Polaris at 52° up means you are at about 52° N.

By the noon sun, anywhere, on any clear day. Measure the sun's altitude at local noon — the angle between the horizon and the sun at the moment of shortest shadow. Then:

• If the noon sun is due south of you: latitude = 90° − altitude + declination
• If the noon sun is due north of you: latitude = altitude + declination − 90° (a negative result means south latitude)

Declination is how far north or south of the equator the sun is on that day. It swings through the year:

A star's declination is its latitude on the sky, and it passes straight overhead for anyone standing at that latitude. So watch a bright star cross the meridian, due north or south: if it passes through the zenith, your latitude equals its declination; if it passes an angle z south of the zenith, your latitude is the declination plus z (for a star crossing north of the zenith, minus z). Measure z with the same quadrant used for latitude from one angle.

• Brightness is in magnitudes: smaller is brighter, and each step of 1 is about 2.5 times.
• Positions drift slowly through precession, by at most about a degree every 180 years, so the whole degrees below will serve for generations.
• Positions are from the Hipparcos catalogue (European Space Agency, 1997).

Dead reckoning is where you are = where you started + direction × distance, updated at every change of course. Its error is typically around 10% of the distance travelled for a careful walker, which is why it is always checked against landmarks when there are any.

Distance by pacing. Count every time the left foot lands. Most adults take about 60–70 of those counts per 100 m on flat ground. Calibrate your own count by walking a measured 100 m three times. Then correct for ground: add 10–20% going uphill, through rough ground, soft sand or snow. Tie a knot in a cord, or move a pebble between pockets, every 100 m, so the count survives a distraction.

Time by Naismith's rule. 5 km per hour on the flat, plus 1 hour for every 600 m of climb — that is, 12 minutes per kilometre and 10 minutes per 100 m of ascent. Add rests. Descents over about 12° slow you down too.

Aim off. When heading for a point on a line — a bridge on a river, a gap in a ridge — deliberately aim a few degrees to one side of it. When you reach the line you then know which way to turn, instead of guessing whether you have overshot or undershot.

Handrails and catching features. Follow a stream, ridge or valley that runs the way you want to go, and pick a feature beyond the target — a river, a road, the sea — that tells you when you have gone too far.

A compass points to magnetic north, not true north. The difference — magnetic declination — depends on where you are and slowly changes year by year. It is a few degrees in much of the world and more than 20° at high latitudes. At 10° uncorrected, the table above says you are 1.76 km off after 10 km. Find the local declination from a recent map, and check it by comparing the compass with Polaris or a noon shadow once.

Keep compasses away from iron and steel — a knife, a belt buckle, a vehicle — which pulls the needle.

Making a compass:

1. Take a steel needle or a thin piece of steel wire.
2. Magnetise it: stroke it with one end of a magnet 30–50 times in the same direction only, lifting the magnet clear at the end of each stroke. Without a magnet, stroking it firmly on silk or wool in one direction gives a weak charge; a coil of insulated wire across a battery for a few seconds gives a strong one.
3. Float it on a leaf, a piece of cork or bark in a bowl of still water, sheltered from wind.
4. It swings to lie north–south. It does not tell you which end is north — check once against the sun or stars and mark that end.

Planting, lambing, hay-making and preserving all run on the solar year, and a group that loses track of the date loses a harvest.

The numbers that make calendars hard:

• Solar year: 365.2422 days. That fraction is why leap years exist: one extra day every 4 years, dropped three times every 400.
• Lunar month (new moon to new moon): 29.53 days.
• Twelve lunar months: 354.4 days — about 11 days short of the solar year. A calendar kept by moons alone drifts right through the seasons in about 33 years. Lunisolar calendars add a 13th month 7 times in every 19 years, because 19 solar years and 235 lunar months come out equal to within about 2 hours.

Finding the solstices and equinoxes by observation:

• Mark sunrise on the horizon from one fixed spot, with a stake or a notch on a distant skyline, every few days. Through the year the sunrise point walks north and south along the horizon. At a solstice it stops and turns back. It moves very little for several days either side, so bracket the turning point and take the middle.
• The noon shadow of a fixed vertical post is shortest on the June solstice and longest on the December solstice in the northern hemisphere, the reverse in the southern. A line of marks on the ground records the year.
• At the equinoxes the sun rises due east and sets due west, and a stick's shadow tip traces an almost straight east–west line all day.

Once one solstice is fixed, count days. Mark it on something that lasts — a notched stick, a stone line, a written record — because one missed winter is enough to lose the count.