How Does a Sundial Work? A Shadow Aligned With the Earth's Axis
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A stick in the ground casts a shadow that moves through the day, and using it to tell the time accurately requires one specific piece of geometry: the shadow-casting edge must point at the celestial pole, parallel to the earth's axis. Get that right and the hour lines are fixed for the whole year. Get it wrong and the dial reads differently every month.
The crucial alignment
The sun appears to move across the sky because the earth rotates about its axis, so a rod aligned parallel to that axis, pointing at the celestial pole, is the only orientation whose shadow sweeps at a constant rate regardless of the season. That rod is the gnomon, or more precisely its upper edge is the style, and aligning it means tilting it from horizontal by an angle equal to the local latitude, pointing towards true north in the northern hemisphere and true south in the southern. A dial made for one latitude does not work correctly at another without adjustment, which is why a souvenir sundial taken home is decorative rather than functional. On a correctly aligned horizontal dial the hour lines are not evenly spaced, with the spacing calculated from a formula involving latitude, while on an equatorial dial, whose face is parallel to the equator, they are evenly spaced at fifteen degrees per hour, which is the simplest case and the least convenient to build.
Why sundial time is not clock time
Even a perfect dial disagrees with a watch, for three separate and cumulative reasons:
- •The equation of time, a correction of up to about sixteen minutes either way over the year, caused by the earth's elliptical orbit making its orbital speed vary and by the tilt of its axis, which together mean true solar days differ slightly in length
- •Longitude within a time zone, since clock time is uniform across a zone spanning many degrees while solar time varies by four minutes per degree, so a dial in the west of a zone reads substantially behind the clock
- •Daylight saving, which shifts the clock by an hour for part of the year and which no dial accounts for
- •Together these can put a correctly built dial more than an hour away from a watch, which is why dials carry correction tables or an analemma, the figure-of-eight curve tracing the equation of time through the year
- •A dial reads apparent solar time, which is what the sun is actually doing, and clocks read mean time, which is an average invented for convenience
- •Before railways forced standardisation, towns kept their own local solar time, and the dial was the authority against which clocks were set rather than the other way round
The forms they take
Dials are built in several configurations to suit where they are mounted. Horizontal dials, the familiar garden type, work all day in summer and are read from above. Vertical dials mounted on walls are extremely common on churches and public buildings, and their hour lines depend on which direction the wall faces as well as on latitude, so a south-facing dial and a south-east facing one are different instruments. Equatorial dials have the simplest geometry and require the face to be flipped between summer and winter as the sun crosses the equator. Polar dials have the face parallel to the style. Analemmatic dials use a vertical gnomon that must be moved along a date scale, and are frequently built at human scale so a person standing on today's date becomes the gnomon. Portable dials with a compass and adjustable latitude were carried as travelling clocks for centuries, and nocturnals performed the same function at night using the rotation of stars around the pole.
What they were for
Sundials were the primary timekeeping instrument for most of recorded history, with Egyptian shadow clocks dating from around 1500 BCE and Greek and Roman versions widespread, and ancient designs frequently divided daylight into twelve unequal hours that changed length with the season, which suited a society organising itself around daylight rather than around an abstract standard. Islamic astronomy advanced the mathematics considerably, partly because prayer times are defined by the sun's position and require accurate determination. Medieval European churches carry scratch dials marking the times of services. The invention of mechanical clocks did not immediately displace dials, because early clocks drifted badly and had to be reset regularly against the sun, so a dial on a church wall and a clock in its tower coexisted for centuries with the dial as the authority. Only when clocks became more accurate than the correction procedure was worth did the relationship reverse, and dials became ornaments, which is what almost all modern ones are.
The takeaway
A sundial works correctly only when its shadow-casting edge is parallel to the earth's axis, tilted at an angle equal to the local latitude and pointing at the pole, which is why a dial made for one latitude fails at another. Hour lines on a horizontal dial are unevenly spaced and their spacing depends on latitude. Even a perfect dial differs from a clock by the equation of time, by longitude within the time zone and by daylight saving, and it was long the authority clocks were set against.