Mountain sundial

A sundial with a real mountain in the middle. A rod set in the summit points at the pole star, and its shadow tells the time on hour lines that run over the real ridges and valleys, worked out for the place where it will stand.

Pick a mountain

Drag and zoom the map: the rod goes in the highest point inside the dashed square, and the circle is the land on the dial. Click near a peak to put the rod there.

Where it will stand

Clock time zone (standard time, without summer time)

The model

Plate

Height of the summit

A taller mountain looks grander, but when the sun is low the rod’s shadow then falls past the dial.

Date lines: the longest day, the equinoxes and the shortest day The noon figure-8 24-hour numbers Engrave terraprinter.com underneath

Colours

In the 3MF the dial, the engraved lines and the rod are each their own named part.

How to set it up

Put it on something level in the sun, where it gets the most sunny hours.
Turn it so the rod points to true north (true south in the southern hemisphere): use a phone compass set to true north, not magnetic north.
Or wait for solar noon (on the instruction card for every two weeks): the shadow of a plumb line then points due north or south. Turn the dial so the line from the summit to the notch at N lies along it.
Read the hour where the rod’s shadow falls, and add the correction for the date from the card. In summer time, add an hour.

Download

Instruction card

One page to keep with it: how to set it up, how to read it, the correction for every two weeks of the year, the rod’s length and how to print it.

Free for personal use, and for selling up to $5,000 a year with a TerraPrinter credit. Bigger sellers need a commercial license. Keep the data credits. License

How the mountain sundial works

The rod points at the pole

The rod is tilted to point at the celestial pole, the spot in the sky the stars turn round (close to the pole star in the north). The sun goes round that same axis once a day, so the rod’s shadow turns steadily through the day, at the same hour in the same place all year. That is why a bare mountain can’t be a sundial on its own, but a mountain with a rod can.

Why the lines bend over the mountain

Each hour the rod’s shadow lies in one flat slice of space through the rod. Where that slice cuts the plate the line is straight; where it cuts the mountain it follows the ground up ridges and down valleys. The page works out every line on the shape you print, so the shadow lands on them wherever it falls.

The figure-8

A sundial shows the sun’s time, which runs up to 16 minutes ahead of the clock in November and 14 minutes behind in February, because the Earth’s orbit is an ellipse and its axis is tilted. The tip of the rod at 12 o’clock on the clock traces a figure-8 over the year. The date lines show where the tip’s shadow runs on the longest day, the equinoxes and the shortest day.

Made for one latitude

The rod’s tilt and every line depend on how far north or south the sundial stands, so it is made for one place. It tells the right time within about 2° of latitude (around 200 km north or south). The hours are moved for your longitude within your time zone, so it reads the clock’s standard time.

When the shadow falls off the dial

The rod starts at the summit, high above the plate. When the sun is low, early or late in the day or in winter, its shadow can fall past the edge. That is why the summit sits off-centre, towards the equator, as the pointer does on a garden sundial: the shadows fall the other way, so they get most of the plate. The page counts how many sunny hours of the year it can be read, and picks a summit height that keeps that high. Make the summit lower to read it more often, or taller for a grander mountain.

In the classroom

Make one for your school and check it against the clock every week: does the gap follow the figure-8? Why does the noon line not point exactly north? Compare a dial made for your town with one made for a town far north: how do the rod and the lines change?

Elevation: Copernicus DEM GLO-30 (© DLR e.V. & Airbus) and Mapzen Terrain Tiles on AWS (SRTM, GMTED2010, ETOPO1 and others). Map © OpenStreetMap contributors, © CARTO. Sun positions: NOAA’s solar calculator method. More to make: an erupting volcano, a terrain zoetrope, the TerraPrinter app or more 3D map gift ideas.