Sundial Park Genk

8. Digital sundial

Digital sundial

Be it accidental or not, the four most innovative sundials line the high side of the Sundial Park: the digital dial, the conical dial (nr. 9) and the shadow plane dials (nr. 10 and nr. 11).

"What in heaven is a digital sundial?" That was the title of an article in Scientific American (August 1991), which prompted a flurry of mental activity in many a smart brain. One answer is on display here: a sundial that displays the time, not by throwing a shadow on a set of lines, but in plainly readable digits. The dial functions from 8:00 to 5.55 hr, in 5 minute steps. There is a smooth transition from one reading to the next. In the picture above, the "0" from 3:20 is still faintly visible.

The sundial has been invented by Hans Scharstein and Werner Krotz-Vogel (Germany) and Daniel Scharstein (USA). See for more information the website of Digital Sundials International.

My comments:

A real black box!

Black box up in the sky When we first visited the Sundial Park, I saw this shallow black box high on a pole, still needing support apparently. The weather was heavily overcast, and the object gave no indication of any sundial functionality, be it that the short rod carrying the box seemed to be pole-stylish. It looked as if something could be displayed on the black screen, but no electrical connection could be seen. Sine sole sileo (I am silent without sun) would be a most adequate motto for this device!

Principle of the digital dial

The sundial consists of two closely spaced parallel masks. The first mask, facing the sun, has a regular array of thin vertical slits, which cast a striped light pattern onto the second mask. That mask, facing the visitor, is composed of narrow stripes, cut from the digits to be displayed. These stripes are intermingled, so that they are illuminated consecutively. The figures below illustrate this in a simplified example for the right-most numeral, which is either a "0" or a "5".

mask facing sun
Slits in the first mask
mask facing visitor
Intermingled stripes from 0 and 5

In one position of the sun, the stripes cut from the "0" are lit. Five minutes later the sun has moved over 1.25° and the stripes derived from the "5" are illuminated. Again 5 minures later, the stripes from the "0" are again illuminated, but the light falling through a given slit has advanced one stripe to the left.

Principle of digital dial

A translucent screen behind the second mask helps diffusing the thin light lines and enables the numerals to be read from a broad angle. Narrow your eyes, if necessary, to simulate this effect.

Fine stripe pattern In reality the twelve numbers for the minutes display: 00, 05, 10, ..., 50, 55, are cut and intermingled together. So only after one hour will the light falling through a given slit has advanced one stripe to the left. Similarly, the ten hour numbers: 8, ..., 12, 1, ..., 5 are mixed in the left half of the box. The fineness of the fabrication process is obvious from the picture at right, showing a detail from the top one: between each pair of light lines, eleven others will appear successively in one hour time.

The slits and the stripes are pointing to the celestial pole, therefore the date (declination of the sun) does not play a role. The principle and construction of the digital dial is described in more detail in the patent application.

The trick that makes it really work

That sounds not too complicated, isn't it? No, but it wouldn't work very well this way...
In fact, each slit in the first mask is the gnomon of a small polar dial. The stripes in the second mask are the time lines: 5-min lines for the minute numbers, 1-hour lines for the hour numbers.

First, have a look at the dial face of a polar dial, such as the Book of Time (nr. 12). The hour lines are not equally spaced, but their interval increases considerably to the sides. The shadow of the pole-style moves slowest across the dial face around noon, and faster in the morning and the afternoon.
Now have a look at the right-most panel in the figure above, the one with the three sun icons. Assume that we are here somewhere in the afternoon. The effect of increasing velocity of the lines of light would cause them to hit the next stripes just somewhat too early. The effect would get stronger as the sun moves further to the west, so that the time would advance at an increasing pace. And that is not what a clock is expected to do...
What is needed is a way of linearizing the relationship between solar angle (corresponding to time) and the velocity of the light across the second mask.

Refraction of light at boundary This problem can be solved by profiting from an oddity of nature, and that is in my view the real heart of this invention. This 'oddity' is Snell's law of refraction, which describes how light traverses the boundary between two media. The relationship between angle a (in air) and b (in some transparent medium) depends on the index of refraction n of the medium:
  sin(b) = sin(a)/n .

The larger a gets, the more b will lag behind. The solution thus is to fill the space between the masks with a transparent medium. The effect can be seen in the following graph, where the distance of the light line (expressed relative to the height of the pole-style above the dial face) is plotted versus the time. The curve for n = 1.0 depicts the common polar dial in air. The refraction index of water is n = 1.33; for many transparent solid substances, like glasses and plastics, the value is between 1.4 and 1.6. A transparent medium between the masks, such as a sheet of plexiglass, effectively linearizes the time scale, up to at least 4 hours before and after noon.

Linearization of polar dial

Four large digital dials installed

The digital dial in Genk was the first one on public display world-wide. Next, the Sundial Garden in the Deutsches Museum in Munich (Germany) had one installed, followed by the Municipal Museum in Köln (Cologne, Germany). The latest one is in front of a house on Martha's Vineyard, an island off the coast of Massachusetts (USA).

The window-sill version

A smaller version of the digital dial has been developed that can be placed on the window-sill of a south-facing window. The minutes now are displayed in a column to the right of the hour numbers, in 10 min steps. The advantage is that the transition from one number to the next does not occur at the same place. This enables accurate reading, by interpolating the observed intensities. In the example below, it is between 12:35 and 12:40 hr.

Window-sill version

A new type, or just a multiple polar dial?

Grand piano Is this just a multiple polar dial, comparable to multiple dials like the polyhedron dial (nr. 4)? Some people think so. In my view, that does not do justice to the degree of organization of this instrument. Using an array of hundreds closely spaced, interacting polar dials to get pictures out of the instrument is quite an innovative step. As a metaphor, compare a single string under tension that produces a single tone when hit with a piano on which a Beethoven sonata could be played (or a boogie-woogie if one preferred).

Other 'digital' dials

Several sundial designers have called their product 'digital'. Examples are:

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