gnomonic map projection | Helios Sundials

First sundial with a world map with gnomonic projection by Franz Ritter, published in the magazine Speculum Solis (1640). Source and copyright: Austrian Academy of Sciences

The Qibla, the direction of prayer towards the Kaaba in Mecca, is a great circle that is depicted as a straight line on the gnomonic map. The plane of incidence of sunlight also always intersects the earth's surface in a great circle and the map plane always in a straight line.

The sun crosses the equator at the equinox at 2 pm GMT. The sub-solar point is projected onto the gnomonic world map.

A horizontal sundial with a gnomonic map projection. The 47mm high gnomon shows the subsolar point at the tip of the shadow.

$The sunlight is refracted in the transparent body. The shadow of the pinhole is shifted to shorter distances.$

The sunlight is refracted in the transparent body. The shadow of the pinhole is shifted to shorter distances.

$In one experiment, the gnomon of the horizontal sundial is replaced by a transparent body with a pinhole aperture. The optical density in the body initially corresponds to that of the surroundings (refractive index n=1.000).$

In one experiment, the gnomon of the horizontal sundial is replaced by a transparent body with a pinhole aperture. The optical density in the body initially corresponds to that of the surroundings (refractive index n=1.000).

$If the refractive index is increased (here n=1.101), the solar event horizon is reduced from infinity to a diameter of 204 mm.$

If the refractive index is increased (here n=1.101), the solar event horizon is reduced from infinity to a diameter of 204 mm.

$With a refractive index of n=1.333, the refractive index of water is reached. The distortions of the world map are significantly reduced.$

With a refractive index of n=1.333, the refractive index of water is reached. The distortions of the world map are significantly reduced.

$With n=1.491, the refractive index of acrylic glass, we reach our goal, the gnomonic world map of ORBIS SOLARIS. The solar event horizon has a diameter of only 85mm.$

With n=1.491, the refractive index of acrylic glass, we reach our goal, the gnomonic world map of ORBIS SOLARIS. The solar event horizon has a diameter of only 85mm.

The ORBIS SOLARIS with undistorted gnomonic world map shows the subsolar point exactly.

The gnomonic map projection and its special use in the ORBIS SOLARIS sundial

The ORBIS SOLARIS world map is a gnomonic map projection of the globe. Gnomonics is the science of sundials, which predestines this map projection for use in a sundial. Nevertheless, this rarely happens because it only shows the world in a highly distorted and incomplete way.

The video clearly explains the gnomonic projection, its extraordinary properties and its convincing use in the ORBIS SOLARIS sundial due to the refraction in the acrylic glass body:

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A video by Carlo Heller. Speaker: Richard Martin

If the video does not run in your browser, then watch it on YouTube.

The ORBIS SOLARIS is available in our sundial store.

A brief history of sundials with gnomonic projection

The story begins two years before the publication of Johannes Kepler's ASTRONOMIA NOVA (1609). In 1607, the theologian Franz Ritter from Nuremberg published the first sundial with display of the subsolar point on a gnomonically projected world map in SPECULUM SOLIS (Sun Mirror). A later edition of this sundial from 1640 can be downloaded from the Austrian Academy of Sciences and is shown above.

William Andrewes launched a modern version of a horizontal sundial with a gnomonic map projection. In 2003, he completed his first prototype of the “Longitude Dial”. The sundial shows the zonal solar time with the shadow of a wire rope, the standard time can then be calculated taking into account the equation of time. A small sphere mounted on the wire rope indicates the subsolar point. However, as on the historical model, only part of the continents are shown on the distorted world map, which theoretically extends to infinity.

Heinz Schilt took the first step towards reducing the expansion of a horizontal sundial by refraction in water in 1956 with his “sundial in the bathing pond”, which used a “water lens” (water flowing out of a pipe) to project a bright spot of light onto the dial drawn on the flat bottom of the pond.

His compatriot Ernst Lobsiger, who knew the famous Swiss sundial expert from several encounters, took up the principle with a new idea in 2024. He used a horizontal dial with a gnomonic world map in a water basin. The world map was created from NASA satellite data and makes it possible to track the subsolar point when the sun is shining. In addition to the true local time, the dial of the sundial also shows UTC, the Italian and Babylonian hours and the position of the sun in the zodiac.

When Ernst Lobsiger approached Carlo Heller in May 2024 with a question about the long-term stability of Dibond under the influence of the weather, he was immediately enthusiastic about Lobsiger's sundial idea. As water was out of the question as an optical medium for a sales product, Carlo Heller used acrylic glass for his first prototypes. He quickly developed the ORBIS SOLARIS sundial, which was launched on the market before Christmas 2024.

Read the article "In the footsteps of Heinz Schilt" by Ernst Lobsiger in our sundial blog. In addition to the exciting story of Heinz Schilt's gnomonic work, Lobsiger also goes into detail about his sundial in the water basin. The sundial ORBIS SOLARIS by Carlo Heller has also received his tribute.

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The gnomonic map projection and its special use in the ORBIS SOLARIS sundial

A brief history of sundials with gnomonic projection