# Elevation sundial

Cylinder sundial for φ = 52 °

With an elevation sundial , the elevation angle of the sun is measured. On the date lines of the dial - the date of the year must be known - the time of day can be read off instead of the angle of elevation. Since the sun has the same height twice in one day, it must also be known whether it is morning or afternoon.

An elevation sundial must be aligned with the sun, which makes it suitable as a portable sundial .

## Measuring principle

With a sundial , the hour angle τ of the sun, which is a direct measure of the time of day, is also measured directly. Often the second equatorial coordinate (stationary system), the declination angle δ , is also measured directly and displayed as an approximate annual date.

The elevation angle h and the azimuth a are the two sun coordinates in the horizontal coordinate system . Sundials that measure these coordinates and thus allow conclusions to be drawn about the time of day are elevation sundials or azimuthal sundials .

A conversion equation between the two coordinate systems is

• sin h = sin δ sin φ + cos τ cos δ cos φ .

The conversion

• cos τ = (sin h - sin δ sin φ ) / (cos δ cos φ )

shows the hour angle τ as a function of the elevation angle h and the declination angle δ . The declination δ is therefore used as an input variable in order to determine the hour angle τ - that is, the time of day - via the elevation angle h . The parameter δ appears on the dials of the elevation sundials as a family of date lines.

Altitude sundials are also dependent on the geographical latitude φ. They are set up for a certain width, so they can only be used to a limited extent as travel sundials.

## Types of elevation sundials

The scale is a network of intersecting date (declination) and hour lines with an infinite number of possibilities. The dial usually adopts a vertical position with the advantage that it does not have to be set up for very long horizontal shadows in the morning and evening.

Only a few of the known versions are listed below:

Side light sundial

### Side light sundial

The grazing light sundial (see picture opposite) from ancient Egypt is the oldest known elevation sundial. The dial is inclined, has vertical rows of declination and oblique hour point rows. The height of the sun is indicated by the edge shadow of a block in front of the dial. The clock must be directed towards the sun so that the side walls receive grazing light.

### Cylinder sundial

The cylinder sundial was widespread in the late Middle Ages and early modern times . Shepherds used them in a smaller version, called the shepherd's sundial . The cylinder sundial was developed by Hermann von Reichenau (1013-1054).

The date lines are straight lines parallel to the axis. The clock is held vertically and with the horizontal shadow stick against the sun. The shadow stick is placed over the valid date line by rotating it. The intersections of the date lines with the hour lines form a scale from which the morning or afternoon hour can be read. The display point is the end of the stick shadow.

The figure above shows a cylinder sundial for latitude 52 °. The dial also shows how the length of the day changes over the course of a year.

The solar quadrant is a quarter disk that has to be held vertically . Quarter circles are drawn on it as date lines, which are intersected by S-shaped hour lines.

The intersection of a perpendicular with the valid declination line is used for reading. The plumb bob is attached to the center of the declination circles. The quadrant is set to the height of the sun when the sun touches one of the two radial edges of the sundial, which is controlled with a reticle (shadow of a “grain” falls on a “rear sight”).

The solar quadrant was invented in Spain around the year 1000.

### Pawn ring

With the pawn's ring , the dial is on the inner cylinder surface. The pointer is the image of the sun, which is created by means of a hole made in the cylinder wall. Most of the time, the date lines are circles around the cylinder axis.

In the standard version, the pawn's ring is held with a horizontal axis and rotated around the vertical so that the light spot falls on the valid declination circle.

### Habermel's sundial

The elevation sundial invented by Erasmus Habermel is a disc with radial date lines starting from the center and evenly distributed over the circumference. They are intersected by closed hourly curves that enclose the midpoint.

In the center there is a normally mounted shadow bar. The target is to be held in such a way that the valid declination ray falls straight down. It is to be turned towards the sun in such a way that the rod shadow hits the declination ray. Its end shows the time of day there.

### General clock tablet

General clock tablet

The German astronomer Regiomontanus has a particularly remarkable construction known as the “general clock panel”. It is a pendulum quadrant with the pivot point of the pendulum slidable on a surface so that the clock can be set to the current date as well as the latitude of the location. The pendulum length must also be set depending on the date and location. The time is read on a flat scale with straight hour lines, it results from the hour line to which the tip of the pendulum points. Sunrise and sunset can also be read.