Sundial calculation

A study of sundial calibration for eight selected altitude dials

Mathematical diagrams for the circular altitude dial.

This dial has circular graduations for dates. The gnomon is fixed, and the hour point on a circle is where the nodus shadow falls. A series of calculations for coordinates (X’, Y’) give the calibration for the whole dial. These calculations are by numerical iteration on computer.

Altitude dials are an intriguing type of sundial. There are many individual types, and they mainly date from around the 1600s or earlier. Our own design for a full-scale altitude sundial for the garden is a circular dial. It follows the same working principle as a circular brass dial in The Augustine Museum in Germany. We decided to investigate the calibration of eight different altitude dials, including the one from the museum, and we have now completed a study of their mathematics. We submit the report of our study in full for wider interest here: A Study of Altitude Sundial Calibration.

 

 

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A circular altitude sundial at full-scale for the garden

Altitude sundial in the garden

The altitude sundial in sunshine on 21st July 2026. The dial reads 3:50 pm, which is only 4 minutes difference from clock time, with corrections made for BST, Longitude, and EOT. The reading point is the tip of the shadow, which is the shadow of the gnomon nodus. 

The altitude sundial is an intriguing instrument. It relies on measuring the height of the sun to tell the time. It also requires the user to adjust for the time of year before making a reading. There are many altitude sundials and there is one particular one with a circular dial, from around the year 1600, which we find very interesting. We have now designed and built one like it at full-scale for the garden. Continue reading

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Inverkeithing Mercat Cross – sundial restoration complete

Inverkeithing Mercat Cross, the capital stone, cube sundial, and unicorn fully restored.

The Inverkeithing Mercat Cross is a tall stone column in the centre of the town. The capital stone, cube sundial, and unicorn sculpture are at the top of the column. There has been no ‘Cross’ as a Christian symbol on the column since the Reformation. Photo: Graciela Ainsworth.

The Inverkeithing Mercat Cross is a tall and handsome piece of historic town architecture. The Mercat Cross in Scottish towns was a symbol of licensed authority to trade in goods, and the trading place was at the Cross. The sundial would be a 17th century addition, now fully restored, together with the heraldic capital stone and the symbolic unicorn of Scotland.

The sundial is a cube stone which is ideal for a prominent place in a town. It is visible from all sides and it shows the time at all hours of the day. Continue reading

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Haddo House cube stone sundial restored and reading solar time

Haddo House stone cube sundial

This sundial cube stone has fine carving detail. Each of five faces can read the time. The horizontal dial carved in the stone on top indicates an ornamental piece for a garden. A cube set on a tall pillar or on a wall will have the side dials only. Photo: Graciela Ainsworth.

This cube stone sundial stands in the garden of Haddo House, the National Trust for Scotland property in Aberdeenshire. When we examined it at the workshop, it had broken and missing gnomons and moss obscured the dials. After restoration the dials can now read solar time properly again.

A cube dial has the mathematical attraction of reading time by the sun on south, east, west, and north faces. As a result, as the sun moves round, the cube sundial is an excellent device for showing time Continue reading

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Restoration of Inverkeithing Mercat Cross, finding true North

The azimuth sundial instrument

The azimuth sundial used as a measuring instrument for finding north. The cursor is set for the date, the cursor arm is turned to set the time. The gnomon shadow and cursor are in line.

The Mercat Cross at Inverkeithing in Scotland is a tall stone column that dates from the 14th century. The top of the column has a sundial stone in the form of a cube and a unicorn. Restoration of the whole column is now complete. To re-install the sundial stone correctly we had to find a true north line.

The north line is the direction that shadows will fall at noon, and Noon is the exact time of day when the sun is in the south. Continue reading

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A design of azimuth sundial to go in a garden

Azimuth sundial on 10 October at 11.10am

On 10 October the autumn equinox has passed and the cursor reading point has moved out from the inner circle of the dial towards winter solstice at the circumference. The sighting arm carries a short vertical gnomon which casts its shadow in line with the sun.

The azimuth sundial is an intriguing instrument. It finds the time from the direction of the sun. This idea sounds simple, the sun rises in the East, at Noon it is due South, and it sets again in the West, but it is complicated by the time of year. This note is about a new design for a precision azimuth sundial to go in a garden. Continue reading

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A modern altitude sundial after Erasmus Habermel

A modern circular altitude sundial after Erasmus Habermel of Prague

Modern reconstruction of a 16th century altitude sundial for studying its mathematics and accuracy. An altitude dial uses the height of the sun to find the time. The dial is double-sided with the two half-years back-to-back.

Erasmus Habermel was a renowned scientific instrument maker working in the court of Emperor Rudolf II in Prague in the 16th century. He made instruments for all disciplines including astronomy and navigation. One of his sundials is an altitude dial in the clocks collection of the Augustine Museum in Freiburg im Bresgau*. It is an elegant circular dial and the mathematical construction is intriguing. Continue reading

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Calibrating a new obelisk sundial in stone

Inclined test dial facing east

This dial stone is a test piece for the new obelisk sundial, and is on a board at the correct angle for one of the faces of the obelisk. It faces East and inclines 61° to horizontal so the shadow of the temporary plastic gnomon will show the time.

Obelisk sundials carved in stone were popular in Scotland in the 17th and 18th centuries. Quite recently stonemasons in Fife have done the work to carve a new obelisk sundial for one of their clients. Its dials have remained blank for mathematical calibration. Macmillan Hunter are responsible for the calibration and have supplied detailed dial instructions and drawings for the mason to use together with the required set of geometric bronze gnomons. Continue reading

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North alignment on a Victorian pedestal

Sun direction measured with an angle finder

The direction of the sun measured against one edge of the octagonal stone pedestal using the angle finder and light slit

A Victorian sundial pedestal stands in the gardens of Riccarton estate outside Edinburgh. It once held a beautiful octagonal dial which is now in safe storage. A replacement dial is to go on show and it must be in a correct orientation. The gnomon on a sundial must point north. A wrong alignment will make the sundial inaccurate, and nothing on the 19th century pedestal actually marks the north. Continue reading

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Wall sundial at Royal Square in St Helier, Jersey

Wall sundial at St Helier, Jersey

Wall sundial in Royal Square at St Helier, Jersey, Latitude 49.1839° N, Longitude 2.1057° W. The inscription reads: REGULATE YOUR CLOCKS BY THE SUN DIAL. CORRECTION MUST BE MADE FOR THE EQUATION OF TIME WHICH IS GIVEN IN ALL THE ALMANACKS.

This beautiful sundial is set into the wall of the old Picket House in Royal Square, St Helier, Jersey. Historical records show it was made by a talented Jerseyman called Elias Le Gros in the 1820s. In spite of being plastered over at one time by the military authorities and then restored again in 1875 after a public outcry over the dial’s obliteration, it is now in excellent condition, as our photo shows. Our host for lunch that day told us: “The dial is much admired but of course it isn’t accurate.” Poor old Elias Le Gros, now was the time to rescue his reputation! Continue reading

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