Article of the month June

Constant daily insolation

The graph below shows daily insolation over the year for a south dial in Utrecht, on 52 degrees north latitude. The graph uses apparent time.

In autumn and winter, the insolation equals the time that the sun is above the horizon, with a maximum of twelve hours.
In spring and summer, the sun is above the horizon for longer than twelve hours, but the insolation of the south dial reduces to approximately nine and a half hours on the longest day.
This comes about because the sun is behind the sundial face for part of the time.

We see the sundial insolation vary over the year.
In general, insolation should be examined for any surface in order to determine which hour lines would be useful on it.
More about this is in
Article of the month for February in the 2003 archive.

We will now present a sundial for Utrecht that has the same insolation every day of the year.
For Utrecht, that is approximately seven and a half hours.

The proposed sundial surface both inclines and declines.
For Utrecht, the numbers are:
inclination: 118,384 degrees
declination: -40.249 degrees.
Like an old wall, the surface leans towards us by 28 degrees from the vertical.
The extension of the wall intersects the horizon in the northeast, where the sun rises on the longest day.
The style height for this sundial is -52 degrees. The sundial face is parallel to the horizontal plane at 52 degrees south latitude.

The next graph shows the daily insolation for this surface. It is from sunrise to approximately seven and a half hours later, for every day of the year.

A design sketch shows what such a sundial could look like in reality.
The sundial reads apparent time.
Observe that the noon hour line is not vertical.

Remark 1:
The surface with:
inclination: 118,384 degrees
declination: + 40,249 degrees
also satisfies the requirements for equal daily insolation.
For this surface, that would be from about seven and a half hours before sunset, to sunset.

Remark 2:
There are more surfaces with constant daily insolation, but the duration would be less.
The example achieves the maximum constant daily insolation.