Article of the month May

Flash sundial

This wooden indoor sundial is located on a latitude of 45 degrees north and is aimed north.
The view through the window is almost south and we can expect the sun there.
The sundial receives no direct sunlight, but it does use sunlight to show the time.

Over the sundial, a special construction is visible.
There is a small motor, the axis of which is parallel to an imaginary pole style.
It runs at a speed of approximately 10 rotations per minute and is powered by solar cells.
If there is no sun it stops, but then the dial does not need it anyway.

A small mirror is fixed to the axis. Two side walls reduce its width to only 2 mm. The length is arbitrary.

The motor rotates the slit so formed through all possible hour planes, once every six seconds.
Now suppose, for instance, that the time is true noon. When the rotating slit passes through the meridian plane, the mirror will reflect the sunlight and a flash of light falls on the corresponding hour line on the sundial.

This is true for any other time as well. The rotating mirror will only reflect the sunlight when the slit it is in the hour plane of the sun.
The flash of light on the sundial moves with the sun and is visible every six seconds.

The sketch below shows the principle of the set-up.
The calculation of this special sundial is done as if the latitude were zero.
For any other latitude, the entire sundial is inclined accordingly.

Note: the angles in this sketch are not correctly drawn.
It appears as if the mirror is parallel to the sundial face, but that is in fact not the case in this example.
There is some freedom in the choice of the angles that are here marked 18 and 33 degrees.