Hello Roger,
Any thoughts on how one should calculate solar coordinates to be
most precise/accurate? Most solar coordinates are computed for the
center of the solar disk, I would like to hear feedback (since I don't
believe this topic has come up yet) on using coordinates based of the
solar limb (instead of the center) to increase precession and accuracy
in resolving the cast shadow. I await another stimulating thread.
Best Regards,
Luke
Roger Bailey wrote:
>
> Dear John Carmichael,
>
> Well done John, Your simple question again triggered an avalanche* of
> responses from us nit picking old timers.
>
> By now the difference between accuracy and precision is well defined. I
> would like to return the discussion to sundial design. The accuracy of a
> dial depends on the skill of the designer, builder and installer. It should
> take into account the latitude, longitude and orientation of the dial.
>
> The precision of a sundial is limited by the fact that the sun is not a
> point source of light but is a disk about half a degree wide. The shadow
> edge is fuzzy for half a degree as the sun is partially covered (penumbra
> shadow) and then totally covered by the umbra shadow. Size does not matter.
> A small dial seems to have a sharper shadow but it cannot be read as
> precisely. A large dial allows division into smaller units of time but the
> shadow is too fuzzy to read precisely. For a rod type of gnomon, the
> problem is even worse. It may be too narrow to completely cover the sun
> and produce the dark umbral shadow.
>
> There is a simple demonstration of this phenomenon that I observed one
> morning. Stand by a window with the sun at your back and casting your
> shadow on the floor. Move away from the window until the shadow of your
> head is about 4 inches (10 cm) from the shadow of the top of the window.
> Then slowly more to bring your shadow up to the window shadow. As the
> penumbra shadows of your head and the window start to intersect, the dark
> shadow will grow. The top of your head will seem to swell upward as the
> shadows come together. Repeat to confirm the phenomenon. This is best done
> in the privacy of your own home.
>
> In that twilight zone of partial shadow, a sundial cannot be precise. Half
> a degree is two minutes of time. But there are techniques to minimize the
> problem and read a dial to a precision of less than a minute. One is to use
> a disk or ball on the gnomon to cast the shadow. A properly sized disk will
> project a small dark umbral shadow at the center of the large fuzzy
> penumbral shadow. The Romans used this technique by topping their obelisks
> with spheres.
>
> Cheers from a swelled headed, nit picking, old timer,
>
> Roger Bailey
> Walking Shadow Designs
> N 51 W 115
> *where triggering an avalanche is not just a figure of speech!
