Fernando,
Fellow diallists,
>>> Fernando asked:
Given a certain latitude, how can we find the "best" angles for
a sundial?
For "best" I mean those that offer:
a) the longest insolation during the day
b) the longest insolation at the various seasons
c) the best azimuth (declination) and the best reclination so the
dial
can be place as high as possible and still get to be
seen comfortably (based on the angle, not on the size).
and with the sundial in the top of a 6-meter tall (19' 8") column
so as it can be the best possible visibility from the ground.
At the same time it should work all year round for a certain
latitude (in this case, 15 d 45' 5"S), from sunrise to sunset.
<<<
in trying to find a single plane dial;
At the Arctic [Antarctic] Circle the sun just does not set on the N [S]
horizon at midsummer.
Therefore a single dial must face generally N [S] of horizontal otherwise it
will not intercept that light.
However, at the Arctic [Antarctic] Circle the sun just rises on the S [N]
horizon at midwinter.
Therefore a single dial must face generally S [N] of horizontal otherwise it
will not intercept that light.
>From this we can see that only a horizontal dial will work in the polar
regions to (just) satisfy both requirements. This is clearly the case at
either pole where the sun travels along the whole horizon at the equinox.
And, in fact, a horizontal dial will work in all regions (because while the
ground is illuminated, so will be the dial) - the only problem here being
that it will be out of sight on the top of the pillar, unless you either
a) make it transparent and look at it from underneath or
b) place a mirror above it and look at the reflection (BTW, is this a new
(if rather impractical) idea of mine - can anyone cite an example?)
In the Northern [Southern] hemisphere above the tropics, a direct S [N]
vertical dial will not show earliest and latest hours at midsummer (or
indeed at any summer date between the equinoxes). If we take a horizontal
dial and tilt it towards either S or N, then the E-W line through the gnomon
will be higher than that part of the dial to the S or N of the gnomon foot
and will therefore shade the dial at sunrise and sunset either in summer or
winter. Therefore I do not think a single dial will suffice unless it is
actually horizontal.
Two vertical dials will solve the problem - at 51 deg N a SW and SE pair
work nicely. However as you go further towards the pole the angle between
them must decrease until in the polar regions they have to be back to back
e.g. N and S or E and W and sunlight arrives at one just as it leaves the
other with a glancing illumination, so three (or more) become preferable if
you wish at least one surface to be well lit at all times.
Typically in England pillars or other structures (e.g. above a church
parapet or roof) with four vertical dials (N, S, E, W) are reasonably
numerous, while occasionally one finds a larger number of equally spaced
ones (e.g. 6, Covent Garden, London; and 8, Douglas, Isle of Man). Omitting
the N dial is often no great loss as the E and W ones can be used for more
of the time anyway and there are quite a few of such E, S, W triplets (as
well as some approximately SW, SE pairs).
The complex multiple dials of Scotland are another subject altogether!
I think that a vertical S (N) dial just works on the northern (southern)
tropic. However, between the Equator and the Tropic, (and hence for
Fernando's actual problem ;-) ) I'll now leave it to others to discuss the
possible range of angles of a single inclining vertical dial, or between the
pair of vertical dials required.
Regards
Andrew James
