The Universal Dialist’s Companion
A really useful device
© Mike Shaw
Incorporating many additions,
suggestions and graphics from
Tony Moss
of
Sundial Equations – there’s a lot of them
sin(A) = sin(L) sin(D) + cos(L) cos(D) cos(HA)
cot(Z) = {cos(D)sin(HA)}/cos(A)
cos(HA) = - tan(L) tan(D)
But what do they all mean?
Can you visualise what they represent?
I couldn’t, but
then I found this
book by
Peter Drinkwater
…and inside
was this
diagram that
explained it all
With a bit of refinement, and a few additions,
it can help you find out all sorts of things for
any Northern Latitude.
But first, let’s recap on what we know …
We know that the earth goes round the sun like this …
… and that it is tilted at about 23.5 degrees from the vertical
We also know that
the earth rotates
once on its axis
each day, with
every 15 degrees
of longitude
representing one
hour
So from the top it
looks like this …
… or this could be a
slice representing
the equator
Usually the earth is
shown tilted at 23.5
degrees like this
Which is OK if
you live at the
Arctic Circle
But I think that I
live at the top,
like this
Actually,
everyone thinks
that they live at
the top, that’s
what makes
designing dials
difficult.
So what do things look like from where I live?
How does the sun appear to move across the sky?
How does the time and direction of sunrise and
sunset change with the seasons?
What are the dial limits at my location?
We need a Dialist’s Companion
This is how
you construct
one
Everyone carries a sphere around with them
It’s the sky above them, and the
earth beneath their feet
On a flat surface, we represent it as a circle.
This is the horizon, you can’t see anything below this line
You are looking due east into the screen, with north to
your left, south to your right and west behind you.
If you point at the pole star with your left hand,
you are pointing along the axis around which
the earth rotates
53’22”
In Bebington, where I
live, that is 53 degrees,
22 minutes North
This vertical line is the
end of a wall that runs
due east : west.
So this is a
direct south
facing wall
and this is a
direct north
facing wall
The line perpendicular to
the earth’s axis is in the
same plane as the equator
23.5
23.5
Lines drawn 23.5 degrees from
the plane of equator mark the
northern and southern limits of
the sun’s travel, the tropics of
Cancer and Capricorn.
If we extend these
lines parallel to
the equator, and
draw a circle
within the limits,
this then
represents the
earth’s annual
path around the
sun
We can use this to find the sun’s
position throughout the year
We do this by
dividing the circle
into 12 equal
parts, starting at
the equator (the
equinox)
These now
represent the
dates covered
by the 12
signs of the
zodiac
We extend these
divisions
parallel to the
equator, they
then represent
the sun’s path
on the surface
of our sphere on
the respective
date.
Next the equator is
rabatted and laid
flat at the base of
the axis of rotation
We then divide
it to show the
hour lines, and
bearings (in
degrees) from
North
And use it to
determine
where the hour
lines intercept
our sphere
So that we can
draw “hour lines
in the sky”
Now we’re
ready to use
our
Dialist’s Companion
Remember
that you
can’t see
anything
below the
horizon
This is
the sun’s
path on
the
longest
day
At the equinox
it’s here
On the
shortest
day
Longest day
But, of course,
it’s really in 3
dimensions,
like this
Equinox
Shortest
day
On the
longest day,
the sun rises
at 03:20 and
sets at 20:40
All times are local
apparent time
These are the
overall dial
limits for this
latitude
On the shortest
day the sun
rises at 08:20
and sets at 15:40
As this is the
pivot point,
this happens
at every
latitude
At the equinox, the
sun rises at 6am
and sets at 6pm.
Limits for a
direct north
dial are 03:20
to 07:20 then
16:40 to 20:40
What about other Northern latitudes?
What you need is a
Universal Dialist’s Companion,
one that can be easily adjusted for any
latitude.
It looks
like this
The rebatted
equator is
discarded, and
the new circle
at the bottom is
the rebatted
local horizon.
The bottom
circle has the
azimuth
marked in
degrees from
due south.
The circles
show
altitude;
effectively
we are
looking
down on the
top of our
sphere
Let’s have a
look at the
top part.
There is a
pivot in the
centre, so
that any
latitude can
be selected.
The latitude
scale has
moved to
the bottom
to get it out
of the way,
here set at
51 degrees
Note that a
scale of the
sun’s
declination
has been
added.
And the date
scale now
shows
calendar
months rather
than zodiac
signs
The
previous
latitude
scale is
now used
to find the
sun’s
altitude …
… and there are
crepuscular
lines showing
civil, nautical
and
astronomical
twilight
We are in the South of England at 51º Latitude
It is 9 am on 1st August
So what can we find out?
The sun’s
altitude is
42º
9am on 1st
August
The sun’s
declination is
+18º
Sunrise
was at
04:20 and
sunset will
be at 19:40
Civil twilight
is at 20:20
Nautical
twilight is at
21:15
Astronomical
twilight is at
22:45
Note that the sun does not reach astronomical twilight
at this latitude near the summer solstice
We use
the lower
circle to
find
azimuths
Sunrise is at
121 degrees
east of south
Sunset is at
121 degrees
west of south
The dial
limits for a
horizontal
dial at this
latitude are
03:55 to
20:05
Dial limits for
a direct North
dial are
03:55 to
07:15
and
16:45 to
20:05
The lower
circle can
be used
to find the
dial limits
for a
declining
wall.
A wall
declines
14º east
of south
Draw in
the wall
Project up to
the upper
circle
Dial limits for
51º latitude
are 05:15 to
17:10
The lower
circle can
be used to
plot the
sun’s path
on our
sphere,
here
plotted for
the
longest
day
Drop a
vertical
wherever
the sun
crosses an
altitude
line and
mark the
position
This can be
used to
find the
azimuth at
any time on
that day.
Drop a
vertical
down to the
sun’s path
Here, at
9am the
azimuth is
73º east
Then draw a
line from the
centre
through to
the azimuth
scale.
But the great thing about the Universal
Dialist’s Companion is that we can go
anywhere we like – lets start at the North
Pole, and see what we can discover
At the north
pole, the sun
is above the
horizon from
the spring to
the autumn
equinox.
Set the
pointer to 90
degrees
It maintains
the same
altitude all
day.
The sun’s
altitude is
equal to the
declination
At the Arctic
circle
The sun never
sets on the
longest day
At the Arctic
circle
And the sun
never rises
on the
shortest day
At the
northern
tropic
The sun is
directly
overhead only
on the longest
day
The sun shines
all day on a
north facing
wall at the
summer
solstice.
At the
equator
The sun shines
on a north
facing wall for 6
months, and a
south facing
wall for the
other six
months
The sun rises at
6am and sets at
6pm every day
There is very
little twilight
And you can look at any northern latitude
So, with this simple device, you can, for any chosen date:
Find the time and azimuth of sunrise and sunset.
Find the time of Civil, Nautical and Astronomical twilight.
Find the sun’s altitude and azimuth at any time.
Find the sun’s declination.
Find the dial limits for horizontal, declining and
direct north dials.
That’s really all there is to it …
and not an equation in sight.
Thanks for your attention