A PLOTTING INSTRUMENT FOR SUNDIALS TO LAY
OUT ON SMOOTH OR IRREGULAR SURFACES
I) SUNDIALS ON IRREGULAR SURFACES… ................................................................. 2
II) INSTALLATION STYLE Two different techniques are possible................................... 3
III) THE LATITUDE SETTING............................................................................................ 4
IV) DEFINITION OF THE PARAMETERS USED TO GET A BETTER
UNDERSTANDING ........................................................................................................................... 8
V) DRAWING OF THE HOUR LINES: ............................................................................. 10
VI) DRAWING OF THE DIURN CURVES: ...................................................................... 10
VII) OTHER POSSIBILITIES ............................................................................................. 10
VIII) OTHER PRATICES: ................................................................................................... 10
After several months of work and much thought (sometimes helped by friends and after the
exhibition of a laser apparatus that Sir Vercasson presented at the meeting of our committee in Paris
the 12th of may 2001) I have the pleasure to present to you for your analysis an apparatus able to lay
out sundials on smooth or irregular surfaces.
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Gérard Labrosse , Les Varennes, 42460 VILLERS (France)
Member N° 35 967 C of the French Sundials Committee mailto:captainbrosse@hotmail.com
I) SUNDIALS ON IRREGULAR SURFACES…
THIS APPARATUS ALLOWS THE LAYING OUT OF SUNDIALS ON ALL KINDS OF
SURFACES WHICH HAS BEEN UP TO NOW IMPOSSIBLE.
The normal software cannot handle all surfaces that dialists need to use. Special software is
generally the solution for ordinary surfaces.
In all cases when the surface is irregular to trace the sundial (sculpture), the lay out becomes a
big problem.
The correct use of this apparatus requires a very methodical set-up and of course the
indispensable presence of the sun during the installation.
The design of this instrument differs from that of the “Astro-laser” and eliminates some
difficulties.
1) MODIFICATIONS BROUGHT ABOUT:
The centre of the Equatorial axis is now reachable.
The distance between the base of the gnomon and the centre which supports the lasers equals
the length of the polar style U. The layout of the diurnal curves must be respected so that it has real
meaning.
The size was particularly calculated to allow easy reading of the adjustment of the sliding
gauges. The lay out then permits a good precision.
Pointing towards the pole is now possible.
2) NEW POSSIBILITY:
The style can be positioned without wedges. It
is not necessary to make an outline or precise pattern.
One need only change the disc on which are the lasers,
by a half disc on which is in its centre a nail and a
thrust. This system allows the style to be put in the
correct position during the sealing. The point of
introduction of the style is indicated by the light point
and generated by a second laser which is
perpendicularly installed on to the one implanted at the
centre of Equatorial.
To permit this, a second laser is perpendicularly
installed.
The possibility exists to trace the sundial in
larger dimension in a higher position
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Gérard Labrosse , Les Varennes, 42460 VILLERS (France)
Member N° 35 967 C of the French Sundials Committee mailto:captainbrosse@hotmail.com
II) INSTALLATION STYLE
Two different techniques are possible
1) Style installation for a sundial with only hours lines
In a general way the meeting point of the hour lines is indicated
by the second laser which can be seen on the photo above.
In fact when the large disc is fixed in a vertical position with
corresponds to the date of equinoxes, the luminous point projected by
the laser show the exact position of installation of the style.
As you can see the style has a rotating feture, which allow to move and fix in certain location.
The style is positioned in a way that the laser point can be seen on the end of the style.
All is left is to remove the surrounding disc by sliding out over the style which is in a fixed
permanent position.
2) Style installation for a sundial with diurn's lines
Setting. up the style in the case of the sundial completed with diurnal curves. The tracing
device is installed within the area of the tracable surface allowing the other technique of installation.
We can then remove the twin laser disc and replace by a semi disc in which the center of the equatorial
axis is materialized by a centring pointed tip.
The following configuration :
The end of the style is fixed on the meeting point of the line representing the hours (example in a hole
pre drilled in the wall).
The other end is in center position as shown in the photo below.
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Gérard Labrosse , Les Varennes, 42460 VILLERS (France)
Member N° 35 967 C of the French Sundials Committee mailto:captainbrosse@hotmail.com
All is left is the fixing of the axis style in a permanent fixed position.
It is not necessary to follow the angle of which the support is placed. Therefore it’s not
necessary to prop before fixing.
III) THE LATITUDE SETTING
This adjustment can be
done with a precision of a 5
minutes arc thanks to the addition
of an other sliding gauge
juxtaposed over the first one
marked in degrees (calliper
square system) . The twelve
intervals of the upper sliding
gauge, graduated by sets of 5
minutes arc, match to a graduated
sector of 23° of the lower sliding
gauge.
WARNING: The value
you must consider is the value of
the complementary angle of the
latitude.
4/10
Gérard Labrosse , Les Varennes, 42460 VILLERS (France)
Member N° 35 967 C of the French Sundials Committee mailto:captainbrosse@hotmail.com
IV) BILLSTICKING OF THE HOUR ANGLES H
The positions of the standard hour angles usually used in
dials science (15° and 7,5°) can be done with a ball pushed by a
coil spring in notches made in the outer edge of the graduated
disc.
Any hour angle can be laidout by using chosen colours
with the help of the lower disc made in bronze. The described
system is easily put out of activation.
V) BILLSTICKING OF THE DECLINATION :
The declination of the solstices or equinoxes can be positioned with
respect to the three 7,87 inches holes of the vertical disc and the two other holes
made in the structure which support the disc.
An axis with symbol  in one of its end, then takes place in this alignment
and makes the two parts integral with each other.
The disc carrying the two lasers can be locked in
each position of the sun declination with a small plastic
stopper which is pushed with a milled screw made in
brass (with a sun for decoration). A part of the graduated
disc from + 23,26° to – 23,26° is visible through the
hollow which is made on the base of the support of the
disc.
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Gérard Labrosse , Les Varennes, 42460 VILLERS (France)
Member N° 35 967 C of the French Sundials Committee mailto:captainbrosse@hotmail.com
The entire upper part is based on a tray made with aluminium with 15,75 inches on each side
and including three screws that can be used for the adjustment of the horizontal
line.
A double spirit level is perpendicularly fitted into the tray in aluminium to allow dial readings.
The final dial reading will be done with a very precise spirit level.
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Gérard Labrosse , Les Varennes, 42460 VILLERS (France)
Member N° 35 967 C of the French Sundials Committee mailto:captainbrosse@hotmail.com
In a corner of this tray a compass is fitted into it and allows the first approach to the alignment
on the local meridian line.
So there will be practically no important move during the final alignment.
The materials composing of screws for the dial and the tray will not create magnetic
disturbances on the compass.
The final positioning (alignment of the 0 on the local meridian line) will be made with the
following procedure:
On the disc which carries the two lasers is placed an assemblage witch is composed of a
viewfinder with a lense allowing to focus a bright point on a target positioned at a distance.
The first step consists in sliding away the bronze disc supporting the upper part of the
predetermined angle (corresponding to 0 of the graduated crown).
This angle will correspond to the azimuth of the sun clearly defined for a given precise
moment.
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Gérard Labrosse , Les Varennes, 42460 VILLERS (France)
Member N° 35 967 C of the French Sundials Committee mailto:captainbrosse@hotmail.com
It would be necessary to work out the time difference between the time of instalation and the
true local sun time.
Let us consider H = the hour converted in degree (+ 15° for 13h or – 15° for 11h) minus the
equation of time written with its sign (+ or -) with minutes and seconds and divided by 4 (if 1 hour =
15°, 1 minute = 4’) and finally minus one or two legal hours (minus 15° or 30°) according to whether
it is summer or winter.
Example:
It is the 17th of November and the equation of time this day is – 15minutes and 4’. I want to
put my apparatus in position at 2 o’clock in the afternoon of my watch. The longitude  where I am is
4’ East, in fact it is a negative sign.
I use the formula to write the specific values.
H = 30° - (- 15° 4s / 4) – (- 4°) – 15° then H = 22°46’)
Now, we need to evaluate the azimuth of the sun indicated by A corresponding to the hour
angle H previously calculated.
The 17th of November the declination of the sun is – 19°. The latitude where we are drawing is
46° North, and so a positive sign.
Since we know the value of H, the declination and the latitude , the calculation of the
equation allows us to know the azimuth of the sun and gives as result:
A =tan-1 (sin H ((sin  * cos. H) – (cos. * tan ))) then A = 23° 12’
OBSERVATIONS:
The use of the ephemeredes values, is preferred to get better accuracy with respect to standard
values generally used.
VI) DEFINITION OF THE PARAMETERS USED TO GET A
BETTER UNDERSTANDING
H: s the hour of the sun calculated positively towards west from south meridian from 0 to 180
and negatively towards the east, from 0 to – 180. The hour angle is set to 0 whenever the sun passes
through the meridian of the spot of set up (true noon). We use the following standard convention: 12h
is set to 0 and we add 15° from it.
A: is as the azimuth of a star measured positively from the south meridian towards the west,
from 0 to 180 and negatively towards the east from 0 to –180.
 : this denotes the geographical latitude of the original location computed positively from the
equator in the northern hemisphere and negatively in the southern hemisphere.
 : this defines the declination of the sun. In dial science, we consider the declination of the
sun very constant during a day. The arcs of declination or diurnal arcs are generally drawn to show
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Gérard Labrosse , Les Varennes, 42460 VILLERS (France)
Member N° 35 967 C of the French Sundials Committee mailto:captainbrosse@hotmail.com
special values.  matches with the dates when the apparent longitude of the sun is a multiple of 30°, in
fact in decimal degrees: -23°44’; -20°15’ ; -11°47’ ; 0° ; +11°47’ ; +20°15’ ; +23°44’.
 : is the geographical longitude of the original location computed positively from the
international Greenwich meridian towards the west (from 0 to 180) and calculated negatively towards
the east from 0 to –180. The longitude of a place is used for the calculation of the orientation of a wall
for the conversion of the solar time into a legal time or for the sundials to be drawn from a
conventional meridian.
U: it is defined as the length of the polar style. In other words, it is the gnomon kept parallel to
the globe axis. In the particular case of a dial set up for a polar gnomon the whole shadow shows the
time by covering one line. The hour lines converge towards the so called “dial centre”. The sundials
which don’t have the polar style impregnated into the table are said to have an inaccessible centre.
The chosen moment and measurement of the starting point:
The lower disc is at first displaced from the angles drafted from Z in relation with 0 marked on
the graduated ring. The upper part of the apparatus has to pivot on the aluminium base, in a way to
bring into alignment the bright point on the vertical line situated on the target surface.
Because of this it is not necessary to adjust the declination delta at the sliding gauge to put the
apparatus in function. As an example if the upper vertical disc had been at first placed with the value 
of the day – 19° (little window with binding screw), the light spot would be exactly at the intersection
of two perpendicular lines in the centre.
When this operation is done, dismantle the target mechanism so that it does not obstruct the
moves necessary to do the different manipulations.
The apparatus is then correctly set up and the imaginary line passing by points 0 and 180 of
the graduated ring, will be aligned on the meridian line of the place you are based.
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Gérard Labrosse , Les Varennes, 42460 VILLERS (France)
Member N° 35 967 C of the French Sundials Committee mailto:captainbrosse@hotmail.com
VII) DRAWING OF THE HOUR LINES:
To do this, you just have to adjust the position of the lower disc (made in bronze) to the values
of the hour angles (i. e. +15° for 13h , -15° for 11h) and then, to pivot the upper disc perpendicularly
from the top to the bottom.
The light spot produced by the laser and placed at the centre of the equatorial axis will indicate
the route of the hour line you have to layout.
VIII) DRAWING OF THE DIURN CURVES:
We have seen that the upper vertical disc (blue) has at its’
base a little graduated sliding gauge to show the values of
the sun declinations. It is necessary to put the upper disc
in alignment to the chosen value delta opposite to the
value of the fixed index which is engraved at the bottom
of the alignment control viewer situated on the base of the
disc. For certain common adjustments (common values of
 ) the manipulation is easy, but for other adjustments the
specific value of  is held in position during
manipulations by a binding screw.
When this operation is done, you just have to
pivot the entire upper part from left to right. The route of
the laser on the drawing plane matches the diurnal curve
you have to trace.
Both of the lasers are supplied with current
independently and automatically with the help of a switch
situated on a small box.
IX) OTHER POSSIBILITIES
All around the lower graduated disc, there is a
graduated ring (in degrees) to allow the drawing of the hour
lines. This makes possible a shifting of the 0, taken as a
reference to put the apparatus in function.
It’s possible to trace the hour of an other destination
or the average local sun time.
X) OTHER PRATICES
I take for example, the measurement of a wall which
is perfectly vertical. Actually, the angle of the equinox line in
comparison with the horizontal line varying according to the
declination gives us an angle which can be calculated.
The set-up for the height of a dial decorated by its
diurnal curves is possible with the help of a scaffolding. But it
must be very stable
An 80 pound weight helps to give good stability. All parts in aluminium have received special
treatment called “anodising” which gives them good protection against oxidising.
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Gérard Labrosse , Les Varennes, 42460 VILLERS (France)
Member N° 35 967 C of the French Sundials Committee mailto:captainbrosse@hotmail.com