ANALEMMAS
Analemmas on the style or dial plate of an armillary dial, ditto for the
equatorial dial, and analemmas on an hour line for a horizontal dial, and with
two adjustments for a v-dial, and with more thought, for a v-dec dial.


The EOT or equation of time (clock and solar time differences) when plotted
against the sun's declination forms a figure of eight. This figure of eight is
called an analemma. Do not confuse this with the analemmatic dial.   Read
Declining Shadows for a good understanding of the sun's declination, and
how to use it.
This analemma can be depicted on a
sundial by either figures of eight on
each hour line, or it can be done with
some accuracy by a style shaped as
a figure of eight.
When placed on a dial plate, the dial plate can get rather busy, especially if
calendar information as well as Italian hour lines are included. The gnomon with
a figure of eight shape declutters the dial plate but has other issues.

Some sundials have an EOT chart or table, which simplifies mean time reading.
The problem with the figure of eight correction is that you must also know whch
side of the figure of eight to use, depending on the date, since except for WOTs
of 0, two dates exist for each EOT value.

To help with the figures of eight, this web site has some support material.
This DeltaAD program displays analemma charts and tables.
NOTE:  The DeltaCAD h-dial analemma in this suite works well and the X,Y pairs match closely
those in the Excel and Open Office sheet.
NOTE:  This same DeltaCAD program also includes a full h- and v-dial plate, with declination (calendar)
curves, and analemmas.They are all included in the zip file

Excel
spreadsheets, as well as the master Illustrating Shadows spreadsheet provide tabular and graphical
analemma support.

Some very good
notes on analemmas are here, however, the notes provided with Illustrating Time's Shadow are best.

For those with the Cortona vrml plugin,
The
3d gnomon in vrml is here
The
dial plate analemma is here
The
differences between the two are here

Most Illustrating Shadows sundials are made of ceramic or glass and copper, and the table or graph approach is more
realistic than a dial plate analemma. Engraved dials benefit more for analemma on the dial plate. And 3d analemma
on the gnomon's style take some effort and have drawbacks, see the notes in the ZIP file for a full discussion of the
pros and cons of analemma on a gnomon style.

The armillary was nice in that its analemma, be it on the plate or on the gnomon, uses the same formula with the axes
reversed.

The equatorial dial differs from the armillary in that  the formulae for the dial plate analemma and the gnomon based
analemma are not interchangeable.

This is discussed in the
notes here on analemmas.

The master Excel spreadsheet and the Open Office master sheet have always handled the h-dial

The v-dial is the same as the h-dial except
use the co-latitude
reverse the longitude and meridian
The analemma
DeltaCAD macro handles horizontal and vertical dials with calendar and analemma
data, and for completeness, the main
DeltaCAD macros handle the horizontal and vertical
dial with calendar and analemmas.

The vertical decliner is the same as the h-dial except
use the SH as the latitude for the h-dial
but you need a longitude difference which is not the same as for the v-dec value - play with it
or use the DL figure provided by the v-dec spreadsheet or the v-dec DeltaCAD macros.
and slide an h-dial for SH latitude along the SD line, as described in the free
calendar notes
here and here also. Also the main analemma notes cover the analemma process
for vertical decliners in much more detail with a complete example of a full set of analemmas
for a 45 degree vertical decliner.  As always, these free notes are not as complete as those
provided with the book Illustrating Time's Shadow.  
NOTE: Choice 0 will aid in v-dec design, and choice 8 does almost everything for v-dec dials  

Polar and meridian dial option added, menu cleaned up, and all dial types now have full dial plates with analemmas,
and calendar curves.

Northern hemisphere and southern hemisphere differences noted .
For other dial furniture, look at the declination or calendar line page
For other dial furniture, look at the Italian line page page
A DeltaCAD horizontal dial with calendar curves and
with the analemma, also we have a v-dial with
analemmas also.
Use this ZIP file for all analemma
related material.
All these analemma spreadsheets and
DetaCAD files (general analemma, h-dial
analemma, and v-dial analemma)  and
documentation
in one ZIP file.
For just calendar curves on any hour angle dial, but with
no analemmas, check this page here.  
The vertical decliner choice in the analemma as well as the
vertical dial DeltaCAD macros.
A very good analemma page is at:-
http://www.analemma.com/
For what an analemma looks like on
a dial plate    
The main spreadsheet in Excel, which also works in Open Office, have a worksheet that shows what the analemma would look like in the
sky. It has two charts. One is the analemma as would be seen by a human, in other words on a curved photo where azimuth is linear. The
other is as it would appear on a flat photo, where azimuth is not linear but is the tan(azimuth). These two worksheets are marked as still
being tested. Have fun with them. Hours where azimuth in the summer is on the polar side of the equator are not shown correctly yet.
NOTE: At low latitudes the summer sun can be higher than a camera could ever capture. This is not a bug in the spreadsheet, it is simply
how cameras work.    
 
For what an analemma looks like in the sky...
see page 294 Illustrating Times Shadow
This is a wide gnomon with the double S
analemma, sometimes called a spider dial.

Note how the dial center switches.
June 10, 2016

The macro issues a warning if an analemma spans
the east west line, otherwise all is good.

An excellent link to Carl Sabanski's Sundial Primer
page of wide gnomons.
Sometimes called a spider dial (not to be confused
with the spider azimuth dial).
June 3, 2016

This has the analemma as two S curves from Jan 1
to Dec 31.

The time is read by the intersection of the style's
shadow and the date. Month circles are for the first
of the month.

This was produced by a DeltaCAD macro in the H
dial macro "MAIN-h-dials.bas" choice 9
also as     "spiderH-by-itself.bas and
    "analemma.bas" choice 7
style's shadow and date
circle indicates clock time,
not a nodus
nodus indicates clock time
style's shadow and date
circle indicates clock time,
not a nodus