THE NOMOGRAM
Some nomograms for sundials use a logarithmic portrayal because the
nomogram is often an additive device, and multiplication is done by adding
logarithms. However, some nomograms use division directly (N or Z) and some
use multiplication directly (circular), so, there is variety. Here are several types:-
type 1 | | | additive nomogram C = L + R must use logs for * and /
type 2 | \ | dividing nomogram C = L / R no logs for division
type 3 ( | ) multiplying nomogram C = L * R no logs for multiplying
type 4 \ /_ adds reciprocals 1/C = 1/L + 1/R
NOTE: nomogram.BAS was running out of memory on XP systems, it is fixed.
For those who wish to design nomograms, and sundial plates using nomograms,
here are some notes on doing it. The process for the horizontal dial is shown, the
vertical dial being the same but co-latitude, which is also shown. Further, the
DeltaCAD macro: nomogram.bas builds vertical and horizontal dials, but since
DeltaCAD (as I have it) only does natural logs as opposed to base 10, these
macros use Napierian logs.
nomogram is often an additive device, and multiplication is done by adding
logarithms. However, some nomograms use division directly (N or Z) and some
use multiplication directly (circular), so, there is variety. Here are several types:-
type 1 | | | additive nomogram C = L + R must use logs for * and /
type 2 | \ | dividing nomogram C = L / R no logs for division
type 3 ( | ) multiplying nomogram C = L * R no logs for multiplying
type 4 \ /_ adds reciprocals 1/C = 1/L + 1/R
NOTE: nomogram.BAS was running out of memory on XP systems, it is fixed.
For those who wish to design nomograms, and sundial plates using nomograms,
here are some notes on doing it. The process for the horizontal dial is shown, the
vertical dial being the same but co-latitude, which is also shown. Further, the
DeltaCAD macro: nomogram.bas builds vertical and horizontal dials, but since
DeltaCAD (as I have it) only does natural logs as opposed to base 10, these
macros use Napierian logs.
| July 25, 2010 |
All nomogram files in one ZIP
file, includes the notes,
DeltaCAD maco, and the
Lazarus/Pascal source and
executable, test skeleton
programs, and more.
file, includes the notes,
DeltaCAD maco, and the
Lazarus/Pascal source and
executable, test skeleton
programs, and more.
| type 3 |
| type 2 |
| type 1 |
DeltaCAD macro is a complete v and h dial, a sunrise/set, a polar/meridian
dial with calendar data nomogram (both the three vertical line as well as the N
or Z nomogram), and a vertical decliners SD, SH, and DL with the v-dec hour
lines worked using SH and DL. The DL macro choice has two variations, the
second showing the use of differing line separations (xL, xC, xR) and the
modulus (scale) of the right line (mR) which you may change. Also has the
analemmatic dial nomogram. Does nomograms type 1,2, and 3.
Lazarus/Pascal code for the h, v, m/p, v-dec dials, and sunrise/set times all in
one ZIP file. Does nomograms type 1, 2, and 3. In essence, everything the
DeltaCAD macro does except exporting the images, which needs a screen
screen capture program such as this (I have NOT used it, I use PhotoMax Pro).
Printed nomograms from both DeltaCAD and Lazarus/Pascal are in PDF form.
The nomograms are also in the free appendices. This book of printed
nomograms may be lower quality print than if you run the DeltaCAD or the
Lazarus based program, which you are encouraged to do. the appendices
however have very high quality nomograms.
NOTE: Chapter 31 in Illustrating Time's Shadow covers more detail
than these notes. The notes here are good, and supplement chapter
31, however chapter 31 goes into more detail on line separation,
modulus (line scaling), and details on where "0" is on the three
common nomogram types. The free appendices to Illustrating Time's
Shadow have the nomograms in appropriate sections, and the formula
appendix also has a short summary of the three nomogram types,
their formulae supported, and where '0' is, and other issues with 0.
Documents online for nomogram design are:-
The Art of The Nomogram - read this first
Graphical and Mechanical Computation
Creating nomograms with pynomo software
JAVA online nomogram builder
dial with calendar data nomogram (both the three vertical line as well as the N
or Z nomogram), and a vertical decliners SD, SH, and DL with the v-dec hour
lines worked using SH and DL. The DL macro choice has two variations, the
second showing the use of differing line separations (xL, xC, xR) and the
modulus (scale) of the right line (mR) which you may change. Also has the
analemmatic dial nomogram. Does nomograms type 1,2, and 3.
Lazarus/Pascal code for the h, v, m/p, v-dec dials, and sunrise/set times all in
one ZIP file. Does nomograms type 1, 2, and 3. In essence, everything the
DeltaCAD macro does except exporting the images, which needs a screen
screen capture program such as this (I have NOT used it, I use PhotoMax Pro).
Printed nomograms from both DeltaCAD and Lazarus/Pascal are in PDF form.
The nomograms are also in the free appendices. This book of printed
nomograms may be lower quality print than if you run the DeltaCAD or the
Lazarus based program, which you are encouraged to do. the appendices
however have very high quality nomograms.
NOTE: Chapter 31 in Illustrating Time's Shadow covers more detail
than these notes. The notes here are good, and supplement chapter
31, however chapter 31 goes into more detail on line separation,
modulus (line scaling), and details on where "0" is on the three
common nomogram types. The free appendices to Illustrating Time's
Shadow have the nomograms in appropriate sections, and the formula
appendix also has a short summary of the three nomogram types,
their formulae supported, and where '0' is, and other issues with 0.
Documents online for nomogram design are:-
The Art of The Nomogram - read this first
Graphical and Mechanical Computation
Creating nomograms with pynomo software
JAVA online nomogram builder
| A nomogram that is not type 1, 2, nor 3. This is a quadrant of an equatorial dial. |
| Not really a nomogram, more a teaching aid for correctly drawing some h-dial (and v-dial) hour lines from an equatorial dial. |