>A branch of mathematics in which methods of graphical representation of functional dependencies are studied. The resulting designs are called nomograms. Every nomogram is constructed for a definite functional dependence within specific limits of variation of the variables. In nomography computational work is replaced by the performance of the simplest geometric operations indicated in the instructions and an evaluation of the answers.
>The accuracy of answers by nomography depends on the form of the nomographic presentation of the dependency, the limits of variation of the variables, the dimension of the design, and on the chosen type of nomogram. On the average, nomograms can provide answers to 2–3 true digits. When the accuracy of nomograms is insufficient, they can be used for provisional calculations, for finding zero-order approximations, and for the control of computations with the aim of discovering gross errors.
>Nomograms can also be used to study functional dependencies, putting the nomograms at their foundation. Often such a study can be carried out by nomograms in a considerably simpler and more intuitive way than by other methods. By means of nomograms one can investigate the influence of various variables on the required variable, give an intuitive interpretation of some previously known properties of the dependency in question, and establish previously unknown peculiarities of it. Nomographic methods of investigation can be applied, for example, in problems on the selection of parameters in empirical formulas on the results of observations, in the approximation of one function by another, and for finding extremal values of functions.
Re:The Lost Art of Nomography (2009) [pdf]
by kqr on Monday January 02, 2023 @07:38AM
(#34217286)
I don't have the image at hand but the most impressive nomogram (?) I've seen was in a pilot's operating handbook for some version of the DC-3.
It allows you to calculate take-off ground run distance as a function of no less than four variables! Namely,
- gross weight,
- altitude,
- headwind, and
- softness of ground surface.
The same POH also had two more useful (but simpler) nomograms:
- density altitude as a function of temperature and altitude, and
- rate of climb as a function of density altitude and gross weight.
The reason I remember these two is not that they were particularly cool on their own, but because they were placed side-by-side in the POH so you could also think of them as a single nomogram that let you compute rate of climb as a function of temperature, altitude, and gross weight.
Re:The Lost Art of Nomography (2009) [pdf]
by el_nahual on Monday January 02, 2023 @09:22AM
(#34218125)
If you like Nomograms or other mechanical mathematical curiosities, do check out @ChrisStaecker on YouTube. He does short, funny reviews/how-to videos for his collection of nomograms, measuring tools, mechanical and paper calculators.
Unfortunately his channel also mixes his university lectures, so you have to check out his playlist [0].
Here's a nomogram for solving a quadratic equation. Check out the O-riginal video on YT! [1]
Re:The Lost Art of Nomography (2009) [pdf]
by Valgrim on Monday January 02, 2023 @09:45AM
(#34218372)
In the Pixar movie "Lightyear", at some point we see Buzz using an E6B calculator to quickly calculate a trajectory correction in space.
The E6B is some kind of nomogram/slide rule hybrid, still widely in use by pilots in flight training for dead reckoning.
Funny fact, the chart that Buzz uses in the film is used to calculate wind correction...in space. (Well he does get 'pushed' off course by the wind of an explosion).
Re:The Lost Art of Nomography (2009) [pdf]
by doodlebugging on Monday January 02, 2023 @11:39AM
(#34219936)
This takes me back. The first bit of programming I ever did that wasn't RPN on an HP-11C involved digitizing nomograms from technical tool output interpretation guides published by oil and gas service companies for each of their downhole tools. We located guidebooks in the university library, at estate sales and garage sales, by visiting service company offices, etc and had a large collection that eventually allowed us to code, in BASIC (later QuickBASIC and eventually QuickC and C++) the equations for each of the lines involved in the interpretation. We even did the most complicated tornado chart corrections on a Compaq Deskpro sewing machine cabinet style 8086 or 80286 PC back in the mid-late 80's. Mainframe interpretation suites couldn't do the things we did.
Our process was pretty convoluted and involved the PC and a 128k Mac (upgraded to 512k later) with some Mac software that didn't exist in PC world at the time. We would digitize the nomogram curves or lines top to bottom and include any points where value were known by example in the guidebooks. Then those digitized points were fed to an equation solver on the Mac that would take the input points and output an equation for that line that fit the example data across the range. Then we would code all equations for the tool nomogram and test outputs to make sure that it calculated exactly as the chart books specified. Then we would feed downhole log data and crosscheck for any calculation bugs, overflows, etc and make sure it all fit into a reasonable geological/geophysical situation.
I don't remember the name of the software used on the Mac. I would have to go out to the box and check for the disk. I still have the computer and other stuff including some dot matrix printouts of a lot of the code we used in debugging. Not sure why I kept all that.
I never made a nickel from all that though I know that it was used commercially after I went to grad school. It was fun though and helped launch my career in geophysics. Being a geophysicist in the late 80's who could code, identify bugs, run all the software and operating systems without someone needing to babysit them was a clear advantage.
Re:The Lost Art of Nomography (2009) [pdf]
by riedel on Monday January 02, 2023 @05:02PM
(#34224286)
Wonder why the art was "lost" (maybe between 2008 and now, as the title does not contain th word)? I guess it is true that with computer program one does not have to rely an books. However, looking at the civil engineering books of my wife, which a full of nomograms, I would not consider it lost. I guess they follow a similar fate as logarithmic tables.
In the meantime I think we can change the URL to https://deadreckonings.files.wordpress.com/2008/01/nomograph..., which has an earlier version of the same piece.
>A branch of mathematics in which methods of graphical representation of functional dependencies are studied. The resulting designs are called nomograms. Every nomogram is constructed for a definite functional dependence within specific limits of variation of the variables. In nomography computational work is replaced by the performance of the simplest geometric operations indicated in the instructions and an evaluation of the answers.
>The accuracy of answers by nomography depends on the form of the nomographic presentation of the dependency, the limits of variation of the variables, the dimension of the design, and on the chosen type of nomogram. On the average, nomograms can provide answers to 2–3 true digits. When the accuracy of nomograms is insufficient, they can be used for provisional calculations, for finding zero-order approximations, and for the control of computations with the aim of discovering gross errors.
>Nomograms can also be used to study functional dependencies, putting the nomograms at their foundation. Often such a study can be carried out by nomograms in a considerably simpler and more intuitive way than by other methods. By means of nomograms one can investigate the influence of various variables on the required variable, give an intuitive interpretation of some previously known properties of the dependency in question, and establish previously unknown peculiarities of it. Nomographic methods of investigation can be applied, for example, in problems on the selection of parameters in empirical formulas on the results of observations, in the approximation of one function by another, and for finding extremal values of functions.
Thanks!
It allows you to calculate take-off ground run distance as a function of no less than four variables! Namely,
- gross weight,
- altitude,
- headwind, and
- softness of ground surface.
The same POH also had two more useful (but simpler) nomograms:
- density altitude as a function of temperature and altitude, and
- rate of climb as a function of density altitude and gross weight.
The reason I remember these two is not that they were particularly cool on their own, but because they were placed side-by-side in the POH so you could also think of them as a single nomogram that let you compute rate of climb as a function of temperature, altitude, and gross weight.
Unfortunately his channel also mixes his university lectures, so you have to check out his playlist [0].
Here's a nomogram for solving a quadratic equation. Check out the O-riginal video on YT! [1]
[0] https://www.youtube.com/playlist?list=PLLFpXNanTP9X6lHrX9qoJ...
[1] https://www.youtube.com/watch?v=swCy6pQSEpk&list=PLLFpXNanTP...
http://lefakkomies.github.io/pynomo-doc/introduction/introdu...
The E6B is some kind of nomogram/slide rule hybrid, still widely in use by pilots in flight training for dead reckoning.
Funny fact, the chart that Buzz uses in the film is used to calculate wind correction...in space. (Well he does get 'pushed' off course by the wind of an explosion).
Our process was pretty convoluted and involved the PC and a 128k Mac (upgraded to 512k later) with some Mac software that didn't exist in PC world at the time. We would digitize the nomogram curves or lines top to bottom and include any points where value were known by example in the guidebooks. Then those digitized points were fed to an equation solver on the Mac that would take the input points and output an equation for that line that fit the example data across the range. Then we would code all equations for the tool nomogram and test outputs to make sure that it calculated exactly as the chart books specified. Then we would feed downhole log data and crosscheck for any calculation bugs, overflows, etc and make sure it all fit into a reasonable geological/geophysical situation.
I don't remember the name of the software used on the Mac. I would have to go out to the box and check for the disk. I still have the computer and other stuff including some dot matrix printouts of a lot of the code we used in debugging. Not sure why I kept all that.
I never made a nickel from all that though I know that it was used commercially after I went to grad school. It was fun though and helped launch my career in geophysics. Being a geophysicist in the late 80's who could code, identify bugs, run all the software and operating systems without someone needing to babysit them was a clear advantage.
http://www.projectrho.com/nomogram/index.html
Thank you for sharing such an intriguing source of information.