Basics

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Nomography

A nomograph is a graphical computer. By using nomograph, straight edge (or ruler) and pen, one can see (or compute) how parameters relate to each other. There are two major uses for nomographs. First, they can be used as calculators. Second, they can be used to illustrate complex problem as a picture. The latter use is today probably the most important.

Nomography was invented in the end of 19th century and nomography was workhorse in engineering up to the 1960s. During the 1970s computers were more and more used for computations and nomography turned out to be a forgotten state of the art. Today we use spread-sheet calculators in computers and compute with them relationships between parameters. However, by using spread-sheet approach, we have difficult to understand relations intuitively. We may not grasp the problem. We may lose touch of orders of magnitude and what really matters in a problem.

It is today very difficult to present graphically how more than three variables relate to each other. In practice xy-scatter graphs for two variables and contour plots for three variables are used. Other types of graphs are more rare. We have almost lost a way to present laws (nomos) graphically (graphy) of variables above three.

Nomography can in many cases be used to illustrate problems having many more than three variables. Below are two examples of the use of nomography in order show how nomographs may be used in practice.

Example 1

This is a classic nomography example. The question is about body-mass-index that is a measure of over- or underweight. The index is calculated from height and weight, and if it turns out to be between 20 and 25, person has normal weight.

In the example we have person with weight 85 kg and 183 cm. By drawing a straing line between the points in the scales, one can read that body-mass-index is some 25.5. It means the person just crossed the limits of normal weight and has slight overweight. The red line for calculation is drawn in the nomograph below.

Body mass index
Ex BMI line.png
Generated portable document file (pdf): File:Ex BMI.pdf

This example is one of the more simple examples illustrated in Examples. One may see how it was constructed with PyNomo at the following page.

Example 2

The second example represent a use of a complex nomograph. The question to be asked is the following. A photographer wants to travel to Helsinki (Latitude 60) to take outdoor photographs around 2 pm First of May (Vappu). The sky is often dark gray (it's Helsinki, not Silicon Valley) and one wants to take photographs of people at open place. The photographer plans to use zoom lenses with maximum aperture f/4 and wants to shoot with speed ISO100 in order to have low grain or noise in pictures. How does he find out what is the estimate for shutter time? Are the pictures taken by hand to become blurred? He uses the following nomograph to answer the questions. See the nomograph in portable document format: File:Ex photo exposure.pdf

Ex photo exposure.png

First he draws line from time 14.00 via grid point of latitude 60 and month May. He finds out that solar zenith angle is around 50 degrees.

Photo crop.png

Next he draws horizontal line until it hits the line "Sky dark gray".

Photo crop1.png

Next one he draws vertical line until it hits the line "Person at open place" and then horizontal line until he hits edge of the "contour plot"

Photo crop2.png

He finds that lightning corresponds to EV100 value around 10.5. He draws a line via point ISO100 to axis R. There he draws a second line to aperture point f/4. The crossing of the line in time axis or shutter speed tells that value is around 1/80s.

Photo crop3.png

In order to determine if the shutter time is small enough for focal length of 30mm of his image stabilized (IS) zoom lens in his cropped sensor digital single-lens reflex (DSLR) cameran he plans to use, he draws line to the maximum focal length point vial DSLR IS point. Maximum is above 200mm, so it is safe to take handheld photographs in this focal length and shutter time.

Photo crop4.png

If he wanted to use 200mm zoom of his lens with maximum aperture of f/5.6, he finds out, that maximum focal length with these conditions is around 110mm and shooting 200mm would turn out to be blurred pictures even with image stabilization.

Photo crop5.png

This example uses many blocks of PyNomo and maybe considered such complex that it is a question, is it practical in real use. Maybe in some cases.

The theory, references, mathematics, nomography construction and PyNomo source code is elaborated at the following page.

Further information on Nomography

See links.