How to make a slide rule (or log-log or semilog graph paper)
1. Take an ordinary ruler, and put decimal points before the numbers marking the inches. (Ignore the last two inches on the ruler.)
2. To position the major (black) divisions on the logarithmic scale, calculate the base-10 logarithm of each integer from 2 to 9 and plot the integer at that place on the ruler.
log_(10) 2 = .30103,
log_(10) 3 = .47712,
...
3. To get the secondary (red) divisions, calculate the base-10 logarithm of each integer from 11 to 99, discard the number before the decimal point (1 in this case), and locate the rest on the ruler.
log_(10) 11 = [1].04139,
log_(10) 12 = [1].07918,
...
4. Continue to the desired precision. (At the third level, the discarded part of the logarithm will be 2, and so on.) Obviously you will plot fewer numbers at the right end of the rule than on the left, because the points are much closer together there.
5. When you have made two of these logarithmically scaled rulers, you can position them beside each other so as to multiply numbers by adding the lengths corresponding to their logarithms. Yes, before calculators we really did this (using the slide rule on homework and tests, not the do-it-yourself construction).
I have used the example on page four of essay I on making Nomograms:
The nomogram will use the metric scale and be accurate to 1mm; therefore, decimals are rounded to the nearest 10th, which will be 1mm.
Formula: 4/3πabc = V, where a, b, and c are the length, width and height of an ellipsoid.
Height and width are combined into one term, as they are multiplied together. It would be easier to provide a simple multiplication nomograph than to add a fourth axis. 4/3πLD=V
One option would be to have a nomogram for the user to multiply values up to 300, resulting in a "6" scale nomogram, but it would really be two 3-scale nomograms, on one "page.
Size of nomogram: 25cm in height, 16 cm in width.
Term u (4/3πlength) 50<L<1000 (Min-max length of an airship)
Term w (Height x width) 100<w<90,000 (min-max product of width and height)
Term v (Volume) 5000<V< 9,000,000 (Min-max values for volume)
Log (4/3πL) + Log (D) = Log (V)
M1 = 25/ (log 1000 - Log 50) = 19.2
M2= 25/ (log 9,000,000,000 - log 5000) = 6.6
M3= (19.2 x 6.6) / (19.2 + 6.6) = 5.0
a/b = 19/2/6.6 = 3
a=3b
a+b = 16, 3b + b = 16, a=12, b=4
Scales:
u=19.2(log1000-log50) = 25
v=6.6(log 9,000,000-log5000) = 21.5
w=8.4(log 90000 - log 100) = 16.4
I am still stymied by constructing the scales.
I will pay in chocolate for help constructing this Nomogram. I have a project where I wish to make "rules" for players to "construct" their own Airships in the Victorian/Steampunk era.
I will need:
Volume of an Elipsoid (this Nomogram)
Area of an ellipsoid (Very crucial)
Heat/steam lost through the AREA
Drag produced by travel, at speed(s) by the AREA
Weight of the infrastructure (derived by AREA, mostly)
Bouyancy (determined by volume)
I really want to learn how to create my own nomograms, I'd like someone to "teach me to fish" and not give me a fish. I have other purposes for nomograms.
Nomograms can illustrate the relationship between numbers: If nothing else, I can use this when I help teach people skills. (In real life, I am a Social Worker. I have had math through calculus, some work in matricies, lots of Statistics. I like Math, but I don't get to use it as much as I would like, and I am rusty.)
Squeek Squeek.
