Slide Rule Scales
Scales for building your own slide rule
Due to popular request, the following 75 reference scale images are combined into one file that you can download: SR_scales.zip. Just right-click and save target to your computer, then you can un-zip them.
Ying won a reward for this innovative application. His son is shown cutting out one of the disks.
For more details on the construction and use, go to Patrick's TK5EP Home Page.
Visit John Savard's Web Page,
a mathematically oreinted web site that focuses on cryptology, ciphers and map
projections along with many topics in mathematics, science, computers and Chess.
Note: The scale identifiers (A, B, C, S, T, etc.) are added to every scale at the half interval marks (an unusual visual technique, but very effective). In this way, the scales are identifed no matter where the rule is positioned.
|The first of three templates to build a circular slide rule background. This one is for a general-purpose rule, except that hyperbolic functions are present, and log-log scales omitted. This is peculiar, but it is intended that this rule will be used in conjunction with the one with two four-decade log-log scales, normal and reciprocal, as part of a set.|
|This is the second of three possible backgrounds for the circular slide rule. This one features a logarithmic scale for multiplication that makes five turns around the rule. Unlike earlier versions of my circular slide rule, I put it far enough towards the outside that I could graduate it for a 20 inch rule instead of as for a 10 inch rule. Given the binary capability of the overlay design, it can indeed be used for accurate multiplication.|
|This is the third of three backgrounds for the circular slide rule. This one contains conventional log-log and inverse log-log scales. The log-log scales, but not the inverse log-log scales, are graduated for a 20" rule, except the last little bit.|
|This file is the one that needs to be printed on clear plastic as the overlay for the family of three circular slide rules. Note the cursor line on the main disc, as well as the cursor templates (for which no border is given). This allows the rule to be used both in the simple fashion of a conventional slide rule for combinations involving one of the scales on the overlay, and as a "binary" type slide rule for any arbitrary pair of scales on the base as well.|
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Thacher Cylindrical SR c1910
Thacher Scale Example
Thacher Bars, full-sized, prints on single sheet 18.5" x 20"
Thacher Drum, full-sized, prints on single sheet 13.5" x 20"
Thacher Bars, legal sheet size, multiple pages
Thacher Drum, legal sheet size, multiple pages.
Kinko's print ready Adobe format .KDF Thacher Bars, full sized, prints on single sheet 18.5" x 20"
Kinko's print ready Adobe format .KDF Thacher Drum, full sized, prints on single sheet 13.5" x 20"
David White of Essex, Massachusetts, built this beautiful rendition of a Thacher using the above Thacher scales.|
Click on the pictures and pdf to see how he did it. Contact: whitey5656 [at] hotmail.com
Bob Wolfson of Marietta, Georgia, built another beautiful rendition of a
Thacher using the above Thacher scales.|
Contact: bobwolfson [at] gmail.com
Peter Monta made this scale sheet using a 'C' file to create a postscript file of Otis King Model L scales. to fit rigid tubing.
In the first column is the scale name. In the second column is the formula used for that scale. Any simplification is left as an exercise for the reader. The convention used is that R denote the length of the rule and # denotes the number on the scale whose position is being calculated. The final column contains notes about the particular scale.
Derivation of the scales was not always easy, and I have not shown here how it was done. Essentially, I went in knowing that the whole thing was based on logarithms, and then played around until I came up with something that worked. Generally I started out quite close -- it became mainly a matter of playing with constants. Jason.
|A/B||(R/2)*log(#)||Used to calculate squares and square roots with the D scale, used to calculate the sine of an angle with the S scale on a Mannheim slide rule|
|C/D||R*log(#)||Used in multiplication and division, and also used with many other scales in various operations|
|CF/DF||(log# - logPI)*R if # less than R then add R||The folded scales used as a shortcut in multiplication and division|
|CI||abs[R*log(10/#)-R]||The inverse of the C scale, often used as a shortcut in division|
|The inverse of the CF scale|
|K||(R/3)*log(#)||Used with the D scale to find the cube or cube root of a number|
|L||#*R||Used with the D scale to calculate the logarithm log10(#) of a number|
|LL0||log(ln(#))*R + 3*R||Contains all numbers greater than or equal to 1.001 and less than or equal to 1.01; these scales (LL0-LL3) are used for logarithms, roots, and powers|
|LL1||log(ln(#))*R + 2*R||Contains all numbers greater than or equal to 1.01 and less than or equal to 1.105|
|LL2||log(ln(#))*R + R||Contains all numbers greater than or equal to 1.105 and less than or equal to e|
|LL3||log(ln(#))*R||This contains all numbers greater than or equal to e|
|LL/0||log(ln(1/#))*R + 3*R||This contains all numbers greater than or equal to e-0.01 and less than or equal to e-0.001|
|LL/1||log(ln(1/#))*R + 2*R||This contains all numbers greater than or equal to e-0.1 and less than or equal to e-0.01|
|LL/2||log(ln(1/#))*R + R||This contains all numbers greater than or equal to e-1.0 and less than or equal to e-0.1|
|LL/3||log(ln(1/#))*R||This contains all numbers greater than or equal to e-10.0 and less than or equal to e-1.0|
|R1||log(#)*2*R||Used with the D scale to find squares and square roots; those numbers greater than about 3.13 are on the R2 scale|
|R2||[log(#)*2*R] - 25||Used with the D scale to find squares and square roots; those numbers greater than about 3.13 are on the R2 scale|
|Smannheim||(R/2)*[2 + log(sin(#))]||Used with the A scale to calculate the sine of a number, or the tangent of a number less than 5.7 degrees|
|S,T||[log(100*sin(#))]*R||Used with the C scale to calculate the sine or the tangent of a number less than 5.7 degrees|
|S||[log(10*sin(#))]*R||Used with the C scale to calculate the sine of a number greater than 5.7 degrees|
|T||R*log[10*tan(#)||Used with the D scale to calculate the tangent of angles greater than 5.7 degrees|
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