This note compares the results of a calculation performed on some of my slide rules, especially the ones offering high accuracy. The candidates are:
The calculation was: 300 x 2.543 (the cc equivalent of an American 300-cubic-inch car engine).
The calculation was performed as a chained series of multiplications: 300 x 2.54 x 2.54 x 2.54. On the 12 and 25cm linear slide rules it was performed using the minimum number of steps using C, D and CI scales. On the 50cm it was performed using C and D scales. There is no choice on the others.
From any electronic calculator, the result is: 4916.12 to 6 sig fig.
| rule | result | error |
|---|---|---|
| 12cm | 4910 | -0.12% |
| 25cm | 4920 | +0.08% |
| 50cm | 4915 | -0.02% |
| Fowler short scale | 4910 | -0.12% |
| Fowler long scale | 4915 | -0.02% |
| Fuller | 4914.5 | -0.03% |
| Otis King | 4915 | -0.02% |
In which the disappointment is the Fuller. With its 13-metre scale it has scale marks for four sig fig and can be estimated to five, so it's not reading error, there is actually a systematic error of about -0.03%. That's a linear error of about 1.5mm. I did it twice and got the same result each time.
Clearly some more detailed research is needed. There is other work available on the web, including scales taken off an Otis King, scanned and compared with computer-generated log scales. I shall have a go myself sometime.
On a logarithmic scale of length L a reading error of x amounts to the same ratio error at any point along the scale, by the nature of logarithms. The actual percentage error resulting from a linear error of x is given by: error (%) = 100 * (10(x/L) - 1). A good rule of thumb on a 25cm scale is that 1mm is 1%; the distance between scale marks 1.00 and 1.01 is roughly 1mm. On the Fowler's 750mm scale 1mm is 0.3% and on the Fuller's 13 metre scale it's 0.02%
My slide rules + How to use a slide rule
2008-04-19 .. 2008-08-28
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