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Scales (Slide Rule): Difference between revisions
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5⁴ = 625 | 5⁴ = 625 | ||
5(LL3) | I → 4(C) = 625(LL3) | 5(LL3) | I → 4(C) = 625(LL3) | ||
</syntaxhighlight> | </syntaxhighlight>Because the LL scale is split up into four sections, it reads from e<sup>0.001</sup> up to e<sup>10</sup>, which is a range of about 1.001 to 20000. This leads to some accuracy problems at the high end, but on the low end it becomes incredibly accurate. One interesting thing to note is that for sufficiently small values of x (such as those less than 0.001), we have the approximation e<sup>x</sup> ≈ 1+x, which means that for values below LL0, the C or D scale itself can act as a sort of "LL00" by showing the fractional portion of the value. | ||
== List of Common Scales == | == List of Common Scales == | ||
Below is a list of the common scales used on this page, as well as a few others. For a more complete list, see the [[List of Scales and Scale Marks]] | |||
{| class="wikitable" | |||
|+Common Scales | |||
!scale | |||
!relation to primary scales | |||
!Common Location | |||
!Notes | |||
|- | |||
|D | |||
|Primary scale (x) | |||
|body, directly adjacent to C | |||
|This is the most commonly used scale on the body of most slide rules. it is identical to C | |||
|- | |||
|C | |||
|Primary scale (x) | |||
|Slide, directly adjacent to D | |||
|This is the most commonly used scale overall. Often found on both sides of duplex rules | |||
|- | |||
|CI | |||
|Reciprocal (1/x) | |||
|Slide, usually adjacent to C | |||
|identical to C, but increasing from right to left. incredibly common, and very helpful in chaining operations together | |||
|- | |||
|A | |||
|Square, "quadratic" (x²) | |||
|Body, directly adjacent to B, usually above C and D | |||
|two decade scale, squares are performed D → A, square roots are performed A → D | |||
|- | |||
|B | |||
|Square, "quadratic" (x²) | |||
|Slide, directly adjacent to A | |||
|two decade scale, it is identical to A | |||
|- | |||
|K | |||
|Cubic scale (x³) | |||
|Body, in various locations, usually on the same side as A and B for duplex rules | |||
|three decade scale, one of the only purely logarithmic scales without a slide counterpart | |||
|- | |||
|DF | |||
|Folded scale (πx) | |||
|Body, usually on the opposite side of A and B, directly adjacent to CF, not common on simplex rules | |||
|identical to D, shifted by a constant. only has one index near the center of the scale. Can be used to "rescue" operations that otherwise need a change of indices. Useful for finding areas and circumferences of circles. | |||
|- | |||
|CF | |||
|Folded scale (πx) | |||
|Slide, directly adjacent to DF. | |||
|identical to DF. This scale can be used in place of C because of its single index on rules without scale extensions. | |||
|- | |||
|CIF | |||
|Folded Reciprocal (1/πx) | |||
|Slide, usually adjacent to CF | |||
|Identical to CF, but increasing from right to left. Can be used with CF and DF to chain operations similar to C, D, and CI. Not found on rules without other folded scales. | |||
|- | |||
|S | |||
|Sine scale (arcsin(x)) | |||
|either body or slide | |||
|nearly always in degrees, both DMS or decimal. Usually used by reading sin(θ) on the scale, then using the equivalent value on C or D for other operations. Usually reads from 5.7° (arcsin(0.1)) to 90°. Cosine values are often printed on the same line, increasing from right to left. | |||
|- | |||
|T | |||
|Tangent scale (arctan(x)) | |||
|either body or slide, usually with S | |||
|Same function as S scale, but for tangents. Usually has range from 5.7° to 45°. Values greater than 45° can be read by taking the complement of the value, occasionally this is marked either on the same scale or on a "T2" scale. | |||
|- | |||
|ST | |||
|Small Angle scale (arcsin(x)≈arctan(x)) | |||
|usually between S and T | |||
|uses the approximation that for sufficiently small angles, sin(θ)=tan(θ)=θ when measured in radians. Used to find very small angles, and convert small angles in degrees to radians. has a range from 0.57° to 5.7°, below this limit, the ST scale effectively wraps on itself, giving arbitrarily small angles. | |||
|- | |||
|LL | |||
|Log-Log scale (e<sup>x</sup>) | |||
|Body, found on the slide of Darmstadt rules | |||
|Usually used with C to find arbitrary bases and exponents. LL is split into 3 (sometimes 4) scales, labeled LL1, LL2, LL3, sometimes LL0. Each portion has a range of e<sup>cx</sup> from 1≤x≤10, where the constant C is 1/1000, 1/100, 1/10, or 1, in ascending index order. | |||
|- | |||
|LL/ | |||
|Reciprocal Log-Log scale | |||
(e<sup>-x</sup>) | |||
|Body, often found opposite LL scales | |||
|reciprocal of the LL scales, increases from right to left, using the negative exponents of the same divisions as the LL scales. | |||
|} | |||