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Scales (Slide Rule): Difference between revisions
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Added section on folded scales
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=== Folded and Split Scales === | === Folded and Split Scales === | ||
Similar to how the A and B scales are the C and D scales shrunk down to fit "two decades" on the rule, other rules may have similar transformations that allow them to cover different ranges or have other nice properties. The general name for these scales are "folded" scales, because they "fold" up to fit onto the rule in the space provided. These folded scales come in two general forms: simple folded scales, and "split" scales. | |||
==== Folded Scales ==== | |||
A simple folded scale takes advantage of the "wrapping around" property of the C and D scales, usually being a copy of them that is shifted to align the index to a different point on the scale. The most common of these scales are the CF and DF scales, which are traditionally folded at the value of π ≈ 3.1416 and only have a single index near the middle of the rule. This is advantageous for two reasons: | |||
First, pi is very close to the square root of 10, which is the value at the exact middle of the C and D scales, meaning that values normally very far apart on C and D (like 9 and 15) are brought much closer together and can facilitate easier chaining of operations without having to perform changes of index. | |||
Second, moving from one of the primary scale to its associated folded scale has the effect of multiplying the value by pi, which can lead to more accurate results involving pi that remove the potential error involved with extra slide manipulations. | |||
Other common points to fold the scales are at √10 ≈ 3.16, log(e) ≈ 2.301, or ln(10) ≈ 0.434, each with their own advantages and disadvantages, depending on the layout of the rule | |||
==== Split Scales ==== | |||
Instead of shrinking to fit multiple copies of a scale on a single line, the reverse process is also possible. Scales that have been cut or split and placed on multiple lines help to improve the resolution and accuracy of the rule without making the rule unreasonably large. The most common scales with this feature are the Log-Log scales, commonly abbreviated to LL. The LL scales are related to the C and D scales such that for any number found on the LL scales, the natural (or, rarely, the common) logarithm of that number is found on D. The "Log-Log" name comes from the fact that the C and D scales are already logarithmic, meaning the LL scales are doubly so. Other split scales include sine and tangent scales, which usually have their lowest range combined into a single "ST" scale; square root scales, sometimes called "W" scales, which are twice as long as D; and cube root scales, which are three times as long as D, and are most common on high end Pickett brand rules. | |||
===== LL Scales ===== | |||
The LL scales are unique in that they do not wrap around on themselves, and instead have a set decimal place present directly on the scale. | |||
== List of Common Scales == | == List of Common Scales == | ||