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Scales (Slide Rule): Difference between revisions
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==== Chaining Operations ==== | ==== Chaining Operations ==== | ||
As a single operation tool, the slide rule is already capable of speeding up calculation time. However, because of the analogue nature, each calculation has a margin of error. In order to both increase the power and accuracy of slide rule calculations, many operations can be "chained" together for complex procedures. Let's look at one such procedure that may require chaining.<blockquote>Calculate the volume of a sphere with radius 2.48 using the following formula: V=4πr³/3</blockquote>Notice here how we have a total of two multiplications, a division, a cube, and a special constant. This can most easily be accomplished on a rule with the following scales: C, D, CI, and a cube root scale, which here will be denoted R. With careful planning we can develop the following solution:< | As a single operation tool, the slide rule is already capable of speeding up calculation time. However, because of the analogue nature, each calculation has a margin of error. In order to both increase the power and accuracy of slide rule calculations, many operations can be "chained" together for complex procedures. Let's look at one such procedure that may require chaining.<blockquote>Calculate the volume of a sphere with radius 2.48 using the following formula: V=4πr³/3</blockquote>Notice here how we have a total of two multiplications, a division, a cube, and a special constant. This can most easily be accomplished on a rule with the following scales: C, D, CI, and a cube root scale, which here will be denoted R. With careful planning we can develop the following solution: | ||
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2.48(R) | 3(C) → 4(C) → X (D) | π(CI) → i(C) ≈ 63.8 | |||
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Notice how the cubing and division are done together first. We can skip going to the index like we normally would, because we immediately need to multiply again, which starts by aligning the index to our number, which is already in place. | |||
In general, chaining operations come in pairs that follow a pattern: divide then multiply. Align two numbers on scales, then move the hairline to the third number. Treating this new result as the first value of another chain, we can continue chaining values by alternating between moving the slide and hairline to tackle most complex products. Thanks to the inverse scales and how they interchange the multiplication and division processes, we can even perform long strings of multiplication or division in a much shorter set of steps. The only limit to this chaining ability is the user's creativity, familiarity with the tool, and the layout of the slide rule itself (which scales lie on the slide vs the body of the rule to facilitate the multiplications). | In general, chaining operations come in pairs that follow a pattern: divide then multiply. Align two numbers on scales, then move the hairline to the third number. Treating this new result as the first value of another chain, we can continue chaining values by alternating between moving the slide and hairline to tackle most complex products. Thanks to the inverse scales and how they interchange the multiplication and division processes, we can even perform long strings of multiplication or division in a much shorter set of steps. The only limit to this chaining ability is the user's creativity, familiarity with the tool, and the layout of the slide rule itself (which scales lie on the slide vs the body of the rule to facilitate the multiplications). | ||