Editing Slide rule (section)

==Physical design==
{{further|Slide rule scales}}
===Standard linear rules===
[[File:Teaching sliderule comparison.jpg|thumb|A normal-sized slide rule sitting inside a {{convert|7|ft|m|adj=on}} teaching model]]

The width of the slide rule is quoted in terms of the nominal width of the scales. Scales on the most common "10-inch" models are actually 25&nbsp;cm, as they were made to metric standards, though some rules offer slightly extended scales to simplify manipulation when a result overflows. Pocket rules are typically 5&nbsp;inches (12&nbsp;cm). Models a couple of metres (yards) wide were made to be hung in classrooms for teaching purposes.<ref>{{cite web |url=http://www.tbullock.com/sliderule.html |title=Slide Rules |publisher=Tbullock.com |date=2009-12-08 |access-date=2010-02-20 |archive-url=https://archive.today/20130203202414/http://www.tbullock.com/sliderule.html |archive-date=2013-02-03 |url-status=dead }}</ref>

Typically the divisions mark a scale to a precision of two [[significant figures]], and the user estimates the third figure. Some high-end slide rules have magnifier cursors that make the markings easier to see. Such cursors can effectively double the accuracy of readings, permitting a 10-inch slide rule to serve as well as a 20-inch model.

Various other conveniences have been developed. Trigonometric scales are sometimes dual-labeled, in black and red, with complementary angles, the so-called "Darmstadt" style. Duplex slide rules often duplicate some of the scales on the back. Scales are often "split" to get higher accuracy. For example, instead of reading from an A scale to a D scale to find a square root, it may be possible to read from a D scale to an R1 scale running from 1 to square root of 10 or to an R2 scale running from square root of 10 to 10, where having more subdivisions marked can result in being able to read an answer with one more significant digit.

===Circular slide rules===
{{Uncited section|date=March 2025}}
Circular slide rules come in two basic types, one with two cursors, and another with a free dish and one cursor. The dual cursor versions perform multiplication and division by holding a constant angle between the cursors as they are rotated around the dial. The onefold cursor version operates more like the standard slide rule through the appropriate alignment of the scales.

The basic advantage of a circular slide rule is that the widest dimension of the tool was reduced by a factor of about 3 (i.e. by [[pi|π]]). For example, a {{cvt|10|cm}} circular would have a maximum precision approximately equal to a {{cvt|31.4|cm|}} ordinary slide rule. Circular slide rules also eliminate "off-scale" calculations, because the scales were designed to "wrap around"; they never have to be reoriented when results are near 1.0—the rule is always on scale. However, for non-cyclical non-spiral scales such as S, T, and LL's, the scale width is narrowed to make room for end margins.<ref>At least one circular rule, a 1931 Gilson model, sacrificed some of the scales usually found in slide rules in order to obtain additional resolution in multiplication and division. It functioned through the use of a spiral C scale, which was claimed to be 50 feet and readable to five significant figures. See http://www.sphere.bc.ca/test/gilson/gilson-manual2.jpg {{Webarchive|url=https://web.archive.org/web/20061230062132/http://www.sphere.bc.ca/test/gilson/gilson-manual2.jpg |date=2006-12-30 }}. A photo can be seen at https://www.hpmuseum.org/srcirc.htm. An instruction manual for the unit marketed by Dietzgen can be found at http://www.sliderulemuseum.com/SR_Library_General.htm {{Webarchive|url=https://web.archive.org/web/20070214152423/http://www.sliderulemuseum.com/SR_Library_General.htm |date=2007-02-14  }}. All retrieved March 14, 2007.</ref>

Circular slide rules are mechanically more rugged and smoother-moving, but their scale alignment precision is sensitive to the centering of a central pivot; a minute {{convert|0.1|mm|abbr=on}} off-centre of the pivot can result in a {{convert|0.2|mm|abbr=on}} worst case alignment error. The pivot does prevent scratching of the face and cursors. The highest accuracy scales are placed on the outer rings. Rather than "split" scales, high-end circular rules use spiral scales for more complex operations like log-of-log scales. One eight-inch premium circular rule had a 50-inch spiral log-log scale. Around 1970, an inexpensive model from B. C. Boykin (Model 510) featured 20 scales, including 50-inch C-D (multiplication) and log scales. The RotaRule featured a friction brake for the cursor.

The main disadvantages of circular slide rules are the difficulty in locating figures along a dish, and limited number of scales. Another drawback of circular slide rules is that less-important scales are closer to the center, and have lower precisions. Most students learned slide rule use on the linear slide rules, and did not find reason to switch.

One slide rule remaining in daily use around the world is the [[E6B|E6-B]]. This is a circular slide rule first created in the 1930s for aircraft pilots to help with [[dead reckoning]]. With the aid of scales printed on the frame it also helps with such miscellaneous tasks as converting time, distance, speed, and temperature values, compass errors, and calculating fuel use. The so-called "prayer wheel" is still available in flight shops, and remains widely used. While [[Global Positioning System|GPS]] has reduced the use of dead reckoning for aerial navigation, and handheld calculators have taken over many of its functions, the E6-B remains widely used as a primary or backup device and the majority of flight schools demand that their students have some degree of proficiency in its use.

Proportion wheels are simple circular slide rules used in graphic design to calculate [[aspect ratio]]s. Lining up the original and desired size values on the inner and outer wheels will display their ratio as a percentage in a small window. Though not as common since the advent of computerized layout, they {{cns|are still made and used.<!-- please add {{as of}} or equivalent when sourcing -->|date=March 2018}}

In 1952, Swiss watch company [[Breitling SA|Breitling]] introduced a pilot's wristwatch with an integrated circular slide rule specialized for flight calculations: the [[Breitling Navitimer]]. The Navitimer circular rule, referred to by Breitling as a "navigation computer", featured [[airspeed]], [[rate of climb|rate]]/time of climb/descent, flight time, distance, and fuel consumption functions, as well as kilometer—[[nautical mile]] and gallon—liter fuel amount conversion functions.
<gallery>File:Vintage Concise Model 28 Circular Slide Rule, Made In Japan, Circa 1960s (16240893439).jpg|A simple circular slide rule, made by Concise Co., Ltd., Tokyo, Japan, with only inverse, square, and cubic scales. On the reverse is a handy list of 38 [[Metric system|metric]]/[[Imperial units|imperial]] conversion factors.
File:Slide rule pocket watch.jpg|A Russian circular slide rule built like a pocket watch that works as single cursor slide rule since the two needles are ganged together
File:Rechenschieberring.jpg|A two-scale slide rule built into a ring
File:Circular slide rule.JPG|Pickett circular slide rule with two cursors. (4.25&nbsp;in/10.9&nbsp;cm width) Reverse has additional scale and one cursor.
File:Breitling Navitimer slide rule.jpg|''[[Breitling Navitimer]]'' wristwatch with circular slide rule
File:RotaRule-Photo-Front-04.jpg|alt=RotaRule 510 Front|The front side of a Boykin RotaRule Model 510
File:RotaRule-Photo-Back-04.jpg|alt=RotaRule 510 rear side|The rear side of a Boykin RotaRule Model 510
File:Keuffel & Esser - Sperry, Model 4016 Pocket Calculator - MIT Slide Rule Collection - DSC03581.JPG|Pocket watch style Sperry 4016 Pocket Calculator
</gallery>

{{anchor|Cylindrical slide rule}}

===Cylindrical slide rules===
Cylindrical slide rules are made in two styles: those with helical scales such as the [[Fuller calculator]], the [[Otis King]] and the [[Bygrave slide rule]], and those with bars, such as the Thacher and some Loga models. In either case, the advantage is a much longer scale, and hence potentially greater precision, than afforded by a straight or circular rule.
<gallery>
File:Fuller's calculator.jpg|Fuller calculator, 1928
File:Otis King Model K (horizontal).jpg|Otis King Model K
File:Suwak Bygrave.jpg|Bygrave slide rule
File:Senator John Heinz History Center - IMG 7824.JPG|Thacher slide rule, {{circa|1890}}
</gallery>

===Materials===
Traditionally slide rules were made out of a relatively dense, stable hardwood such as [[mahogany]] or [[boxwood]] with cursors of glass and metal. Aluminum was used, and at least one high precision instrument was made of steel.

In 1895, a Japanese firm, Hemmi, started to make slide rules from [[celluloid]]-clad bamboo, which had the advantages of being dimensionally stable, strong, and naturally self-lubricating. These bamboo slide rules were introduced in Sweden in September, 1933,<ref>{{cite web|url=https://runeberg.org/tektid/1933a/0348.html|title=336 (Teknisk Tidskrift / 1933. Allmänna avdelningen)|publisher=Runeberg.org|access-date=2010-02-20}}</ref> and probably only a little earlier in Germany.

Scales were also made of celluloid or other polymers, or printed on aluminium. Later cursors were molded from [[acrylyl group|acrylics]] or [[polycarbonate]], sometimes with [[polytetrafluoroethylene|Teflon]] bearing surfaces. 

All premium slide rules had numbers and scales deeply engraved, and then filled with paint or other [[resin]]. Painted or imprinted slide rules were viewed as inferior, because the markings could wear off or be chemically damaged. Nevertheless, Pickett & Eckel, an American slide rule company, made only printed scale rules.{{cn|date=March 2025}} Premium slide rules included clever mechanical catches so the rule would not fall apart by accident, and bumpers to protect the scales and cursor from rubbing on tabletops.