![\"PADT-TechSupport-Team-Prop\"](\"https:\/\/www.padtinc.com\/wp-content\/uploads\/2022\/02\/PADT-TechSupport-Team-Prop.webp)
<\/picture><\/p>\nThis thing is huge, over 6 feet (2 m) from side to side, in its un-extended position hanging on the wall.<\/p>\n
In theory a gigantic slide rule could provide more accuracy, but our trophy, a Kueffel & Esser model 68 1929 copyrighted 1947 and 1961, was intended for teaching purposes in classrooms.\u00a0 Most engineers had essentially pocket size or belt holder sized slide rules, also known as slip sticks.\u00a0<\/p>\n
For the real thing, here is a picture of a slide rule used by Eric Miller’s father Col. BT Miller while at West Point from 1955 to 1958 as well as\u00a0during his Master’s program in 1964.<\/p>\n
Why do we care about the slide rule today?\u00a0 Have you ever seen World War II aircraft, submarines, or aircraft carriers?\u00a0 These were designed using slide rules and\/or logarithms.\u00a0 The early space program?\u00a0 Slide rules were used then too.\u00a0 Some phenomenal engineering was accomplished by our predecessors using these devices.\u00a0 Back then the numerical operations were just a tool to utilize their engineering knowledge.\u00a0 Now I think we have a tendency to focus on the numerical due to its ease of use and impressive presentation, while perhaps forgetting or at least de-emphasizing the underlying engineering.\u00a0 That\u2019s not to say that we don\u2019t have great engineers out there; rather it\u2019s a call to energize you all to remember, consider, and utilize your engineering knowledge as you use your simulation tools.<\/p>\n By contrast, here is a picture of PADT\u2019s brand new server room, with cluster machines being put together in the big cabinets.\u00a0 Hundreds of cores.<\/p>\n What about the giant slide rule?<\/p>\n My father found a thick book at an estate sale a few months ago.\u00a0 There are a lot of retirees living in Arizona, so estate sales are quite common and popular.\u00a0 They occur at a life stage when due to death or the need for assisted living, folks are no longer able to live in their home so the contents are sold, clearing out the home and generating some cash for the family.\u00a0 This particular estate sale was for a retired engineer.\u00a0 The book caught my father\u2019s eye, first because it was quite thick and second because the title was, Mechanical Engineers\u2019 Handbook.\u00a0 Figuring it was a bargain for the amazing price of $1.00, he bought it for me.\u00a0 This book is better known as Marks\u2019 Handbook.\u00a0 It\u2019s apparently still in publication, at least as late as the 11th<\/sup> Edition in 2006, but the particular edition my father bought for me is the Fifth Edition from 1951.<\/p>\n Although the slide rule is mostly a curiosity to us today, in 1951 it was state of the art for numerical computation.\u00a0 While Marks\u2019 has a couple of paragraphs on \u201cComputing Machines\u201d, described as \u201celectrically driven mechanical desk calculators such as the Marchant, Monroe, or Friden\u201d, the slide rule was what I will call the calculator of choice by mechanical engineers at the beginning of the 2nd<\/sup> half of the 20th<\/sup> century.\u00a0<\/p>\n As an aside, these mechanical calculators performed multiplication and division, using what I will describe as incredibly complex mechanisms.\u00a0 Here is a link to a Wikipedia article on the Marchant Calculator:\u00a0 http:\/\/en.wikipedia.org\/wiki\/Marchant_Calculator<\/a><\/p>\n Marks\u2019 Handbook devotes about 3 pages to the operation of the slide rule, starting with simple multiplication and division and then discussing various methods of utilization and various types of slide rules.\u00a0 It starts off by stating, \u201cThe slide rule is an indispensable aid in all problems in multiplication, division, proportion, squares, square roots, etc., in which a limited degree of accuracy is sufficient.\u201d\u00a0<\/p>\n The slide rule operates using logarithms.\u00a0 If you\u2019re not familiar with using logarithms then you are probably younger than me, since I recall learning them in math class in probably junior high in the late 1970\u2019s.\u00a0 The slide rule uses common logarithms, meaning the log of a number is the exponent needed to raise a base of 10 to get that number.\u00a0 For example, the common log of 100 is 2.\u00a0 The common log table in the 1951 edition of Marks shows us that the common log of 4.44 is 0.6474.\u00a0 For the sake of completeness, the \u2018other\u2019 logarithm is the natural log, meaning the base is the irrational number e, approximated as 2.718.<\/p>\n Getting back to common (base of 10) logs, the math magic is that logarithms allow for shortcuts in fairly complex computations.\u00a0 For example, log (ab) = log a + log b.\u00a0 That means if we want to multiple two fairly complicated numbers, we can simply look up the common log of each and add them together.\u00a0 Similarly, log (a\/b) = log a \u2013 log b.\u00a0<\/p>\n Here is an example, which I will keep simple.\u00a0 Let\u2019s say we want to multiple 0.0512 by 0.624.\u00a0 On a calculator this is simple, but what if you are stranded on a remote island and all you have is a log table?\u00a0 Knowing the equations above, you can look up the log of 0.0512 which is 0.7093-2 and the log of 0.624 which is 0.7952-1.\u00a0 We now add: Writing that sum as a positive decimal minus an integer is important to being able to look up the antilogarithm or number whose log is 0.5045 \u2013 2.<\/p>\n Looking up the number whose log is 0.5045 we get 3.195, using a little bit of linear interpolation.\u00a0 The \u201c-2\u201d tells us to shift the decimal point to the left twice, meaning our answer is 0.003195.\u00a0 Thus, using a little addition, some table lookup, a bit of in the head interpolation, and some knowledge on how to shift decimal points, we fairly easily arrive at the product of two three digit fractional numbers.\u00a0 Now you are free to look for more coconuts on the island.\u00a0 Or maybe get back to a hatch in the ground where you need to type in the numbers 4, 8, 14, 16, 23, and 42 every 108 minutes.\u00a0 Oops, I\u2019m really becoming Lost<\/em> here\u2026<\/p>\n Getting back to the slide rule, one way to think of it is a graphical representation of the log tables.\u00a0 In its most basic form, the slide rule consists of two logarithmic scales.\u00a0 By lining up the scales, the log values can be added or subtracted.\u00a0 For example, if we want to multiply something simple, like 4 x 6, we simply look from left to right on the scale on the \u2018fixed\u2019 portion of the slide rule to get to 4, then slide the moving portion of the slide so that its 1 lines up with the 4 found above on the fixed portion.\u00a0 We then move left to right on the movable scale to find the 6.\u00a0 Where the 6 on the movable slide lines up with on the fixed portion is our solution, 24.\u00a0 What we\u2019ve really done is add the log of 4 to the log of 6 and then find the antilog of that result, which is 24.\u00a0 Now that we\u2019ve found 24<\/em>, we\u2019re not Lost<\/em>!\u00a0<\/p>\n We don\u2019t intend to give detailed instructions on all phases of performing calculations using slide rules here, but hopefully you get the basics of how it is done.\u00a0 There are plenty of online resources as well as slide rule apps that provide all sorts of details.\u00a0 Besides multiplication and division, slide rules can be used for squares and square roots.\u00a0 There are (were) specialty slide rules for other purposes.\u00a0 Note that with additional knowledge and skill in visually interpolating on a log scale, up to 3 or even 4 significant digits can be determined depending on the size of the slide rule.<\/p>\n![\"Burt-Miller-SlideRule-D2\"](\"https:\/\/www.padtinc.com\/wp-content\/uploads\/2022\/02\/Burt-Miller-SlideRule-D2.jpg\")
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