How Slide Rules Work | Hacker News Reader

How Slide Rules Work

amenzwa.github.io

203 pointsColinWright60 comments

In the UK there was a time (late `70s) when slide-rules were allowed in examinations but calculators weren't, no-brainer to learn how to use one just for that. Even better, if you added "(SR)" after your calculations, that indicated that you had used a slide-rule so small errors were permitted.

Deep dive, for sure. I suspect Cliff Stoll is enjoying this site.

I played with creating a logarithmic slider thing [1] in Javascript that I hoped I could package up as a kind of "widget" people could use on their web pages. But I don't really know Javascript that well—or rather how to make an API out of a Javascript thing.

Anyway, to test it I tried to make an Ohm's Law calculator [2].

I would love to see a site like the one in this post have some kind of interactive slide rule on the web page itself.

[1] https://github.com/EngineersNeedArt/SlideRule

[2] https://www.engineersneedart.com/ohmslaw/index.html (the yellow slider is not directly user-moveable in this example)

It works well enough to get the idea of "set the voltage, set the resistance, read the current off the voltage scale above the 1 on the resistance scale". It might be a little easier to do if the rules were closer, which would probably require a little noodling about with the code to make the "resistance" box sit below the rule scale.

> I missed my slipstick. Dad says that anyone who can’t use a slide rule is a cultural illiterate and should not be allowed to vote. Mine is a beauty—a K&E 20″ Log‐log Duplex Decitrig. Dad surprised me with it after I mastered a ten-inch polyphase. We ate potato soup that week—but Dad says you should always budget luxuries first. I knew where it was. Home on my desk.

Robert A. Heinlein, Have Space Suit—Will Travel (1958)

Here one can play with many slide rules in the browser https://www.sliderulemuseum.com/VirtualSR.shtml

My Dad is a retired R&D chemist who worked at the DuPont corporation's Experimental Station. When I was a kid he would bring his old slide rules home from work when he got a new one, and at one point he explained to me how they work but I forgot it all long ago.

I still have the slide rules, so this post was a great rabbit hole to go down. In software there's no need for them but I still find them fascinating as a window into how engineers used to get their work done.

> In software there's no need for them...

... but in the Real World they work pretty well for the sort of calculations you might need to do in the field (literally, in a field, sometimes) and don't require batteries, are reasonably waterproof, and reasonably robust if dropped.

The all plastic ones are intrinsically safe in a potentially flammable environment, they don't require power, they're an education in how most engineering materials in the real world have surprisingly wide tolerances so they are far more than accurate enough for most work, for people who learn graphically/visually they are the logical next educational step after counting on fingers.

They're pretty useful for teaching amateur people how to implement algorithms. Multiple ways to solve problems, some easier than others, some more efficient than others, with immediate rewards of faster higher accuracy.

> The all plastic ones are intrinsically safe in a potentially flammable environment

Never thought of that, and I used to work in an ATEX environment where calculators powered by watch batteries had to be carefully logged and carried across to a "safe" area inside a special (horribly expensive) Peli case.

Me neither. Similar to the drill floor on oil rigs where there's tracking of every tool in use to make sure it is non-sparking.

There were also all manner of specialty "slide rule" calculators of various kinds for special purposes. I used to have a bunch of them especially from the oil business. Don't know if I still have any at this point.

Somewhere I have a circular one for flight calculations that you velcro to the knee of your trousers.

To add to this, there's a great set of resources by Joe Pasquale explaining the mathematical theory behind how various functions can be computed by slide rules:

* https://cseweb.ucsd.edu/~pasquale/Classes/SlideRule/

* Mathematical Foundations of the Slide Rule (PDF): https://cseweb.ucsd.edu/~pasquale/Papers/IM11.pdf

* Why Does A Slide Rule Work? (PDF): https://cseweb.ucsd.edu/~pasquale/SlideRuleTalkLasVegas14.pd...

The gist of it is:

1. First, define a way to represent any univariate monotonic function f(x) on a graduated scale. (Specifically: select a discrete set of x values, and for each of these x values, place a mark with label x at a distance proportional to (f(x) - f(x_L)) from the left endpoint, where x_L is the leftmost x value.)

2. Then, if we have two such scales f(x) and g(x) that can slide relative to each other, we can compute functions of the form h(x, y, z) = f_inverse(f(x) + g(y) - g(z)).

It ends up being surprisingly versatile -- the above resources show how you can compute:

1. Multiplication: x * y using f(x) = log(x) and g(y) = log(y), with z fixed at 1

2. Hypotenuse: sqrt(x^2 + y^2) using f(x) = x^2 and g(y) = y^2, with z fixed at 0

3. Parallel resistors: 1/(1/x + 1/y) using f(x) = 1/x and g(y) = 1/y, with z fixed at +infinity

4. Exponentiation: x^(y/z) using f(x) = log(log(x)) and g(y) = log(y)

This education film from 1957 gives a good overview of using one:

* https://www.youtube.com/watch?v=oYQdKbQ-sgM

"Professor Herning" (?) also has a good series of videos on the use of various scales as well:

* https://www.youtube.com/@ProfessorHerning/videos

His playlist starting at the beginning (C and D scales) with a Manheim layout:

* https://www.youtube.com/playlist?list=PL_qcL_RF-ZyvWJJkJOk_O...

* https://sliderulemuseum.com/Manuals/M37_Post_Manheim_Instruc...

Some manuals / books on slide rules:

* 1909: https://archive.org/details/mannheimsliderul00coxwrich

* 1922: https://archive.org/details/cu31924002978561/mode/2up

I also like (and was lucky enough, as a young man, to find a physical copy of) Asimov's "An Easy Introduction to the Slide Rule." It's my favorite introductory text. PDF copies can be found on the web.

Slide rules are super cool. Such an easy gift to give the engineer in your life.

I never spent the time to get quick with it, but I could absolutely see it being quicker than a calculator. You’d just have to be aware of the limits to its precision if you were in a field that required it.

Quicker than an algebraic calculator, maybe, but very few people could get. faster with a slide rule than an ergonomic RPN calculator. like the HP 41 series. And I say that as an enthusiastic and experienced slide rule user, before I switched to a calculator.

One problem with a slide rule is that it only performs operations on normalized mantissas. You have to keep a parallel exponent calculation in your head, and that slows you down. Also, maintaining best precision slows you down.

I used an HP-41CV for many years. I needed the financial calcs module which I used in place of the dedicated HP financial calculator in grad school. Eventually gav out on me but was a good calculator for a long time.

I did keep a slide rule as a backup for exams in college when calculators were still LED but never really used one after a couple of years in high school.

The financial people I know all own 12Cs and they've been in continuous production since '81 although the innards are just a very boring ARM processor now.

They do what people want, the keyboard feel is infinitely smoother than tapping on a phone, etc.

I have an HP-41 app on my phone that the author gave to me when I was doing some product reviews early-on in the smartphone days. But definitely not the same as the physical HP calculator.

Yeah, the 12C was the standard in business school. But I needed a new calculator and the 41 with its various modules worked fine and was more general purpose.

When using a slide rule, keeping track of the number of digits to the left of the decimal point (DLDP) in the result is fairly simple if you know the basic rule:

For multiplication, the DLDP in the result is:

- the sum of the DLDPs of the multiplicands MINUS 1 if the multiplication is done with the slide sticking out to the right of the ruler's body (for example 2.0 x 3.0 = 6.0).

- the sum of the DLDPs of the multiplicands if the multiplication is done with the slide sticking out to the left of the ruler's body (for example 5.0 x 4.0 = 20.0).

There's a similar rule for division, but that's left as an exercise for the student.

> You have to keep a parallel exponent calculation in your head, and that slows you down

We were taught to estimate and use the rule to refine. I date back to the early electronic calculator era and we still had textbooks referencing slide rules etc.

"I want a dropping resistor for a plain old 1980s LED in a car" (back in ye old red LED 20 mA days) "Well experience indicates that will be far more than 500 ohms and somewhat less than 1K and IRL you're probably going to install a 680 and call it good" If you want an actual calculation for engineering purposes you calculate the ideal value under worst case conditions as about 585-ish ohms or whatever using the slide rule, purchasing LOLs at the idea of buying 0.1% precision resistors for mere LEDs, installs cheap 680 ohms and ships it. Maybe 680s if you want it bright to see in daylight or 820 if you want better odds to survive an alternator field winding dump or open battery (about the same thing). You can at least use the slide rule to verify everyone rounded in the "safer" direction to handle the worst case scenario.

You still have to be aware of the difference between precision and accuracy, and how to propagate precision through calculations to maintain accuracy. It's a forgotten skill that lets us now create data out of whole cloth and call it actionable information but back when slide rules and log tables ruled the day the difference was stressed over and over in math and science classes and you would fail an assignment or a test question if you had the wrong precision in a result.

We have speed electronic calculators now instead of slide rules, but they give a wronger answer and people aren't even aware of it or know why.

For people into watches, check out this video (and the whole series of watch and learn) on slide rules on watches: https://www.youtube.com/watch?v=RuK_77DEUfw

Wow, I really want a slide rule watch now.

In my head: “Oh yeah, I forgot how to use one of those”

This article: “lol, is that the depth of your commitment”

I have one at home, which is the one we had to buy to use in highschool. In the math classrooms we had a 6 feet version that could be mounted on the blackboard such that the teacher could used for instruction. See for a picture on the Dutch page https://rekenlat.barneveld.com/rekenliniaal.htm

These TMSLs were also reasonably common in classrooms in the United States in the 1950s.

Two Meter Slide Rule

Wow that's fascinating! Crazy how things change, no wonder my grandma thinks math is black magic!

It is worth keeping one around.

When the "cloud" is raining and your laptop and phone batteries are drained and you suddenly need to navigate your 4823 times table - its got you covered.

You will also need to work out how to write with a pen or pencil on paper or try and fix up your atrophied ability to remember arbitrary "facts" short term.

Honestly the scenarios where this becomes likely are dwindling with the advent of solar and batteries. Offline knowledgebases and the ability to use them long term are getting increasingly stable, and the likely low point in a societal collapse is probably getting high enough that a slide rule would not be necessary.

I have a Casio fx-991ES calculator, and twenty years later I have yet to need to replace the button cell in it thanks to the tiny solar cell.

And when the EMP washes over your home/office it will most likely be off and most likely survive. If you are doing your monthly finances at the time and it is on, it will be destroyed. The slide rule rules!!! I keep a pocket Pickett for fun...the window has a small crack, and it is missing a very tiny screw (1 of 8). I brought it to my engineering company one day and showed the 20-30-something group how it worked. I then did a full page of calcs they did in Excel, and even with the limits of visual resolution came within an acceptable percentage of their calc.

That's not quite how EMPs work. The wire traces act as antennas, and long wires like power transmission lines will have huge power surges, and small devices like calculators will have basically none. The miniscule increase in length of conductive material if the battery happens to be conducting at the moment won't impact the amount of current induced.

Solar EMPs won't be powerful enough to impact electronics. A nuclear EMP can impact electronics, but only over a small geographic area; close enough that if you are in the electronics-frying radius of a nuclear weapon explosion, you either have much larger problems to worry about, or nothing at all to worry about ever again.

Here's info from Los Alamos Lab on it: https://www.lanl.gov/media/publications/national-security-sc...

Thanks for the information and link. I was, however, being facetious and making puns (slide rules!)

I have a little collection of them. I keep the small Hemmi bamboo on the navigation table at all time.

https://wiki.xxiivv.com/site/slide_rule

Last year I made my own rotary slide rule for playing Balatro, the poker roguelike!

My version has a couple interesting properties compared to ordinary linear slide rules:

1. It has three octaves, so it can scale from 1 to 1k or from 1k to 1m, or from 1m to 1b. This is great for calculating point values

2. It's rotary

3. It can be easily 3d-printed!

Source code and .STL files here: https://www.printables.com/model/1026662-jimbos-rotary-slide...

When I was in 5th grade, calculators had become pretty affordable and there was this huge discussion whether kids should learn slide rules or use calculators. At the time it was decided we should learn slide rules and I am happy about this because it gives you some level of number intuition.

It reminds me a little of AI now. The question of whether students should use AI will probably soon go away and everybody will use AI. Not sure what the results will be.

Calculators went from something that was really expensive to something that was relatively affordable over a very short period of time. In about 1974, a 5-function TI was about $100 (in 1975 currency). By the next year a full scientific TI calculator wasn't much more and no one, at least in engineering school, was still using a slide rule though I brought one to exams as a a backup. By a couple years later, I was able to buy a discontinued HP calculator for about the same.

Last week I donated several slide rules to Goodwill; a few were very nice. Meanwhile, I still have a pristine HP-41cx and HP-15c, and an HP-25 app on my iPhone.

I have an HP-15c as well as a 16c and I've been using the latter on a daily basis while writing a byte-level network protocol client. I'm getting faster by the day and on the verge of writing some programs for shortcuts on the calculator. I still use the excellent PCalc as well, but seem to be faster on the physical calculator, which is kind of surprising.

When I was writing a shareware program in x86 assembler and doing a fair amount of bit twiddling, the 16C was really handy. Presumably I still have it around somewhere.

I came up on the cusp of the calculator take-over, so although slide rules were around, and we were taught how to use them in school, I never really used them for any practical purpose. However, since they were the buggy whips of that day, you could pick up nice fancy ones for cheap in stationary stores (also now gone). So somewhere I have a good collection of them.

A sort of non-logarithmic slide rule, the E6B Flight Computer, was still in use when I was a student pilot 20 years ago. I still carry one: they don't require electricity (although using one in the dark requires a light source).

https://en.wikipedia.org/wiki/E6B

The main part of the E6B is a very standard logarithmic slide rule. Having it loop unto itself is a neat trick but very ancient.

But perhaps you were referring to one of the many other parts of the E6B which I am not familiar with.

These fascinates me, it's one of the highest simplicity / abstraction level ratio I can think of. A few marks well spaced on two bits of wood, and you get "linearized" multiplication. Nicest ~analog computer I can think of :)

I still have the wooden 10" Keuffel and Esser that I inherited from my father and that I used in college. These days I use my HP15C unless I want to provoke glee and amusement in my younger colleagues by sporting my Pickett slide rule in my shirt pocket.

K&E's are classic. What do you think was the most popular Pickett model?

The microline series, antique stores are full of them. Every high school or lower undergrad boomer had one or a similar clone and they show up in antique stores and on ebay all the time. The 80 and 120 are about the same size and sell for about $20 and I don't bother buying them anymore when I see them. The 80 puts the T scale on top and the 120 more usefully puts it in the slider IIRC so you can chain calculations.

Grad students or undergrad STEM students would have something like a 900 series, I have several, very nice. This is a desk rule it will not fit in a pocket. Something like a 600 series is a short pocket model, anodized aluminum, very nice and desirable.

The microline series was definitely made to a price point and unless you find one in unusually good condition or its your first collector rule I would not bother picking it up. They stick very strongly and the cursor cracks after half a century and they are slippery in the hand and warp more than most rule and I don't think they're easy to read. They were cheap to make and cheap to buy.

Slide rules in the 2020s are an efficient market; something that barely works "the walmart solar calculator of its generation" like a microline series sells for around $20 today, a VERY desirable N600 series sells for like a hundred bucks and I think its a bargain at that price.

If you mean most popular as in most desired today not most sold back in the day, that's probably the 600 series or specialty rules like I have a N-16-ES with the electronics engineering scales. The latter sells for about as much as a working HP48 calculator, which is interesting. If you mean popular as in attractive that is surely the Faber-Castell short 83N series, I think that's a 62/83N. I would like one of those LOL. Unleash 1960s German graphics artists on industrial design and tell them to make the coolest looking slide rule possible under 60s industrial design rules, you get the 83N series, very very cool way to spend $300 or so, its the kind of thing you put in a lighted display case to admire.

Wow, thanks. This is an incredible deep dive and I obviously came to the right place for that question. This kind of detailed comment is why I still appreciate HN so much...

I think MIT ended up with the K&E collection. I haven't had a chance to tour the MIT Museum in its new digs so I'm not sure what's on display.

While I'm a bit too young to have used one in school, my dad did give me his slide rule from when he was a student. It's one of my most prized possessions, if only to show how far humanity has come in terms of computing devices.

My mother (who ran a biochemistry lab) had a longish one--extra digit of precision I guess. Unfortunately my anti-packrat dad must have chucked it in some move or another. In addition to some cheap student stuff, I think I still have a couple of "normal" professional slide rules but they're not in very good shape if serviceable.

For the past 10 years, I've worn a slide rule every day. It's a small circular one modeled after the E6B aviation slide rule, with markers for common aviation conversions.

Anyone know of a good place to buy a new linear slide rule? I know there's a circular slide rule manufacturer but am not sure if any linears are being made any longer.

They won't be new, but Ebay has a lot of old linear rules.

As per sibling comment: not much of a market for new ones. Would be curious about someone trying to make some: use Kickstarter to gauge interest perhaps?

For used, see perhaps "Where to Buy Slide Rules?":

* https://www.sliderule.ca/buy.htm

The used ones aren't that expensive on eBay, especially if you just want a functional one and not a pristine show piece. There's a few 3D print models available for them too, and honestly they are rudimentary technology, you could probably make one with hand tools and patience.

I bought a newly manufactured one from ThinkGeek several years ago, some geek-catering company will pop up and supply pent up demand eventually. Curiosity Box fills that niche right now.

Faber-Castell had new-old stock in the mid 20-teens, but they ran out (of stock or patience) around 2016–2018. Picked up a 2/83N for under $100, and I wish I'd gotten more. I'd suggest some of those are on eBay now.

Most of my like-new rules came from antique malls, though I've also purchased one from Etsy. Estate sales are occasionally fruitful. As long as they were stored properly (e.g., in a desk drawer, like it seems they mostly were after the electronic calculator took over), they don't degrade. Occasionally you see minor yellowing that is cured by some time in the sun. Carrying cases (often leather) are typically more affected by time. I soak new (to me) leather cases in neatsfoot oil and give them at least a week before putting the rule back.

You could make your own with prints from the Slide Rule Museum [0]. 3D printing would make quick work of it, but I'm sure wood or metal units could be accomplished. The cursor benefits from spring loading,

They also have some pretty nice simulators [1], if that's your thing.

[0] https://sliderulemuseum.com/SR_Scales.shtml [1] https://www.sliderulemuseum.com/VirtualSR.shtml

The HP-35 wasn’t programmable- it was just a scientific calculator.

This would have been helpful for Sam Cooke.

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