If the Otis King slide rule in [Chris Staecker’s] latest video looks a bit familiar, you might be getting up there in age, or you might remember seeing us talk about one in our collection. Actually, we have two floating around one of the Hackaday bunkers, and they are quite the conversation piece. You can watch the video below.
The device is often mistaken for a spyglass, but it is really a huge slide rule with the scale wrapped around in a rod-shaped form factor. The video says the scale is the same as a 30-inch scale, but we think it is closer to 66 inches.
Slide rules work using the idea that adding up logarithms is the same as multiplying. For example, for a base 10 logarithm, log(10)=1, log(100)=2, and log(1000)=3. So you can see that 1+2=3. If the scales are printed so that you can easily add and then look up the antilog, you can easily figure out that 10×100=1000.
The black center part acts like a cursor on a conventional slide rule. How does it work? Watch [Chris’] video and you’ll see. We know from experience that one of these in good shape isn’t cheap. Lucky that [Chris] gives us a 3D printed version so you can make your own.
Another way to reduce the scale is to go circular, and you can make one of those, too.
Ah, the diddy pocket slide rule. Why not get a “full-size” one?
The Fuller calculator has a scale that is nominally[1] equivalent to a 1000inch/25.4m scale standard straight slide rule. Over 14000 were made during the 94 year production run, ended when the HP35 put the final nail in slide rules in general. https://en.wikipedia.org/wiki/Fuller_calculator
There are always some for sale on fleabay, but look carefully at the condition of the scale; many are OK, some are good, some are unusable.
[1] Personally I think that is marketing speak; the scale’s length is 500inch long.
I used to, and still kind of, went on about how multiplying numbers is pretty trivial with paper and pencil and will give you the exact solution instead of the roughly +/- 1% or so (depending on where on the log scale you are working). I also maintain that adding numbers is only slightly “easier” than multiplying numbers. And if you are at all doing complex computations, then certainly multiplying numbers with paper and pencil should be well within your wheelhouse.
So I never really understood how a slide rule is “better” with adding logs instead of just paper and pencil. faster maybe, but with the trade off of uncertainty that is most likely fine anyway. And at least in my scientific career, “exact” solutions were way more critical than rapid estimates. Almost nothing was time-sensitive that the extra couple minutes to do computations on paper was any kind of downside.
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UNTIL I started using the slide rule for trig functions! The it is waaaayyyy faster then using sine tables and stuff. Plus the ability to chain calculations together became super handy. I mean, it is all academic anyway these days but I could easily buy that “back in the day” slide rules were super rad. Not at all for simple arithmetic but when you start dealing with engineering functions, trig functions and actually working with logs (ln or base 10.. doesn’t matter) themselves instead of as a proxy for simple multiplication, they are king.
Pencil and paper for exact results are fine…except when taking an hour-long chemistry exam with 30 problems…
And in all my chemistry courses as well as grad school research I recall only one instance where more than four significant figures were needed. Three sig figs was far more common. The approximate answer given by a slide rule was ordinarily sufficient.
Especially for multiple-choice exams!
More like 0.5% with a 10″ slide rule.
Plus you can divide, do square roots, trigonometry, etc., and calculate powers if you have a log-log rule.
On the C and D scales of a 10″ rule, there’s no reason you shouldn’t always be able to get 0.1%. Otherwise, it does depend partly on the slide rule, and of course on which scale we’re talking about, and which end of the scale. It seems like slide-rule manufacturers would have tried to make their products accurate enough that the only limitation would be a good user’s close-up vision and judgement of proportion, for example that the cursor is 11/20ths (55%) of the way to the next tiny mark. Unfortunately, I’ve been disappointed more than once. The most recent is a Concise model 300 circular slide rule I got recently just for fun, since I’ve never had, or even personally seen, a circular one; but when you line up the 1’s on the C and D scales, it’s very visibly off at the other side of the circle, especially in the 2.5 to 3 area, and the 3.000 on the C scale points at about 3.003 on the D scale, as you can see in the last picture of it on my slide-rules page at http://wilsonminesco.com/SlideRules/SlideRules.html .
At the left end of the LL1 scale, you should be able to get a lot more than 2-3 digits, like 1.01068. That’s not to say the last digit will necessarily be correct; but it’ll be more accurate than if you didn’t try at all.
There is a way to microadjust, with extreme accuracy, not just the cursor, but the slide also, a vernier-like way I’ve never seen anyone do in any of the online instructional videos. I come up short trying to describe it in text. I guess I should make my own video, or at least a sharp still photo.
The real challenge with circular slide rules is getting the center points for all of the scales to coincide with the mechanical pivot, which is where most of the error comes in. A linear rule only has to be adjusted on one axis, but that second axis on a circular ‘rule’ is the bastard.
I have one of these I picked up on eBay years ago… cool retro gadget.
Sorry, can’t post while drooling …
I’ve got a couple. The thing about the Otis King is … it’s not accurate. The scales were drawn by hand and they’re a bit off, making the extra length moot.
It was a good idea though, and a cool gadget.
867 by 309. Why does that sound familiar?
That’s Jenny’s number.
When comparing geometries for slide rules, it’s a tradeoff of volume vs. area vs. maximum dimension (length), where excess volume means bulk, excess area means you can’t put it in a given pocket even by letting it stick out the top, and excess length means you can’t put it in your backpack, lunchbox, or whatever fixed-size container you prefer. The cylindrical rule is the winner for length, and pretty good for area, but it sucks for volume (think about the tradeoffs between cylindrical lithium-ion 18650 cells and flat lithium-polymers). Maybe this could be mitigated by making the core accessible for storing small items and pencils. The circular (disc) does well on volume and good for length, but is poor in area, with most of the middle area being unusable. The straight rule has low volume and okay area, but the worst length. When it comes to accuracy, with only one degree of freedom you can’t beat a straight rule for repeatability and accuracy.
I can’t help but be reminded of the Hewlett-Packard frequency meters (https://en.wikipedia.org/wiki/Frequency_meter) that we used for precisely determining the frequencies of microwave oscillators, where we didn’t have a prescaler/counter that could handle them. These were transparent cylindrical devices with input and output coaxial or waveguide connectors. Signal connects to input, output goes to power meter. Twist the top of the cylinder, which had a helical scale with an effective length of several meters, and look for a dip on the power meter.
Heck, we even had a procedure for plotting out the spectrum of a pulsed magnetron, by plotting the frequency and depth of each dip, which I did only one time, ever. When you’re looking for dips that are about 500 kHz apart on a 2700 MHz maggie, you start to appreciate that kind of precision.
Now for a sundial to go with it:
https://www.youtube.com/watch?v=IMrhNv0qj8g
https://www.thingiverse.com/thing:1068443