How did scientists and engineers actually use slide rules, in the old days?

Factual Questions
1

Somebody in one of my FB groups recently posted a vintage ad for a slide rule. A number of folks posted about a parent who had been an engineer back in the day, and one or two older engineers, themselves, also commented on how indispensable the old “slipstick” had been for them. The humble slide rule got us to the moon, baby!

All this makes me curious about how, exactly, that was so. I think I understand the basic principle of a slide rule; i.e. by sliding one logarithmically calibrated scale against the other, you can perform multiplication quickly. But given the limits of human dexterity and visual acuity, how did that help 1960s engineers in determining the optimal shape of space capsule? Or in calculating a midflight course correction during a moon flight? Were the actual calculations more typically performed with paper, pencil, and log tables, with the slide rule serving more as a sanity check on the results? Or was it that, if you had a big enough slide rule, you really good perform calculations down to the level of precision required for planning spaceflights and other engineering tasks?

I understand enough about calculus to thoroughly appreciate that the necessary mathematical models were possible. But how did the slide rule fit into the process of using those models?

2

They’re useful for chain calculations. Convert miles to feet, and then feet to meters.

Multiply the sides of a big rectangular volume to find out how many cubic feet it measures, then multiply by the weight per cubic foot of concrete, to tell you how much it weighs.

Figure how many times 30 goes into 360, multiply by 2, divide by 24, multiply by 60, and that’s how long it takes the moon to travel through its own width against the background stars.

3

Intriguingly naive.

Here’s the main (most complicated) function… rapid fire (approximate) use Napiers Logarithms…
(The method of logarithms was publicly propounded by John Napier in 1614, in a book titled Mirifici Logarithmorum Canonis Descriptio … Description of the Wonderful Rule of Logarithms)
A* B = X^(logX(A)+LogX(B))
So find A on the fixed part of the slide rule, then put the slides 0 there… SO you find B on the slide, and read off the Value (where B is) on the fixed part of the slide … thats A*B… Multiplication done by addition.

Of course the slide rule lets you evaluate functions too… a few log’s, sin, cos,tan…
and that

4

I used one through college - my aunt gave me one as a present. I was never an expert, but they were great at getting quick answers to a few places of precision, doing sins etc and conversions as mentioned. Anyone wanting real accuracy would see if the result looked reasonable with a slide rule first, and then work it out precisely.

The only qual I flunked during my first pass in grad school was circuit theory, for which I used my slide rule. I bought a TI calculator and whizzed through the retest. That shows why slide rules did not survive the advent of calculators - they were better than paper and pencil for calculating quickly, but not match for silicon.

5

My dad was a physics professor and had several fairly fancy slide rules. (He’s over 90 now)

With a good one, he said you could get two digits of accuracy, and with a little mental agility and math tricks, produce the third digit. Three digits is pretty darned good. However, when the HP handheld programmable calculator with little program cards came out he got one of those and put it to good use.

6

For anyone slide-rule curious, slip sticks on YouTube.

7

My slide rule had sin, cos, x**2 etc as well as multiplication scales. But the fact is that when I was in high school we mostly chose to use our 4-digit tables for calculations, rather than the slide rule. I don’t know why people prefered slide rules to sets of tables, and I no longer know anyone old enough to ask.

8

When I was at school, our maths teacher had worked during WW2 calculating trajectories to aim anti-aircraft guns at the bombers over London. They worked in an underground bunker and were given the speed, course and height of the plane, and they told the gunners what settings to use.

To do these complex calculations fast enough to be useful, they used a large spiral slide rule wrapped around a tube. He showed as a photograph.

We used the straight ones, but only for estimating. Logs, sines, cosines etc. were all in the essential book of tables.

9

I used one through my first two years in college (at MIT). In high school, I could calculate faster with my slide rule than the guy who had the electronic calculator.

Slide rules gave you a quick way of multiplying numbers together, raising numbers to second and higher powers, taking square and cube roots (and other roots, too) and doing trigonometric calculations, all to three-place accuracy. What it didn’t let you do was add or subtract (although there were mechanical devices for that, if you wanted, including the abacus and various ingenious yet simple devices).

Multiplying two numbers together won’t design a space capsule for you, or calculate expected yields of chemical reactions, but it will let you perform the above-mentioned numerical calculations (chiefly the multiplications) easily and rapidly.

The reason I didn’t get an electronic calculator earlier was that any of them that did anything beyond multiplication, division, addition, and subtraction initially cost a lot. The venerable HP-35, which did logarithms and trig operations, cost $395. When my college chemistry lab started requiring four-place accuracy, I borrowed someone’s HP-45. (The HP-65, which was programmable, cost a whopping $695).

I didn’t buy a calculator until the HP-25 came out. 49 steps of programming, all the functions, and it only cost $195. (But you couldn’t store the programming on cards, as the HP-65 could. It was in non-volatile memory, but if you needed a new program, you had to write over the old one)

Scary to think that you could get an infinitely more capable PC for the cost of an HP-65 today.

I still have my collection of slide rules. Even after the prices of calculators came down, the good slide rules were still being sold, with no reduction in price. The cheap plastic ones disappeared from stores, though. You used to be able to buy a plastic slide rule in the stationary department of something like a Target or Wal-Mart. I buy old ones at flea markets and garage sales.

10

A slide rule only gives you about three digits of precision, and that’s a feature, not a bug. There are new generations of engineers who don’t know how to round. If your calculations go all the way out to eight digits, and your parts only come in increments of a millimeter, you’re not going to know which one to use.

EDIT: I still have my collection of slipsticks, too, and I’m a lot younger than Cal. I’ve also actually used them for tests.

11

When I was a freshman engineering student (1966), the first major financial decision you had to make at the bookstore (*) was which slide rule to buy. I dimly recall that the two kinds available there were Decilon and K&E.

(*) books were not a decision. You wandered down the aisles, found the locations where your classes were listed, and bought the books you were told to buy.

12

That would be an HP-25C (for continuous memory.) Fellow HP-25 owner here. I loved that machine. Still have it, and last time I had it out my fingers still knew where all the functions were. (I now have a mini-collection of HP calculators. Also have a teaching slide rule that hung from the top of a blackboard and is about four feet long.)

Something that I liked about the discipline of using a slide rule was that you had to do your own decimal place calculations. So you got to grips with orders of magnitude very quickly, and you got good at sanity checking calculations. Something that was lost with calculators. It remains altogether too easy to mess up with a calculator and not twig to a miss-key or similar error.

13

Sounds like a Thatcher’s calculating instrument, good to 4 digits IIRC.

14

http://www.americanartifacts.com/smma/advert/az461.htm

15

Alleged football cheer for MIT -

Cosine, secant, tangent, sine,
3.14159,
E to the X, Q E D,
Slide rule, slip stick, M I T!

Regards,
Shodan

PS - I had the round one.

16

Close – it was

e to the u du dx
e to the x dy
secant, tangent, cosine, sine
3.14159
(something, something)
Slipstick Slide Rule
MIT!
This site gives the following, to fill in the gap in my memory:

http://www.anvari.org/shortjoke/Science_Humor/1106_other-cheers-e-to-the-x-dx-dy-radical-transcendental-pi-secant-cosine-tangent-sine-3.html

17

My HS physics teacher made us use one. This was 1972 and TI calculators were just hitting the consumer market. I actually used one all thru college, but we never used numbers all that much in physics. (My HS teacher purposely made us use actual numbers so you couldn’t do the tests without a slide rule.)

Once you get the hang of it, chain calculations, as noted, are very simple and you get used to flipping the thing over to do trig functions. I can’t remember how many functions mine had, but quite a few. And, as Chronos noted, you get good at working with significant digits.

18

Minor correction. You put the slide’s 1 there. None of the scales (except teh L scale (which was for taking logs and was linear) had a zero on them.

Two digits accuracy was quite easy and you could do it even with a lesser slide rule. On the main scales (the C and D scales), the numbers above 4 had marks for 405 410, 415 etc. Between 2 and 4 the marks were for 202 204 etc. Between 1 and 2 you had marks for each three digit combination starting 101. At least that is true for my K&E which admittedly was a pretty top of the line model.

Why yes it is still sitting on my desk. I even used it recently during a power failure.

19

Those fancy aviator watches look like that because the outer ring is actually a circular slide rule, with markings for statute vs. nautical miles etc. A student pilot has to learn to use the WW2-era E-6B even if he’ll never touch one afterward.

20

Here is one of my favorite sites. I use it occasionally when I feel “old school”.