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appleciders
07-29-2006, 02:15 PM
Digging through a box of my dad's high school leftovers, I ran into his slide rule. He has no recollection of how to work it by this point, and I can't figure the darn thing out. Plus, I read a lot of R. A. Heinlein and have never been able to visualize someone actually working a slipstick. So how do I use this thingy?

Q.E.D.
07-29-2006, 02:18 PM
Here (http://www.sliderules.clara.net/a-to-z/a-to-z.htm) is a good page with links to basic slide rule use for various functions.

RealityChuck
07-29-2006, 03:09 PM
Essentially, a slide rule is a ruler with markings set on a logarithmic scale. As you know, logs are exponents and when two logs are added together, it's the same as multiplying the two original numbers.

As an example, the log(2) = .3010 Log(4) = .6020 Log(8) = .9030 Log(2) + Log(4) = .9030 = log(8).

Assuming 10 inches of space for the scales, you put a "2" at 3.010 inches, a 4 at 6.020 inches, and an 8 at 9.030 inches. You generally use the C and D scales for multiplication: they are identical, but next to each other. Move the slide to make the "1" on the C scale aligned with the "2" on the D scale, then move down the C scale to the "4." A slider with a hairline was used for this. With it precisely on the 4 on the C scale, it will also cross the 8 on the D scale because of the addition of numbers: 3.010 in. along the D scale, plus the C scale used as a ruler to measure off another 6.020 inches.

The A and B scales used the same principles to find squares and square roots; the K scale was used to find cubes and cube roots. Everything was logarithmic, so adding the linear values as represented by the marks allowed you to multiply values simply by moving the slide.

The main issue with slide rules was keeping track of the decimal point; you had to remember if an answer meant 120 or 1200. Also it was limited in precision.

Lumpy
07-29-2006, 05:01 PM
Here's a more "dumbed down" explanation:

Slide rules take advantage of the fact that for exponents, adding is the same as multiplying numbers. For example, 10^2 (=10x10) multiplied by 10^3 (10x10x10) equals 10^5 (10x10x10x10x10). This isn't limited to whole or even rational numbers either; for another example, the square root of 10 multiplied by the square root of 10 equals 10 of course. So the square root of 10 can be considered 10^(1/2), which gives 10^(1/2) x 10^(1/2) = 10^1.

A slide rule has two scales of numbers which have alogarithmic spacing: the spacing of the numbers is constant in terms of exponents. The distance from 1 to 2 is the same as the distance from 2 to 4, from 4 to 8, etc. (2^1, 2^2, 2^3, etc.) So this allows you to do multiplication by adding the exponents in a manner similar to the way early math students learn addition using number scales.

Slide rules' main limitation is accuracy; the scale can only be so fine which limits how exactly the numbers can be set or read. But you get the most significant digits first, so if all you needed to know was about how much 352 X 127 is, a slide rule gave you a ballpark figure quickly.

Since many other mathematical functions like trig ratios and square and cube roots can be expressed by logarithims, slide rules were handy for those as well.

PBear42
07-31-2006, 12:15 AM
In the days before electronic calculators, and for several years after when the latter were very expensive, a slide rule was the only convenient way to do multiplication. Engineers, for example, used them routinely. In the hands of a skilled user, it is quite accurate, though as has been mentioned, limited in precision. Basically, it is accurate to three significant digits, But, in those days, most measurements also were only accurate to three significant digits, so this wasn't much of a problem. If greater precision was required, a computer, a log table or hand calculation was used.

BTW, slide rules come/came both straight and circular. The latter had the advantage of "wrapping" the calculation and were, I believe, more popular.

Giles
07-31-2006, 08:26 AM
Slide rules' main limitation is accuracy; the scale can only be so fine which limits how exactly the numbers can be set or read.
Hence the old joke that when you ask an engineer to multiply 2 by 2, he (engineers were always "he" in those days) pulls out his slide rule, and says "About 4".

PBear42
07-31-2006, 10:32 AM
Followed, in the electronics age, by "What do you get when you multiply 2 times 3?" The kid (usually), punches it in and gets 5.999... "Ah, heck, call it six."

Dewey Finn
07-31-2006, 10:44 AM
[pointless anecdote]Mr. Hovey, my high school physics teacher, taught us to use slide rules specifically because doing so forced one to get good at reading scales. I graduated from high school in 1984, so we were trying to buy them in the early 1980s when they were already obsolete. Several of my classmates got laughed out of the stationery stores when they asked if the stores had any. (I think I got mine from my older brother, who had already been through his physics class.)[/pointless anecdote]

Kevbo
07-31-2006, 11:10 AM
Basically, it is accurate to three significant digits, But, in those days, most measurements also were only accurate to three significant digits, so this wasn't much of a problem.

One of the really good things about slide rules was that they forced you to think about what level of resolution was appropriate.

Also, you had to track the magnitude of the calculation seperately, so you tended to notice if you got an absurd result.

Today I routinely see results expressed to 5-6 significant digits when the data used to generate them was only good to at best 1%. I also talk to a lot of young engineers who have absolutely no clue the hoops you have to jump through if you really need 4-5 digits of real world accuracy maintained over time, temperature, manufacturing tolerances, etc.

Side note: One interesting slide rule variant is therotary slide rule (http://en.wikipedia.org/wiki/E6B) , AKA "whiz wheel". Still used by many pilots the standard "E6B" version allows you to set, for example, your speed, then read off the distance for any amount of time without having to make any further adjustments. Similarly for fuel consumption, etc. Because of this, it can actually be faster than a calculator if you are making a series of "what if?" calculations.

flex727
07-31-2006, 11:38 AM
Today I routinely see results expressed to 5-6 significant digits when the data used to generate them was only good to at best 1%. I also talk to a lot of young engineers who have absolutely no clue the hoops you have to jump through if you really need 4-5 digits of real world accuracy maintained over time, temperature, manufacturing tolerances, etc.
I work in the semiconductor industry and the source of much hilarity amongst my cow-orkers is the data output from various metrology tools. When I measure a dielectric film, the result will generally be in angstroms and carried to 4 decimal places (e.g. 3,142.7968 angstroms). I'm surprised that the software people at KLA haven't figured out yet how stupid they look when they output a result like that.

CalMeacham
07-31-2006, 12:56 PM
I used a slide rule in high school, and for my first two years of college -- at MIT. I eventually stopped when a.) I needed better than three decimal place precision ; and b.) The price came down to where I could afford one (prior to the HP-25, calculators that could do trig functions cost \$400 and up)

In high school, I was faster with my slide rule (I never knew anyone who called it a "slipstick") than the guy with the calculator when it came to anything more complex than multiplying two numbers.

I still have my slide rules from high school and college, and have added to them - I can pick up slide rules cheap at yard sales.

Speaking of circular slide rules, I have a cylindrical one (It's also a pencil cup). The spacing is the same on all scales, so, in principle, the accuracy is the same for all scales, unlike your typical circular slide rule. Unfortunately, it's not really very good on any of them, so they're equally crappy.