Of course the designers also used digital computers, but in the 1960s computers were giant machines that you programmed with punched cards, and they were strictly reserved for only the most complex mathematical calculations. As the 40th anniversary of the Apollo 11 mission approaches, we are constantly reminded of how incredible that voyage was. Add to the incredulity the slide rule: the basic mathematical tool that helped get the astronauts to the moon and back.

The visitors who gathered around the Command Module on Space Day generally fell into two camps. Older visitors told me that they used a slide rule in school but hadn’t seen one in years, and they had completely forgotten how it worked. The younger visitors (i.e., those under 40!) had never seen one before, although a few had heard of them. I belong to the former group, having once been quite proficient while in high school. For this presentation, I got out the manual and taught myself all over again how to use it. It was not easy.

The National Air and Space Museum has preserved a few slide rules, including one carried by Apollo 13 astronauts on their April 1970 journey. The Museum also has on display the slide rule owned by Wernher von Braun, who headed the Marshall Spaceflight Center in Huntsville, Alabama during the Apollo era. It shows signs of heavy use. One other favorite of mine is the “Space Vehicle Pocket Designer,” a specialized circular rule that computes spacecraft payload and range, based on fuels and rocket engine efficiency. It was given to me by a mathematician who had just retired from a northern Virginia technology firm. When he gave it to me, the retiree said, “Congratulations, Paul, you are now officially a rocket scientist!” If only it were that easy.

Apollo astronauts carried slide rules, but by the time of the last mission to the Moon in 1972, the pocket calculator had been invented. On the Apollo-Soyuz mission in 1975, the last to use Apollo hardware, the crew carried a Hewlett-Packard pocket calculator that had more power than the on-board Apollo Guidance computer.

*Paul Ceruzzi is a curator specializing in aerospace computing and electronics in the Division of Space History at the National Air and Space Museum.*

Tags: apollo 11, ceruzzi, slide rule

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The slide rule story brings back fond memories for me. I was an undergraduate at the very competitive Harvey Mudd College (HMC) in Claremont, California at the time of this revolution. I used my prize winnings from my entry in the 1969 International Science Fair and money earned cutting lawns to purchase a Pickett Log-Log Decitrig slide rule at Cal State Fullerton prior to entering HMC. I would walk around on campus with the slide rule proudly hanging from my belt. I wore a white shirt, complete with a crammed pocket protector back then. (I blended in perfectly at HMC!)

I had to occasionally insure that the three metal strips were properly aligned, using a screwdriver from my pocket protector to tighten the housing screws as necessary. Occasionally, I used a pencil lead on the metal grooves to provide dry lubrication. The slide rule is an application of the concept that adding logarithms of a pair of numbers is the same as multiplying those two values. (Division is the same as subtracting logs.)

In my senior year at HMC, my room mate was given one of the first HP-35s produced as a gift by a friend of his family. The speed and accuracy of his calculator impressed me. It was alot faster and quieter than the mechanical calculators we could use in the computer lab. (I was the senior operator of HMC’s IBM 1620 in the computer lab from 1972-1973. The HP-35 had comparable computing power to the IBM 1620.) By 1978, slide rules were only used to crack walnuts and stir beverages, according to a popular HMC quip. I still have my original Pickett slide rule.

While I was working at NASA-JPL during the summer of 1974, I purchased a HP-25C calculator. It was such a big deal that I was able to get one of my buddies there to engrave my name in the plastic housing to show that it was my personal property, not NASA’s. I purchased a number of scientific calculators since 1974. I keep a spare scientific calculator in my luggage now. It cost me $3.00 on sale.

As I continue to work with ever more powerful and compact computers as an information technology professional in 2009, I appreciate the revolution that the HP-35 began.

While most people under 40 have no clue how a slide rule works, there are a few of us that do!

Around the age of 20, I found my Dad’s slide rule (which he had briefly used in his younger years but had completely forgotten how to use) and set out to use my math and physics training to reverse engineer what everything did.

Now, at the age of 31, I have a collection of four slide rules (not including the E6-B flight computer that is actually used for flight training), and am happy to acquire as many as I can afford!

I am also attempting to gain some proficiency in using them for day-to-day calculations, just for the fun of saying I can. Indeed, I’m writing a little piece of software to give me ten minutes of practice problems each day so that I can impress all the other geeks out there.

I, too, enjoy showing people this tool, and have even learned an appreciation for these fine machines. They may not be nearly as fast as my computer, but they give an appreciation for numerical relationships that random digits on a screen cannot give.

Amusing as the last comment was on a B-day, and he also worked @JPL as have I.

My comment specifically about slide rules is that we have to know how to make them, and that to be useful the mechanism is logarithms. I’ve found asking students about logs is useful to determine their math knowledge.

I was able to get thru UCSB w/o resorting to an HP-35 or 45 (friends had those, and I had TI stat calc access in my work-study job) but on taking a photogrammetry class a couple of years later I broke down and bought an HP-41C.

Now, I use my Palm cell phone calculator.

Slide rules have certain nice approximation advantages which digital calculators don’t have.

I was in high school in the late 1970s when calculators were just coming into widespread use. Still, we had one chemistry teacher who insisted that we use slide rules in his class, even though some of us had calculators. He taught us how to use the the slide rule, and loaned school slide rules to those who couldn’t afford them.

A couple of years later I’m in the middle of a Physics exam in college, and the battery in my brand-new TI SR-52 calculator died! No problem, the prof allowed me to get out my slide rule (which I kept for just such a contingency), and I was able to finish the exam in the allotted time.

Sometimes, low tech is just as good, or even better!

Astronomer Clifford Stoll made a memorable appearance at TED a few years ago where he used demonstrated with a slide rule that you don’t have to have a computer to do physics:

http://www.youtube.com/watch?v=Gj8IA6xOpSk

I wore my slide rule in High School. I recall not being very popular with the surfers until they realized that I was also on the freshman football B-team. I didn’t survive freshman year on the team, of course, but I still have my K&E slide rule!

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I used the slide rule during my high school years. I have to admit it was a very useful tool that allowed me to ace a lot of exams.

I used the slide rule during my high school years. I have to admit it was a very useful tool that allowed me to ace a lot of exams.

The great thing about a slide rule is that it does NOT tell you where to put the decimal point. This forces you to understand the problem at hand well enough to be clear on the order of magnitude of the answer. The digital calculator, in contrast, gives a precise answer which too many students happily accept, regardless of the accuracy of the inputs.

With a slide rule, you can’t mistake precision for accuracy – two very different things!

Here’s video with the slide rule explanation:

http://www.youtube.com/watch?v=waiprjueVpQ

On July 20 th 2011, Mr Frank Van Haste wrote :

« …slide rule does NOT tel you where to put the decimal point. »

A quite simple method exists !

For a multiplication, using the slide rule’s right side, the number of digits of the product is equal to the sum of the number of digits of the factors.

8 400 x 12.5 gives a number of digits of the product of 4 + 2 = 6 digits, reading the slide rule, the answer is 105 000.

For a multiplication, using the slide rule’s left side, the number of digits of the product is equal to the sum of the number of digits of the factors minus one digit.

12.5 x 0.45 give a number of digits of the product of 2 + 0 – 1 = 1 digit, reading the slide rule, the answer is 5.625.

For a division, using the slide rule’s right side, the number of digits of the quotient is equal to the difference between the number of digits of the dividend and the divisor.

2600 / 0.0042 gives a number of digits of the quotient of 4 – (-2) = 6 digits, reading the slide rule, the answer is around 619000.

For a division, using the slide rule’s left side, the number of digits of the quotient is equal to the difference between the number of digits of the dividend and the divisor plus one digit.

625 / 2.4 gives a number of digits of the quotient of 3 – 1 + 1 = 3 digits, reading the slide rule, the answer is around 260.

I once had one in hand when I was in high school, at that time It was great to have such a tool in hand, I completely forgot how to use it. How sorry I am.

Enormously educational thanks, I do believe your visitors will likely want further blog posts like this maintain the excellent effort.

I appreciate the above mention of Clifford Stoll, Ph.D. He and I attended SUNY Buffalo as graduate students in different depatments. I recall talking with Cliff while he ran the planetarium and related equipment. Cliff later wrote he very engrossing nonfiction book, “The Cuckoo’s Egg.” http://en.wikipedia.org/wiki/The_Cuckoo's_Egg_(book)

The last time i used a slide rule was in June 1972. I used a 6 inch RICOH log log the I purchase din Japan in July 1968. The occasion was the descent of a QUANTAS 707 V-Jet into Brisbane on a non-stop flight from Honolulu. I had eyeballed the angle of descent observing the nose down tilt of the cabin and estimated altitude of 42,000 plus feet, speed of 550 mph in throttled back glide.

The leveling off would occur at about 3,000 feet and somewhere between the estimations and the slide rule I came out dead on. The flaps started to extend and the engines increased in power as the sweep second hand on my wristwatch which Mom had used as a WAC Sargent in WW2 ticked past the last 5 seconds of my prediction.

There is certainly a lot to find out about this

subject. I like all the points you made.

Electronic calculators are great, still use my old HP11C, and have a couple of others that I’m hardly on speaking terms with. That being said, slide rules, which I’m slightly familiar with, require no outside power, and while they aren’t good for more than a couple of decimal places, a great many structures have been designed with them. In conclusion, I guess that one could describe them as “crude but useful to this day, and likely beyond”. Sort of sad that they are no longer made, however there are lots of them floating around.