Circular Slide Rule Watch Tutorial
by Dave Gauer
First, Determine Your Type of Circular Slide Rule
If both the outside and inside circular rules have identical scales with a full range from 10 to 90, then you have what are known as "C" and "D" log scales. These are useful for multiplication and division as well as ratios and percentages (which are really just multiplication.) Great, this is the type of slide rule discussed in this tutorial!
If the outside rule is the reverse of the inside rule, then you have the "C" and "CI" or inverse scales. Sadly, this page will not be helpful to you. But a quick Google search for "slide rule CI scale" should get you going.
Understand Slide Rule Basics
The most important thing to remember when using the circular slide rule is to ignore decimal place when entering values. Always select the two-digit number closest to the two most significant digits in your value. Let's take a look at some examples to make this clear:
|Number to input||Select on the slide rule|
Of course, you'll have to remember to shift the answer by an appropriate power of ten when you get it back. Here's an example: 5,000 * 6 will be entered on the slide rule as 50 * 60 and will return 30. You have to figure out the appropriate amount of zeroes to get the correct answer of 30,000.
Using the slide rule for a while improves your ability to estimate correct answers!
Multiplying numbers on the slide rule is easy. Basically, you set a multiplier on one scale that creates a lookup table on the other scale. Here's how to do it. (My instructions will refer to the inner and outer rules. Since the C and D scales are identical, you can actually swap them and it'll still work!)
Let's do 5 * 6:
- Align 10 on the inner rule with 50 on the outer rule. This sets the multiplier to 5.
- Now look at 60 on the inner rule. It should line up with 30 on the outer rule. 60 here represents the 6 from our equation. 30 is our answer.
- Now we double check the decimal place of our answer. As it happens, 5 * 6 does equal 30, so there's no need to adjust.
What's handy is that we have now set up the slide rule to multiply any number by 5 without making any more adjustments. We just need to look at a number on the inner rule and see the answer in the outer rule (for example, 24 is currently aligned with 12 because 5 * 24 = 120.) As you have probably figured out already, you have also set the rule to multiply by 50, 500, 50,000 and 0.005... Remember, it's up to you to keep track of the decimal place.
Let's try another one. 3.5 * 4,000:
- Align 10 on the inner rule with 35 on the outer rule.
- Now look at 40 on the inner rule. It should line up with 14 on the outer rule.
- Knowing that our answer should be in the thousands, let's adjust 14 so that it makes sense by shifting it to the left three decimal places: 14,000. Now it's correct!
Try a few others and check your answers with a calculator. You'll quickly get a hang of it.
Dividing is just the reverse of multiplication. This time we align the two numbers of our problem, and the answer will appear next to the "10".
We'll start with 60/3:
- Align 60 on the outer rule with 30 on the inner rule. I like doing it this way because it lets me visualize "60 over 30."
- Now look at 10 on the inner rule. It aligns with 20 on the outer rule.
- 20 is the correct answer, so there's no need to adjust the decimal place.
Now let's try something without a nice, clean integer answer: 5/7:
- Align 50 on the outer rule with 70 on the inner rule.
- Now look at 10 on the inner rule. It aligns just a little past 71 on the outer rule.
- Adjusting the decimal point correctly gives us roughly 0.71. The correct answer is actually 0.714286... Obviously, the slide rules on watches are so small that it is hard to get more than two digits of accuracy. Still, it's a wonderful estimation tool.
Distance and Volume Conversions
If your watch has them, you can use the unit conversion marks to convert amounts of one unit to another. All of the conversions work the same way and they're very simple. Note: my instructions assume that the unit indicators are on the outer rule. If they are on the inner rule, simply reverse my instructions.
Let's convert nautical miles to kilometers. We'll start with 22 nautical miles.
- Align 22 on the inner rule with the nautical miles (Naut) indicator on the outer rule.
- Now look at the kilometer (Km) indicator of the outer rule. It aligns just slightly past 40 on the outer rule.
- There is no need to adjust the decimal. 40 is right. The precise answer is 40.744.
Use this same method to convert any of the following (if indicated on your watch):
- Nautical miles, statutory miles, kilometers, and 1000s of feet
- Pounds of fuel, pounds of oil, imperial gallons, U.S. gallons, and liters
- Kilograms and pounds
Any slide rule watch will allow you to do these calculations. Some make it simpler by including a time scale on one of the rules which translates from minutes to the familiar HH:MM format. One of the many original uses of flight computers was to estimate time of arrival. Here's how you might calculate ETA. Note: my instructions assume a time scale (if any) is on the inner rule.
Let's say you have a ground speed of 43 miles per hour and you know that your destination is 50 miles away. What's your ETA?
- Align 60 (for 60 minutes per hour) on the inner rule with 43 (your speed) on the outer rule.
- Now look at your distance, 50, on the outer rule. It aligns roughly with 70 and with 1:10. The answer is that you'll arrive in about 70 minutes (or one hour and ten minutes).
Of course, the HH:MM time scale only works if the number of minutes is in range. If we had 500 miles to go instead of 50, the answer would have been approximately 700 minutes, which is obviously NOT 1:10!
Conversely, You can figure out how far you'll go in a given amount of time at a given speed. Say we're going 70mph and we'll be doing it for 1:30 (one hour and thirty minutes - or 90 minutes):
- Align 60 on the inner rule with 70 (your speed) on the outer rule.
- Now look at the time of 1:30 or 90 on your inner rule. It aligns roughly with 10.5 on the outer rule. The answer is that you'll travel about 105 miles.
Lastly, if you know how far you went and how long it took, you can figure out how fast you were going. Say we went 250 kilometers and it took two hours:
- Align 2:00 (or 12 for 120 minutes) on the inner rule with 25 (for your distance of 250) on the outer rule.
- Now look at 60 on the inner rule (to solve for minutes). It aligns with about 12.5 on the outer rule. That's the answer. You would have gone 12.5 kilometers per hour
Like the unit conversions, calculating percentages is simple to do and comes in handy in stores and restaurants. Say you see a $70 item marked 20% off. You can find out what it would cost by aligning 10 on the inner rule with 80 (you'll pay 80% if it's 20% off) on the outer rule. Now you can see the 70 (for $70) on the inner rule lines up with the sale price of $56 on the outer rule and so forth. If everything is 20% off, you never have to turn the rule again to see the sale prices of all of the items in the store! A 17% tip in a restaurant is easily calculated by aligning 10 on the inner rule with 17 on the outer rule. A $25 meal shows 42.5 on the outer tip rule. The tip would be $4.25.
The trick is to always apply the common-sense shift of the decimal point as needed. Once you get proficient, it's fast and easy.
A Little Bit About These Watches
I'd always been fascinated with the apparently complexity of "pilot" style watches, but it wasn't until fairly recently that I finally got the urge to learn more about them. I actually had no idea that these watches contained slide rules! The geek-factor of having a slide rule on your wrist as well as the aviation and space-race connections sold me on the concept.
I purchased a Seiko SNAB67 Flight Master chronograph in 2009. It has a slide rule bezel styled after the famous Breitling Navitimer (which in turn borrowed features from the "E-6B" manual flight computer carried by pilots). The standard features are:
- "C" and "D" (or fundamental) scale log rules
- A time scale matching hours to minutes
- Markers for converting from nautical to statutory miles and to kilometers and thousands of feet
- Conversions for U.S. gallons to Imperial gallons or liters or pounds of fuel or oil
- Conversions from pounds to kilograms
Breitling still makes the Navitimer, but many manufacturers made or currently make watches with slide rule bezels such as (in no particular order):
|Breitling||Swiss||The Navitimer was created in 1952 and to the best of my knowledge, it is the origin of all circular slide rule "flight computer" watches. Breitling still makes an array of excellent flight watches.|
|A.I. Wajs||Swiss||They make some extremely attractive O&W aviation watches.|
|Hacher||Swiss||The "Aviateur" series of flight computer watches feature slide rules.|
|TAG-Heuer||Swiss||They make several excellent slide rule watches. Interestingly, a Heuer stop watch became the first Swiss watch to make it into space via John Glenn.|
|Tissot||Swiss||They have made some slide rule watches, but I don't believe they currently offer any.|
|Ikepod||Swiss||Designed by Marc Newson (as are all Ikepod watches), the Megapode is a beautiful watch with a slide rule.|
|Ventura||Swiss||Their current V-matic Loga is a very elegant slide rule watch.|
|Zeno||Swiss||Offers several attractive flight calculator models in the "Oversized" line.|
|Torgoen||Swiss||They brand themselves as "Professional Pilot Watches" and have a number of nice slide rule models.|
|Chase Durer||Swiss||Apparently based in the United States. Offers a number of flight watches with slide rules.|
|Movado||Swiss||Has one model, the ESQ Beacon watch with a traditional flight computer slide rule.|
|Formex||Swiss||Has a square AS6500 series model with a slide rule.|
|Wenger||Swiss||The "other" Swiss Army Knife maker (besides Victorinox). Wenger has a nice Commando watch with a slide rule.|
|Sector||Italian||They have several models, including the Mountain Master with a circular slide rule.|
|Aeromatic 1912||German||Has inexpensive aviator-style watches including at least one Flight Computer model with a slide rule.|
|Detomaso||German||Has a wide variety of reasonably-priced watches, including the attractive Teramo Chronograph with slide rule and Seiko guts.|
|Seiko||Japanese||Great value. The Flight Master series has slide rules. Have also produced slide rule watches under these brands:|
|Orient||Japanese||Owned by Epson (as in the printers) and part of the Seiko Group which includes Epson and Seiko Watch Corporation. Crazy. Has made several slide rule watches.|
|Citizen||Japanese|| Offers several excellent slide rule watches including the Skyhawk series. Also produces under the brand:
|Casio||Japanese||Known for all things electronic. Makes several inexpensive watches such as the Aviator series with slide rules.|
|Kentex||Japanese||The SkyMan watches have slide rules.|
|Timex||Japanese||The Expedition Military Chrono series features a slide rule (other Expedition models do not).|
|Poljot||Russian||Offers several aviator watches with slide rules.|
|Vostok||Russian||The Energia series has a slide rule.|
|Invicta||U.S.||The brand was originally Swiss. The Force Flight series is cheap and has a slide rule.|
|Nautica||U.S.||Either a brand of Timex or of the VF clothing company. Not sure. Has at least one slide rule model with Japanese movement.|
|National Geographic||U.S.||Watches are of unknown manufacture. Has an Aviator model which runs on solar power and has a slide rule.|
The prices of watches by the above manufacturers range from $50 (Casio) to thousands (many of the Swiss brands.) Many but not all slide rule watches have the time scale and unit conversions of the Navitimer.
My watch did not come with any instructions regarding the use of the slide rule. The instructions I found online for using slide rule watches or slide rules in general were confusing, loaded with math terminology or (in one case) simply wrong! I have strived to make this tutorial succinct and accurate.