Beyond The Dial is pleased to welcome mathematician, aerospace enthusiast, and physicist, Gary Bedrosian, PhD to assist the watch enthusiast community with a deep dive into the slide rule instructions for the Breitling Navaitimer. Gary also happens to be my father and it was truly special to collaborate with him on something that we are both passionate about. I’m going to let my Dad take it from here…
The slide rule functions of the Navitimer are the definition of retro. Back in my day, learning to use a slide rule was considered essential for high school students aiming for college majors in engineering and science. Today, nearly everyone carries a smartphone with a built-in calculator app. Why bother with analog slide rules?
If you are reading the instruction section, we assume you are intrigued by the complications of the Navitimer and want to learn more. Perhaps you would like to master the analog functions of the Navitimer’s circular slide rule for nostalgia, fun, a back-up for your electronic devices, and finally − let’s be honest − a touch of showing off. You will need two skills to make the best use of the circular slide rule on the Navitimer.
The first skill to learn is how to read and interpolate the number hash marks. Interpolation of the hash marks is a fancy way of saying that you estimate the values between the marks.
Look at the region on the outer white dial between 10 and 11, near the crown. This region has nine hash marks representing 10.1 through 10.9. Your first new skill is to estimate numbers between the hash marks. For example, halfway between 10.5 (the dark hash mark) and 10.6 is approximately 10.55. With practice, you should be able to estimate to the nearest one-quarter of the interval between hash marks. (Some old-timers have claimed that they can distinguish ten steps between hash marks, but I never believed them.) Using the same example, you can distinguish among 10.5, 10.525, 10.55, 10.575, and 10.6 without too much trouble.
The number of digits you can determine by interpolation depends on where you are on the dial. To pick another example, look at the 60 on the white dial at the 12 o’clock position. There are four hash marks between 60 and 65, representing 61, 62, 63, and 64. Between 61 and 62, you can interpolate 61.25, 61.5, and 61.75 with practice.
The second skill you need is estimating the overall size of the expected result so that you know where to put the decimal point in your answer. On a slide rule, the number you read on the scale has an indefinite decimal point. The number 61.5 could easily be 6.15 or 6,150 or 0.615 depending on the problem you are solving. For example, suppose you want to multiply 55 times 45. (We’ll get to the how-to next.) You know 50 times 50 is 2,500. When you multiply the numbers on the Navitimer and interpolate between the hash marks, you will get a number between 24.6 and 24.8. With good interpolation, you will get 24.75. Knowing that the answer should be near 2,500, you mentally move the decimal point two places to get 2,475.
multiplicand × multiplier = ?
Example: 45 x 55 = 2,475
Multiplying two numbers is accomplished in two steps: First, rotate the bezel until the second number (the multiplier) on the white (outer) dial is adjacent to the red 10 on the black (inner) dial. The red 10 is called the unit index. Second, read the digits of the answer on the white (outer) dial adjacent to the first number (the multiplicand) on the black (inner) dial. You will use your hash mark interpolation and decimal point skills to get the final answer.
dividend ÷ divisor = ?
Example: 2,475 ÷ 45 = 55 (adjacent to the unit index)
Dividing two numbers is also accomplished in two steps: First, rotate the bezel so that the first number (the dividend) on the while (outer) dial is adjacent to the second number (the divisor) on the black (inner) dial. Read the answer on the white (outer) dial adjacent to the red 10 (unit index) on the black (inner) dial. Again, you will use your hash mark interpolation and decimal point skills to get the final answer.
In addition to the basic multiplication and addition operations of any circular slide rule, the Navitimer has special marks on the black dial and a few on the white dial that provides convenient functions. We will go through a few special functions here. For the full list, consult the Navitimer User Manual (scan courtesy of Breitlingsource.com).
If you own a Navitimer (or would like to), the odds are that you have traveled or will travel outside of the United States. Converting between kilometers and miles will be a frequent activity on your visit. On the black (inner) dial, you will see two red hash marks labeled STAT (near 38) and KM (near 61). STAT stands for statute miles and KM stands for kilometers. If you rotate the bezel until the red STAT hash mark is adjacent to the miles or miles per hour value on the white dial, the red KM hash mark will be adjacent to the kilometers or kilometers per hour value on the while dial. This also works to convert from kilometers to miles.
There is a red hash mark labeled NAUT (near 33) for nautical miles. Use a similar process to convert statute miles and kilometers to and from nautical miles and nautical miles per hour (knots).
You will notice that the 60 and 36 hash marks on the white (outer) dial are in red for convenience because multiplying and dividing by 60 and 360 are common in navigation. 36 is also marked in red on the black (inner) dial. The 60 on the black dial has a large and stylish hash mark.
A nautical mile was originally defined as one minute (1/60) of one degree of a great circle of the earth. Let’s estimate the circumference of the earth in miles using the skills and concepts we have discussed.
First, we determine the number of minutes of arc in a complete circumference of the earth. Multiply 60 minutes of arc in one degree times 360 degrees in a complete circle. Rotate the bezel so that 36 (360) on the white (outer) dial is adjacent to the unit index (red 10) on the black (inner) dial. Find the 60 on the black (inner) dial and read the answer on the white (outer) dial = 21.6. To place the decimal point, we notice that 360 is very approximately ⅓ of 1,000, so the answer should be in tens of thousands = 21,600 minutes of arc or nautical miles.
Rotate the red NAUT mark on the black (inner) dial to 21.6 on the white (outer) dial and read the answer in miles on the white (outer) dial adjacent to the red STAT mark on the black (inner) dial = 24.85 (approximately). Using the same decimal point placement, the final answer is that the circumference of the earth is approximately 24,850 statute miles.
Not bad for a tiny circular slide rule that you wear on your wrist!