The Aspiring Pilot’s Guide To Using The Breitling Navitimer Slide Rule Bezel
If this doesn’t make you feel grateful for modern flight instruments nothing will.
There are complications that make life easier, and then there are complications that make you work. Some complications take more getting used to than others – the ins and outs of the Gregorian calendar aren’t particularly anything you need to know if you own a perpetual, although if you do know why there’s a leap year every four years, it’ll give you better appreciation of the ingenuity behind the mechanism. Most complications are designed to be as simple to use as possible and are in general pretty intuitive; once you realize that a chronograph is just a watch with a stopwatch bolted on top (quite literally) using one is easy.
However, there are some complications that take a little more study. Regatta timers, for instance, don’t make a whole lot of sense unless you know how sailing races are organized. A tachymeter bezel is usually said to show average speed over distance for a measured elapsed time, but if you know that it can be used for any general units per hour calculation you can use if for … well, any general units per hour calculation. Elapsed time bezels are easy – for a dive watch, for instance, you just set the zero mark at the minute hand and watch the elapsed minutes count up.
Slide rule bezels on pilot’s watches, however, are a different story and I think of all complications, they must be the one most widely worn and least understood. The Breitling Navitimer is best known slide rule bezel watch, and even if you know absolutely nothing about how to use the bezel, you can’t help but feel like a natural-born stick-‘n’–rudder type, when you strap one on. The slide rule bezel on the Navitimer is a miniature version of the pilot’s circular slide rule, the E6-B flight computer, which pilots still learn to use today.
Let’s look at how the Navitimer bezel works, how it works, and how you can do actual flight plan calculations with them. But first a refresher in the basics.
Parts Of The Bezel
The slide rule bezel consists of an outer, rotating scale and an inner fixed scale, which I’ll call the outer bezel and inner scale. Inside the inner slide rule scale is a tachymeter scale as well, which you can use in conjunction with the chronograph. There are slide rule bezel watches that don’t have a tachymeter scale –generally these are non-chronographs; but you don’t need a chronograph for a slide rule bezel to work.
On the Navitimer, the numbers on both the outer bezel and inner scale are organized on a logarithmic scale. A logarithm to the base 10 (the common logarithm) is the exponent to which a number is raised to produce a given result; the log base 10 of 1000 is 3, since 10 raised to the third power is 1000.
What Is A Logarithmic Scale On A Watch Bezel?
A logarithmic scale is one in which the difference between two numbers is logarithmic rather than linear, and on the Navitimer bezel, the scale, which is base 10, shows the logarithmic rather than the linear distance between two numbers. (The distance between two numbers on a standard ruler, by contrast, is linear; the distance between 35 and 36 inches is the same as the distance between one and two inches).
The logarithmic distance between 10 and 20, for instance, is greater than the logarithmic distance between 50 and 60, so the distance between 10 and 20 is greater than between 50 and 60 – which is why the distance between numbers shrinks as you go around the dial.
The numbers can also be thought of as increasing infinitely as you go around the dial, thanks to this logarithmic progression. Thus, 20 can mean 20, 200, 2000, and so on (increasing by powers of 10). This is the first and maybe most important point to keep in mind about using the Navitimer – you have to have a general idea of the answer you’re expecting so you get the order of magnitude correct. This is not as hard as it sounds, though – usually common sense will tell you that, say, 60 gallons of fuel burned over one hour is more realistic than 600 or 6000.
This also means that the bigger the numbers get the more you are guesstimating both input and output – reading off 24 is easy; reading off 243 is much harder as the tick marks get very crowded together.
There are some special markers on the inner and outer bezels which are useful for both general and specific calculations. The first is a red 10 on the inner scale at roughly 2:30 – this is the Unit Index, which is used for multiplication and division operations. At 12:00 on the inner scale, we have a pointer labeled in all caps, MPH, which is used for calculations involving speed. Also on the inner scale, you’ll find two indexes labeled STAT and NAUT, which are used for measurements involving statute or nautical miles, and for conversions between the two, along with the red KM (kilometers) on the inner bezel, just to the right of the MPH marker at 12:00.
Let’s look and some basic calculations, and then, let’s do some more flight operations-centric calculations, for which I’ll incorporate some of the performance values of one of the great classic propeller driven fighters of all time, the P-51 Mustang.
How To Multiply
Multiplication is easy – actually none of the operations we’re going to look at are hard, it’s remembering how to do them that’s hard. Multiplying consists of the number you want to multiply, or multiplier, and the number by which you multiply it, the multiplicand. The result is the product (I can see my third grade teacher Mrs. Neff giving me the stink eye even as I type this). This is where that Unit Index comes in.
If you want to multiply 18 by 20, for instance, just rotate the outer bezel until 18 is lined up with the Unit Index. Then find 20 on the inner scale and read off the number next to it on the outer scale – which is 360 in this case, the correct answer.
- Line up the multiplier with the unit index
- Find the multiplicand on the inner scale
- Read the product off the outer bezel
If you want to multiply 182 x 20, though, you’re going to need better eyes than mine. The tick mark to the right of 18 represents 182 (remember, 18 can mean 180 also, or 1800) and lining it up with the Unit Index is a chore. Reading off the correct answer is basically impossible, although you can get close – it’s 3640 although even through a loupe, the inner 20 is barely noticeably offset enough from the outer 3650 tick mark for you to guess that 3640 is the right answer.
How To Divide
This is easy too, since it’s just the reverse of multiplication. Set the dividend, or number you want to divide, next to the divisor you want on the inner scale, and read off the quotient on the outer scale next to the Unit Index. If you want to divide 360 by 20, for instance, just line up the outer 360 with the inner 20, and you can read off 18 on the outer scale next to the Unit Index.
- Align the dividend on the outer bezel with the divisor on the inner bezel
- Find the Unit Index on the inner bezel
- Read off the quotient opposite the Unit Index.
The dire warnings about multiplying 182 by 20 apply to the division as well. These old eyes ain’t got it no more.
You probably noticed that the arrows in the pics for multiplication and division point to the same numbers; that’s because they’re inverse operations and to divide, you just do the operation in reverse.
How To Convert Kilometers To Miles
Again, not an especially complicated maneuver. Pick the number for miles, set it next to the tick mark for NAUT or STAT, depending on which you’re using, and read off the equivalent in kilometers on the outer bezel next to the red KM at 12:00. Fifty statute miles is about 80.5 kilometers.
- Align the number of miles (statute or nautical) with the STAT or NAUT index
- Find the KM index on the inner dial
- Read off kilometers on the outer dial
Nautical miles by the way, are used in both nautical and air navigation, which is why conversions are shown on the Navitimer.
How To Calculate Ground Speed
Another fairly straightforward but useful calculation, and this one is flight ops-specific. Ground speed is the speed of an aircraft measured against the ground, as opposed to airspeed (which is your apparent speed taking into account windage; if you have a headwind your airspeed will be less than your ground speed). To calculate ground speed, you need to know the time it takes to go a certain distance.
To calculate ground speed, find the distance traveled on the outer scale, and line it up with the time traveled on the inner scale; ground speed is read off at MPH, at 12:00 on the dial.
- Align distance traveled on the outer scale with time traveled on the inner scale
- Find the MPH index on the inner scale
- Read ground speed off the outer scale
If I’m in my trusty, glorious P-51 Mustang and it takes me 45 minutes to go 300 miles, then my ground speed is 400mph. The speed in the calculation is about par for the Mustang, which flew as a bomber escort and fighter during World War II and which could hit speeds in excess of 430 mph at over 30,000 feet.
How To Calculate Flight Time
Another pilot-worth calculation; to calculate your flight time, you just need to know your speed and the distance between two points. Let us say we are in our Mustang and flying from London to Berlin. The distance is about 580 miles and the Mustang as we have seen could cruise at altitude at 400 mph. Set the speed – 40 on the outer bezel, which remember is the same as 400 – next to MPH and then read off the desired distance – 580 – on the outer bezel as well. With some squinting, you will see that 580 is right next to 87 on the inner scale, giving us a flight time of 87 minutes, or one hour 27 minutes.
- Align speed on the outer scale with the MPH index on the inner scale
- Find the known distance from point A to point B on the outer scale
- Read off travel time in minutes on the inner scale
I would have thought getting in a World War II era fighter from London to Berlin would have taken a lot longer than that, and of course the calculation doesn’t take into account climbing to altitude and accelerating to cruising speed … but still, the pilots could be Over There a heck of a lot faster than I’d thought.
How To Calculate Miles Per Minute
Let’s say you’re in your trusty Mustang and watching the fields of France roll away beneath you, and you’re wondering just how many miles are going by every minute. There’s a calculation for that too. For this you need your old friend the MPH index again. Set your speed in miles per hour against the MPH index, and then jump over to your other old friend, the unit index. Opposite the unit index, you can read off your speed in miles per minute.
- Align speed on the outer scale with the MPH index on the inner scale
- Find the unit index on the inner scale
- Read off speed in miles per minute on the outer scale
The number as it turns out is a messy one if you’re doing 400 mph – on the Navitimer bezel, it looks like around 6.7 miles per minute. According to my iPhone calculator this is close enough for gubmint work, as they say – 400 divided by 60 is 6.666… miles per minute.
Fuel Consumption
Here’s a pretty mission critical calculation for the intrepid aviator. How much fuel will you need to fly a certain period of time, if you know your rate of consumption? For this you do need to know your average rate of fuel consumption, as well as the amount of time you intend to travel. Our P-51 Mustang has wildly different fuel consumption figures depending on what the plane is doing, whether or not it is carrying drop tanks (which cause more drag and increase fuel consumption) and so on, however, I have seen several sources that converge on about 60 gallons per hour at cruising altitudes and speeds.
OK, so we want to make it to Berlin from London – in our long-suffering Mustang. We know that on average we will be drinking 60 gallons of fuel per hour and that it takes 87 minutes more or less to make the trip. So we set gallons per hour against the MPH index, and then find the minutes on the inner scale. Reading off from 87, we find that it takes – unsurprisingly – 87 gallons of fuel to get over there, since at 60 gallons per hour we’re basically burning a gallon per minute.
- Set the figure for known gallons per hour on the outer scale against the MPH index on the inner scale
- Find known minutes of flight time on the inner scale
- Read off fuel consumption in total gallons need on the outer scale.
The P51 had two 92 gallon tanks in the wings, so you can see why for long range bomber escort missions they used drop tanks – assuming the average rate of consumption of 60 gallons per hour would be consistent throughout the mission is a huge “if” and leaves little margin for error and damned little extra for things like air combat maneuvering, or evasive maneuvers if some enterprising opponent gets behind you.
Rate Of Climb
This is a useful thing to know in a lot of scenarios – I guess one would be where you have taken off to intercept an inbound bunch of bandits who are coming in at a certain altitude, and you want to know if you can climb fast enough to catch them in time. You must know your average rate of climb in feet per minute, and the desired altitude and the slide rule bezel will tell you how long it will take you to get up there.
The rate of climb of the Mustang varies depending on altitude but a good average seems to be around 3,200 feet per minute. How long will it take to climb to 40,000 feet from zero altitude?
To find out, set the rate of climb (32, which is 3200) opposite the inner Unit Index; then find the altitude (40, or 40,000) on the outer scale.
- Align known rate of climb on the outer scale with the Unit Index
- Find desired altitude on the outer scale
- Read off total rate of climb to the chosen altitude on the inner scale
The Navitimer’s slide rule bezel says that it will take just about 13 minutes, read off those little hash marks with the naked eye; the iPhone calculator says 12.5 minutes; I attribute the discrepancy to operator error (meaning, me). If therefore you are not already airborne, you are in a Mustang, and the opposition is at 40,000 feet and you have detected them with less than twelve minutes before they darken the skies overhead, you may as well save yourself the trouble of kicking the tires and lighting the fires.
The Slide Rule Bezel Today
Obviously, the slide rule bezel and the slide rule calculator have been made obsolete by digital flight calculators and instruments. The bezel of the Breitling Navitimer and other pilot’s watches with slide rule bezels is based on the E6-B flight computer, a task-specific analog circular slide rule which for practical purposes has been replaced by hand held flight computers costing around a hundred bucks.
Purely from a practical standpoint it amazes me that anyone could actually use the slide rule bezel for flight operations although that is the perspective of a non-pilot with progressive presbyopia. I think from a very non-systematic pass through online forum remarks that there are certainly pilots who find the slide rule bezel useful although often it is with the caveat that learning to use the E6-B slide rule first makes child’s play of a wristwatch slide rule bezel (except for legibility). The E6-B is much larger than the Navitimer bezel and much easier to read but if you learn how to do flight calculations on the E6-B I’m sure it’s a huge help in being able to use the Navitimer slide rule bezel efficiently and reasonably accurately. It’s tough though – the Unit Index for instance is printed in red against a black background and unless the light’s pretty good and at the right angle, it’s hard to see – I suspect if one were trying to use such a bezel for calculations in flight, in the oft-cited hypothetical scenario of a total failure of your $20,000 Garmin Glass Cockpit, that you would fly into a mountain while squinting at the read-off. I would anyway.
However, there is a lot to be said for going through the process of working out how to use the Navitimer bezel for flight calculations. For me it was instructive to use the slide rule bezel in the context of a specific aircraft – the P-51 seemed like a good choice since it sits right on the cusp of the transition in aviation from internal combustion engine-powered propeller aircraft, to jets. (The jets did not necessarily have the upper hand at first. The German ME-262 was an aviation revolution but it was also vulnerable at different times in its flight envelope – the late Chuck Yeager famously said, “The first time I ever saw a jet, I shot it down.”)
It should be borne in mind that the numbers resulting from the calculations in this article with respect to the P-51, are essentially fiction. Actual performance would depend greatly on the characteristics of any given mission and as a bomber escort the Mustang would have had to coordinate with bomber groups consisting of a variety of aircraft, departing from different airfields in different locations and on the way to different targets; all of this makes assuming that Mustangs were routinely arriving over Berlin 87 minutes after takeoff, ridiculous.
Running the numbers is an abstraction but running them, even with an absolute ton of simplifying assumptions, is an education in the realities of flight and the sometimes very narrow margins separating glorious victory from ignominious (and often instantaneous) defeat, and to wear a watch with a slide rule flight bezel – and to understand its operation – is a gateway to understanding the fundamental principles that govern aviation even today.
And yes, if you must, you can calculate tips with it.