CPR For DR: Breathing Life Back into Dead Reckoning

Dead reckoning, the most basic form of navigation, seems to be at death’s door, in need of extreme measures if it is to be kept alive. And I know what you’re thinking: So what? With all the great new nav systems out there, not the least being universal, affordable, VFR and IFR capable GPS, who cares about dead reckoning any more? No one elects to navigate using dead reckoning. Dead reckoning is something student pilots have to do because the FAA says they have to and that’s the only reason anyone uses dead reckoning for navigation at all anymore.

Actually, there probably is some truth to the argument that the only reason student pilots still have to learn DR is because the FAA is so reactionary—maybe conservative would be a better word—and the truth is, that’s not such a bad thing. DR has been an important part of air navigation since Wilbur and Orville left Kitty Hawk. And having served aviation so well and so importantly for so many years, decades stretching into centuries, before we let it die we had better be sure of two very important things: one, will we never ever need it again, and, two, will we always have something at least as good to replace it? Can we really live without it? I want to show you that the answer is almost certainly, “No.”

First, before we get too far ahead of ourselves, let’s make sure we all know what we mean by dead reckoning—DR. The phrase “dead reckoning” comes from the phrase “deduced reckoning.” “Deduced” means to start with known facts or figures, and use logical reasoning to come to a conclusion. “Reckoning” means a counting or computation. So dead reckoning, then, as a navigational method, means to start with known facts and figures, and to then compute certain outcomes based on those facts and figures. What are those known facts and figures? They include a starting point, a desired course to an end point, an estimated airspeed and forecast winds aloft. We can use the principles of dead reckoning, which are based on fundamental laws of motion, along with basic algebra and trigonometry, to plan a flight along that desired course, and to then execute that flight.

More specifically, dead reckoning is often defined in navigation books, including mine, The Aviator’s Guide to Navigation, now in its fourth edition, as a navigational method that uses laws of motion and basic mathematics to “advance a position.” What does that mean, to advance a position? It means essentially what we just said: to start with a known fact, a given position, normally, in our case, our departure airport, and then to advance that position, based on what we know about our airspeed and direction of flight and winds aloft, to another position, and then another, until we reach our desired position, normally another airport.

In practical terms, it means all the stuff we did as student pilots to plan a cross country flight and then to execute it without using any external aids to navigation like VOR or GPS. Pure navigation: I am at this airport, I want to go to that airport, using this airplane, and I’m going to do it by flying a course of so many degrees for this many minutes, and if I have everything figured out correctly and the winds aloft are as forecast, at the end of that number of minutes I should be over that airport. That’s a pretty simple explanation of what dead reckoning is: I am here, I want to go there, to do that I have to fly this heading for this many minutes.

Where does pilotage fit in here? The two always seem to go together, “pilotage and dead reckoning”, like a single thing. They almost are. Pilotage means looking out the window. Pilotage is navigation using terrain features. Basic IFR: I Follow Roads, I Follow Rivers. You can, of course, navigate using pilotage alone—not real smart, but you can. You can just take off, look for something familiar along your route of flight and keep doing that until you get to where you wanted to go. This works best when you have something very distinctive to look at, like the Mississippi River, and a full tank of gas. You could also, in theory, navigate using dead reckoning alone, but that would be even stupider. Why wouldn’t you look out the window and verify your dead reckoning computations if you could? So, in practice, the two go hand-in-hand: dead reckoning provides initial estimates of heading and time, pilotage corrects and verifies: you estimated, for instance, that it would take 8 minutes to fly between Oshkosh and Fond du Lac on a heading of 171, but in fact it took 10 minutes and you had to adjust the heading by 3 degrees to the right. The winds aloft were not exactly as forecast, they seldom are, and in this case they were blowing a little harder and more from the right than forecast. That’s how pilotage and dead reckoning work together and why we always think of them as one system.

It is at least theoretically possible to navigate using DR in instrument conditions, meaning little or no opportunity for pilotage, but it is becoming increasingly rare. You have to go to some pretty obscure parts of the earth where instrument flight plans can be filed over routes without any external navigational aids. But back in the ‘70’s, when I was a young copilot flying Cessna Citations, we used to fly between New England and Bermuda with a substantial section in the middle that was pure dead reckoning. We lost the Nantucket VOR about 200 nautical miles out, and picked up the Bermuda VOR about 200 miles from Bermuda, and the section in between, a distance of over 200 nautical miles, we navigated using dead reckoning. Pilotage over water is an exercise in futility: you can look out the window, but what you see is a bunch of water. So that section was pretty much pure dead reckoning. You can’t do that anymore. For all practical purposes, pilotage and dead reckoning always go together now.

So dead reckoning is a method of navigation that advances a position from a known starting point to a desired end point, and verifies its progress with pilotage. How is that different from other nav systems? Well, it’s quite a bit different than VOR navigation, where we go to and from fixed, ground based nav aids, zig zagging our way from A to B. And it is also fundamentally different from GPS navigation. How so? Doesn’t GPS take us directly from A to B, advancing our position as we go? Isn’t the only real difference between a DR course and a GPS course is that the DR course is a rhumb line course—a straight line on a flat map—and the GPS is a great circle course—the shortest distance between two points on a sphere? That is true, but it is not the only difference, in fact the two are fundamentally different in how they work. So, before we look at dead reckoning in more detail, let’s look at GPS.

GPS stands for Global Positioning System. GPS is a satellite system comprised of 24 primary units plus spares. Each satellite transmits a long series of numbers called a pseudo random code. The onboard receiver has the same code, along with a clock. The onboard receiver notes how much later the satellite code arrives compared to its code, and the difference in time corresponds to distance from receiver to satellite: The greater the difference between the two codes, the greater the distance. The actual engineering to do this is hideously complicated stuff involving differential and integral calculus, matrix algebra, and the simultaneous solution of equations with four unknowns. Relativity must be taken into account, because the satellites are going very fast and time slows for objects approaching the speed of light. Relative to other objects, anyway. Don’t ask me to explain all this, I can’t. In fact, I can’t imagine how smart you have to be to figure this stuff out. But the basic theory behind GPS is simple: once you know your distance from something, you can establish an initial estimate of position somewhere on a sphere with that distance as its radius. Distance from a second satellite establishes a line of position along that sphere. A third satellite distance crosses that line and establishes a point, but only a rough point because, unlike the satellite, which has a nearly perfect atomic clock, the onboard receiver only has a quartz clock, which is relatively inaccurate. A fourth satellite removes that error, and any additional satellites provide reliability testing. That’s the basic GPS system.

The point I want to make here about GPS, though, is that GPS provides only one bit of information: position. It tells you where you are. That’s why it is called a Global Positioning System. And that’s all it does. The only way it can figure out anything other than where you are is by looking at changes in your position. And it can’t even do that by itself, it needs another computer, and guess what kind of computer that is? It’s a DR computer. That’s not what it’s called, but that’s what it is. What we call “our GPS navigation system” is really a DR computer with GPS inputs. The computer part takes changes in position to figure out actual track, groundspeed, and winds aloft. With a data base of known fixes, it can build routes, and it can compare present position, provided by the GPS input, to keep the aircraft on course, or report how much off course we are in terms both of distance and direction. All great stuff, but all GPS itself is doing is telling you where you are, and it does that only in terms of latitude and longitude—basic data. The computer does all the rest. If the nav computer is the dead reckoning part, then the GPS receiver is the pilotage part, except that it works backwards: the pilot navigating with dead reckoning uses pilotage to check his computed position. But the nav computer says to the GPS, “Keep telling me where I am, and I’ll figure out the navigation from there.”

I want to talk just for a little bit about INS as well—inertial navigation systems, including INS’s rich relations, the IRS’s, or inertial reference systems. The reason I want to talk about INS as well is because these three nav systems, DR, GPS, and INS, are, for all practical purposes, the only way we have to navigate without reference to ground based nav aids. Every other existing system of air navigation—NDB, VOR, DME—requires an external, ground based nav aid to function. And GPS requires an external, space based nav aid. Which means dead reckoning and INS are the only systems that can operate completely independently from any outside reference. Think about it: dead reckoning, the student pilot’s old friend, is in the same league with INS, the heavy metal crowd’s best friend.

A quick review of INS. What is it, how does it work? Inertial navigation works by detecting changes in direction and velocity to advance a position. Sounds an awful lot like dead reckoning, doesn’t it? In simple terms, an INS says, “If I know where I am—my starting position—and if I can keep track of every movement after that, then I can keep a runny tally of where I am at all times.” INS detects movement with accelerometers—there are various kinds but they all act like pendulums, swinging with movement—and it then compares that movement to a stable platform which is a basic reference separate from the aircraft itself. Platforms are stabilized with gyros, originally mechanical gyros, similar to the gyro in an artificial horizon, only many times better and many times more expensive. Nowadays the platforms are normally stabilized using lasers, and are called ring laser gyros. The lasers aim beams at each other in a ring pattern and interference patterns among the lasers result as the platform tilts, and computers use those patterns to correct the tilt and maintain stability. INS is very simple in principle, but like GPS, with which it is often paired, it is enormously complicated in practice, made even more so by the fact that the earth is round, which means the platform needs to tilt somewhat as it moves to maintain its alignment with the earth—with its so called “local vertical”—and also with the fact that the earth rotates, which means that some movement is normal even standing still, and that movement varies with latitude—a lot at the equator, none at the poles. To work properly the INS has to separate the earth’s rotation from the movement of the aircraft. The actual process of making all this happen is the kind of thing that gets Double E’s—electrical engineers—all excited and puts the rest of us to sleep. But INSs do work and they work extremely well: typical performance for a well maintain ring laser INS is accuracy to within 0.1 nautical miles per hour. That means that after a typical five hour crossing from the West Coast to Hawaii, the INS would know where it is to within a half a nautical mile. That’s without any additional help from GPS or DME. Early navigators to Hawaii just wanted to get close enough to the islands to pick up an NDB and track it in. That meant enroute navigational accuracy to within 100 miles or so. With just an INS, you can not only find the islands after five hours, you can hit a specific spot on one of those islands to within a half a mile: standard ILS minimums. Pretty impressive. But with a pretty big price: a single ring laser INS can cost close to a half a million dollars, and three are typically installed, for increased accuracy and reliability.

What’s an IRS? IRS stands for “inertial reference system.” IRS takes INS beyond a navigation system and uses the core—all the expensive stuff like the accelerometers and the stable platform—to drive a variety of other components and systems in the aircraft: the vertical and horizontal gyros, the autopilot, even the anti lock braking system—any component that can benefit from a highly accurate stable platform or from changes in acceleration can benefit from IRS. The nav system is then just one of the components the IRS serves. So the only real difference between an INS and an IRS is that INS is a stand alone inertial navigation system, while IRS is a source of inertial information driving any of a number of other systems, including navigation.

So we’re back to dead reckoning and INS, the only nav systems capable of operation entirely from within the aircraft and without the need for any external source of information, and we have seen that the two do, indeed, operate in a very similar manner, in each case starting from a known position and using speed and direction, in the case of dead reckoning, to advance that position along a route of flight, and acceleration along three planes in the case of INS to advance its position. In fact, INS is often described as a highly accurate dead reckoning system, and that is true, it is. We could say that the two are not exactly the same though, that dead reckoning works with speed whereas INS works with acceleration, but in fact the difference is less than it appears. We actually do work with acceleration in dead reckoning as well, we just tend to ignore it or round it off. We know, for instance, that when we take off we start from zero and accelerate from there to climb speed and later to cruise speed, but we don’t include every bit of that acceleration in our computations. We just assume we go from zero to climb speed virtually instantaneously and use that speed for the climb segment of our flight planning. (In fact, if we want to be as accurate as possible, we look that information up in our performance manual, which allows for the time to accelerate.) At top of climb we assume we transition instantly from climb speed to cruise speed, even though in practice that might take a minute or so. We allow for these inaccuracies—these assumptions that aren’t literally true—as a practical matter and because the errors are minor. But they are one of the many reasons dead reckoning is less accurate than INS: INS takes even the tiniest change in acceleration into account. So INS and DR really aren’t different at all, it’s just that INS has better information.

What is the other main reason DR is not as accurate as INS? The single most important factor affecting the accuracy of DR is wind. In fact, wind is the only reason we have other nav systems at all. Think about it: if we could eliminate the wind, or more realistically, if we could forecast and measure the winds aloft with near perfect accuracy, dead reckoning would be all we would need to get from here to there—a perfectly accurate, long range, area navigation system. We wouldn’t need VORs, NDBs, INS, or GPS, just a highly accurate true airspeed indicator, a very accurate gyro compass, and a nav computer, which could even be an E6-B. And that’s all.

How could that be? We all know how inaccurate dead reckoning is; it’s not all due to wind. No, it’s not all due to wind. Some is due to compass error, to gyro precession, to inaccurate airspeed indicators, to rounding off errors and to less than perfectly accurate timing measurements, but these errors can all be eliminated with more accurate instrumentation. To understand this better, let’s start with the simple case of no wind. Navigation by dead reckoning immediately becomes quite a bit easier, because a couple of factors are eliminated. First, our course and our heading will always be the same. Whatever course we fly will also be our track, because the only thing that blows us off course is wind. Fly 090, get 090.

Second, our airspeed and our groundspeed will always be the same. With no wind, 100 knots true airspeed is 100 knots groundspeed. Navigation planning would consist of plotting a course, measuring the distance, selecting an airspeed, spinning the “whiz wheel”—the E6-B—and distance divided by airspeed equals time enroute. For enroute navigation we would start the clock, take off, select the heading desired, set power for that airspeed, watch the progress enroute as a function of time enroute—a third of the time gone would equal a third of the way there—and when the time runs out, or just before, look for the desired airport and land. If there were no wind, that’s all there would be to air navigation.

Now, I have oversimplified what would happen in the real world for the sake of argument—I didn’t allow for a climb or descent segment, for instance, and I assumed you were able to hold both heading and airspeed perfectly, but the point I’m trying to make is that most of the little things that add up to make DR fairly inaccurate can be eliminated. It takes money, but it can be done. Air data computers, for instance, can provide true airspeed to within a knot of accuracy. A good autopilot with a decent gyro coupled to a flux gate can maintain magnetic heading to within a degree of accuracy and an INS quality gyro can do even better. And without the need to fill our cockpit with other stuff—NDBs, VORs, DMEs, GPSs, and so on—there would be money to spare for these items. The real problem is, we can’t make the wind go away and we can’t forecast it accurately enough to totally compensate for it, and probably never will be able to.

Never’s a long time but I doubt if we will ever be able to forecast the winds aloft accurately enough to navigate via dead reckoning alone. To understand why, let’s digress a little here into an area known as chaos theory, but bear with me, it relates directly to aviation and, in particular, to weather forecasting. The classic question that chaos theory poses is, “If a butterfly flaps its wings in China, will it effect the weather in Maine?” And the answer has to be, “Yes,” it has to have some effect, and in return the weather in Maine has to ultimately effect how the butterfly flaps its wings, but how could we ever account for these effects? For one thing, the butterfly and the weather create an endless iteration: one effects the other which effects the other, which effects the other and so on forever (or until the butterfly dies, but there will be more). And this is just one butterfly. Everything effects everything, and in quantities and qualities so small that they can’t possibly all be accounted for.

The butterfly effect is an extreme case, but a simple example we can all relate to is pouring cream into coffee: each time we do it, it will produce a similar result—we recognize a particular pattern that we know is cream swirling in a cup of coffee. But each time it will also be different—no two swirls of cream will be the same, and we certainly can’t predict, before we pour the cream in, what any given swirl will look like. Why? Because there seems to be an element of chaos in the universe which, by definition, cannot be predicted. And why is that? Because there are butterflies is the short and simple answer. I don’t have a better one.

Winds aloft act like cream swirling in coffee, inherently chaotic. We will never be able to perfectly forecast the winds aloft, or any other weather phenomenon—visibility, cloud cover, precipitation, and so on—no matter how many observations we make and no matter how many super computers we put on the job. So a certain element of uncertainty will always effect the accuracy of our navigation when using dead reckoning. And that means that we will always need something to complement it, normally pilotage, but it could be VOR, DME, GPS, or INS.

So if INS is just a very sensitive dead reckoning computer, how does it get around this problem? How does INS deal with the wind in ways dead reckoning by itself can’t?

The simplest explanation is that INS senses accelerations, including those caused by the wind. What is the primary factor affecting acceleration? For an airplane, it’s the power plant. That’s what makes it go. What is the next factor? Drag. That’s what makes it slow down and eventually stop. Without drag we’d just keep accelerating until we reached the speed of light. Wind, as an additional accelerating factor, acts like the power plant when it’s behind us, and like drag when it’s ahead of us, helping or hurting.

Imagine an INS equipped blimp. Let’s assume we start with it tied to its moorings with the engines off—it’s standing still. We enter it’s position, let it stabilize, and then we cast off the moorings. It will start to drift with the wind, airspeed zero, groundspeed the same as the wind speed. The INS will sense that the blimp is being moved by the wind—it will sense the acceleration from zero to wind speed, and then will sense no further acceleration except for changes in the wind. But it’s keeping track of where the blimp is all the time based on those measurements. Now we turn the motor on and accelerate again. Again the INS senses that acceleration, but it doesn’t know that it is because we switched the engines on and not because the wind increased, nor does it care—it’s all the same to the INS. And if it’s all the same to the INS in a blimp, then it’s all the same to the INS in an airplane, just a little more dynamic.

My father learned to fly back in the forties at a little airport in Coffeeville, Kansas, home of the Funk Aircraft. He said that they used to think it was great fun on a really windy day to try to land one backwards—the wind down the runway blowing harder than the airspeed, a negative groundspeed. As kids my brothers and I had trouble believing that, for several reasons. One, who would name an airplane, a “Funk”? Second, he also told us that when he was a kid there was a cowboy movie star named Tom Mix, and we knew that couldn’t be true. Tom Mix? What kind of name was that for a cowboy? So we figured the Funk landing backwards was probably a story too. But if you could get an INS into a Funk and still get it to fly, it would work as well forwards as backwards.

So INS can, in effect, “feel” the wind. Not directly, but it includes the effects of wind in what it senses. How does it then separate the wind components from aircraft movement?

Very simple: it has a stable platform that isolates accelerations, resulting in groundspeed, and it has true airspeed and aircraft heading inputs. It looks at the difference between true airspeed and groundspeed, and that gives it a tailwind component. It looks at the difference between where the aircraft is pointed and where it is actually going, and the difference in degrees is drift angle. With drift angle and tailwind component it computes winds aloft.

So in simplest terms, the only significant difference between a half million dollar INS, and a $15 E6-B, is that the INS can sense wind, whereas we have to observe it. But “observe” is just another way of saying “sense”, isn’t it? Isn’t sight one of our senses? And how do we observe the wind? Pretty simple, really. We look out the window. And what do we see? We see two things. First, we see that we are passing things, and second, we see that where we are pointed and where we are going is not exactly the same. At least they usually are not, and even when they are, that tells us something. The passing by things means we can determine our groundspeed. All we have to do is time ourselves from one identifiable landmark to another, measure the distance between those two landmarks on a chart, whip out the old E6-B, put distance on the outer ring over time on the inner ring, and groundspeed is over the pointer. If we know our true airspeed, something we can also figure out fairly accurately with the E6-B, correcting indicated airspeed for altitude and temperature, then the tailwind component is the difference between true airspeed and groundspeed, a negative tailwind component being a nice way of saying headwind.

Drift angle is a little more difficult to figure out, but not impossible. In the old days, by which I mean before my time, back when DR was a primary form of navigation for all aircraft, aircraft were often fitted with drift meters, for just this purpose. A drift meter was basically a downward facing periscope with grid lines on it that could be turned in order to align those lines with the actual movement of the aircraft over the ground. The drift angle of the aircraft, the amount the aircraft was drifting off course, could then be seen by comparing the difference between the grid lines and the longitudinal axis of the aircraft: I’m pointed this way, but I’m actually tracking several degrees to the right or left of where I am pointed, and that is my drift angle. The drift meter also had two parallel lines called “timing lines” that were used to determine groundspeed. To do this an object on the ground was timed as it moved from one line to another, and then that time was referenced to a chart that corrected for altitude. The result was groundspeed.

Once you knew drift angle and groundspeed, you could determine the actual winds aloft. Drift angle is the opposite of the wind correction angle—it’s the same thing really, just looked at in a different way—and it can be used just like a wind correction angle, along with groundspeed, to work a wind triangle backwards. That is, instead of using forecast winds aloft, true airspeed, and true course to compute a wind correction angle and groundspeed, we use true course, groundspeed, true heading and true airspeed to compute actual winds aloft.

Aircraft don’t come equipped with drift meters anymore, for several reasons, but the main one is we really don’t need them. We can determine drift another way, mainly by flying a desired course. We note landmarks along our route of flight, fly the aircraft—that is, adjust the heading as necessary—to fly directly over those landmarks, and note the heading necessary to do that. The difference between the aircraft heading and the desired course is the drift angle, and the difference between the desired course and our heading is the wind correction angle. Take out the old E6-B, convert IAS to TAS, then flip it over to the wind side, plot the wind triangle, and the result will be winds aloft.

What if we can’t see the ground, either because we are on top of the clouds or are in the clouds? How could we figure groundspeed and winds aloft then? Easy, we have to substitute electronic fixes for visual fixes. We could time ourselves between VOR passages, for instance, to get groundspeed and we could fly a VOR course with the needle centered and note the difference between heading and course. The calculations are the same, we just got time between fixes and drift angle using external nav aids instead of visual sightings.

This has been a lot of words to come to a very simple conclusion: with DR navigation we can do everything an INS can, we just need to be able to see the ground or have one other source of nav information. We can’t do it as accurately, or as quickly, which is why dead reckoning isn’t allowed in controlled airspace or on long over water routes where INS shines, but we can do it. It isn’t different, it’s just slower and less accurate. Big deal. And I saved a half a million bucks.

I have to assume that everyone here has some idea of what I am talking about when I say “dead reckoning”, but I can’t assume that everyone has the same idea or the same amount of knowledge. So, this isn’t meant to be ground school, but for the record let’s do a quick review of what navigation by dead reckoning for airplanes is all about.

First, what are we trying to do? Very simple: We want to go from one place to another. So we need a starting point, normally the airport where our airplane is parked, and an end point, normally our destination.

An ex-Navy guy was being interviewed for a Cessna Citation Captain’s job at the aircraft management company where I was then employed as a very inexperienced copilot—I heard this story later while flying with the boss. As part of the interview this guy was given a very complex situation involving an instrument approach, certain aircraft system problems, and rapidly deteriorating weather on approach. The alternate weather was good but fuel was going to be very tight if he diverted, and he would still have the system problems. They wanted to know what he would do, continue or divert. There was no right or wrong answer, they just wanted to examine his thought process. He thought and thought, weighting this against that, trying to figure out if one course was definitely better than another, and finally said, “I don’t know, I guess it would depend on where my car was parked.” He got the job anyway.

Our end point is normally our destination airport. We locate these points on a Sectional Chart, a chart designed specifically for visual air navigation, and then we draw a line connecting the two, which defines a course. We make sure that course doesn’t take us anywhere we don’t want to go, like through a Restricted Area or mountains we can’t top or a large body of water—anything we should or must avoid. We determine the direction of that course by placing a plotter along the course, and then we read the direction given by the plotter using either the north south or east west grid lines, whichever is easier given the direction of flight. We then have to use common sense to make sure we are reading the proper direction of flight since the plotter isn’t smart enough to know which one of our two points is the origin and which one is the destination. So we have a number for our course, which represents its direction, but it’s direction relative to what? The answer is, direction relative to true north, because that is the way sectional charts are designed. The vertical grid lines that are used to measure the course point to true north and true south, while the horizontal lines are aligned with true east and true west.

Great, but all we have is a compass, and a compass points to magnetic north, not true north (unless you happen to live along a particular line where the two just happen to coincide, which in the US runs along a line from the U.P. of Michigan to Florida). The reason true north and magnetic north are not the same is, number one, the magnetic north pole is only close to the true north pole and is actually several hundred miles south of the true north pole, and, number two, magnetic strength varies across the globe—it doesn’t radiate out in exact degrees of magnetism the way lines of longitude do from the north pole. So if we want to use a magnetic compass to track a true course, we are going to have to account for this variation, and fortunately that variation is printed right on the sectional chart in the form of a magenta line with a number and direction, either east or west. The number represents the number of degrees magnetic direction varies from true north, along and to either side of that line, and the direction, W or E, means magnetic north varies to the west or east by that number of degrees from true north.

So how exactly do we use that information? If our course falls along a line that is marked “15 W”, what do we do with that? Every student pilot learns the memory aid, “East is least and west is best,” meaning subtract easterly variation from true course, and add westerly. That’s fine, and aviation is full of memory aids because there is an awful lot to know and to remember and, in any case, we don’t always have the time to think through how a relationship works every time—we need a quick and practical method and memory aids like “East is least and west is best” work well. But at least just once it’s also a good idea to think it through and try to see where the memory aid comes from. So if we say, in this case, that our course is 45 degrees true north, which we found out with our protractor/plotter, and if the variation for our area is 15 degrees west, that means that magnetic north is actually 15 degrees to the west, or to the left, of true north. Our chart needs to be titled 15 degrees to the left, or counterclockwise, if we want to use magnetic north instead of true north, and if you can visualize leaving our course line on our sectional chart where it is, but rotating the grid lines 15 degrees left, or counterclockwise, toward magnetic north, our course will now be 15 degrees greater, 45 plus 15 or 60 degrees. And if we check that with the “East is least and west is best” rule, 15 west means adding 15 to our true course, 45, and the result is 60 degrees. It works.

The sectional chart makers could have eliminated this conversation by aligning the grid lines with magnetic north instead of true north, but as a practical matter that is very difficult to do since magnetic lines don’t radiate in straight lines from magnetic north the way true north lines do—they bend—and they vary with time. True north grid lines are always the same, so it’s much easier to use that reference and simply add the variation to it. Just remember to adjust true course for magnetic course, unless your aircraft just happens to be equipped with an inertial reference system and a switch to select true north.

So we now know that in this case if we want to fly from A to B along a course that measures 45 degrees true, we have to actually fly the airplane so that the magnetic compass reads 60 degrees. (And even if you’re using a directional gyro, it has to be set to agree with the magnetic compass.) So we go out to the airplane and we look at our compass, and there underneath it is a little card that says, “TO FLY N, STEER 000, TO FLY 030 STEER 031,” and so on at regular intervals all the way around to North again. What’s that all about?

There was an ad a couple of years back, I don’t remember for sure what they were selling, maybe Quicken bookkeeping software, but the ad started with a big guy standing in front of a huge wall chart with colored strings going all which ways across it. Standing beside him is a somewhat puzzled looking little guy and both are staring at the chart. Big guys says to little guy something like, “Trevor, this is The Grid. We use The Grid to plot our costs: blue is labor, red is materials, gold is administration, and so on. Got it?” Trevor stares at the chart for awhile, then says, “How do we know what our total costs are?” Big guy stares at the wall chart for a while, looks down at Trevor, then back to the chart, and finally says, “Trevor, The Grid is not perfect.”

Well, Trevor, the compass is not perfect either. It is effected by other materials in the aircraft: radios, cables, the engine. Some of these errors can be eliminated with little compensation magnets, but inevitably some error still remains, and by a process called swinging the compass, the remaining errors are distributed as evenly as possible around the compass. Then a little card is printed up saying what all those remaining errors are. So we want to fly a compass course of 60 degrees, and we look on our compass card and it says, TO FLY 060 STEER 061; the heading to actually maintain will be 61 degrees not 60. Not a real big deal, and it’s hard to hand fly an airplane to within one degree of accuracy anyway, even in still air, but that’s the number we’re going to try to fly.

And that would be the end of it if the air were perfectly still. But it’s not, there is always some wind, which is just high pressure and low pressure air trying to equalize. They never ever actually reach equilibrium because the surface is always being heated differently creating different areas of pressure, but they are always trying, and the result is a constantly changing wind. And wind affects both our track—where we actually go versus where we are pointed—and our speed: flying into the wind slows us down—relative to the ground anyway, and that’s what matters in navigation, movement over the ground—and helps us along when flying with it—free extra speed.

This, to me, is where the real fun begins in DR: adjusting for wind. Adjusting true course for variation and deviation is just a practical matter, something we’re forced to do because our only directional aid is a magnetic compass and installing a gyro compass stable enough to maintain a true course just isn’t practical, not for most aircraft relying on dead reckoning for navigation at any rate. Maybe someday it will be and then all you’ll have to do is measure your true course, align your gyro to true north (which is easier than it sounds—all you need is a spot somewhere on the airport that you taxi over and align your gyro as indicated), and then you could fly that course directly. But you would still need to account for the wind.

So how do we do that? We use vector algebra and trigonometry, either graphically, with an E6-B with a wind slide, or, for high performance aircraft, using the back side of a Jeppesen CR-3 nav computer, or, electronically, with a handheld nav calculator. (Electronic calculators work great until the batteries run down.)

I’m not going to review here how to account for wind with an E6-B or a CR-3—the handheld calculator is easy, you just enter the data and it figures it out—but essentially the nav computers graphically plot the true course and true airspeed versus the winds aloft to show wind correction angle and groundspeed. What are the winds aloft? Those are the forecast winds for various altitudes, as provided by the National Weather Service. They can be obtained from Flight Service Stations or over the internet at a government sponsored site known as DUATS, which stands for Direct User Access Terminal Service. It’s free for all licensed US pilots, even student pilots. Go to www.duats.com.

So we now have a course, corrected for variation and deviation so we can fly it using our magnetic compass, we have a wind correction angle to keep us on that course, and we have an estimated groundspeed. We use that to estimate our time enroute, and that means we need to know our total distance enroute which we measure on our Sectional chart using our plotter. Time enroute is then a simple calculation with our DR computer, essentially a problem in proportions: ground speed is to 60 minutes as distance is to X, time enroute. You can also do it in your head pretty quickly, if not always completely accurately, by thinking of your groundspeed in terms of miles per minute: 120 knots GS is two miles per minute, 180, three miles per minute, and so on. It works at all speeds—I would frequently convert L-1011 or 757 groundspeeds to miles per minute, 540 knots GS is 9 nautical miles per minute, for instance, and use that to make rough estimates to the next fix, or on oceanic crossings to the mid point between waypoints, where we had to do a check. At 540 knots GS with a midpoint check coming up in 275 nautical miles, dividing 275 by 9 gives me 30 minutes plus a little. To check that, my little plastic E6-B gives me 30.5, the CR-3 looks closer to 30.6 and the calculator says 30.55555555556. The rough estimate of 30 minutes plus a few seconds is pretty good.

And by the way, what did we do at the midpoint between waypoints check on oceanic crossings? We noted, on the flight plan, the actual winds aloft, as indicated by the INS or IRS, the true airspeed and the groundspeed. We also checked our estimate to the next fix to make sure it was still within limits: two minutes for the North Atlantic, three minutes for all others. The winds and speeds were entered to have a record of actual conditions, versus forecast conditions, in case we had to revert to basic DR navigation—the failure of all inertial and GPS navigation. The estimate to the next fix was a basic DR computation. So even with all that other stuff in the airplane, we were still using DR.

We now have everything we need to plan our cross country using dead reckoning for navigation. How do we use this in flight? It would be nice to think that we could just take off, take up the heading we computed, and then just sit back and wait for the time to run out and land. It would be nice, but we know from experience that it just isn’t that simple.

For one thing, the compass isn’t very stable. It bounces around, it tilts, it swings back and forth—as a primary reference it will drive you pretty batty. So normally we use a directional gyro for heading guidance, a much more stable reference, but it drifts—it precesses—and has to be regularly reset to the magnetic compass, which is still bouncing around, giving us an average heading at best. Even if we are lucky enough to have a “slaved” directional gyro—a gyro that is continuously corrected for magnetic heading by a remote magnetic sensor, we still have to try to fly that heading, not a perfect task given anything less than total concentration on that one task alone, never a good idea anyway. And even if we are really lucky and have an autopilot to track the continuously updated slaved directional gyro, we still haven’t allowed for changes in true airspeed which will result in changes in groundspeed. And even if we are flying a sophisticated turbine aircraft with all of this stuff plus an auto throttles system—something that will maintain a constant airspeed—we still have to account for the real wind versus the forecast wind. In other words, no matter how well equipped our aircraft is, if we want to navigate using dead reckoning, we need to allow for differences between the forecast winds aloft and the actual winds aloft, and we do that with pilotage: we look out the window and we correct our heading as necessary to stay on course, and we recompute our groundspeed by timing our progress over a known distance,. We use that to reestimate our times enroute. And that’s the quick review of basic DR navigation.

So, we’ve covered a lot of ground here so far, and maybe it’s time to step back and look at what we have covered so far, and then finish up with where that takes us.

First, we looked at what dead reckoning is, and how it is like inertial navigation and how it is unlike satellite navigation. A quick recap: satellite nav, GPS, is a positioning system that uses DR to figure out how its doing and where its going. Inertial nav is a DR system that senses movement directly to keep track of where it is at all times and correct as necessary to stay on course. Dead reckoning uses fundamentals of physics and mathematics to advance a position from a known point to some other point. The most important variable in those calculations are the winds aloft, and pilotage is generally relied on to correct for inaccuracies in those winds. All three are area navigation systems: they take you in direct line from one point to another. Ground based navigation systems like NDB and VOR require the aircraft to over fly the associated nav aid, the NDB or the VOR station. Others, like DME or VOR combined with DME provide information that requires further computation in order to navigate. An area navigation system is inherently more efficient than a non-area system, which means that DR navigation has certain advantages over ground based systems, so long as we have sufficient visibility to back it up with pilotage.

If INS is the ultimate DR system of navigation, what is the minimum? That is, let’s assume a basic aircraft with no electrical system and no vacuum system. Something like that Funk my father used to fly. Or maybe we have all that stuff, but one by one they go inop. What is the minimum equipment required to navigate using dead reckoning?

Let’s start by looking at the minimum equipment required by Part 91 for aircraft operating under visual flight rules during the day. And in fact, very little is required: an airspeed indicator, an altimeter, and a magnetic direction indicator—what you and I call a compass—and that’s it—the rest of the required items under that part are either related to the power plant or are unrelated to navigation, like seat belts and ELTs. So, can we navigate with that? Can we navigate with just an airspeed indicator, an altimeter, and a compass? I guess the answer has to be, “Sort of.” With that equipment you can fly a magnetic course at the proper altitude for the direction of flight and at an indicated airspeed that is within the normal, or safe, operating range. But that really doesn’t add up to navigating by dead reckoning. Why? Well, for one thing, you have no clock, so you have no idea of your progress and you have no way of knowing what your actual groundspeed is. That’s not really navigation, that’s just humming along. So, in addition to the minimum instrumentation, we need a time keeper, and in order to use that information we need a navigation computer, an E6-B or the equivalent.

With a clock we can time ourselves between two checkpoints with a known distance between them, and use the calculator side of the E6-B to determine actual groundspeed. Now we’re getting somewhere, we’re starting to navigate. We can fly a magnetic course, correcting our computed wind correction angle for actual winds aloft with pilotage, and we can compute our actual groundspeed and use that to revise our times between checkpoints and total time enroute. So we’re navigating using dead reckoning with just an altimeter, an airspeed indicator, a compass, a clock, and an E6-B.

Can we determine actual winds aloft with that? What do we need to figure winds aloft? We need groundspeed, and we have that, we need true course, and we can figure that, starting with magnetic heading and working backwards, subtracting deviation and variation, and we need true airspeed. We don’t have true airspeed but we do have indicated airspeed. What do we need to convert indicated to true? We need altitude and temperature. We have altitude, but we don’t have temperature. We need an outside temperature gauge. If we had one of those we could compute actual winds aloft, which we don’t have to have, but they are certainly nice to have and make the adjustments to our estimated wind correction angles much easier and more accurate. So that’s it, our minimum equipment list for DR navigation, five items plus one “good to have”:

• altimeter

• airspeed indicator

• compass

• clock

• E6-B

• outside temperature gauge.

Would I ever actually do that? Fly cross country with nothing more to navigate by than an altimeter, an airspeed indicator, a compass, a clock, an E6-B, and maybe an outside temperature gauge? Of course I would. Maybe not with only three or four miles of visibility, maybe not with rain showers forecast enroute, maybe not around a restricted area, and maybe not to an airport or an area I’d never been to before. But on a good day in an area that I was familiar with, of course I would. It would be fun. I’d be spending most of my time looking outside, not chasing a VOR needle or staring at a little moving map. It would be efficient—a straight line course, area nav on the cheap. And it’s reliability would be in direct proportion to the amount of effort I put in to it. With careful preflight planning, a good log of times and headings enroute, careful attention to pilotage, there is no reason why it shouldn’t be completely reliable, with the outcome never seriously in doubt, as they say in the flight test guides. I like to think of it as the fly fishing of air navigation: there may be better ways to feed yourself than to stand in a cold river while casting a hand-tied fly that you hope will fool a very smart fish, but there aren’t many that are more fun. Or so I’m told.

And what if the weather isn’t severe clear, or what if my destination is to an unfamiliar airport? Would I just ignore DR and go back to chasing VOR needles or stick the Garmin on the panel? No, of course not. I might well want to have external nav aids available, just in case, but it would still be fun, and efficient, to plan and execute the flight based primarily on DR, with the VOR or GPS there as a backup. And in any case, for routine VFR navigation, the combination of DR and GPS is as logical and complementary as INS and GPS is for commercial aviation and the military. The two go hand in glove, with the DR navigation providing the planning and the enroute guidance—advancing the position—and the GPS backing up the pilotage. One knows where you are going and the other knows where you are.

You know the question I hated the most as an airline captain? “Where are we?” You get it all the time. Guy looks out the window and sees a lake or some mountains and wants to know where he is. So he flags down a flight attendant. The flight attendant doesn’t know—he or she has been pushing carts up and down the aisles and can’t see out the windows anyway. So the flight attendant calls up front. “Don, this is Julie, in the back. Guy wants to know where we are.” You can’t say you don’t know. But 23 DME east of the Keene VOR doesn’t really answer the question, nor does N43 30.7 W 076 44.1. One flight attendant told me she just always tells them they’re over Wyoming because no one knows what it looks like and no one knows where it is, and it seemed to work. The fact is, at FL 370 on an IFR flight plan, you often don’t know exactly where you are in terms of the terrain. I used to tell the flight attendants, “We don’t know where we are, but we know where we’re going, so that’s good.” Some thought that was funny and others just walked away with a worried look. With DR for primary nav and GPS information available, you have the best of both worlds: you know both where you’re going and where you are. The GPS is just another form of pilotage.

I want to leave you with one final thought, and if it’s all you get out of this discussion that’s fine, because it’s important. DR as primary navigation may be close to death, but DR will never go away completely because, whether you realize it or not, you can’t not DR. Even if all you do is estimate that it’s going to take you about an hour to get where you want to go, and you have checked that you have about three hours worth of fuel on board, and you know the route so well that you just plan on using pilotage to get there, you are still using DR. How did you estimate an hour enroute? You probably did it in your head using an average TAS of 100 knots, typical for your aircraft. You knew that your route was generally eastbound and you knew that a cold front had just blown through which would give you a nice tailwind component enroute, and you knew from past experience that the total distance was about 110 nautical miles, and from that you were able to rough out that it would take about an hour. And how did you know you had about three hours worth of fuel? Easy, the tanks were full, which meant 36 gallons of fuel, and the most you ever burn is about 10 gallons an hour, plus a little more maybe for the climb, so roughly you’ve got three hours plus a little. You took off and set course to the northeast and immediately saw that the winds were from the northwest, so you put a little crab to the left into your heading, and you watched your progress over familiar ground toward your destination, confident that your groundspeed was a little better than your airspeed so you knew your hour estimate was very conservative, and when you got close you started looking for the airport and you landed. On the surface, all you used for navigation was pilotage, but in fact, you were using DR as well, you just didn’t think of it that way.

I had a car years ago that had one of the first trip computers in it. That was really one of the main reasons I had bought it. Just after I got it the family had set out from Northampton, Massachusetts, where we lived, to go to Hanover, NH, where we used to live, a trip we had made many times. After we had left town and had gotten up to highway speed, I entered the distance to Hanover and checked the time of arrival. My younger daughter, Hilary, who was about six at the time, wanted to know what I was doing. So it told her I had told the computer how far it was to Hanover and it would tell us when we would get there. She wanted to know how it could do that, so I told her it knew how fast we were going and I had told it how far it was, and with that it could figure it out. “So what does it say?” she asks. “It says we’ll get there in about two hours,” I said. “Two hours?” she says. “Tell it we want to get there sooner!” Even six year olds have an intuitive understanding of DR navigation.

So I say, if you can’t not DR, why not do it right and have fun with it at the same time? Why do most of us fly, anyway? Is it just to get from here to there? Sometimes, yes, that’s what it’s for. And that’s fine and DR still has an important role to play there both in flight planning, for progress checks enroute, and as an ultimate navigational backup. But for many of us the main reason we fly is because it’s fun. The airlines will get you from here to there, if that’s what you need to do. But flying ourselves from here to there is fun. So put the fun back in navigation: you can’t not DR, so why try? Give the fly fishing of navigation a try, and enjoy the chaos.

*Based on a talk given at EAA AirVenture 2007, July 24, 2007, in the Sporty’s Pavillion.