Lis is a highly respected member of the x-pilot.com forums whose knowledge of pilotage is legendary in the X-Plane world. He's written a wondrous guide to that blackest of the pilot's art, ded reckoning (reproduced and edited below with lis' permission. The URL for the original article is [ http://forums.x-pilot.com/index.php?topic=1377.0 ] should you want to diff them). Read it, you will learn things:
Prerequisites: what?First, let me say that there are no special skills or magic when it comes to this type of navigation. In fact, you have all the skills you need already or should develop them anyway as a part of good airmanship. This tutorial assumes that you can hold a heading within +/- 5 degrees, maintain level flight within +/- 50 feet and fly at constant airspeed within +/- 5 knots from desired values. You can use autopilot in heading and altitude hold modes if you like, and practice your manual flying skills another time, but if you want to fly manually, proper trimming of the plane is absolutely crucial! You really don't want the plane to do aerobatics on it's own when you let go of the controls to make calculations or consult with the map. Also, I'm going to deliberately "forget" about a few additional things in order to make this tutorial as easy as possible and to keep myself on the topic. All right, are you ready to walk in the footsteps of the great aviation pioneers?
When you don't reckon, you're deadYou may have seen the term "dead reckoning" and have read all kinds of jokes and more or less funny sentences based on that term. In fact, the proper name of this navigation technique is "ded" - from deductive. Like a detective, you have some clues and with their help you try to deduct your position in space, with regards to your planned route. In my native language it's called "calculative navigation", because you have to use known values, like time, distance and speed, to calculate actual position in relation to takeoff or beginning of route point. Whatever the name, the overall concept is in fact simple.
Three amigosYou may have noticed that airspeed is always expressed in distance per time format. Even knots are in fact nautical miles per hour. That means if you fly, for example, at 100 knots you cover 100 nautical miles in an hour. The same distance could be flown in 30 minutes at 200 knots, or flying at 50 knots would require 2 hours to cover it. As you can see, there is a direct relation between the three values airspeed, distance and time of flight, but what is even more important is that you can always calculate a missing third value in cases where you know only two of them. Have you ever wondered what to say when ATC asked for ETA to a waypoint? Or how much fuel you need to load, knowing distance from the map and your speeds and fuel consumptions from POH? Right
D-recko's LairOk, time to get down to business. Take your map and choose two airfields: take-off and landing. Forget about transatlantic routes for now
- Honolulu PHNL to Molokai PHMK will be enough. My map says that the distance between them is 47,5NM and that the heading required to fly to Molokai is 92 degrees. Even if you're lazy and prefer to fly staight 'n' easy East, it won't make a difference for such short flight. Let's assume that we're going to fly a Cessna 172 Skyhawk; it is very popular training plane, with a nice 100KIAS cruise speed. This will make our task a lot of easier.
So, we take off from Honolulu, point the nose directly east and now what? How long do we have to fly that direction - there are other islands around, other airfields, how would we know that we're at the right spot when it comes to landing? In order to do that, we have to calculate flight time. I usually cheat at this point and grab my E6-B flight computer (yeah, a real one) and it says 28 minutes 24 seconds. A quick memory check - at 100 knots we'll need about 30 minutes to cover about 50 nautical miles, so that looks good, but before I finally got the E6-B, I had to use a regular battery powered pocket calculator to get enough accuracy with calculations than would be possible with my head alone, already overloaded with trying not to fall out of the sky
The method to do it is as follows:
Our speed is 100knots (100 nautical miles in 1 hour), which is equal to:
100miles in 60 minutes
Our problem is:
47,5miles will take how many minutes?
So we set up a simple equation:
100miles - 60 minutes47,5miles - x minutes
Now we rearrange it:
100 * x = 47,5 * 60
x= (47,5 * 60) / 100
x= (pocket calculator online...) 28,5 minutes
If you want to convert this 0,5 minute into seconds, all you have to do is to multiply it with 60:
28 minutes 30 seconds.
Now, usually you don't need the seconds, 28 minutes will suffice, but on longer flights minutes become hours and seconds become minutes, and suddenly it is vitally important to know if it is 15 minutes or 30 minutes and the methods to convert decimals to minutes is the same. 1,35 hour? 1 hour 21 minutes. 2,7 hours? 2 hours 42 minutes.
So, now we're flying a hot racing piston at 275kts and the race course is 10,5 nautical miles long. How long it would take to complete the track?
275miles - 60 minutes10,5miles - x minutes
x= 2,29 minutes = 2 minutes 17,4 seconds from start to finish. Pretty hot, alright!
And that's it - you fly on a specific heading, at a specific airspeed, for a specific time and every time you'll arrive at your destination no sweat, no lame GPS, no crazy NDBs & VORs
A word of caution: you really want to use your simulator's clock. Simulations don't always run at exactly the same speed as real time and the differences that inevitably build up during a flight can and will bite you at some point.
Always use sim-time for navigational calculations!
Now you're ded reckoning apprentices. Planes with just a compass, airspeed indicator and a clock suddenly become fully equipped
Let's have a short break with some of the best planes from a more civilised and elegant navigation era
Say airspeed. What airspeed?As you may know, the higher you fly, the thinner air becomes, which in turn has some important effects on your plane. One of them is the higher you fly, the more the airspeed indicator is lying to you, because in reality it doesn't measure how fast you fly, but how strong the airflow is beating against the Pitot tube. So, the thinner the air, the more gentle the beating, and less airspeed indicated on the gauge. Hence the name - Indicated Air Speed (or IAS).
Smart folks quickly recognized that the airspeed indicator is lying at altitude and they invented another type of airspeed - a true airspeed (as opposed to lying airspeed, I guess...), which means how fast you are flying over the ground, and that is the airspeed we're going to use during navigation calculations. Now, the problem is: how do we know the true airspeed? Easy
For navigation fanatics, there is the E6-B... For normal folks, there is a simple and effective calculation that is accurate enough for everyday flying and for our purposes.
Read your altitude from the gauge, divide it by 1000 and multiply by 2. The number you've got is a percentage of IAS you need to add in order to get TAS. So, let's just say we're doing 100KIAS at 10000ft. That's 100KIAS + 20%. So the TAS is 120knots. If we were in a Corvalis, doing 163KIAS at 18000ft, then TAS would be 222knots. Cool, eh?
Reality check: this is not the most accurate method of estimating true airspeed, but the most easy and efficient one. Also you remember that it's accurate for a standard day, as the IAS/TAS relationship depends on the air temperature at altitude, because temperature affects pressure and thus the beating the Pitot gets. The colder the day, the less the IAS/TAS difference, and the hotter - the greater. My E6-B says that for the 100IAS-120TAS example to be true, the air temperature at 10000ft needs to be +10C or +50F.
Tokyo Drift styleSo far, all of our exercises have assumed a windless, calm day. However I'm yet to see that in the REX or XSquawkbox weather systems
Winds are the most irritating part of navigation, but they also make it so much more challenging and addictive; the feeling of accomplishment after you've prevailed over the winds trying to push you off track makes up for all the hair pulling and stick yanking you've got during the flight.
The way you're going to fight the winds depends on whether you know their direction and strength or not. Since there is always plenty of weather information in flight simulators, we're going to concentrate on the known winds techniques.
As you may have guessed already, an E6-B can calculate winds for you and it will even be so nice as to tell you how many degrees you have to add or subtract from your heading in order to stay on track. However for the purpose of this tutorial, we'll do it the old school pocket calculator way. Even an abacus with beads will be fine, unless you fly in turbulence
Mastery Of The WindsThe greatest evil the winds can do to you is to push you off-track. Even if you have maintained perfect airspeed and heading, for a precise amount of time, you end up everywhere but your intended destination. Since you don't have the help of purple GPS line nor VOR radial needle, you will have to calculate how much influence the wind is having on your plane in order to counter it. The method I'm going to show you is again not the most accurate, but more than enough and actually easier to perform on-the-fly, so to speak.
First, for the simplicity, let's consider that the wind is blowing at 90 degrees from our intended heading. Remember that Hawaii scenario? We're flying 90 degrees and the winds are from the south, 180 degrees. In order to stay on track, we have to point the nose to the right, but by how much?
Let's assume the we're flying so low that IAS=TAS, at 100knots and with winds blowing at 10knots. The formula to calculate required "counter=heading" is TAS/10/6=a; wind_speed/a=degrees to turn INTO the wind in order to maintain desired ground track.
So:
100/10/6=1,66; 10/1,66=6 - the required correction is 6 degrees, so we need to fly 98 degrees of magnetic heading in order to reach Molokai (remember, that the real heading was 92 degrees? In our previous iteration we could let go off the two, but now 2+6=8, which is almost 10 degrees - a considerable error in ded reckoning, which could become nasty even on short flights).
Another situation, we're flying the same trip, but this time at 20 000ft, 120KIAS and the winds are from the south at 38 knots.
120KIAS + 40% = 168KTAS
168/10/6=2,8; 38/2,8=13,5 - now we need to fly heading 105 (decimals of 0,5 or lower are converted to the lower full degrees, over 0,5 are converted to higher full degrees). Had the winds been from the North, we would have to fly 92-13=79 degrees of heading. Piece of cake
(unless the calculator batteries go down... Does anyone on-board have an E6-B manual?)
All right, before we take the final last brain twist, let's have a break:
This time DON'T even think of clicking any of the "related videos" and get back to the class ASATME (as soon as the movie ends)!
Let's twist again, like we did last summerNow, as you may know, winds rarely cooperate and they tend to blow from every possible direction, mostly from the forward plane hemisphere, to kill as much of TAS as possible. How can we defend against it? Again, the E6-B flight computer does all the maths, but often I just use a premade chart that is printed on my kneepad. However, before I got all the goodies, the pocket calculator and a little bit of math magic did the trick.
Actually, after all these explanations, this last part of this tutorial is quite easy. First you need to calculate the heading correction as if the wind was blowing perpendicularly to your plane. That's called "maximal wind correction angle" (or something like that, as I'm translating it from Polish. It's funny, because part of what I know is in Polish and part is in English, with not everything overlapping between the two of them). Since the wind is blowind at some angle, only part of it's strength is used to push you off track and the rest is used to increase or decrease TAS, but how much of the wind does what? It could be precisely calculated but for our purpose it's enough if we use the following simplified chart.
| Hdg Difference | Percentage |
| 0 or 180 | 0 (all the wind is used to slow you down or speed you up) |
| 30 or 150 | 50% |
| 45 or 135 | 70% |
| 60 or 120 | 90% |
| 90 | 100% (perpendicular, described previously) |
On the left you have the difference between desired heading (or ground track) and wind direction. For example, heading of 20 degrees and wind from 135 would produce a difference of 115 degrees. On the right is how much percentage of the wind is being used to push you off-track.
So, our 115 degrees of difference between desired heading and wind direction means that we use a value of 90% as the closest one. The remaining 10% of wind speed affects TAS and TAS with the added wind effects is called ground speed or GS. That's the speed usually displayed on your GPS, but now you don't need satellites to know that
The chart may look counter-intuitive; it would seem that an angle difference of 45 degrees should produce 50% wind difference, but I guarantee that the chart is correct.
What about the speed? Take note of the ground speed and calculate the fuel amount and fuel flow against it; it may be necessary to land earlier if you have a small reserve and strong headwinds. Don't just add power to counter headwinds, as you'll move the engine out of it's economic power range, making fuel usage even worse. Also, don't tslow down (with tailwinds), as that will also be less effective and you may even stall the plane, especially at higher altitudes. Just fly as usual, at normal cruise power settings, taking into account time differences over subsequent waypoints than planned, as well as a different overall flight time. If, for example, winds took away 10% of the airspeed from you, recalculate time to next waypoint being 10% longer and fuel burn being 10% higher. Need to fly a leg for 20 minutes? Then fly it for 22 and you'll arrive on mark, just a little bit later. Fly the plane and calculate where you actually are, not where the flight plan says you should be.
One last bit of advice: don't try to fly ded reckoning for more than 200-300NM at a time. Over that you'll enter a world of great circle navigation and changes in magnetic variation during flight, both of which will seriously complicate your life. Either fly shorter trips, or divide a long flight into shorter legs, with distinctive land features along the route, like lakes, cities, rivers, mountains and so on, to help you fix actual position and correct any errors that arise. During a recent long An-24 flight I had a radar that showed me the drift angle - all I had to do was to turn heading knob by the same amount of degrees. And the gyro-inductive compass has taken care of great circle and magnetic variations problems. That plane was the right tool for the job, even without GPS and that's the real secret behind the success of that flight. By the way, it was very similar to what Lindbergh did, just the details were different.
HOMEWORK!Load your simulator and go to Midway Atoll PMDY. Set real weather (with whatever winds you'll get along with it) and fly a default Cessna 172/182. In order to maximize range and endurance, fly at 2300RPM, higher than or at 6000ft and lean accordingly. IAS will be around 100mph (=87knots). You can squeeze many hours of flight out of it
Exercise 1Fly to Kure Island Seaport (it has a runway also). Course (=desired track) 275, distance 50NM. Then back to Midway.
Exercise 2There is a group of small islands nearby, find them and fly back to Midway. Course 95 to the islands, distance from Midway 84NM.
Exercise 3A classic "navigation triangle". Take off from Midway and fly for 20 minutes course 120, then 20 minutes course 240 and last 20 minutes course 360. See if you can make it back to Midway
If you like, we could do it on Vatsim next weekend, with BK117 ready for the rescue, should something unfortunate happen
Also you could post screenshots from the location map, to show how you did with the homework
Ta-Da!Now you're the master of ded reckoning
It's lengthy to describe (all right, half of this tutorial is actually me trying to stay on topic, instead of writing anything useful
) and it seems a little bit complicated at first (try Orbiter freeware space simulator if you haven't had enough flying by mathematics for today
) but ded reckoning in it's essence is very simple and rewarding - it's easier than mastering a real Garmin 1000 (or so I've been told...). Thanks for reading and above all - enjoy your new skills
See you in the airspace!
NOTE: This "version" of lis' article has been edited for grammer, typography and spelling (lis is Polish, so I forgive him ).
(And a tiny bit of advertising - pilots in the UK that want a real E6-B flight computer could do worse than looking at TransAir [ http://www.transair.co.uk/ ], it's where I bought mine, and my UK 1:250,00 charts. )
