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Learning hub · General Navigation · Lesson 4

Dead reckoning, track error and position fixes

Dead reckoning means working out where you are from where you started, the heading you flew, your speed and the time. It is never exact, so the skill is in checking it against the ground, finding out how far off you are and correcting early with a small turn.

About 15 minutes, plus the quiz. Part of General Navigation. It follows the wind triangle.

1. What dead reckoning is

You choose a heading from the wind triangle, hold it, and count the minutes. From the heading, the groundspeed and the time you can say how far along the track you should be. Every part of that is a little wrong: the forecast wind is not the wind you meet, the heading wanders a few degrees, and the clock starts a minute after the wheels leave the ground. The errors do not cancel themselves, so the track you make good slowly drifts away from the one you planned.

Two habits keep this under control:

  • Check the ground against the plan at every point you can name: a town, a lake, a motorway junction. Do it at least every ten minutes.
  • Correct as soon as you see a trend, not after you have flown off the edge of the chart.

2. Heading, time and ETA

The navigation log has three numbers for each leg: the heading to fly, the groundspeed, and the estimated time interval (ETI, also called the estimated time en route). The estimated time of arrival (ETA) is the time you passed the last point plus the ETI to the next one.

Time = distance ÷ groundspeed × 60 (minutes, with groundspeed in knots and distance in nautical miles)

The ETA is a promise that you update. Each time you identify a point, write down the actual time, work out the groundspeed you really made over that stretch, and revise the ETA for the rest of the leg. If your groundspeed is 10 knots lower than planned you will be late, and you want to know that at 20 minutes out, not at 60.

3. Track error and closing angle

At a fix you can see that you are not on the planned track. Two angles describe it.

  • The track error is the angle between the planned track and the track you have actually made good since the start. It tells you how wrong your heading has been so far.
  • The closing angle is the angle, measured at your present position, between the planned track and the line from where you are to the point where you want to be back on it, usually the next turning point or the destination. It tells you how much extra you must turn to get there.

Both come from the one-in-sixty rule you met in the wind triangle lesson. One degree of angle moves you about one nautical mile sideways for every sixty nautical miles you go.

Track error ≈ distance off track ÷ distance flown × 60
Closing angle ≈ distance off track ÷ distance to go × 60

The rule is good to a few tenths of a degree up to about 20° of error. Beyond that, work from the chart with a protractor.

4. Regaining track

Turn first by the track error, and you fly parallel to the planned track: you stop getting worse, but you are still the same distance off. Then add the closing angle, and you converge on the planned track. When you have turned by the track error plus the closing angle you are flying straight to the point you chose.

Turn towards the track = track error + closing angle

There is a useful shortcut. If you choose to rejoin the track at the same distance ahead as the distance you have already flown, the closing angle equals the track error, so you turn by double the track error. Fly that heading until you are back on the line, then turn the other way by the track error alone to hold it.

Do not wait. A 3 nm error found 30 nm from the start is a 6° correction; the same error found 10 nm from the destination is a much bigger turn, and you have less time to see whether it worked. A small early correction is also the one you can make without leaving the area you planned for: airspace, high ground and the weather you briefed are all near the track.

Try it: set the airspeed, the wind along the track, how long you have flown and how far off track you are. The green line is the planned track and the dashed orange line is the track you made good. The grey dashed line is the heading that would keep you parallel, and the blue line goes straight from you to the destination. The two arcs are the track error and the closing angle, and the readout gives the turn and the revised time. Press a preset to start from a typical case.

This diagram needs JavaScript to move. The explanation above and the exercises below cover the same ideas.

5. Position lines and fixes

A fix is a position you are sure of: you are directly over a named town, or over the crossing of a railway and a river. It is the best check on the plan and the point from which the next leg starts.

Often you only have part of that. A railway that runs across your track tells you that you are somewhere on the railway but not where along it. That is a line of position. A second line of position that crosses the first, such as a road or the edge of a lake, gives a fix where they meet. Lines that run nearly along your track tell you about your sideways error but not about your progress, and lines that cross your track tell you about progress but not sideways error. Use both kinds.

  • Choose features you can recognise from the air and that are on the chart: rivers, railways, large roads, lakes, towns, wind turbines, masts.
  • Be wary of a single feature that looks right. Look for a second one that agrees.
  • At each fix, note the time, work out the groundspeed over the last leg, and revise the ETA and the fuel you expect to have left.

If the ground does not match the chart, stop forcing the plan to fit. Hold your heading, check the time since the last fix and read the position off the chart as a patch of ground, not a point: as a rule of thumb taught to student pilots, the error after a stretch of dead reckoning is up to about one-tenth of the distance flown. Then follow your school’s uncertainty of position procedure and see the lesson on Pan-Pan and lost communications for what to say and to whom.

6. A worked example

The leg is 80 nm. The planned TAS is 100 kt and the plan assumes no wind, so the planned time is 80 ÷ 100 × 60 = 48 minutes. All numbers in this lesson are invented.

After 20 minutes you identify a fix that is 30 nm along the track and 3 nm to the right of it. The groundspeed over that stretch was 30 ÷ 20 × 60 = 90 kt, so there was a 10 kt headwind component.

  1. Track error = 3 ÷ 30 × 60 = 6° right of the planned track.
  2. Distance to go along the track is 80 − 30 = 50 nm. Closing angle = 3 ÷ 50 × 60 ≈ 3.6°, call it 4°.
  3. To fly straight to the destination, turn left by 6 + 4 = 10°. To fly parallel only, turn left by 6°.
  4. The distance direct is about 50 nm (the 3 nm sideways adds almost nothing). At 90 kt that is 50 ÷ 90 × 60 = 33 minutes.
  5. The new time for the leg is 20 + 33 = 53 minutes against a plan of 48, so you will be about 5 minutes late. Check that the fuel still agrees with that.

The diagram above starts from these numbers if you press the second preset.

Dead reckoning is only as good as your last fix. If more than ten or fifteen minutes pass without one, treat your position as less certain and look harder, do not trust the arithmetic more.

7. Try it yourself

Work each one out on paper first, then open the answer to compare. The numbers are invented.

  1. After 25 nm along the track you are 2 nm to the left of it, with 50 nm still to go. Find the track error, the closing angle, and the turn to fly direct to the destination.
    Show the answer

    Track error = 2 ÷ 25 × 60 = 4.8°, about 5° left of the planned track.

    Closing angle = 2 ÷ 50 × 60 = 2.4°, about 2°.

    You are left of the track, so the turn is to the right, by the track error plus the closing angle: 5 + 2 = 7° to the right.

  2. You find a track error of 4° to the right after 20 nm. You want to rejoin the track in another 20 nm. How far off track are you, and how much do you turn?
    Show the answer

    Distance off = track error × distance flown ÷ 60 = 4 × 20 ÷ 60 ≈ 1.3 nm.

    Closing angle = 1.3 ÷ 20 × 60 = 4°. The distance to rejoin is the same as the distance flown, so the closing angle equals the track error and the turn is double it: 8° to the left. When you reach the track, turn right by 4° to stay on it.

  3. You leave A at 1000 on a leg of 80 nm. At 1030 you identify a fix 45 nm from A. What groundspeed did you make, and what is the revised ETA at B?
    Show the answer

    Groundspeed = 45 nm in 30 minutes = 90 kt.

    Distance to go = 80 − 45 = 35 nm. At 90 kt that is 35 ÷ 90 × 60 = 23 minutes, so the revised ETA is 1030 + 23 = 1053.

8. Check yourself

Five original practice questions. Answer them, press Check answers and read each explanation.

1. After 20 nm you find you are 2 nm off the planned track. About what is the track error?

Track error ≈ distance off ÷ distance flown × 60 = 2 ÷ 20 × 60 = 6°.

2. You are to the right of track and turn left by exactly the track error. What happens?

Turning by the track error makes your new track parallel to the planned one. To close the gap you must turn further, by the closing angle.

3. The track error is 4° right and the closing angle to the destination is 2°. What turn flies you direct to the destination?

You are right of track, so you turn left, by the track error plus the closing angle: 4 + 2 = 6°.

4. You leave at 1000. At 1030 a fix shows 45 nm flown of a 90 nm leg. What is the revised ETA, assuming the same groundspeed?

45 nm in 30 minutes is 90 kt. The remaining 45 nm takes another 30 minutes, so the ETA is 1130.

5. A single railway crossing your track at right angles gives you:

One line is not a fix. It does tell you how far along the track you are. A second line that crosses it, or a named point on it, turns it into a fix.

Next: time, speed, distance and magnetic variation if you have not read it yet, or back to the learning hub.

For training and situational awareness only. Not certified for navigation. Always use official charts, the AIP, NOTAMs and a proper weather briefing for real flights.