Returning to track
Once a reliable fix shows that the aircraft is off the planned track, the 1 in 60 rule provides a measured correction. The pilot can regain the old track by a chosen point or fly a new track directly to the destination.
Planned track, track made good and heading
The planned track is the intended path over the ground. Track made good, commonly shortened to TMG, is the line actually followed over the ground from the last reliable on-track position to the fix. The track error angle is the angle between planned track and TMG.
Heading is the direction in which the aircraft nose points. Drift is the angle between heading and track. Track error is therefore not drift. Expected drift is the angle between heading and planned track, while actual drift is the angle between heading and TMG. A track error can arise when the actual wind differs from the forecast wind, when the heading was not held accurately, or when the previous turn was inaccurate.
Before making a correction
- Hold a steady heading while confirming the fix. Do not chase an uncertain position.
- Decide which point is the last reliable on-track position.
- Measure distance gone along the planned track and distance off perpendicular to it.
- Identify whether the aircraft is left or right of track.
- Choose whether to regain the original track or proceed directly to a future point.
Drift Correction
| Angle | Formula | Purpose |
|---|---|---|
| Track error angle | 60 x distance off / distance gone | Stops the existing divergence and makes the aircraft parallel the planned track |
| Closing angle | 60 x distance off / distance to go | Turns the parallel path towards the selected point on the planned track |
| Total heading alteration | Track error angle + closing angle | Combines both actions into one turn at the fix |
For small corrections the rapid method assumes that a heading change of a given number of degrees produces approximately the same change of track. In reality the drift also changes slightly after a heading change, but the approximation is suitable for normal visual navigation corrections.
Double Track Angle Error Method
If the fix is obtained halfway to the point where the aircraft must be back on track, the closing angle equals the track error angle. The first heading alteration is therefore twice the track error.
Why merely cancelling the error is not enough
Suppose the aircraft is 4 NM left of track after 30 NM. The track error is 8 degrees left. A turn of 8 degrees right stops the divergence, but only places the aircraft parallel to the planned track, still 4 NM left of it. A further closing angle is needed.
If the aircraft is to regain track after another 30 NM, the return triangle is the same size as the error triangle. Its closing angle is also 8 degrees. The turn at the fix is therefore 8 degrees to cancel the track error plus 8 degrees to close, giving 16 degrees right.
What to do at the intercept
At the planned track the aircraft must remove the closing angle. In the example, turn 8 degrees left. The aircraft then remains on track on a heading 8 degrees right of the original heading, which compensates for the wind that caused the first error.
| Stage | Heading action | Result |
|---|---|---|
| Fix obtained | Turn 16 degrees right | Cancels 8 degrees of left track error and adds 8 degrees of closing angle |
| Return leg | Hold the corrected heading for the same time used outbound | The aircraft closes through the equal triangle |
| Track regained | Turn 8 degrees left | Removes the closing angle and leaves a net 8 degree right correction |
Track Error Angle and Closing Angle
When the aircraft should fly directly from the fix to the destination, or when the remaining distance differs from the distance already gone, calculate a separate closing angle.
Closing Angle and the distance split
Distance gone and distance to go must be measured along the planned track. Their sum is the total leg distance. Distance off track is perpendicular to the planned track. The same cross-track distance forms the opposite side of both the error triangle and the closing triangle.
Total Correction to destination
A leg is 78 NM long. After 30 NM, a fix places the aircraft 4 NM left of track. Distance to go is 78 minus 30, which is 48 NM.
- Track error angle = 60 x 4 / 30 = 8 degrees left.
- Closing angle = 60 x 4 / 48 = 5 degrees.
- Total heading alteration = 8 + 5 = 13 degrees right, towards the track.
The first 8 degrees stops the left divergence. The remaining 5 degrees establishes the track from the fix to the destination.
Regaining track after a chosen distance
The destination need not be the return point. If the aircraft is 5 NM left after 50 NM and the pilot wants to regain track 30 NM farther ahead, track error is 60 x 5 / 50 = 6 degrees and closing angle is 60 x 5 / 30 = 10 degrees. Turn 16 degrees right at the fix. At the intercept, turn 10 degrees left to remove the closing angle, leaving the required net 6 degree heading correction.
Combined Track Error Angle and Closing Angle Single Calculation
The track-error-plus-closing calculation can be collapsed into one step when the closing angle and the fraction of the leg already flown are easy to see.
Derivation of the shortcut
Let the total leg distance be D, distance gone be G, distance to go be R and distance off track be X. Track error is 60X/G and closing angle is 60X/R. Adding them produces the same total correction as multiplying the closing angle by D/G.
Equivalently, estimate the fraction of the leg already flown, invert that fraction, then multiply by the closing angle.
| Fraction of leg flown | Invert the fraction | Total correction |
|---|---|---|
| One quarter | 4 | 4 x closing angle |
| One third | 3 | 3 x closing angle |
| One half | 2 | 2 x closing angle |
| Three quarters | 4 / 3 | 1.33 x closing angle |
The 78 NM example in one calculation
The aircraft is 4 NM left after 30 NM of a 78 NM leg. Distance to go is 48 NM, so the closing angle is 60 x 4 / 48 = 5 degrees. The combined correction is 5 x 78 / 30 = 13 degrees. This is the same result as adding the 8 degree track error and 5 degree closing angle.
When the shortcut is quickest
The method is particularly fast when the fix lies close to one quarter, one third or one half of the leg. If the fraction is awkward, calculating track error and closing angle separately is often less prone to mental error.
Direction never comes from the arithmetic alone. If the fix is left of track, the correction is right. If the fix is right of track, the correction is left.
Using These Methods Practically
Good preparation reduces airborne arithmetic. Angle guides and distance-to-go marks allow the pilot to recognise a correction directly from the chart.
Preflight chart preparation
Five-degree and ten-degree guidelines can be drawn from each end of the planned track, but a full set may clutter the chart. A practical arrangement is one 10 degree guideline at each end. Mark distance to go at 10 NM intervals, because that is the denominator needed for the closing angle. The same 10 NM spacing also provides a useful scale for judging cross-track distance.
| Chart mark | What it gives | Airborne use |
|---|---|---|
| 10 degree guide from departure end | Approximate track error | Compare the departure-to-fix line with the guide |
| 10 degree guide from destination end | Approximate closing angle | Compare the fix-to-destination line with the guide |
| 10 NM distance-to-go marks | Remaining distance without subtraction | Use directly in the closing-angle calculation |
New Track Reference
New Track Reference treats the line from the confirmed fix to the destination as the new desired track. First estimate how much of the original leg has been flown. Invert that fraction and multiply it by the closing angle. Apply the result towards the destination.
A second fix establishes another new reference
After the first correction, a later fix may show that the aircraft is displaced from the new fix-to-destination track. Repeat the process using the new track, not the original one. Estimate the fraction travelled from the first fix to the destination and measure the new closing angle to the destination.
For example, the first fix is one quarter of the way along the original leg and gives a 5 degree closing angle. The initial alteration is 4 x 5 = 20 degrees towards the destination. A later fix halfway along the new track gives a new closing angle of 2 degrees. The further alteration is 2 x 2 = 4 degrees towards the destination.
Worked in-flight corrections
The following examples show distance, time and direction handled together. Keep the left or right sense beside every intermediate answer.
Example 1: a direct correction from a pinpoint
An aircraft is 11 NM left of track after 85 NM on a 160 NM leg. Distance to go is 75 NM.
- Track error = 60 x 11 / 85 = 7.8 degrees left.
- Closing angle = 60 x 11 / 75 = 8.8 degrees.
- Total correction = 7.8 + 8.8 = 16.6 degrees right.
The values are close because the fix is near the halfway point. At exactly halfway the two angles would be equal.
Example 2: correction using time
An aircraft has flown for 2 hours 40 minutes at 360 kt groundspeed and is 30 NM right of track. Remaining flight time is 45 minutes at 240 kt. The original heading is 358 degrees.
- Distance gone = 360 x 160 / 60 = 960 NM.
- Distance to go = 240 x 45 / 60 = 180 NM.
- Track error = 60 x 30 / 960 = 1.9 degrees, rounded to 2 degrees right.
- Closing angle = 60 x 30 / 180 = 10 degrees.
- Total correction = 12 degrees left. New heading = 358 minus 12 = 346 degrees.
Example 3: a complete Oxford-style leg
A 96 NM leg has planned track 250 degrees, heading 260 degrees and groundspeed 180 kt. Twelve minutes after departure, the fix is 3 NM right of track.
| Step | Calculation | Result |
|---|---|---|
| Distance gone | 180 x 12 / 60 | 36 NM |
| Track error | 60 x 3 / 36 | 5 degrees right |
| Track made good | 250 + 5 | 255 degrees |
| Distance to go | 96 minus 36 | 60 NM |
| Closing angle | 60 x 3 / 60 | 3 degrees |
| Direct correction | 5 + 3 | 8 degrees left |
| New direct heading | 260 minus 8 | 252 degrees |
If the double-track-error method is chosen instead, turn 10 degrees left to heading 250 degrees. After another 12 minutes the aircraft reaches the planned track. Then turn 5 degrees right to heading 255 degrees, the original heading corrected for the track error.
More worked checks from the source chapters
| Given | Working | Answer |
|---|---|---|
| 20 NM off, 600 NM gone, 300 NM to go | TE = 60 x 20 / 600; CA = 60 x 20 / 300 | 2 degree TE, 4 degree CA, 6 degree total correction |
| 15 NM off, 225 NM gone, 135 NM to go | CA = 60 x 15 / 135 | 6.7 degrees, rounded to 7 degrees |
| 20 NM right, 600 NM gone, 240 NM to go, heading 270 degrees | TE = 2 degrees; CA = 5 degrees | 7 degrees left, new heading 263 degrees |
| 7 NM right after 35 NM on a 95 NM leg | TE = 12 degrees; CA over 60 NM = 7 degrees | 19 degrees left; drift cannot be found because heading is not given |
| Track 074 degrees, heading 065 degrees, 4 NM left after 30 NM on a 70 NM leg | TE = 8 degrees left; CA = 6 degrees | TMG 066 degrees, expected drift 9 degrees right, actual drift 1 degree right, turn 14 degrees right to heading 079 degrees |
Where a whole-degree heading is required, Bali's worked method rounds a fractional correction to the next whole degree. Always preserve the left or right sense before applying the rounded value.
Choosing the right correction
Each method uses the same geometry. The best choice depends on where the fix occurs, where the aircraft must next be on track, and how much reliable information is available.
Method selection
| Situation | Use | Reason |
|---|---|---|
| Fix is halfway to the required return point | Double-track-error method | The return triangle equals the error triangle, so closing angle equals track error |
| Fly directly from the fix to destination | Track error plus closing angle | It uses the actual distance gone and distance to go |
| Fraction of leg flown is obvious | Combined calculation or New Track Reference | Multiply closing angle by the inverted fraction |
| Return to track at a nominated point | Track error plus chosen closing angle | Use fix-to-intercept distance as the closing denominator |
| Fix is past halfway and destination is near | Direct-to-destination correction | Doubling the track error would regain track beyond the destination |
Direction and reasonableness checks
- A fix left of track requires an initial turn right, towards track.
- A fix right of track requires an initial turn left, towards track.
- Closing angle grows as distance to go becomes shorter.
- Track error grows when the same distance off occurs after a shorter distance gone.
- At halfway, with destination as the intercept point, track error and closing angle are equal.
- After regaining track, remove the closing angle, not the whole correction.
Common errors
| Error | Why it fails | Correct action |
|---|---|---|
| Calling track error drift | Drift needs the heading as a reference | Keep planned track, TMG and heading as three separate lines |
| Using total distance for both angles | Neither triangle has total distance as its adjacent side | Use distance gone for error and distance to go for closing |
| Turning only by track error | The aircraft merely parallels the track | Add a closing angle |
| Using the old track after a second fix | The first correction created a new reference line | Measure from the new fix-to-destination track |
| Correct arithmetic, wrong direction | The numerical angle carries no left or right sense | Sketch the fix and turn towards track |