Track error adjustments

The track plot below shows the first leg of our planned flight between Oxford and Tottenham. The green lines are the 10° drift lines and the pink marks along the track are the 10 nm distance marks. In this example the first three marks are distance from Oxford, the last three are distance from Warraway Mountain, and the longer mark is the track midpoint. For the colour blind amongst us the track is orange.

Instead of distance marks some navigators favour time marks at, say, 10 minute intervals. However time marks really don't co-relate that well with charts – time notations are more properly confined to the log.

As it is remarkably easy to set off in the wrong direction – reversed application of variation for instance – it is advisable to note a landmark as a means of verifying that, at the set course point, you really are setting off along the required track. The sun's position provides a gross indication of heading which will at least confirm that you are not flying the reciprocal course. Starting off in the wrong direction, without realisation, really makes progress monitoring difficult when you are flying over relatively featureless terrain. In addition a position fix must be acquired within 15 to 20 minutes of the set heading time.

At any time after departure, when the aircraft's position has been pinpointed and found to be off track, heading adjustments will be necessary: initially to regain the required track and then to maintain it or, alternatively, for a new heading to track directly to the next turning point. There are several methods for calculating and applying heading adjustments – and I suggest you may now find pencil and paper handy.

Double track error method

This is the recommended method if the position fix shows the aircraft to be less than halfway along the leg – hence the reason for marking that midpoint on the chart. The procedure is as follows:

      1.   Using the diverging 10° drift lines estimate the track error – the difference in degrees between the track required and the track made good. The track error is also referred to as the opening angle or sometimes as the drift angle. (The term 'drift angle' in this context is deprecated as it normally refers to the angular difference between the heading flown and the track made good.)

For example let's say, on our Oxford to Warraway Mountain segment, we find ourselves crossing the railway line at Trida and estimate the track error as 6° north of required track. i.e. the track made good is 077° magnetic. We log the time and note 24 minutes have lapsed since departing the set-course point.

      2.   Double the track error and add or subtract that value from the planned heading to arrive at the heading to regain track or the intercept. If the drift was to the right of track the new heading must be to the left of the original heading and, conversely, if drift was to the left the new heading must be to the right of the old. The time we must remain on this new heading, until intercepting the required track, is roughly equivalent to the time flown on the original heading.

Although we have used the terms 'left' and 'right' you will find it more helpful, when considering position, to think in terms of 'north', 'south', south-west' etc.

For example track error is 6° north [left] and original heading 079° magnetic, thus the heading to regain track is 079 plus 12 = 091° magnetic [096° compass] and we fly that for 24 minutes – the same time as that flown on the original heading.

      3.  After it is visually evident that the required track has been reached, or the required time has passed, subtract the track error and turn onto the new heading to maintain the required track and log the event.

For example the track error was 6° and the heading to regain track is 091° magnetic, thus the heading to maintain track is 091 minus 6 = 085° magnetic [090° compass] and we fly that until either a new position fix is obtained or we reach the waypoint.

Theoretically this method doesn't work if the position fix is past the halfway point because the point at which the required track is finally regained would be past the waypoint.

Track error/closing angle method

The recommended method if the position fix shows the aircraft to be more than halfway along the leg, or if you choose to fly directly to the waypoint at any time, is as follows:-

      1.   Using the diverging 10° drift lines estimate the track error or opening angle – the difference in degrees between the track required and the track made good. Then using the converging drift lines estimate the direct track to the waypoint and the angle between that track (the new required track) and the original required track. This is usually called the closing angle.

For example let's say, on our Oxford to Warraway Mountain segment, we fix our position as one mile south of the Dundooboo Ridge with an estimated track error of 7° north of required track and the closing angle to the waypoint is about 9°.

      2.   Add the track error and closing angle and apply the value as a correction to the original heading. If the drift was to the left of the required track the new heading will be to the right and vice versa.

For example 7 plus 9 is 16°, drift was to the left of the original heading 079° magnetic, thus the heading – to track directly to the waypoint – is 095° magnetic [100° compass] .

Flight direct to landmark

A third method might be employed if after getting a position fix a landmark known to be on, or close to, the required track is positively identified.

      •   Having pinpointed your position use the diverging 10° drift lines to estimate the track error, then fly directly to the identified on-track landmark. To maintain the required track it will be necessary to turn onto a new heading when overhead the landmark. The new heading will of course be the original heading plus/minus the track error.

Utilising the 1-in-60 rule

The 1-in-60 rule provides a rule of thumb based on the reasonably accurate assumption that the sine of any angle, up to about 45°, is equal to 0.1666 times (or 1/60) the number of degrees. e.g sine 30° is 0.1666 x 30=0.5 or 30/60 = 0.5.  The sine is the ratio – in any roughly right angle triangle – of the length of the side opposite the angle, to that of the hypotenuse (the longest side), thus the 1-in-60 rule is handy in the mental arithmetic of flight theory and basic navigation as the angles involved are usually less than 45°. For angles up to 15° or 20° the tangent (opposite side/adjacent side) is practically the same value as the sine.

This rule of thumb can be used to determine track error, given distance travelled and distance off track. It replaces the use of drift lines but the latter is much the easier method to use in flight because the angle is easier to estimate than the on-chart distance off track, and the mental arithmetic is easier. However, just to keep you informed, here is the 1-in-60 method for track error calculation.

      1.   Having pinpointed the aircraft's position, estimate the distance off track and the distance travelled along the leg. The track error = the distance off track [DO] divided by the distance travelled [DT] × 60. i.e. The track error = DO/DT × 60.

Or conversely the distance off track [DO] = track error/60 × DT

For example let's revert to our Oxford to Warraway Mountain segment where, after 24 minutes flight, we pinpoint our position at Trida. Trida is about 3 nm north of required track and 22 nm distant from the departure point. Thus 3/22 × 60 = 8° track error. The track error we estimated using the drift lines was 6°, but that's basic navigation for you.

      2.   To regain the required track double the track error and when the required track is reached, or the time has elapsed, subtract half the error and take up the new heading. In this aspect it's the same technique as the double track error method.

      3.   Or to track direct to the next waypoint calculate the closing angle – which will equal the distance off track [DO] divided by the distance to go [DTG] × 60. i.e.closing angle = DO/DTG × 60.

For example Trida is 52 nm distant from Warraway Mountain. Thus 3/52 × 60 = 3° closing angle. The new heading is the original heading plus track error plus closing angle = 079 + 8 +3 = 090° magnetic – as in the track error/closing angle method.

Each time the aircraft's position is pinpointed and the heading is adjusted, a re-calculation of the ground speed and ETI for the segment should be made on the running log: the 1-in-60 rule has use in this aspect of navigation, see section 7.4 below.

Diversions – 30° and 60° dog-legs

There is another navigation adjustment technique occasionally mentioned as a standard method of diversion around hazards or no-fly areas such as towns. As no such diversions would be necessary if the flight plan is properly prepared such techniques should be of practical use only when something of interest is spotted off track and you divert for a little sight-seeing.

The method is as follows:

      •   When you judge the point of interest is about 30° off your current heading alter course 30° towards the target. Note the time when the target is reached and then turn 60° in the reverse direction and fly that heading for the same time as the first part of the dog-leg, then revert to the original heading. The time lost during the two legs, and which has to be added to the ETI for the segment, is one third of the time flown on the first [or either] leg, and of course you have to add to the ETI any time spent circling over the target.

      •   The 60°dog-leg is much the same except that you alter course when the target is 60° off the original heading, the alteration to return is 120° and the time lost flying the dog-leg is the time spent on the first [or either] leg.

      For example if we were about halfway along our track from Oxford to Warraway Mountain and we thought it a good idea to have a look around the Warranary Hill. Thus we turn 60° left from our original heading of 079° magnetic to 019° magnetic, fly that for say 6 minutes then turn right 120° to 139° magnetic and fly that heading for 6 minutes. Then turn left 60° back on to our original heading of 079° and add 6 minutes to our ETI and/or ETA.