The 1:60
Whilst it may be fashionable to denounce anything that requires thought and structure as a futile waste of effort; the infringements of controlled airspace, danger areas and Red Arrows displays continue and from reports are getting worse. Sadly and most important pilots also become lost and spatially disorientated flying into all sorts of things, the results of which can become tragic.
Whether some of you like it or not structured navigation training is crucial for the basis of by whatever means you navigate. There are of course many ways to skin a cat and just as many navigation techniques. That doesn’t matter; the important thing is that a methodical structure is taught. GPS is based logically using Radians, i.e. 1:60 and Descartes grid, so the pilot should have a basic understanding of the use of the rule just the same when using a GPS and should it fail.
Use of the 1:60 as a working base to navigation is perhaps the simplest available. The number 60, as said, is a rounded up Radian. The actual definition of a Radian is; that its angle subtends the length of arc. To see this; draw a circle and from the centre of the circle draw two lines 60 degrees apart. Between the two points that each line crosses the circumference take a measurement. Compare this measurement to the length of each line (radius). You will discover that the length of the arc is almost the same as the length of each of the two lines. I say almost because the circumference is of course an arc, a curving line. Reduce to angles of less than 20 degrees and discover that the difference between the arc and the straight line is impossible to measure on a standard chart. Incidentally 20 degrees is one third that of 60 so therefore the distance off track would be one third off the distance gone.
Treat one radius line as the intended track and the other as the track made good. At a point 24 miles along the intended track take a measurement between the two tracks and divide the distance gone by the distance apart which we will say equals 2 miles.. E.g. 24 miles flown is divided by 2 miles off track which equals a ratio of 12. Divide the radian 60 by the ratio 12 = 5. You are 5 degrees off track. The1:60 formulae commonly given in the text books is to divide distance off by distance gone and multiply by 60 (2\24x60 = 4.999). You may also divide the degrees off track into 60 to find the distance in miles that you are off track. 60\5 = 12 therefore 24\12 = 2 miles off track.
The simplest way is to pre-determine the points along the track where you will assess your progress known as a ‘pinpoint’ or ‘mid track fix’ which doesn’t have to be half way or quarter way, and draw 5 or 10 degree fan lines abeam the point – no need for any sums other than to double or treble the track error as appropriate to regain track. You will regain track should you double the error in exactly the same time and distance or by trebling the error in half the distance and time. You will now have a point and an ETA to regain track.
The 1:60 allows for velocity as well simple angles. Your aircraft is flying at 100kts with a wind 90 degrees across at 20kts. 100\20=5 therefore 60\5 = 12, your drift is 12 degrees. All sorts of navigation problems can be understood by understanding Radians, the 1:60 rule.