Aero Circus | The 1 in 60 rule: Part 1

The unthinkable long shot

Love it or hate it, in Australia the aviation regulator still thinks that navigation using 1 in 60 is a necessary skill for all pilots to have. Given the proliferation of electronic flight bags, it’s probably going the way of the VHS recorder. But technology sometimes does fail.

History

The 1 in 60 rule is a basic rule-of-thumb aerial navigation skill. To the best of our (limited) knowledge, it’s not widely taught as such anywhere except in Australia. It does appear in some North American publications but does not seem to command the same level of importance as it does down under. This is likely because in Australia there is no other way to get it right if electronic navigation aids fail (you can guarantee this will ‘happen’ during a flying test).

The 1 in 60 rule has likely flourished in Australia as we have vast expanses of nothing between places. Of course, I am talking about the interior of the country. We can usually track in a straight line between most places (DCT). In many European countries military airspace is everywhere and needs to be avoided (unlike ours, these are usually full-time no-go zones). There are also major airport airspaces, towns, mountains, poor weather, etc to avoid.

In Europe, a fixed-wing pilot will usually follow the road like a helicopter pilot. In the US, they used to go from navigation aid to navigation aid. I’m not sure of the continuing availability of VOR and NDB services around the world, but they are certainly disappearing in Australia. This is because they been overtaken by the GNSS.

According to the regulator, the WWII technologies of NDB and VOR are not much good anymore. Some pilots trained before the rise of the computer tend to disagree. I have heard that computer technology is a fad and it is going to go away. Seriously. This statement was made by the same people who claim that using a GPS for navigation is cheating.
Following a road or going from one reference point to another is a technique very useful for a helicopter pilot. This is because they have only two hands, at least one of which is required to be on the controls at all times (I can only speculate as to what they do with the other one).

Practical usage

The 1 in 60 rule can be very easily used in flight. The only pilot requirements are to fly in a straight line at a constant speed. Of course, this is easier said than done, especially for low-hour pilots. This also assumes that the wind is constant throughout the exercise. Obviously, a little variation here and there with speed, direction and wind strength will not have a huge impact on the effectiveness of the technique. But the closer to a ‘stable’ flight that can be achieved by the pilot, the better the results will be.

Defining the terms used

Let’s refresh our understanding of some basic navigational terms used in this article.

• Track
  The straight line between where you started and where you would rather be is called the flight planned track (FPT). Students of Jim Davis may know it as the required track. The line between where you started and where you are now is called the TMG, or track made good.
• Heading
  Where you need to point the nose of the aircraft so that it actually flies along your flight planned track when the wind thinks it should go somewhere else. Usually abbreviated to HDG.
• Course
  In the US this means track and in the UK it means heading. In Australia it means another serving of food and in the interests of clarity is best kept that way by Aussie pilots.
• Variation
  This is the difference between true north and magnetic north and varies depending where on the planet you are flying. The 1 in 60 rule relies on magnetic direction (not true direction) as it uses the compass (or DG) for reference. Therefore, when measuring tracks off aeronautical charts you must adjust for the Variation as shown by the isogonals on the chart for the area you are flying through. The mnemonic “East is Least, West is Best” may help you to remember whether to add or subtract the variation from the true direction to determine the magnetic direction.

• 

• Drift
  This is the difference (in degrees) between the Heading that you steered and the track made good that resulted. Usually caused by Mother Nature. As well as wind strength and direction at the time, its effect varies with your true airspeed (TAS), i.e., the slower your TAS the more drift will result for a given wind strength.

• Track Error
  This is the difference (in degrees) between the flight planned track that you wanted to follow and the Track Made Good that you actually followed. Usually caused by humans.Track error is the difference between where the aircraft is supposed to go and where is actually goes.

Reasons behind

Before we move on, let’s examine the reasons behind why a constant heading and speed are important for the 1 in 60 rule.

• Constant heading
  We may be tempted to think that if we can identify our starting point and current position on a map, we can draw a line between the two and there’s our heading. Alas, that would be our TMG, not our heading. We still have no idea where the aircraft was actually pointing in order to result in the TMG we achieved. There is no other way to determine our heading other than by flying the aircraft in a straight line based on our compass (and DG) readings. Therefore, if we were forced to deviate from a constant heading for any reason (e.g. due to cloud) then the 1 in 60 rule may be of little use for that segment of the flight.
• Constant speed
  Surely we could fly at any speed and the maths would still work out? In a nil wind situation this would be true. But as we vary the speed at which we are flying, the impact of any crosswind component on our TMG will also vary. Incidentally, in a nil wind situation, 1 in 60 would be of much less use as there would be no drift.

Using a simplified example, if we fly slowly at, say, 60 kt for the first 10 minutes (the blue line above), we have travelled 10 NM and the strong winds today might push us 4 NM off track (point C above). Then if we fly at twice that speed (120 kt) for the second 10 minutes (the red line above) on the same heading, we will cover twice the distance (20 NM) in this period. However, that same wind will still push us off track by the same 4NM (point D above). The different speeds will clearly result in different angles (and therefore TMG’s) as shown above. For the purposes of 1 in 60, the average resulting TMG angle (shown in green) is not related to either previous (red or blue) angle.

Correcting an errant flight path

From the weather forecast, we (think we) know the wind speed and direction. We can then use the 1 in 60 rule to make heading corrections when the weather forecast is inaccurate — which is most of the time. It’s better airmanship to expect the forecast to be inaccurate than expecting it to be right. The lesson from this? Only use weather forecasts as a starting point and be ready to adjust inaccuracies with 1 in 60 or resume your own navigation if it’s completely inaccurate.

As pilots we make calculations and all the preparations necessary for a particular flight. When it is time to implement these in the air, we often find that the calculations do not work. We now require a new set of tools so that we can continue with the flight with some dignity. This is where the skills of map reading and revising our heading using an easy technique like 1 in 60 comes in.

Maths behind 1 in 60

Let’s get to the reasons behind this rule. It is called 1 in 60, but why not 1 in 80 or 1 in 1,000? Where does the 60 come from? The answer is very simple — let’s go back to some basic school arithmetic and a little bit of geometry.

The red line is at a 1⁰ angle to the blue line. Therefore, the distance between the red and blue lines at the circumference is 1/360th of the total circumference.

• A full circle consists of 360 degrees.
• π (Pi) = 22/7.
• The circumference (C) of a circle is π multiplied by the diameter (D). You may have learned this as “2 π r” where r is the radius of the circle. Given the diameter is always twice the radius, these are simply 2 ways of expressing exactly the same thing.
• This can be expressed as circumference = diameter x π.
• And rearranged to
  diameter = circumference / π (by dividing both sides of the equation by π).
• Finally, the radius would be half of this result:
  radius = circumference / π / 2

Still awake?

Now assume that 1 degree equals 1 NM

For the purposes of navigation, it would make life easy if each degree of the circle measured one nautical mile (NM) at the circumference of the circle. That way, each NM that you were ‘off track’ would represent one degree.

Therefore, the whole circle would measure 360 NM around its circumference. Big circle!So now we just need to work out how long the radius of this giant circle would be. From our rearranged formula above we can easily calculate that the diameter = 360 NM /Pi. This gives an answer of about 114.54 which is also in nautical miles.

Now given that the radius is half the diameter, half of 114.54 is 57.27. But no pilot in their right mind wants to deal with weird numbers like that while trying to fly an aeroplane, so we round up to 60.

This approximation is more than adequate for practical navigation purposes. Pilots when hand-flying are not often seen to maintain a heading within 5 degrees of accuracy, so let’s not fool ourselves by pretending to calculate within half a degree!

And that is where the 60 in 1 in 60 comes from.

Here’s proof

To make sure, let’s use the original formula we are familiar with: circumference = 2 x π x radius.

Circumference = 2 x 22/7 x 60 which works out to about 377. This is roughly a 4.7% error. So not exactly 360, but certainly close enough for our ‘on the fly’ navigation calculations. Pun intended.

So, there we are: The ‘rule’ of 1 in 60. If you travel 60 NM in a straight line, every 1 NM off track will be equal to 1 degree. Or thereabouts.

There is a limit

Of course, there are limits to this rule. The limit you use will depend on the level of your flying skills. If you are able to maintain a heading within about 5 degrees of your target heading, then a limit of around 30 degrees would be appropriate. If you think 2 degrees is more like it, then a limit of 20 degrees should serve you better. In all cases the earlier in the leg that you do the calculation, the more accurate the result will be. For our full analysis of these issues see our Making One In Sixty More Accurate paper on the aerocircus.com.au website.

The calculations

The calculations required are in two separate parts. If we find ourselves off the FPT, we can easily calculate the track error angle and use that to correct the heading to parallel the FPT. Secondly, we can determine the closing angle required to get to the destination (or resume the FPT at some carefully selected point), then adjust the heading accordingly.

This is paramount in Australia where roads are few and far between, and features like lakes and towns are very limited for navigation purposes. In the outback there are a few cattle stations and many of them have the name of the station painted on the roof. This is to help fellow pilots when they become ‘temporarily uncertain of their position’. Or totally lost.

Using the 1 in 60 rule, a pilot can also find wind speed and direction. This requires two known points and the time interval to fly between them and that’s it! Simple. This was used extensively during World War II as accurate weather forecasts over enemy territory were hard to come by. More on that one in the next issue.

A traditional example

Initially, let’s stick to what you are probably used to with 1 in 60 — a typical exam-style question.

Suppose a pilot departs from point A and flies a constant heading towards the intended destination at point B which is 120 NM away. After 60 NM (the halfway point) the aircraft ends up at point D which is 10 NM left of point C on the intended track. This flight path is represented by the blue line below.

From the 1 in 60 rule we can quickly determine that the aircraft has drifted 10 degrees to the left of track. This calculation is the first part of a two-step process. It determines the track error.

If the pilot now changes the heading by 10 degrees to the right to correct the track error, the aircraft will fly parallel to the desired track. This is represented by the red line below.

This is better than continuing on the original heading but has only fixed half of the problem. The pilot now has to close the angle to be able to arrive at the intended destination at point B. Because there is still 60 NM distance remaining, the closing angle is also 10 degrees.

So, the pilot should turn right by 10 degrees to correct the track error, plus another 10 degrees to pick up the closing angle. Therefore, adjusting the heading at point D by 20 degrees to the right will place the aircraft on the correct track to arrive at the intended destination of B. Allegedly.

Tip: Those new to the concept of 1 in 60 often take some time to realise that two calculations are required here.

More practical viewpoint

You may have noticed that many aviation textbooks, like our example above, use a point about halfway to the destination (or next waypoint) when explaining 1 in 60. While this is OK for the purposes of understanding the technique, it is not how it should be done in practise. Why would you wait until halfway to the next destination (or even 60 NM along the track) before trying to figure out if you are still ‘on track’?

“Early detection = small correction” is a very apt saying that we heard from an instructor many years ago. Because we like to be different at Aero Circus (and this article is not about passing exams), from now on we will use more practical examples that, hopefully, will better reflect how you should actually use this technique in real life.

Increasing the accuracy of 1 in 60

Many textbooks also say that the difference between the distance travelled along the FPT and the TMG are small enough to be ignored for the purposes of One In Sixty. While that is true for small track error angles, the error does increase dramatically as the track error angle increases. It is simple matter to eliminate the error altogether by always measuring distances along the FPT and off-track distance at right angles to this.

As the accuracy of 1 in 60 is affected by large error angles and strong winds, you should be mindful to check your progress more often when these conditions are present.

Finally, as 1 in 60 tends to increase the angles over the trigonometrically correct results, whenever rounding is required, rounding down instead of up will increase the accuracy of calculations.
That concludes the first part of this article. Next time we will look at some more detailed and practical examples of the use of 1 in 60 rule for navigation.

Read part 2 here. 

Aero Circus is run by a small group of pilots who are independent of airlines, employers, flying schools or other industry associations. They attempt to write unbiased articles with the aim of helping pilots of any experience level get more out of aviation. Check them out at aerocircus.com.au.