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APenNameAndThatA

Accuracy of the "1 in 60" rule for navigation.

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Posted (edited)

As you know, the one in 60 rule is that you are off course one degree for every nautical mile you would by off course if you had travelled 60 miles. So, for example, if you are off course one mine after flying 10 miles, you are off course six degrees (6 x 10 = 60). I wondered how accurate the rule is. As far as I can tell, very accurate up until you are 40 degrees off course.  

 

Below is what I hope is the graph of the error of the one in sixty rule. The y-axis (up and down axis) is is error. There is no error at zero and thirty degrees. The x-axis is the course. The black line what the one in 60 rule says is how far off course you. The blue line is how far off course you actually are. As you can see, when you are 90 degrees off course, the one in 60 rule says that you are only 60 degrees off course. At about 17 degrees off course, the rule overestimates by about 0.5 degrees. At 40 degrees, it underestimates by only one degree. Amazingly accurate for something that is supposed to be a rule of thumb. 

1in60.jpg

Edited by APenNameAndThatA

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This article needs proof-reading, Ian. The first couple of sentences don't make sense, due to missing and mis-spelt words.

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2 hours ago, onetrack said:

This article needs proof-reading, Ian. The first couple of sentences don't make sense, due to missing and mis-spelt words.

As you know, the one in 60 rule is that you are off course one degree for every nautical mile you would BE off course if you had travelled 60 miles. So, for example, if you are off course one MILE after flying 10 miles, you are off course six degrees (6 x 10 = 60). I wondered how accurate the rule is. As far as I can tell, very accurate up until you are 40 degrees off course.  

 

Below is what I hope is the graph of the error of the one in sixty rule. The y-axis (up and down axis) is is error. There is no error at zero and thirty degrees. The x-axis is the course. The black line what the one in 60 rule says is how far off course you ARE. The blue line is how far off course you actually are. As you can see, when you are 90 degrees off course, the one in 60 rule says that you are only 60 degrees off course. At about 17 degrees off course, the rule overestimates by about 0.5 degrees. At 40 degrees, it underestimates by only one degree. Amazingly accurate for something that is supposed to be a rule of thumb. 

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Good Heavens - I learnt the 1 in 60 rule 35 years ago, I didn't think anybody bothered these days, especially with the electronic gizmos. The 1 in 60 rule is used to estimate angles to determine track and heading changes. If you're off track by (say) 30 degrees and have been for (say) 10 minutes you would use diversion procedures to get back on track. Pages 14-19 to 14-27 in book 2 - Meteorology & Navigation by Trevor Thom. The 1 in 60 rule is much easier to apply when you have your track marked on a map with lines every 15nm or so. I only ever used it on big navs that required the WAC and covered hundreds of nm. I am glad I stayed awake during geometry/trigonometry class because that's what the 1 in 60 is all about. I love this stuff, it keeps my remaining neuron active...

 

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Given the scale that a WAC is drawn to, how accurately can you measure one NM on it? Also if, say your intended track passed over Smokey Junction Railway Station, how accurately can you measure the distance between intended track and track made good?  That's without a GPS, which is cheating if you are relying on map reading.

 

I still want to read the original article the graphic came from, please. 

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I didn't bother with 1 nm measurements. To fly better than about plus/minus 3 degrees over 60 nm is doing pretty good. Also, without decent ground features to identify the 1 in 60 technique is hard to apply. Here's a track I flew on a wet and windy day. Dodging rain showers made things interesting. The GPS was just logging my track, no display available. 

 

Maybe there is no link to the graph, the dude who posted it may have created it himself. I'd like to know what he used as Excel is crap. I use Python for stuff like that.

Google Earth Track.jpg

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1 hour ago, old man emu said:

Given the scale that a WAC is drawn to, how accurately can you measure one NM on it?

Just grabbed a WAC and scale rule; there's a power line 2 Nm from the geometrical centre of Yass.

The scale is graduated in 1 Nm and you could easily pick 0.5 Nm

However, once you get down to that scale, you can actually see both points.

The WAC and Scale is also more accurate than a swinging compass, and to a much lesser extent with a DG.

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17 hours ago, old man emu said:

Please post a link to the article that contains this graph

 

1in60.jpg

The graphic came from an iPhone app called Desmos. It is a cropped screenshot from my iPhone. 

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17 hours ago, Bruce Tuncks said:

The 1 in 60 rule is only appropriate for small deviations off track. It is good to see this proved mathematically.

What amazes me is that if you are off track by 40 degrees, the one in 60 rule is still less than one degree inaccurate. 40 degrees off course is a lot. 

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The 1 in 60 rule is a nice thing to know if you are flying very long distances at high speed, but to try to apply it for short flights at speeds below 100 kts is making the argument ad absurdum. Have a look at the presentation of the 1 in 60 rule in this video. The track lengths and off-track distances are very small, resulting in off-heading amounts of only a few degrees.

 

 

Now have a look at a typical gyroscopic compass face most people would use to monitor their heading:

image.jpeg

See that the scale is marked off in 5 degree sections. That means that the most accurate heading you can fly is plus or minus 2.5 degrees from planned heading. Given the small size of the compass face, the most accurate is more likely to be 5 degrees. And I won't add in gyroscopic progression.

 

So, for those who day VMC flight, below 10,000 ft at speed below 100 kts, the 1 in 60 rule is a nice bit of theory, but not as practical as map reading.

On 04/01/2020 at 5:32 PM, turboplanner said:

Just grabbed a WAC and scale rule; there's a power line 2 Nm from the geometrical centre of Yass.

The scale is graduated in 1 Nm and you could easily pick 0.5 Nm

However, once you get down to that scale, you can actually see both points.

The WAC and Scale is also more accurate than a swinging compass, and to a much lesser extent with a DG.

 

Using Turbo's information, 0.5 nautical miles is about 925 metres. Since VMC visibility limit is 5000 metres (approx 2.5 nautical miles). Blind Freddy could see that far.

 

Another factor affecting off-track position is wind direction. If a pilot obtains the current weather before planning a flight, then the pilot will have a general idea of which side of the planned track the aircraft is likely to be blown to if the wind is greater or less than forecast. If a pilot is flying with a navigator (usually she who must be obeyed) the navigator can keep an eye on Track Made Good and advise heading corrections. 

Edited by old man emu
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10 minutes ago, old man emu said:

Using Turbo's information, 0.5 nautical miles is about 925 metres. Since VMC visibility limit is 5000 metres (approx 2.5 nautical miles). Blind Freddy could see that far.

 

And if you can see the 5000 metres and see you're off track, why not just adjust your heading slightly to intercept the next on-track feature, then make another small adjustment to have yourself running on track.

 

The 1 in 60 had much more relevence in the pre 5000 metre days when it was popular to get above cloud layers and hopefully down through a hole here and there, and still has relevence over featureless country of which Australia has plenty. 

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Good heading keeping is still the basis of accurate navigation over featureless terrain or holding where offsets for wind effect must be done, at the onset and be corrected when information shows it's not allowed for enough. The only difference with very fast planes is If you are going the wrong way you are getting lost faster.

 I think the term is Gyroscopic precession where you get heading indicator drift and you reset to the compass when it's steady. (which it rarely is when in "live air. Nev

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On 04/01/2020 at 1:53 PM, Bruce Tuncks said:

The 1 in 60 rule is only appropriate for small deviations off track. It is good to see this proved mathematically.

Well you only want to be screwing up in small ways, otherwise you're out there in the ether like the Wackett on the Nullabor, or the RAAF Sabre that set his DG 180 degrees out before taking off from Hobart.

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3 hours ago, facthunter said:

Good heading keeping is still the basis of accurate navigation over featureless terrain or holding where offsets for wind effect must be done, at the onset and be corrected when information shows it's not allowed for enough. The only difference with very fast planes is If you are going the wrong way you are getting lost faster.

 I think the term is Gyroscopic precession where you get heading indicator drift and you reset to the compass when it's steady. (which it rarely is when in "live air. Nev

This is the benefit of drawing in your 10 minute checks. You adjust the DG at regular intervals so precession is all but eliminated, and if you stuff up matching the compass in some rough stuff you can have as many goes as you like to get a match, and you'll still be way better off than just trying to use the compass for navigation.

 

Sometimes Apen seems to be going down the path of over-thinking things.

The erro he's shown probably has it's converse in the  "?" track you'll follow if you just fly with the ADF needle pointed at the destination. Navigation is best handled in a class so the instructor can sttle you down if you get too excited about the parts that don't matter.

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33 minutes ago, turboplanner said:

Sometimes Apen seems to be going down the path of over-thinking things.

But it is good to throw this "over thinking" around on these forums. Now I bet Apen will fly with the map on his knees and his eyes outside. After all, this is recreational flying. We don't have "air races" any more where it is essential to keep "on track, on time" to win the prize.

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5 degrees off track is all you are allowed in CTA and on one engine you have to maintain better than that on the climb after the initial swing. Nev

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25 minutes ago, facthunter said:

5 degrees off track is all you are allowed in CTA and on one engine you have to maintain better than that on the climb after the initial swing. Nev

The danger in these discussions is that in some cases PPL students are reading the posts and can be badly misled when flying standards they require for a pass are played down by people thinking the only audience is local flyers in RA.

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The lost Wackett missed the Nullarbor by more than a little. It was found in semi-desert sandhill country, 200 miles N of Cook, and not that far from the S.A./W.A. border. The Wacketts compass was out by 30°.

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Responding to several posts...

21 hours ago, old man emu said:

The 1 in 60 rule is a nice thing to know if you are flying very long distances at high speed, but to try to apply it for short flights at speeds below 100 kts is making the argument ad absurdum

1 in 60 corrections assume you can hold a heading, so a primary reason is to correct for wind. Wind has more effect on a slower aircraft. A 10 knot crosswind will probably be insignificant for a 150 knot aircraft over 100 miles. It is much more significant for a 50 knot aircraft.

 

21 hours ago, turboplanner said:

And if you can see the 5000 metres and see you're off track, why not just adjust your heading slightly to intercept the next on-track feature, then make another small adjustment to have yourself running on track.

How do you figure out how much you need to adjust your heading? That is where the 1 in 60 rule comes in. The idea of the 1 in 60 rule is that if you are flying e.g. 100 miles and are 5 miles off track after 40 miles, you can make a correction that will put you back on track at the 100 mile point so you fly the shortest distance - or at an earlier point if you prefer.

 

When people track visually to something they can see, they often track in a curve if there is a crosswind because they don't apply enough wind correction. It is better to calculate a heading and fly it. Making adjustments to your heading to follow ground features makes it impossible to use the 1 in 60 rule. It relies on accurately flying a constant heading.

 

21 hours ago, old man emu said:

Another factor affecting off-track position is wind direction. If a pilot obtains the current weather before planning a flight, then the pilot will have a general idea of which side of the planned track the aircraft is likely to be blown to if the wind is greater or less than forecast.

If you use a wind correction you don't know whether it is too much or too little, so you do not know which side of the planned track you will be.

 

It is possible if you are navigating to a linear feature (river, road etc.) crossing your track to deliberately track slightly left or right so you know which way to turn when you reach the feature. The deliberate left or right angle needs to be larger than other possible errors.

 

13 hours ago, facthunter said:

5 degrees off track is all you are allowed in CTA

 

When navigating visually the tolerance is 1 mile left or right of track.

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 Degrees (an angle) act from a  POINT.  An along track tolerance is a fixed distance either side of the prescribed track  Example... You wouldn't want to be a mile off track approaching an aerodrome .  If anyone is doing an exam on air legislation get the appropriate document and study the sections relevant to your licence, in the country you are flying in. Nev

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39 minutes ago, facthunter said:

If anyone is doing an exam on air legislation get the appropriate document and study the sections relevant to your licence, in the country you are flying in. Nev

That is so correct. If you are preparing to undertake an examination on any part of a training system, learn and apply the methods based on what is in the syllabus. That will give the answer that the examiner wants to see, with the added advantage that the theoretical basis for the method will be implanted in your mind. That will provide a fall-back position for when everything else fails.

 

After a pilot has run up a bit of experience, then the application of theory is modified by that experience. Consider how your driving experience has altered the way you drive since the time you were on your Provisional licence. Back then you drove with strict compliance with the road rules (one hopes). But after a few years you learned how those rules are bent a little in the day-to-day flow of traffic. Consider your usual drive to work. Same thing every day. You'll even see the same vehicles every day. You all know where minor delays are likely, and you all adjust your driving to get the best result. 

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The rule is only good for small deviations. 10 miles off in 60 is 9.5 degrees approx.

40 off in 60 is approx. 33.7 degrees.

As others have said it is hard to judge distance off and I would not be waiting until I had gone 60 miles to try to fix my track, unless I had no other option.

It used to work well in the old days, before all the GPS and other gizmos, but we could plot it onto the map and use a protractor.

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1 hour ago, Yenn said:

The rule is only good for small deviations. 10 miles off in 60 is 9.5 degrees approx.

40 off in 60 is approx. 33.7 degrees.

As others have said it is hard to judge distance off and I would not be waiting until I had gone 60 miles to try to fix my track, unless I had no other option.

It used to work well in the old days, before all the GPS and other gizmos, but we could plot it onto the map and use a protractor.

My understanding is that you are supposed to use the hypotenuse for the distance that you have flown, not the distance of the original, intended track. So, if you have flown 60 miles and are off course by 40 miles, you are off course by 42 degrees. (If the original distance that you were supposed to fly was 60 miles and you are off track by 40 miles, then you are off track by 33.7 degrees.) As you say, plotting it on a map is just as effective as using maths. 

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