1 in 60 rule - please explain!
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1 in 60 rule - please explain!
Hello learned aviators!
I am 15 hours into my PPL and I have just completed my solo time in the circuit. My instructor now says that I am ready to start navigation training. He started explaining the 1 in 60 rule to me a few days ago but he went through it so fast that I am still a little confused! As I wont be flying for at least another week perhaps someone can help me out here with an idiot-proof explanation.
Much appreciated.
I am 15 hours into my PPL and I have just completed my solo time in the circuit. My instructor now says that I am ready to start navigation training. He started explaining the 1 in 60 rule to me a few days ago but he went through it so fast that I am still a little confused! As I wont be flying for at least another week perhaps someone can help me out here with an idiot-proof explanation.
Much appreciated.
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The 1:60 rule is basically a procedure for off track situations. It assumes that if you have held a constant heading since your departue, you have travelled in a straight line over the ground. Basically the rule is that for every 60 miles travelled, 1 mile off track is equal to a track error of 1 degree. (eg if you have departed from point A and your planned track is 360 degrees, and at point B which is 60 miles from dep. you find yourself 1 mile right of track, your actual track has been 001 degrees.) So basically if you identify your position and you are so many miles off track you can work out how many degrees of track error you have experienced and make a correction to get back onto track.
eg, You plan to fly a 100nm leg from A to B and the magnetic track is 360 degrees. After a period of time you find yourself at point X, which is 40nm from departure and 2 miles right of track. So you work out your track error. 60/40 x 2 = 3 degrees. so your actual track has been 003. So you need to turn left 3 degrees to stop getting off track ie you will now parrallel your planned track. To fly to your destination (point B) you need to work out another 1:60 using distance to travel (60nm) and your off track dist. (2miles) 60/60 x 2 = 2 degrees. So at point x you need to turn left 3+2= 5 degrees to get back to your destination. BTW that is a 5 degrees heading change, the beauty of the one in 60 is that wind effect is taken care of! Anyway it's easier to describe with diagrams so if you did'nt have a clue about my explanation, well ask your instructor next week!
eg, You plan to fly a 100nm leg from A to B and the magnetic track is 360 degrees. After a period of time you find yourself at point X, which is 40nm from departure and 2 miles right of track. So you work out your track error. 60/40 x 2 = 3 degrees. so your actual track has been 003. So you need to turn left 3 degrees to stop getting off track ie you will now parrallel your planned track. To fly to your destination (point B) you need to work out another 1:60 using distance to travel (60nm) and your off track dist. (2miles) 60/60 x 2 = 2 degrees. So at point x you need to turn left 3+2= 5 degrees to get back to your destination. BTW that is a 5 degrees heading change, the beauty of the one in 60 is that wind effect is taken care of! Anyway it's easier to describe with diagrams so if you did'nt have a clue about my explanation, well ask your instructor next week!
Guest
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Guest
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In simple terms the sine of 1 degree is approximately equal to 1/60. Good enough for air navigation, but not for firing guns. The Artilery use the 1 in 1000 rule where at 1000 metres a 1 metre displacement is one Mil. There are 6400 Mils in a circle, I am sure your instructor will confirm this!
For PPL flying you really don't need to confuse yourself with such complex mathematics, based on the formula:
Wheels off the ground = IQ - 60
For PPL flying you really don't need to confuse yourself with such complex mathematics, based on the formula:
Wheels off the ground = IQ - 60
Guest
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without being properly qualified to comment on this (but I will anyway!) I use a simple rule of thumb as complicated maths or even simple ones don't work for me when I am flying.
I write on the chart as a reminder (memory being poor as well) the following.
1/4 way distance gone is track error times 1.5
1/2 way distance gone is track error times two
3/4 way distance gone is track error times 3.
Then using the ten degree fan lines as a guide I have a quick simple calculation that is good enough in VFR.
Help anyone?
Cheers.
I write on the chart as a reminder (memory being poor as well) the following.
1/4 way distance gone is track error times 1.5
1/2 way distance gone is track error times two
3/4 way distance gone is track error times 3.
Then using the ten degree fan lines as a guide I have a quick simple calculation that is good enough in VFR.
Help anyone?
Cheers.
Guest
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1:60 Principle.
For every 60 units travelled, then being displaced 1 unit to the side = an angle of approx 1 degree off track ie the Track Made Good has diverged from the Planned Track. This is called Track Error
(ignore the . below - they're just for spacing)
The a/c travels in a straight line from the start to the finish points
...+ finishing point:
...|
.1|________________+ start point
.......60
If the a/c heading is adjusted towards the track by the amount the Track Made Good has diverged from the Planned Track, then the a/c will parallel track (but still will be offset from the Planned track - just not getting any further away)
Adjust the heading even more towards the planned track & the a/c will eventually converge. Obviously the more towards track the sooner that the Planned Track will be regained. This is called Closing Angle
Regaining track works similarly to getting off track ie 1:60 can be used to calculate where along track to rejoin.
The amount to alter heading = a bit to stop the divergence (to parallel track) + another bit (to regain track) ie Track Error + Closing Angle.
To do 1:60 in your head:
If you've travelled 60 nm, then 1 nm off track = 1 deg Track Error - ie 1 x Dist. off track
If 2 nm off track then TE = 2 deg
If 3 nm off track then TE = 3 deg
If 4 nm off track then TE = 4 deg, etc etc
If you've travelled 30 nm, then 1 nm off track = 2 deg - ie 2 x the dist. off track
If 2 nm off track then TE = 4 deg
If 3 nm off track then TE = 6 deg
If 4 nm off track then TE = 8 deg, etc etc
If you've travelled 20 nm, then 1 nm off track = 3 deg - ie 3 x the dist. off track
If 2 nm off track then TE = 6 deg
If 3 nm off track then TE = 9 deg
If 4 nm off track then TE = 12 deg, etc etc
If you've travelled 15 nm, then 1 nm off track = 4 deg - ie 4 x the dist. off track
If 2 nm off track then TE = 8 deg
If 3 nm off track then TE = 12 deg
If 4 nm off track then TE = 16 deg, etc etc
So, if you've travelled roughly 60 nm, multiply your distance off track by 1 to get the amount you need to alter HDG to parallel track.
If you've travelled roughly 30 nm, multiply dist. off by 2.
If travelled roughly 20 nm, multiply by 3
If travelled roughly 15 nm, multiply dist off by 4.
If you've travelled about 45 nm then use 1.5 times the dist off track eg 2 nm off track = 3 deg Tr. Error.
Just remember the table:
60 run ----- Times 1
45 run ----- times 1.5
30 run ----- Times 2
20 run ----- Times 3
15 run ----- Times 4
To get closing angle you can use the Track Error again (ie 'double the track error') - which would cause you to regain track in the same distance you took to get off track.
Or, you could pick a feature off the chart that would be good point to regain track, & then use the 1:60 method to find the Closing Angle from your current off-track position to the desired point.
Hope this helps.
[This message has been edited by Tinstaafl (edited 29 November 2000).]
For every 60 units travelled, then being displaced 1 unit to the side = an angle of approx 1 degree off track ie the Track Made Good has diverged from the Planned Track. This is called Track Error
(ignore the . below - they're just for spacing)
The a/c travels in a straight line from the start to the finish points
...+ finishing point:
...|
.1|________________+ start point
.......60
If the a/c heading is adjusted towards the track by the amount the Track Made Good has diverged from the Planned Track, then the a/c will parallel track (but still will be offset from the Planned track - just not getting any further away)
Adjust the heading even more towards the planned track & the a/c will eventually converge. Obviously the more towards track the sooner that the Planned Track will be regained. This is called Closing Angle
Regaining track works similarly to getting off track ie 1:60 can be used to calculate where along track to rejoin.
The amount to alter heading = a bit to stop the divergence (to parallel track) + another bit (to regain track) ie Track Error + Closing Angle.
To do 1:60 in your head:
If you've travelled 60 nm, then 1 nm off track = 1 deg Track Error - ie 1 x Dist. off track
If 2 nm off track then TE = 2 deg
If 3 nm off track then TE = 3 deg
If 4 nm off track then TE = 4 deg, etc etc
If you've travelled 30 nm, then 1 nm off track = 2 deg - ie 2 x the dist. off track
If 2 nm off track then TE = 4 deg
If 3 nm off track then TE = 6 deg
If 4 nm off track then TE = 8 deg, etc etc
If you've travelled 20 nm, then 1 nm off track = 3 deg - ie 3 x the dist. off track
If 2 nm off track then TE = 6 deg
If 3 nm off track then TE = 9 deg
If 4 nm off track then TE = 12 deg, etc etc
If you've travelled 15 nm, then 1 nm off track = 4 deg - ie 4 x the dist. off track
If 2 nm off track then TE = 8 deg
If 3 nm off track then TE = 12 deg
If 4 nm off track then TE = 16 deg, etc etc
So, if you've travelled roughly 60 nm, multiply your distance off track by 1 to get the amount you need to alter HDG to parallel track.
If you've travelled roughly 30 nm, multiply dist. off by 2.
If travelled roughly 20 nm, multiply by 3
If travelled roughly 15 nm, multiply dist off by 4.
If you've travelled about 45 nm then use 1.5 times the dist off track eg 2 nm off track = 3 deg Tr. Error.
Just remember the table:
60 run ----- Times 1
45 run ----- times 1.5
30 run ----- Times 2
20 run ----- Times 3
15 run ----- Times 4
To get closing angle you can use the Track Error again (ie 'double the track error') - which would cause you to regain track in the same distance you took to get off track.
Or, you could pick a feature off the chart that would be good point to regain track, & then use the 1:60 method to find the Closing Angle from your current off-track position to the desired point.
Hope this helps.
[This message has been edited by Tinstaafl (edited 29 November 2000).]
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Lancaster201
Tinstaafl has presented you with a free 1 in 60 text book. Lucky you.
You may also find it helps to try and learn how to assess angles on a map by eye. So when you get a fix (that is off track) you look at where you started from and say I have flown x deg left of track.
With a bit of practice (drawing angles on a bit of paper and estimating them then checking with a protractor) some people with an eye for angles get very good at it. Others will never do it. If you are one of the lucky ones it can turn out quicker and easier than measuring the distance off Vs distance gone and doing the 1 in 60.
Not trying for one moment to suggest that you should not fully understand the 1 in 60 and be able to apply it, Just that the estim thing is another skill you might try to acquire for when your GPS goes 34DD up AS IT WILL ONE DAY.
------------------
Forward CGs are better than aft ones
Tinstaafl has presented you with a free 1 in 60 text book. Lucky you.
You may also find it helps to try and learn how to assess angles on a map by eye. So when you get a fix (that is off track) you look at where you started from and say I have flown x deg left of track.
With a bit of practice (drawing angles on a bit of paper and estimating them then checking with a protractor) some people with an eye for angles get very good at it. Others will never do it. If you are one of the lucky ones it can turn out quicker and easier than measuring the distance off Vs distance gone and doing the 1 in 60.
Not trying for one moment to suggest that you should not fully understand the 1 in 60 and be able to apply it, Just that the estim thing is another skill you might try to acquire for when your GPS goes 34DD up AS IT WILL ONE DAY.
------------------
Forward CGs are better than aft ones
Guest
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Hope that you understood the explanation of the very simple 'Standard Closing Angle'! None of this complicated 'reciprocal of proportion of track flown since last fix' nonsense, just 'how far off track?', turn through SCA, hold for appropriate time, turn back onto original heading, assess, correct, enjoy!!
Guest
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As BEagle mentioned (and I should have 
), don't forget to change heading after regaining track!!
Using the 1:60 method you should adjust heading just enough to stop the convergence ie by the closing angle.
--------------
For those interested in a slightly more technical explanation of the 1:60 rule:
Bear in mind that the 1:60 method is an approximation. It certainly is not an 'accurate' method however the inaccuracies are usually negligable for small heading changes - say, up to 15 deg for each 1:60 calculation.
Imagine (or draw) a circle. Draw a straight line horizontally from the centre to the edge of the circle('circumference'). This is the radius.
Draw a second line the same length as the radius, up from where the radius joins the circumference but curved so that it exactly follows the curve of the circumference.
Draw straight line from where the just drawn curved line ends, back to the centre of the circle.
You should now have a wedge shaped section, with all 3 edges having exactly the same length, although one of the edges will be curved. Like a piece cut from a cake.
The angle that this wedge shaped section makes is called a 'radian' and happens to be 57.3xxxxxxx..... degrees ie about 60 deg.
If you subdivided the curved edge of the wedge into 60 equal pieces, then each slice of the 'pie' would be near-as-dammit to 1 degree.
Since the original lines were all the same length, then this small section of the wedge has a curved side 1/60 the length of the radius.
Approximation 1: The angle caused by subdividing a radian into sixtieths is equal to 1 degree.
Also for the very small size of the curved side in the small slice, it is near enough the same as a a straight line at 90 degrees to the radius
Approximation 2: The curved section of the wedge is equivalent to a straight line at 90 degrees to the radius.
When the new heading is adjusted it is presumed that changing heading by the track error (to parallel track) will not affect drift.
Not so. Imagine flying into a direct headwind. Drift will be zero.
Now imagine turning 90 degrees while still in the same wind. Drift will now be at its maximum.
It doesn't just 'jump' to its maximum. It changes smoothly from 0 to max as the heading is changed, however for small changes the difference is tiny.
Approximation 3: Small changes in heading have no effect on drift after applying the heading correction.
The size of the drift is also related to the speed & direction of both the wind and the the aircraft. If any of these change then so will the drift.
Wind velocity changes continously all over the Earth. Aircraft velocity changes as altitude/Temp/pressure/power settings/weight change.
Approximation 4: The wind velocity & aircraft velocity have been and will stay constant.
The scale of all maths errors are generally less than errors introduced by the pilot in terms of maintaining an accurate heading, and those errors caused by wind variations.
As long as you maintain a reasonably accurate heading/altitude, and limit the calculation to no more than about 15 deg the (ie 15 deg max. calculation for the track error + another 15 deg max. for the closing angle) method is accurate enough.
As always with flying you should continuously &/or periodically assess the accuracy of your calculations. Are you where you expected to be & on time? Have you flown across a significant meteorological or geographic feature that could affect the wind? etc etc.
Hope this helps.
----------
PS: Meant to add:
To calculate the angle the formula is...
ignore the ... They're just for spacing
Dist off track.........................Track Error
______________........=........_________________
Dist run.......................................60
On a whiz wheel put the Dist Off over the Dist Run & Track Error can be read above the 60 mark.
Make sure you use mental arithmetic to get the correct answer from the whiz wheel!!!
[This message has been edited by Tinstaafl (edited 05 December 2000).]
), don't forget to change heading after regaining track!!Using the 1:60 method you should adjust heading just enough to stop the convergence ie by the closing angle.
--------------
For those interested in a slightly more technical explanation of the 1:60 rule:
Bear in mind that the 1:60 method is an approximation. It certainly is not an 'accurate' method however the inaccuracies are usually negligable for small heading changes - say, up to 15 deg for each 1:60 calculation.
Imagine (or draw) a circle. Draw a straight line horizontally from the centre to the edge of the circle('circumference'). This is the radius.
Draw a second line the same length as the radius, up from where the radius joins the circumference but curved so that it exactly follows the curve of the circumference.
Draw straight line from where the just drawn curved line ends, back to the centre of the circle.
You should now have a wedge shaped section, with all 3 edges having exactly the same length, although one of the edges will be curved. Like a piece cut from a cake.
The angle that this wedge shaped section makes is called a 'radian' and happens to be 57.3xxxxxxx..... degrees ie about 60 deg.
If you subdivided the curved edge of the wedge into 60 equal pieces, then each slice of the 'pie' would be near-as-dammit to 1 degree.
Since the original lines were all the same length, then this small section of the wedge has a curved side 1/60 the length of the radius.
Approximation 1: The angle caused by subdividing a radian into sixtieths is equal to 1 degree.
Also for the very small size of the curved side in the small slice, it is near enough the same as a a straight line at 90 degrees to the radius
Approximation 2: The curved section of the wedge is equivalent to a straight line at 90 degrees to the radius.
When the new heading is adjusted it is presumed that changing heading by the track error (to parallel track) will not affect drift.
Not so. Imagine flying into a direct headwind. Drift will be zero.
Now imagine turning 90 degrees while still in the same wind. Drift will now be at its maximum.
It doesn't just 'jump' to its maximum. It changes smoothly from 0 to max as the heading is changed, however for small changes the difference is tiny.
Approximation 3: Small changes in heading have no effect on drift after applying the heading correction.
The size of the drift is also related to the speed & direction of both the wind and the the aircraft. If any of these change then so will the drift.
Wind velocity changes continously all over the Earth. Aircraft velocity changes as altitude/Temp/pressure/power settings/weight change.
Approximation 4: The wind velocity & aircraft velocity have been and will stay constant.
The scale of all maths errors are generally less than errors introduced by the pilot in terms of maintaining an accurate heading, and those errors caused by wind variations.
As long as you maintain a reasonably accurate heading/altitude, and limit the calculation to no more than about 15 deg the (ie 15 deg max. calculation for the track error + another 15 deg max. for the closing angle) method is accurate enough.
As always with flying you should continuously &/or periodically assess the accuracy of your calculations. Are you where you expected to be & on time? Have you flown across a significant meteorological or geographic feature that could affect the wind? etc etc.
Hope this helps.
----------
PS: Meant to add:
To calculate the angle the formula is...
ignore the ... They're just for spacing
Dist off track.........................Track Error
______________........=........_________________
Dist run.......................................60
On a whiz wheel put the Dist Off over the Dist Run & Track Error can be read above the 60 mark.
Make sure you use mental arithmetic to get the correct answer from the whiz wheel!!!
[This message has been edited by Tinstaafl (edited 05 December 2000).]
Guest
Posts: n/a
Lancaster201:
Now that your thoroughly confused, here's a very practical use for the 1:60 rule, especially if your GPS is T.U.
When passing abeam a station you can apply the 1:60 rule to determine your ground speed.
Examle:
You are 60 NM east of a VOR, on the 090 radial. You start your clock and note that it takes 3 minutes to cross 10 radials. Applying the 1:60 conversion ie 10 radials at 60 NM = 10 NM. It took you 3 minutes to go 10 miles therefore your present groundspeed is 200 Kts. (60/3=20 x 10 =200).
Another practical use of the 1:60 rule is using your Radar to determine the approximate tops of Convective Clouds.
Example:
You are 60 NM (radar distance), away from a CB maintaining 9000'. You notice that it takes about 7 degrees of up tilt on your radar to make the image dissappear from your screen. If we apply the 1:60 rule, we arrive at the following. 7 degrees at 60 NM = 7 miles. One mile = 5280' so 7 miles = 36,960'. Now add your a/c altitude of 9,000'+ 36,960' and we get 45,960'. So now you have an approximation of the tops of cloud. This will give you a pretty good idea of how much of a course deviation you will need to avoid the nastier WX.
The above calculation is only a 'rule of thumb' and only for an approximation. I know someone may want to comment on the use of the statute mile conversion of 5280' but I think everyone can remember that one.
Hope this helps.
Cheers, OffshoreIgor
PS. Never let your aircraft take you where your brain hasn't already been in the last five minutes.
[This message has been edited by offshoreigor (edited 07 December 2000).]
Now that your thoroughly confused, here's a very practical use for the 1:60 rule, especially if your GPS is T.U.
When passing abeam a station you can apply the 1:60 rule to determine your ground speed.
Examle:
You are 60 NM east of a VOR, on the 090 radial. You start your clock and note that it takes 3 minutes to cross 10 radials. Applying the 1:60 conversion ie 10 radials at 60 NM = 10 NM. It took you 3 minutes to go 10 miles therefore your present groundspeed is 200 Kts. (60/3=20 x 10 =200).
Another practical use of the 1:60 rule is using your Radar to determine the approximate tops of Convective Clouds.
Example:
You are 60 NM (radar distance), away from a CB maintaining 9000'. You notice that it takes about 7 degrees of up tilt on your radar to make the image dissappear from your screen. If we apply the 1:60 rule, we arrive at the following. 7 degrees at 60 NM = 7 miles. One mile = 5280' so 7 miles = 36,960'. Now add your a/c altitude of 9,000'+ 36,960' and we get 45,960'. So now you have an approximation of the tops of cloud. This will give you a pretty good idea of how much of a course deviation you will need to avoid the nastier WX.
The above calculation is only a 'rule of thumb' and only for an approximation. I know someone may want to comment on the use of the statute mile conversion of 5280' but I think everyone can remember that one.
Hope this helps.
Cheers, OffshoreIgor
PS. Never let your aircraft take you where your brain hasn't already been in the last five minutes.
[This message has been edited by offshoreigor (edited 07 December 2000).]
