1. AIR NAVIGATION
Part 3
The 1 in 60 rule

2. LEARNING OUTCOMES On completion of this unit, you should:
Be able to carry out calculations to determine aircraft distance, speed and time
Understand the principles of vectors and the triangle of velocities to establish an aircraft’s track and ground speed

3. LEARNING OUTCOMES Understand the principles of the 1 in 60 rule
Understand the types of compass systems used for air navigation, how they work and their limitations
Know the hazards that weather presents to aviation

4. Introduction
In modern aircraft it is often necessary to do quick mental calculations to check that the navigational computer is still making sense and that we have not fallen into the garbage in, garbage out trap.
We previously looked at progress along track (DST and ETA); we now need to consider our position across track

5. First though, a couple of definitions.
Track Required
The track required is normally the line drawn on the map between the departure
airfield and the destination, or from one turning point to another on the route.

6. Definitions continued
Track Made Good
If for some reason the aircraft drifts off track and we can establish our position overhead using some unique feature (a pinpoint), then the line joining the departure airfield
and the pinpoint is known as the Track Made Good (TMG).

7. Definitions continued
Revised Track
From a pinpoint, which is off the track required, we have 2 options. One
would be to regain the required track, but more normally we would draw a line from
the pinpoint to the next turning point. This is called the revised track.

8. Definitions Provided Track Required Track Made Good (TMG)
Revised Track

9. 1 in 60 Rule
The 1 in 60 rule states that:
if an aircraft flies a TMG 1º in error from the required track, then after 60 miles of
flying the aircraft will be one mile off the
required track.

10. This can be proved with trigonometry
1 in 60 Rule - cont
This can be proved with trigonometry
(SOHCAHTOA)
but all you need to know is how to use the triangle.

11. An Example After 60 nm the error is 1 nm for every 1° off track
Track Required
60 nm
10 nm
10° Track error
After 60 nm the error is
1 nm for every 1° off track

12. The 1 in 60 rule holds good for track errors up to 23º beyond that the difference in length of the two tracks (TMG and Track required) becomes too great and the approximation will not work.

13. Application of 1 in 60
The simplest application of the 1 in 60 rule is when a pinpoint is taken exactly
halfway along track.

14. Pinpoint
Closing Angle
Track Error A B
Revised Track
TMG
From the diagram above you can see the triangle formed as the aircraft drifts off track is exactly mirrored by the triangle showing the aircraft regaining track.
Track Required

15. to the right by twice the track error
Pinpoint
12° A B
TMG 6°
As the triangles are the same size and shape, it is only necessary to alter heading
to the right by twice the track error
to ensure that the aircraft reaches point B (assuming the wind remains constant). As the pinpoint is taken halfway along track, the actual distances do not affect the results

16. The Pinpoint is less than half-way alongB
Pinpoint 20 40 4
To solve this problem it is necessary to look at each triangle separately and use the 1 in 60 rule as applied to “similar triangles”.

17. A B
Pinpoint 20 40 4
Triangles are “similar” if they are identical in shape and differ only in size.

18. A B
Pinpoint 20 40 4
12°
Track Angle Error
Look at the left hand triangle and how this extends to make a 60 mile triangle. Simple multiplication then shows that if a 20 mile run produces a 4 mile error, a 60 mile run (3 times as far) will give a 12 mile error (3 times as large). Thus the track error angle is 12º.

19. How It’s Done The left hand triangle is extended to make the base 6012
Track error
12° 20 4 40
The left hand triangle is
extended to make the base 60
units long

20. How It’s Done - Continued
Closing angle = 6° 6 4 20 40
The right hand triangle
is extended in the same way

21. Once you understand the method and can do the mental arithmetic, you B
Pinpoint 20 40 4
Once you understand the method and can do the mental arithmetic, you
can then omit the drawing of the triangles

22. Putting these figures back into the original problem – using previous slides
12°
Track Angle Error
Closing angle = 6° 4 A 20 40 B
you can see that the track error angle and the closing angle are added together to give 18, this is the amount that you need to turn right in order to regain track at point B.

23. Practical Application
The 1 in 60 rule is used a great deal in both military and civil
flying.
Because pinpoints are not always available when we want them,
we are often left with awkward numbers that do not lend themselves to mental arithmetic.
Bear in mind that the answer is only needed to whole degrees so
ultimate accuracy is unnecessary
The solution is to use approximate numbers that are easily handled, either round numbers like 20, 30, 40 or those divisible by 6.

24. Remember also, that once a pinpoint
is found, it takes you a measurable time to do the calculations, during
which time you are drifting further off track so if you have any rounding
up to do, ensure that you turn more than the precise calculation rather
than less.

25. Questions

26. If an aircraft flies for 60 nm with an error of 1° in its heading, it will be 1 nm from its
intended track. This is understood as:
a. The vector triangle rule
b. The distance/time/velocity rule
c. The 1 in 60 rule
d. The revised track rule

27. If an aircraft flies for 60 nm with an error of 12° in its heading, how far will it be from its intended track?
a. 1 nm
b. 6 nm
c. 12 nm
d. 60 nm

28. 12
Track error
12° 60

29. to the right by twice the track error
An aircraft when flying from A to B is found to be off track at the pinpoint shown below. The pilot calculates the track error as 8° and the closing angle of 4°. By how much does the pilot need to turn to reach point B?
Pinpoint
TMG A B 8° 4°
As the triangles are the same size and shape, it is only necessary to alter heading
to the right by twice the track error
16°

30. Pinpoint
TMG A B 8° 4°
4 nm A B
30 nm

31. An aircraft when flying from A to B is found to be off track at the pinpoint shown below. The pilot calculates the track error as 8° and the closing angle of 4°. By how much does the pilot need to turn to reach point B? A B
Pinpoint 8° 4°
12°
The track error angle and the closing angle are added together to give 18, this is the amount that you need to turn right in order to regain track at point B.

32. Remember:
An aircraft flying from A to B finds that after 30 nm it is 4 nm off track. If it has a further 60 nm to travel by how much does the pilot need to turn to regain the intended track at B?
It’s the 1 in 60 rule!! 

33. a. 4°
b. 8°
c. 12°
d. 14°

34. Take the triangle on the rightB
30 nm
4 nm
60 nm
Here is the diagram
Take the triangle on the right

35. 4 nm A B
Closing Angle = 4°
30 nm
60 nm

36. Now the triangle on the left
4 nm A B
30 nm
60 nm

37. Now the triangle on the left
8 nm A
30 nm
4 nm
Track error = 8°
30 nm
8 nm error here gives a track error of 8°
Another 30 nm would give an additional 4nm total of 8nm

38. Track error = 8° +
Closing Angle = 4°
Therefore, the pilot needs to turn 12° to the right to get to point B

39. a. 4°
b. 8°
c. 12°
d. 14°