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Estimating ETA

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One in Sixty Rule

If you've never heard of the one is sixty rule your life has been too sheltered. This mathematical phenomenon is an underlying element of several critical formulae we will explore in future articles. It is also useful in its own right.

The one in sixty rule relates distance from a point (such as a navaid) to distance along an arc. It all starts with our high school math, where we learned that the circumference of a circle is . 

Examine the diagram to the left. There is some circle with an unknown radius such that:

  • Each degree of arc along the circumference is one nautical mile
  • An arc distance of x miles sweeps x degrees (see diagram to left.)
  • The circle has a circumference of 360 nautical miles.

All the above really say the same thing. This is a VERY important circle - so we need to know its radius. 

To figure the answer just divide 360 by .  The answer is 57.3.

So the 1/60 rule should really be the 1/57.3 rule - but that doesn't sound as cool.

I have met quite a few pilots who know the 1/60 rule but don't know its mathematical origins. Now you do. So, you know that if you are 60 miles from the station and off track by 1 degree you are just a smidge more than 1 mile off track. Or, if you are 3 degrees off track you are just over 3 miles off track, and so on. You now also know that if you want this "rule of thumb" to be right-on you should actually be 57.3 miles from the station when you use it.

Use the formula in proportions

The 1/60 rule can be used in many ways. One of the most useful is for estimating distance off course. For example if you are 10 degrees off course at 60 miles from the station you are 10 miles off course. But how far off course are you if you are 10 degrees off at 30 miles from the station? The answer is 5 miles.

If you are doing an instrument approach that involves flying a 15 mile arc that sweeps though 90 degrees how far will you be flying on the arc?

To answer this question we start by realizing we would be flying 90 miles if it was a 60 mile arc. But, it is only a 15 mile arc, which is 1/4 of 60, so we will be flying 1/4 of 90 or about 22 miles.

Imagine you are flying along on a cross country and there is a VOR to the side of your track, as shown in the diagram. You time how long it takes to cover 10 degrees of arc. How do you use that information to calculate how far it is to the VOR (this works with NDBs too.)?

If it took 15 minutes and you are flying 100 knots then you flew 25 miles. So, the question is really the same as saying at what distance does a 10 degree arc equal 25 miles? Well, at 60 miles 10 degrees of arc would only have been 10 miles. So, we must be a lot more than 60 miles from the station. In fact we are 25/10 times further away. Therefore, we are 60 x 2.5 or 150 Nm from the station.

Summary

The one in sixty (nay 57.3) rule comes up over and over again in aviation. Those who are mathematically inclined will recognize that it is related to the radian angle system. A basic understanding of the 1in 60 rule is valuable for all pilots.