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I'm working on some math questions for a CPL exam (not the FAA written), and I am curious about the 1:60 rule. How does that math work out? I know that if you're 60 NM from the station and 1 NM off course, you're 1 degree off course. How does this work out for other angles? I'm also wondering if this is the same rule used to derive the VOR time/distance formulas.

Any insight would be helpful, along with derivations of the formulas. I'm just having trouble picturing everything in my head.

Thanks!

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This is a fairly basic question of trigonometry. Imagine a very long but narrow right triangle. Your starting position is the the one degree angle, and you have two very long, near parallel, legs leaving that point. The hypotenuse is the 60NM route you actually fly, and the leg leading to the right angle is the route you planned to fly. The third short leg is the distance between your actual position, and your intended position, in your example, about 1NM.

What we need to do is find the length of the short side opposite the given angle. We have the given angle, and the length of the hypotenuse. This relationship is defined by a mathematical function called the "sine".

For example, we can take the sine of 1 degree, and multiply it by the 60 NM flown, to verify the 1:60 rule. We would plug $ 60 \, \text{NM} \times \sin(1°) $ into a calculator, and the result would be 1.05 NM - very close to the rule of thumb.

At small angles, the sine function is very nearly linear - double the angle, and you double the result. For example, if we use 2 degrees, we get 2.09 NM, and if we use 5 degrees, we get 5.23 NM. Even a 20 degree error leads to a deviation of about 20 NM off of your intended route after 60 NM flown. So, the rule of thumb seems to be useful within a pretty wide range.

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  • $\begingroup$ "... of about 20 NM off your" seems like a typo? sin(20 deg)*60 = 20.52 $\endgroup$
    – ROIMaison
    Apr 24 at 7:30
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    $\begingroup$ So for very small angles you have $\sin (n°) \approx n / (180/pi) \approx n / 57.3$, but as the angle gets bigger that approximation is a little too high, so it makes sense to use a constant that's a bit bigger than 57.3. 60 has a lot of factors so it's easy to do the mental math. $\endgroup$ Apr 24 at 14:27

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