In Air Force instrument instructor school, we learn that the relationship of 60 nautical miles to 1 nautical mile holds magical meaning in the world of flight. See 60 to 1 for a story about how the mathematics was presented to a crowd of pilots normally allergic to all things arithmetic. See TLAR for a story of a child of "That Looks About Right" learning a new set of tricks.

The problem is that the math taught in the instrument instructor school doesn't really hold up. (See Rules of Thumb for the math behind many of these rules of thumb.) As with many things aviation, the pilot doesn't need perfection, the pilot needs a way to achieve precision. If a little mathematical slight of hand is needed, so be it.

As you can see in the figure here, the math isn't that complicated and all you need know is that "almost equals" symbol (≈) works because the difference between 2.83 and 3° is imperceptible on a pilot's instruments. Here then are some math derived from this an other relationships.

2020-12-17

See Bank Angle to Maintain an Arc Around a Point for further explanation.

To fly an arc around a point, use a bank angle equal to the turn radius times 30 divided by the arc length.

See Arc Distance for further explanation.

Rule — The distance traveled along an arc is equal to the arc radius times the arc angle divided by 60.

See Gradient for further explanation.

Flight levels divided by nautical miles equals gradient.

Nautical miles per minute times descent angle times 100 gives vertical velocity in feet per minute.

See Gradient for further explanation.

Nautical miles per hour times ten divided by two gives a good three degree glide path VVI.

Or: Groundspeed times 5 equals VVI

Or: Half your groundspeed, add a zero, equals VVI

See Holding Pattern Teardrop Angle for further explanation.

A holding pattern teardrop angle of 120 times the turn radius divided by leg length will provide an on course roll out, no wind.

See Top of Descent for further explanation.

Start descent at three times your altitude to lose in thousands of feet to achieve a three degree gradient.

Start descent at four times your altitude to lose in thousands of feet to achieve a 2.5 degree gradient.

See Turn Radius for further explanation.

At 25 degrees of bank, turn radius is equal to nautical miles per minute squared, divided by ten.

See Visual Descent Point for further explanation.

A Visual Descent Point is found by subtracting the touchdown zone from the Minimum Descent Altitude and dividing the result by 300.

You don't need an engineering degree to diagram an approach as shown in these examples. If you can plug and chug with a scientific calculator, all you need are some formulas. Here are some handy ones. (Click on the figure to download a PDF version.

Portions of this page can be found in the book Flight Lessons 2: Advanced Flight, Chapter 11.

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