To provide circling offset when approaching from the opposite runway, turn 30° away from heading while starting your stop watch, time for 66 seconds (Category D) or 53 seconds (Category C), and then turn to parallel the runway on downwind.

This is the classic real world situation and most pilots opt for 30° offset for 30 seconds, but that usually ends up with a very tight base turn. There is a reason for that: 30 seconds isn't enough. This rule of thumb lengthens that to 66 seconds (Category D) and 53 seconds (Category C). That is really all you need to know, but if you want to follow through with the proof, you will need to know how to compute turn radius and speed. You can find the turn radius by taking the speed in nautical miles per minute, squaring it, and dividing the answer by nine or ten. More about that: Rules of Thumb / Turn Radius.

I first learned about this rule of thumb at the Air Force Instrument Instructor's Course (AFIIC) where we were told it is derived from the 60-to-1 concept. But is that true? Well let's find out. But first, we'll define the rule, provide an example of its application, and then we'll provide a mathematical proof of the rule.

To provide circling offset when approaching from the opposite runway, turn 30° away from heading while starting your stop watch, time for 66 seconds (Category D) or 53 seconds (Category C), and then turn to parallel the runway on downwind.

Figure: Circling from opposite runway, from Eddie's notes.

A Challenger 604 typically circles at 150 knots. Let's say we are flying to Runway 11 with instructions to circle to Runway 29. The rule of thumb says turn 30°, time for 66 seconds, turn back to the original heading for a downwind, and then turn final at the appropriate time. Your downwind displacement should make the base turn work out perfectly.

You can use a 30° or 45° offset, your choice, but it is important to get to that heading using a standard rate turn to make the timing work. The objective, of course, it to establish a downwind offset. Once you've done that, you need to adjust that heading for wind. I use 30°, reasoning that you don't need 45° and it is too easy to lose sight with that angular offset.

The distance travelled “d” on that 30 degree leg would be equal to twice the turn radius divided by the sine of 30 degrees. Once again everything hinges on turn radius.

$\mathrm{Turn\; Radius\; r}=\frac{{\mathrm{(nm/min)}}^{2}}{9}=\frac{{\mathrm{(150/60)}}^{2}}{9}=0.69\mathrm{nautical\; miles}$The distance to travel a 30° offset leg:

$\mathrm{Distance\; d}=\frac{2x0.69}{sin30}=2.76\mathrm{nautical\; miles}$The time to fly that leg at typical Category D speeds:

$t=\frac{d}{v}=\left(\frac{2.76}{(150/60)}\right)60\mathrm{seconds/minute}=66\mathrm{seconds}$For typical Category C speeds, r = 0.44, d = 1.76, t = 53 seconds.

For more about this rule of thumb, see: Instrument Procedures / Circling Approach.

So what about the claims this rule of thumb is based on 60-to-1? My conclusion: No, it has more to do with trigonometry.

Rule of Thumb | 60-to-1? | Trigonometry | π |

Circling Approach Opposite Runway | ✓ |

60-to-1 — Rule of thumb is based on the mathematical relationship of a 360° circle and/or 6076' to 1 nm.

Trigonometry — Rule of thumb is based on the relationship to a right angle and the derived trigonometric functions.

π — Rule of thumb is based on the relationship of a 360° circle, the number π, and/or 6076' to 1 nm.