We long ago figured out that 3 times your altitude (in thousands) gives a nice descent from en route altitude. When the 60-to-1 gurus came out, they were convinced this was an offshoot of the flight levels to lose technique. Well it isn't, but it does work. Here's why.
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.
Start descent at three times your altitude to lose in thousands of feet to achieve a three degree gradient.
Figure: 3° Top of Descent, from Eddie's notes.
Let's say you are cruising at FL410 and are planning a descent into an airport that is just over 1,000 feet MSL elevation. So you have 40 thousand feet to lose. When should you start your descent?
If you multiply your altitude in thousands of feet by three, you will arrive at the ideal distance to start your descent and end up with about a three degree descent gradient. We've been doing that for years. The 60-to-1 mavens will have you believe this is an offshoot of the earlier flight levels to lose technique:
If you do the math, that would mean:
Figure: Top Descent trigonometry, from Eddie's notes.
That works, but that isn't the "school solution." We can verify the technique using trigonometry. We will use K to represent the altitude in thousands of feet and D for the distance in nautical miles. Of course that means the formulas will require two conversion factors:
For a 3° angle, tan(θ) = 0.0524 and the math works out to:
That is an error of less than 5% from our time-tested rule of thumb.
So what about the claims this rule of thumb is based on 60-to-1? My conclusion: It has more to do with trigonometry.
|Rule of Thumb||60-to-1?||Trigonometry||π|
|Top of Descent (3°)||✓|
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.
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