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

Eddie Sez:

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.


Definition

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


Example

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?

Top of Descent = (Thousands of Feet) 3 = (40) 3 = 120 nm

Proof

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:

Gradient = Flight Levels Nautical Miles

If you do the math, that would mean:

Top of Descent = Flight Levels 3

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:

Top of Descent (D) = ( K tan θ ) ( 1 nm 6076 feet ) ( 1000 feet 1 K )

For a 3° angle, tan(θ) = 0.0524 and the math works out to:

Top of Descent (D) = ( K ) ( 3.14 )

That is an error of less than 5% from our time-tested rule of thumb.


More About This:

For more about this rule of thumb, see: Normal Procedures & Techniques / Descent and Flight Lessons / Top of Descent.


Book Notes

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


Bottom Line

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.