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

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?

$\mathrm{Top\; of\; Descent}=\left(\mathrm{Thousands\; of\; Feet}\right)3=\left(40\right)3=120\mathrm{nm}$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:

$\mathrm{Gradient}=\frac{\mathrm{Flight\; Levels}}{\mathrm{Nautical\; Miles}}$If you do the math, that would mean:

$\mathrm{Top\; of\; Descent}=\frac{\mathrm{Flight\; Levels}}{3}$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:

$\mathrm{Top\; of\; Descent\; (D)}=\left(\frac{K}{tan\theta}\right)\left(\frac{1\mathrm{nm}}{6076\mathrm{feet}}\right)\left(\frac{1000\mathrm{feet}}{1K}\right)$For a 3° angle, tan(θ) = 0.0524 and the math works out to:

$\mathrm{Top\; of\; Descent\; (D)}=\left(K\right)\left(3.14\right)$That is an error of less than 5% from our time-tested rule of thumb.

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

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

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.