Here is a trivial nugget from an airplane manual. Among the operational limitations, the airplane’s maximum runway slope is 2%. Neato. What does it mean?

I say “trivial” because folks working at airlines aren’t involved in measuring runway slopes. This topic truly reflects the work of diagramming airports, generating runway analyses, and automating performance calculations.

Referencing the Pilot’s Handbook of Aeronautical Knowledge, we can see this terminology is missing from the glossary. Instead, it’s presented in the middle of the chapter on Aircraft Performance:

The gradient or slope of the runway is the amount of change in runway height over the length of the runway. The gradient is expressed as a percentage, such as a 3 percent gradient. This means that for every 100 feet of runway length, the runway height changes by 3 feet.

An even more basic idea of slope percentage is: Distance times slope equals height.

For a mile-long runway, take 5,280 ft, multiply by 2%, and arrive at 105.6 ft. The mile-long runway with a 2% slope changes elevation by about 106 ft.

For takeoff performance, sometimes the nautical mile unit is relevant, so we can also check Feet Per Nauitcal Mile (FPNM). In that case, 6,076 FPNM times 2% equals 121.5 FPNM.

Trigonometry

The technical idea behind slope percentage is just a reflection of the tangent ratio. We can invert the slope by calculating arctan(2%) which equals 1.15°, about one degree. Then we can express the tangent of 1.15° as 105.6 ft over 5,280 ft. Honestly, the exact angle is no less trivial than the slope percentage, it just requires a scientific calculator.

In the image above, you can see that I calculated the hypotenuse length to show that the sloped runway is only one foot longer than the horizontal mile.

Why 2%?

My search for an FAA definition of runway slope also turned up an administrative justification for all this. It’s called paragraph 2.b.3.a.8 of AC 25.1581-1 which, “identifies the information that must be provided in the AFM under the airworthiness regulations.” The latest draft from 2012 reads as follows:

Runway slope. Limitations and performance information should normally be restricted to runway gradients up to ±2 percent. Limitations for runway slopes greater than ±2 percent may be approved if the effects of the larger slopes are validated in a manner acceptable to the FAA. (See AC 25-7C for acceptable means of validating the effects of runway slopes greater than ±2 percent.)

The exact regulatory basis for all this is more complicated and beyond the scope of my article. See 14 CFR § 25.1533 if you are curious about that, but don’t expect to find “2%” enshrined anywhere.