How are Class E surface area extensions determined?

Ever looked at a sectional chart and noticed those keyholes of dashed magenta lines sticking out from a Class D or E surface area? Known as Class E extensions, they designate where the Class E airspace extends all the way to the surface, instead of starting at 700 ft AGL or 1200 ft AGL like normal.

How do they get these shapes, and what are they for? Many people can answer the second question, correctly but vaguely, with a "to protect for instrument approaches." This is correct, but why do you see extensions at some airports and not others? And why are some big, some small, some fat, and some narrow?

Look at Ardmore, Oklahoma's Class E extensions (KADM):

If you look at the instrument approaches for this airport, you'll see approaches coming from the NE, SW, and SE. But the Class E surface area extensions only go out to the NW and SW - and the SW one is a lot larger than the NW one. Why?

It has to do with the way the airspace extensions are determined, which depends greatly on both the design of the approach from that direction and the terrain underlying that approach.

Let's assume for right now that the terrain surrounding Ardmore is completely flat - it's not, with variations up to a couple hundred feet nearby, but close enough for now. Ardmore's field elevation is 777 MSL, so let's round off and say that all the terrain around there is right at 800 MSL. Now, we know from our Private Pilot ground school that the shaded magenta means that Class E airspace starts at 700 feet AGL. So in order to protect the aircraft as it descends below 700 AGL, a Class E surface area is created - at the point that the airplane is expected to descend below 700 AGL. In addition, a 300 foot buffer is accounted for in there, so it's actually where the aircraft is expected to descend below 1000 AGL.

The methods for calculating this point are extremely detailed and laid out in FAAO 8260.19F, Chapter 5. If there's a cure for insomnia, this chapter is it! There are variations for procedure turns (before, after, and at the FAF), hold-in-lieu-of-procedure turns, precision vs non-precision final approaches, procedures without Final Approach Fixes (FAFs), ways to account for high terrain in segments before final, and more. But I'll briefly focus on two common situations - vertically guided and non-vertically-guided final approaches, with FAFs.

Vertically guided final (ILS, LPV, LNAV/VNAV):

This is conceptually pretty simple - to determine when the aircraft is going to descend below 1000 ft AGL after the FAF, you just use the established glideslope - the pilot should be following the glideslope, so that's what is used. If the FAF is 1500 feet above the ground and there glideslope is 3 degrees, then at 318 ft per nm descent the aircraft will cross 1000 feet above the ground at 500/318 = 1.57 nm "in" from the FAF. So that would establish where the Class E surface extension starts! 

Non-vertically-guided final (LOC, LP, LNAV, VOR, NDB, etc.):

This is more difficult, because there's no way to know how quickly a given pilot is going to descend down to the MDA. In order to simplify some already complex rules, the equation for this rate of descent doesn't account for the wide variations in charted descent angle, stepdown fixes, or even always realistic expectations. The pilot is assumed to descend at 300 feet per mile when within 7 nm of the runway threshold, or at 500 feet per mile if further than 7 nm from the runway threshold. So a FAF that is 9 miles from the runway will use a combination of both descent rates.

In both of these cases, the 1000-foot AGL point is determined using the highest terrain within the final segment. So if it's hilly, that will likely push the 1000-foot point out further from the airport. Also, if due to terrain the aircraft will descend below 1000 feet AGL before the FAF, there are a whole another set of calculations for that, and the airspace extension will likely be longer (and wider too).

So now we know where the aircraft is going to descend below 1000 feet, and how far out the Class E extension goes, but how wide is it? The width is determined by the size of the obstacle evaluation area. I'm not going to go into that here, but see my other blog post for an example of this calculation for a VOR.

Now back to Ardmore. There is no Class E extension to the southeast. The FAFs for the approaches from that direction are close enough to the existing Class D, the altitude is high enough, and the terrain low enough that the aircraft will not descend below 1000 feet AGL before entering the Class D. So no extension is needed.

The approach from the northwest, the RNAV (GPS ) RWY 13, has LP and LNAV minimums - so no vertically guided final.  The FAF is 2000 feet above the airport, and the final is 6.4 nm long. However, the terrain underneath this final is higher than the airport - a clue is the height of the antenna towers near the FAF - the terrain appears to be almost 1300 MSL in this area. So the aircraft will descend below 1000 AGL before reaching the Class D, and needs to be protected.

Lastly, the VOR approach from the southwest (VOR-B) has the VOR itself as the FAF. It is a long final, 8.8 nm, so the descent rate used for the calculation is the higher 500 feet/nm discussed above, until the aircraft is 7 nm from the runway. This means the aircraft gets to 1000 AGL quicker (further out), the extension needs to be longer, and it is.

Similar calculations are performed for the shaded magenta areas that indicate 700-foot floor Class E airspace. However, in this case they're trying to determine where the airplane crosses 1500 feet AGL (the normal 1200 foot Class E floor + 300 foot buffer). As a result, the areas extend further out from the airport. Also, often the areas merge with those of other airports so the airspace is shaped to encompass all of the other airspace, resulting in some unusual areas.

I think that's enough for now. Keep the questions coming!