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Southport, Manitoba, Canada
Steve Pomroy is a professional flight instructor and aviation writer. He has been teaching since 1995 and holds an Airline Transport Pilot License, Class 1 Instructor and Aerobatic Instructor Ratings, military QFI, and an undergraduate degree in Mechanical Engineering. He's written and published three flight training books through his company, SkyWriters Publishing, and has several other books under development. Steve currently teaches RCAF pilot candidates on their Primary Flight Training course.

Monday, January 24, 2011

How Big and How Fast?

I recently gave some advice to a student pilot on another forum (www.askacfi.com: base-to-final turn). The advice included, among other things, the suggestion that the turn from final to base leg should be planned for 20° of bank. The reasoning was that steep angles of bank lead to high load factors, which in turn increases the stall speed—potentially bad news when operating at the low speeds and low altitudes associated with an approach to land. Planning for a 20° AOB for the turn allows for a 10° margin to correct for misjudging if we wish to limit ourselves to 30° AOB under these conditions.


30° is a good limit to use since the load factor and stall speed increases up to that point are slight. But they increase rapidly at steeper bank angles (1.15g at 30°, 1.41g at 45°, and 2g at 60°, all corresponding to 7.5%, 19%, and 41% increases in stall speed, respectively).

So the question from all of this is, "What difference does it make what angle of bank I use?". The difference is in the radius of the turn. The turn radius indicates how much space the turn takes, and therefore how much we need to lead the turn in order to roll out on a specific track. We have to lead the turn to final in order to roll out on the extended centerline of the runway. This means we have to anticipate how much space the turn will take, and to manipulate that spacing during the turn if we misjudge.

This is one situation where the relationship between airspeed, AOB, and radius of turn becomes important. Because we can't have a zero-radius turn (which would be a perfect corner on our flight path), we need to anticipate the space we take up when trying to turn onto a target track—such as when turning final and aiming to be on the extended centerline of the runway. If we turn too late, we'll fly through the centerline. If we turn too soon, we won't reach the centerline.

In practice, we normally control the radius of turn with angle of bank. Theoretically, we could also change airspeed, but our airspeed is usually constrained by other considerations—such as our selected target airspeed to use for the approach: too low and we risk stalling, too high and we run into landing difficulties. So a higher AOB will get us a smaller turn radius, and a lower AOB will get us a bigger turn radius. Of course, this is only useful if we have the option of increasing / decreasing the AOB. Decreasing AOB is easy—we can always fully or partially roll out of a turn to widen the radius. Increasing AOB, however, can be problematic if we are trying to limit our load factor (and the corresponding stall speed increase).

To allow for an increase in AOB to compensate for any misjudging that might occur, we need to plan the turn at an AOB that is lower than our selected maximum AOB. This is where the 20° rule comes from.

Planning for turn radius when turning final is often a problem areas for new multi-engine students. Because they are now operating at an airspeed that's higher than they're used to, they have trouble leading the turn-to-final adequately. the correction in this case, until the student has fully adapted to the new increased operating speeds, is to reduce the AOB once in the turn to final and turn judgment improves.

It's also worth noting that rate of turn is closely related to radius of turn. In many situations where we don't need to roll out on a specific track, we're often more concerned with rate of turn than with radius of turn. Luckily, the parameters are the same: airspeed and AOB. Lower airspeed and higher AOB correspond to higher turn rates (and smaller radii). Higher airspeed and lower AOB correspond to lower turn rates (and higher radii). There's a rule of thumb here that works well below about 200 knots: AOB for a "Rate-1" turn (3°/s) is 10% of your airspeed plus 7 (if you're working in knots) or 5 (if you're working in MPH).

Happy Flying!

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