Optimizing turn performance

I shared that in, “a true canyon turn, as mountain flyers call it, the pilot slows the airplane, possibly extending flaps to lower the stall speed, and makes the steepest turn while maintaining controlled flight.” That is certainly not the recipe for a chandelle.

One reader protested that my piece promoted the idea that a small turn radius is achieved at a low speed. He is correct. But I didn’t mean for that article to include a discussion of the canyon turn. Optimizing turn performance can be complicated, and the topic deserves its own column.

Let’s start with some ground rules: A normal category airplane has a published stall speed of V_S=100 feet per second (about 59 knots) and flies with flaps retracted, in calm winds, at maximum gross weight, full forward center of gravity on a standard day at sea level. (In particular, this makes calibrated airspeed the same as true airspeed.) Furthermore, we’ll assume the pilot establishes a level turn with airspeed V (feet per second) and bank angle β, and that the engine produces sufficient power to maintain level flight.

For the normal category, the limit load factor (Gs) must stay at or below 3.8 to avoid compromising the aircraft structure. This means banking the airplane no more than 75 degrees as is shown on the vertical axis of Figure 1 (next page). An airplane stalls at a higher speed in a bank, so the velocity must be at least the turning stall speed in level flight that is indicated by the curve on the left side of the maneuver envelope. For example, the turning stall speed in a 60-degree turn is 141 feet per second, and in a 75-degree banked turn, it’s the maneuvering speed of 195 feet per second. For our purposes, “slow” refers to a speed that is close to, but safely above, the turning stall speed.

Each point in Figure 1 refers to a given velocity and load factor. The background coloring is a heat map that codes each point with its associated turn radius. The cooler blues and purples indicate a tight, efficient turn, and the warmer colors correspond to those that take up more real estate
than necessary.

For any given bank angle, slowing the airplane close to the turning stall speed improves turning performance. And, for a given airspeed, increasing the bank has the same effect. The winning combination of airspeed and bank angle to minimize turn radius occurs in the upper left corner of the envelope: Perform a level turn using
75 degrees of bank and maintain the
maneuvering speed (V_A).

Not every condition within the envelope in Figure 1 is available for sustained flight. Many general aviation aircraft have insufficient power to sustain more than 60 degrees of bank at mid-range airspeeds. And getting close to the turning stall speed requires a high angle of attack, and the increased drag will necessitate even more power. At higher density altitudes, where canyon turn situations often occur, an even smaller portion of the envelope is available for practical use. Any abrupt elevator inputs should happen below maneuvering speed. Pulling back on the yoke at a higher speed could send the airplane outside the envelope and result in structural damage.

Think about the airspeeds and bank angles with which you normally fly and you’ll realize that most of your time occurs in a small, lower section of the envelope. In an emergent situation, do you know how you and your airplane will perform near the edge?

At high density altitudes, true airspeed increases as does the associated turn radius, so the heat map represents a best-case scenario. Stall speed, however, is a function of calibrated airspeed.

For smaller bank angles, steepening the turn results in a much tighter turn radius, but that marginal benefit drops off at higher bank angles. For example, assuming that you can fly at the turning stall speed, increasing the bank angle from 25 to 30 degrees shaves 114 feet off the turn radius. But increasing from 50 to 55 degrees improves turn radius by only 26 feet. And the difference in turn radius between 70 and 75 degrees of bank is a measly 9 feet. Even with sufficient power to sustain the higher bank angles (a big if in most general aviation aircraft), the improvement in turn radius is not worth the effort. The only pilots who can execute a turn of minimal radius are those who fly high-performance aircraft with a high limit load factor, like a military fighter. Such bank angles are not appropriate for most general aviation aircraft.

It’s not surprising that the recommended technique takes the pilot nowhere near the upper left corner of the maneuvering envelope. In his Mountain Flying Bible, Sparky Imeson recommends banking between 30 and 45 degrees and maintaining an airspeed safely above, but close to the turning stall speed. Imeson also recommends extending flaps, as a tighter turn can be made with the lower stall speed. Doing so restricts the procedure to airspeeds below VFE and load factors less than 2. A more modest bank angle and airspeed makes controlled flight easier to maintain and turn performance doesn’t suffer greatly.