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Proficiency: Take it to the bank

The anatomy of a turn

On your first flight as a student pilot, you learned to alter course by rolling the aircraft into a banked turn while maintaining altitude. You probably got the hang of it quickly without realizing that the maneuver is one of the most complicated in the private pilot syllabus. Let’s dissect an aircraft turn into its components in order to see why.
P&E May 202

Bank angle. In straight and level, unaccelerated flight, the forces on an aircraft are balanced and lift is equal to weight (slideshow). To effect a turn, that balance is disrupted as the aileron deflection, along with rudder deflection to compensate for adverse yaw, rolls the airplane into a coordinated, banked turn. The diagram on the facing page (top right) shows the aircraft forces once the bank is stabilized.

The vertical component of lift is equal in magnitude and opposite the direction of weight, to keep the altitude constant. The horizontal component of lift provides the unopposed force necessary to continually change the aircraft’s direction of motion.

Notice that the lift vector in the 60-degree banked level turn has twice the magnitude of the weight vector. With this load factor of two, your body will accordingly feel twice as heavy as it normally does, just as you would feel at times on a roller coaster. Incidentally, the version of this diagram in the Airplane Flying Handbook incorrectly shows a force that directly opposes the lift vector. It is probably an attempt to explain load factor, and unfortunately this misleading diagram has been copied in many other texts and online courses. Velocity changes, in magnitude or direction, only from an imbalance of forces.

The bank angle you select will depend on how efficiently you need to reverse course. Turn radius and time spent in the turn are both inversely proportional to bank angle (until you approach very steep turns, where the relationship is more complicated). And that makes sense. For a quick, tight turn, use a steep bank and you’ll be headed in a different direction in no time (slideshow).

Power setting and angle of attack. While aileron deflection rolls the aircraft into the banked turn, a combination of increased power and angle of attack create the greater lift needed to balance the vertical forces. A shallow bank might be accomplished solely by raising the angle of attack, but a steep bank in most general aviation aircraft requires increased power to avoid approaching a stall. Each combination of power setting and angle of attack will result in an airspeed for which the effect on turning performance isn’t as obvious as it is for bank angle.

Time spent in a turn is proportional to airspeed, so fast airplanes take much longer to reverse course than slower ones. Since this time changes with airspeed, the turn coordinator or the turn rate indicator on a glass primary flight display provides information on rate of turn. In instrument conditions, we usually strive for a standard-rate turn, one for which a 180-degree course reversal takes one minute. Thankfully no calculations are necessary.

Airspeed has a profound effect on turn radius, which is proportional to the square of airspeed. Doubling the airspeed, then, means the turn radius is increased by a factor of four (see slideshow).

Anatomy of a turn (click on image for slideshow)

In straight and level,unaccelerated flight, the lift created by the airplane is equal to its weight (above). In a coordinated, banked turn, the vertical component of lift is equal in magnitude and opposite in direction of the weight. In this 60-degree turn (above right), note that the total lift has twice the magnitude of the weight vector. So the occupants feel twice as heavy as they normally do. Airspeed has a profound effecton turning performance. As airspeed doubles, the turn rate is cut in half but the turn radius quadruples. As bank angle doubles,both turn radius and time to complete a course reversal is cut in half. In a turn, the outer wing travels a greater distance in the same amount of time so it has a higher velocity and, compared to the inside wing, experiences more lift. The effect is magnified for aircraft with long wingspan and requires ailerons deflected opposite the turn.

This is why the typical procedure for performing a canyon turn (or any situation that necessitates reversing course in a confined area) involves full power; maintaining a minimal airspeed, usually aided by extending flaps to lower stall speed; and turning into the wind using a bank angle appropriate for a tight turn but without approaching a stall.

Overbanking tendency. In a coordinated turn, the aircraft moves along a cone so that, in any given amount of time, the outer wing moves faster through the air than the inside wing (p. 96). The differential velocity means that the outer wing, with more lift than the inside wing, tends to roll the aircraft more deeply into the turn—so it is necessary to hold aileron against the turn. The wider the wingspan, the more noticeable the overbanking tendency becomes, so glider pilots know it well.

Atmospheric conditions. Any factor that changes the wing’s ability to generate lift will affect the turning qualities of the aircraft. In particular, high air density (low altitude, low temperature, high altimeter setting) means that, for a given angle of attack and velocity, the wing can produce more lift. With increased engine and aircraft performance, the same turn will require a lower power setting and/or a lower angle of attack.

Finally, all the above is predicated on calm air with no vertical movement, but updrafts and downdrafts require you to adjust power and angle of attack to maintain the constant altitude that ATC or your FAA examiner expects.

A recent private pilot candidate reassembled all these components into the steep turn she performed to ACS standards. After clearing the area and pointing the aircraft at the Tullahoma Regional Airport in the distance, Ruth used aileron and rudder deflections to smartly roll the Cessna 172 into a 45-degree bank turn. While rolling in, she increased power and used appropriate back-pressure on the yoke to maintain a constant altitude. Once stabilized, Ruth maintained that 45 degrees by keeping the angle between the glareshield and the horizon constant. She knew where along the glareshield the two should intersect (different for left and right turns) to maintain altitude with only a couple checks of the altimeter. Without realizing it, she maintained slight opposite aileron to compensate for the overbanking tendency. About 25 degrees before the reference reappeared, Ruth smoothly applied aileron opposite the turn while decreasing both power and back-pressure to ensure a constant altitude during a flawless rollout on the original heading.

Considering all the factors that need to be managed to perform such a steep turn, the maneuver demonstrates a mastery of the aircraft. That spot on the glareshield at which it intersects the horizon will be different for every aircraft and every factor we’ve discussed.

Frankly, I find it amazing pilots master the maneuver at all, but thousands of pilot certificates issued each year testify that they do. When checking out in a new aircraft or just knocking the rust off in my own, I go around twice for 720 degrees for a steep turn, as once happens too quickly to see what power settings and back-pressure work. I’ve also learned the importance of allowing myself a few Mulligans before I get it right.

Catherine Cavagnaro is an aerobatics instructor (aceaerobaticschool.com) and professor of mathematics at Sewanee: The University of the South.

Catherine Cavagnaro

Catherine Cavagnaro is an aerobatics instructor (aceaerobaticschool.com) and professor of mathematics at Sewanee: The University of the South.

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