When an airplane is in a bank, three things can happen to its roll attitude. The bank angle can increase, decrease, or remain the same, depending on the airplane's spiral stability. Spiral stability is the airplane's tendency to remain (or not) in an angle of bank without any attention from the pilot. Some people call this phenomenon roll stability, but there's more to the story than roll.
Whether the airplane maintains its bank angle depends on several of its stability characteristics. With most airplanes four of these characteristics are dominant, and they determine the airplane's spiral behavior. Let's build a hypothetical airplane and look at these four characteristics individually to see how they affect the airplane's spiral stability.
Let's put our imaginary airplane in an angle of bank in level flight. It's not turning yet, but we'll begin our examination the moment after the pilot rolls the airplane to this bank angle and then centers the cockpit controls, so the pilot is off the yoke and pedals.
Toward Increased Bank Angle
An airplane in a bank wants to move sideways in the direction of the low wing because its lift is tilted toward that wing. As it slides in that direction, it creates a wind component coming from the low-wing side. This wind component from the side combines with the forward wind component to create the total relative wind acting on the airplane.
An analogy to this would be an airplane flying wings-level in a crosswind. The wind from the side combines with the wind from the front (airspeed) and results in a relative wind slightly off the airplane's nose. For an airplane in a right-wing-down (RWD) bank, the relative wind is coming from a little to the right of the airplane's nose. Therefore, the airplane is in a right sideslip.
An airplane's directional stability is its tendency to point into the relative wind. The vertical tail provides most of an airplane's directional stability, but other things that make an airplane weathervane, such as the aft portion of fuselage itself, also contribute. Because the relative wind is coming from the right, our airplane's directional stability attempts to swing the nose to the right.
As the airplane's positive directional stability swings the airplane nose-right, the left wing swings forward and the right wing swings backward. Of course, the right wing doesn't actually move backward because the airplane is traveling forward. But the combination of the airplane's forward speed and its nose-right yaw rate causes the left wing to move forward faster through the air than the right wing. Because the left wing is moving faster through the air it generates more lift. The differential lift between the wings attempts to roll the airplane RWD. This is called roll due to yaw rate.
another roll-due-to-yaw-rate contribution exists even when an airplane is in coordinated flight, i.e., without sideslip. A constant-bank level turn, after all, is a combination of pitch rate and yaw rate. You can convince yourself this is true by imagining an airplane making a level turn using 90 degrees of bank. Such a turn is the result of pitch rate alone. Now imagine an airplane making a level turn with no bank angle - a flat turn. This turn would be pure yaw rate. Level turns performed with a bank angle between 0 and 90 degrees involve some combination of pitch rate and yaw rate.
As the airplane turns, its outer (high) wing travels farther through the air than its inner (low) wing because it's farther from the center of the turn circle. To keep up with the rest of the airplane (as it must), the outer wing must move faster through the air than the inner wing, just as a propeller tip moves faster than the hub. Again, the differential speed causes differential lift, which tends to roll the airplane toward the inner or low wing during a turn.
The combination of positive directional stability and roll-due-to-yaw rate tends to increase the airplane's angle of bank. Directional stability yaws the airplane toward the low wing, resulting in the differential lift between the wings, which rolls the airplane toward the low wing. The faster the outer wing's speed, the greater this increased-bank tendency.
Toward Decreased Bank Angle
The nose-right yaw rate means the airplane is rotating in yaw as it flies. The air resists this rotation the same way water resists your arm motion in a swimming pool. The air damps the yaw rate and attempts to stop it altogether. The faster the yaw rate, the greater the yaw damping.
Yaw damping resists the motion caused by the directional stability. If the damping was infinitely high it wouldn't allow any yaw rate at all in response to the sideslip. Because the yaw damping opposes the yaw rate, it also inhibits the roll-due-to-yaw rate. The resulting effect of yaw damping is to oppose any increase in bank angle.
An airplane with a positive dihedral effect tends to roll away from the sideslip. Some call this lateral stability. In our example, the sideslip is from the right, so the positive dihedral effect tries to roll the plane to the left, toward wings-level.
You can observe the dihedral effect quite easily in the airplane you fly. When you're flying wings level, step on one rudder pedal. If the airplane has positive dihedral, and most do, you should see the airplane's nose yaw in the direction of the pedal you're pushing. The yawing movement is followed by a roll, which also is in the direction of the pushed pedal. Left pedal causes a left yaw, which creates a right sideslip. The airplane responds to the right sideslip by rolling away from it, to the left.
Total Effect
Let's start again with the airplane in a bank. It slides toward the low wing, which creates a sideslip from the low-wing side. Directional stability tries to swing the airplane's nose toward the low wing. If this happens, the yaw rate causes differential lift between the wings, with the high wing producing more lift than the low wing, resulting in a roll toward the low wing. The combination of positive directional stability and roll-due-to-yaw rate tends to increase the airplane's angle of bank.
As the airplane flies through the turn the outer wing moves faster through the air. Again the differential lift caused by the wings' different speeds through the air tends to increase the bank angle.
While this is going on the airplane's positive dihedral effect is responding to the sideslip. As long as there's sideslip from the low-wing side, dihedral effect tries to roll the airplane toward wings-level. The more successful the airplane's yaw damping, the more inhibited the airplane's directional stability. This means the airplane is in the sideslip longer, which gives the dihedral effect more time to roll the airplane away from the low wing.
Whether your airplane's bank angle increases, decreases, or remains the same depends on the relative strengths of the four stability characteristics discussed. If the product of positive dihedral and yaw damping is greater than the product of positive directional stability and roll-due-to-yaw rate, the airplane will roll out of the bank toward wings-level. If the product of positive directional stability and roll-due-to-yaw rate is greater than the product of positive dihedral and yaw damping, the airplane will roll into the bank toward a steeper bank angle. If the two products are the same, the airplane should maintain its bank angle.
Cockpit Perspective
An airplane that tends to roll out of a bank angle has convergent spiral stability. It converges toward wings-level. To maintain a constant angle of bank in this airplane you must hold a little aileron in the direction of the turn. Or, you can apply a little extra rudder in the turn direction, creating sideslip from the outside of the turn, forcing the dihedral effect into play from the outside of the turn. This would be a skidded turn and can be considered sloppy piloting.
An airplane that tends to roll into the bank angle has divergent spiral stability. A constant-bank-angle turn in this airplane requires a little out-of-turn aileron. This isn't very intuitive and can result in crossed controls, such as right rudder and left yoke for a RWD turn.
There's another insidious and potentially dangerous consequence of divergent spiral stability. As the directional stability yaws the airplane toward the low wing, it also yaws it toward the ground because of the bank angle. Unnoticed, this can result in a steep, ever-tightening spiral dive. Besides the possibility of pilot disorientation, there's the risk of exceeding VNE or the airplane's maximum load factor (G) during the recovery.
An airplane that maintains its bank angle without any extra pilot control inputs has neutral spiral stability. This characteristic is often considered desirable for instrument flying. An airplane with divergent spiral stability can subtly place itself in an unusual attitude, and an airplane with subtly convergent spiral stability can alter the airplane's flight path before the pilot notices it.
Pilots usually deal with slightly convergent or divergent spiral stability characteristics without complaint. An airplane whose bank angle doesn't change very quickly usually isn't a threat because it completes the turn before a substantial bank angle change can occur.
What are your airplane's spiral stability characteristics? Chances are you may never have noticed. Many pilots don't, particularly if all their flying is VFR. To see how the airplane you fly behaves, make several level turns with a heading change of more than 90 degrees - and make them under the hood (and with your instructor or a safety pilot). Notice how well you maintain bank and altitude control, and pay attention to where you hold the yoke and pedals during the constant bank angle.
a host of factors affect the precision of this simple task, but this is often a good way to see how an airplane's spiral stability can affect the ease of performing routine piloting tasks. You may be surprised to discover what you've been doing with the controls all along and just never noticed.
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