In a Dutch roll two major, separate stability characteristics are at work. The first is directional stability, which is the airplane?s weathervaning tendency. When the airplane?s nose points to the left or right of the relative wind, you get sideslip. Another way, sideslip is a condition where the relative wind comes from the left or right of the airplane?s nose. When in a sideslip, airplanes with positive directional stability (which includes every FAA-certificated airplane) want to point their noses into the relative wind, just like a weathervane.
In the Dutch roll the other stability characteristic at work is the dihedral effect, which is the airplane?s tendency to roll when in a sideslip. Because the relative wind is coming from one side of the plane?s nose, one wing generates more lift than the other, and the airplane rolls. Airplanes with positive dihedral effect roll away from the sideslip. Putting it another way, a left roll results from a right sideslip, or when the relative wind is coming from the right of the plane?s nose.
That would be that, except every time there?s a yawing motion, a rolling moment occurs. And every time there?s a rolling motion, a yawing moment occurs. Motion around one airplane axis caused by motion around another airplane axis is ?cross-axis coupling.? Dutch roll is sometimes called a ?lateral-directional oscillation? because of the coupling between the lateral (roll) and directional (yaw) motions.
Here?s the abridged Dutch roll scenario. Something causes a sideslip. It might be adverse yaw, improper rudder coordination, or a lateral gust ? it doesn?t matter. The airplane?s positive directional stability yaws the plane into the relative wind, but it overshoots. The nose swings through the relative wind so it is now in the opposite sideslip. The oscillation continues with each overshoot, with each oscillation getting smaller than the previous one, until the plane settles down with its nose again pointing into the relative wind.
While they are occurring in yaw, similar overshoots occur in roll because of the airplane?s positive dihedral effect. There are other reasons why the yaw and roll feed off each other, such as roll due to yaw rate, tilted lift and drag vectors, differential induced drag, and a few others, but the important point is that yaw and roll overshoot.
Dutch rolls come in a variety of flavors. Some dampen quickly, with a minimal number of yaw and roll overshoots, and others oscillate a dozen times or more before settling down. Some oscillate rapidly, and others sort of mosey back and forth. Some are snaky ? mostly yaw with little roll, and some are rolly ? mostly roll with little yaw.
Airplanes with strong directional stability usually have fairly quick Dutch rolls, with few overshoots in yaw and roll. This may be fine from the Dutch roll perspective, but strong directional stability and weak dihedral effect usually cause spiral instability. That means an airplane in a bank tends to roll off or increase its bank angle on its own, unless the pilot prevents it.
Weaker directional stability is likely to improve the spiral stability but result in more Dutch roll yaw and roll overshoots before the airplane settles down. The relative strengths of an airplane?s directional stability and dihedral effect determine several lateral-directional characteristics. The final airplane design can be a compromise between Dutch roll damping (how quickly the roll/yaw oscillation subsides) and spiral stability.
Pilots seem to prefer snaky Dutch rolls to rolly ones. Several arguments can be made for this preference, but it?s a good bet pilot comfort is the primary reason. Think of yourself flying an airplane whose Dutch roll is frequently excited in light turbulence, and you?re flying in a bumpy sky. Would you rather keep an eye on the plane?s heading as it oscillates a few degrees, or would you rather be rolled back and forth five to ten times every time you encounter a gust?
What Good Is It?
Essentially, the Dutch roll is a nuisance that you can deal with a few different ways. First, you can ignore it. When it happens, you simply wait for it to subside, which can take from a few to probably not more than 10 seconds. That?s not such a long time, unless you are doing something important, like flying an ILS approach in actual instrument conditions. The snaky Dutch roll makes it more difficult to precisely track the localizer, and the rolly one doesn?t help the vertigo or burrito lunch situations.
Another method is to suppress the Dutch roll it once it begins. Usually this is fairly easy and requires one or two rudder pedal inputs. You?ve probably been doing this every time you fly, and just never noticed. How easy it is to suppress the Dutch roll depends on the airplane. Even if bringing a Dutch roll to a halt is easy, it still requires extra work and attention, which means you can?t devote that effort to other flying tasks.
Finally, you can prevent the Dutch roll. If it doesn?t get excited, you don?t have to deal with it. This method works well for planned maneuvers like coordinated turns, but other sideslip sources, such as lateral gusts, don?t give you advance notice. In this case you?ll have to resort to one of the other methods.
The Math
The Dutch roll behavior is mathematically identical to the motion of a pendulum, a car?s suspension, or the traditional stability model of a marble in a bowl, rolling down one side, up the other, then back down again. Engineers characterize this oscillatory motion by a frequency and damping ratio. Frequency is described in cycles or oscillations per second. The higher the frequency, the faster the airplane yaws and rolls back and forth. The damping ratio is a measure of how soon or abruptly the oscillations diminish. The higher the damping ratio, the smaller each subsequent yaw and roll overshoot.
How frequency, damping ratio, and the yaw-roll relationship mix and match does matter to pilots, even though you can do nothing to change these relationships except install a yaw damper or autopilot. The combination of high frequency and rolly Dutch roll may be the least desirable. Generally, the lower the frequency, the more rolly a Dutch roll we pilots are willing to tolerate.
In the Cockpit
The next time you?re cruising straight and level at a safe altitude, displace one rudder pedal, then the other pedal, take your feet off the pedals, and observe the airplane?s response. Start with small pedal displacements, don?t make any aileron or elevator control inputs, and make sure the autopilot or yaw damper is not engaged. The airplane will probably yaw then roll in the direction of the displaced pedal. Once your feet are off the pedals completely, the airplane will probably yaw and roll back and forth several times before it returns to straight and level flight. This is Dutch roll. In fact, this is how it is tested and measured.
If you?d like to see how Dutch roll can affect a piloting task, try this. Configure your airplane for landing and trim for straight and level flight at final approach airspeed. The reason for this configuration is that adverse yaw is usually more obvious at the higher angles of attack typical of landing pattern flight conditions. With your feet off the pedals, turn to a heading and attempt to roll out on that heading exactly. You?ll probably over- or under-shoot the heading. When you try to correct those few degrees, you?ll end up chasing the heading as the airplane yaws and rolls in response to your continued aileron deflections.
The reason you?re making those aileron inputs is because adverse yaw creates a sideslip, which initiates the Dutch roll. Every subsequent aileron deflection creates additional adverse yaw that leads to another Dutch roll oscillation even before the previous one subsides. One suggestion naturally emerges, namely, don?t try to suppress a Dutch roll ? even a rolly one ? with the ailerons. To suppress it you must eliminate the sideslip, and the rudder is the primary control for that task. Naturally, you should fly these experiments at a safe altitude and airspeed and without compromising safety.
So what do you do with this information? Maybe nothing. Then again, next time you?re battling the airplane in a struggle for lateral or directional precision, think Dutch roll. Try eliminating the sideslip and see if it helps.
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