Dutch Roll

Dutch roll is a coupled oscillation in yaw and roll. Disturbed by a gust or a rudder input, the airplane yaws one way and rolls the same way a moment later, then swings back to yaw and roll the other way, and the cycle repeats with the two motions out of step. The FAA's Pilot's Handbook of Aeronautical Knowledge describes the nose making a figure eight on the horizon. In most airplanes the motion dies out within a few cycles; in a swept-wing jet at high altitude it can be so lightly damped that it persists, which is why such airplanes carry yaw dampers.

The mode is introduced, with the sources of dihedral effect and directional stability, in lateral and directional stability. This article goes further: a cycle step by step, why sweep, altitude and speed matter, the certification rule, the yaw damper and the pilot's technique when it has failed.

Dutch roll defined

Every airplane has a few natural ways of moving when it is disturbed and left alone, its dynamic modes. In pitch they are the short-period oscillation and the phugoid. In roll and yaw a pure rolling motion is so heavily damped that it stops almost as soon as the ailerons are centered, the spiral mode is a slow, non-oscillatory change of bank, which in a spirally unstable airplane steadily steepens, and Dutch roll is the oscillation. It is called lateral-directional because it involves both lateral stability, about the longitudinal axis, and directional stability, about the normal axis.

Whether a Dutch roll dies away is a question of dynamic stability. An oscillation whose amplitude decreases with time shows positive dynamic stability; one that keeps a constant amplitude is neutral; one that grows is unstable. The FAA describes Dutch roll as usually dynamically stable but objectionable because of its oscillatory nature, with damping that may be weak or strong depending on the airplane. What makes it a hazard is not usually divergence on its own but a lightly damped mode that turbulence keeps re-exciting, and a pilot who makes it worse by trying to stop it.

One cycle, step by step

The mechanism is easiest to follow through one cycle on a swept-wing airplane, starting with a yaw:

1. A gust yaws the nose right. For a moment the airplane keeps moving along its old path, so the airflow now meets it from the left of the nose: a sideslip.
2. The airplane rolls right. The left wing now faces into the airflow. On a swept wing it presents less effective sweep and more span to the flow, so it lifts more, and the right wing lifts less. This is the dihedral effect: a rolling moment that raises the wing facing into the sideslip. The roll follows the yaw, in the same direction.
3. The fin turns the nose back. The airflow meets the fin at an angle equal to the sideslip, and its side force, acting behind the center of gravity, swings the nose back to the left; the extra drag of the advancing left wing helps. But the fin's restoring moment is weak compared with the rolling moment, so the yaw correction is slow, and the nose swings through the relative airflow and past it.
4. The cycle reverses. With the nose now left of the flight path, the airflow comes from the right, the right wing lifts more, and the airplane rolls left while the fin yaws the nose right again.

Each roll is driven by the sideslip that came before it, so the roll lags the yaw and the two motions stay out of step. Whether each swing is smaller than the last depends on the damping provided by the fin and the wings, which resist the rates of yaw and roll themselves.

View full schematic

Lateral and directional stability interaction

The cycle shows the balance at the heart of Dutch roll. Directional stability, or weathercock stability, is the tendency to yaw back into the relative airflow after a sideslip; the fin is its main source. Lateral stability, measured as dihedral effect, is the tendency to roll away from the sideslip, raising the wing that faces into it; dihedral, a high wing and sweepback all add to it. Dutch roll appears when the dihedral effect is large compared with the static directional stability.

The opposite imbalance gives spiral instability. When directional stability is very large compared with the dihedral effect, the fin yaws the nose into the sideslip faster than the wings can roll level after a small bank; the outer wing then moves faster and lifts more, and the bank slowly steepens into a descending spiral, which uncorrected becomes a spiral dive. This is the airplane's spiral stability, or lack of it. The two modes sit at opposite ends of one design choice: more fin cures Dutch roll but pushes the airplane toward spiral instability, and more dihedral effect does the reverse. The FAA notes that because spiral instability is more desirable than Dutch roll tendencies, most airplanes are designed with it; a slow, steepening bank is far easier to manage than a rapid oscillation.

Some design features follow directly. A wing that is both high-mounted and swept back would have so much dihedral effect that many heavy military transports are given anhedral to take some away. The FAA also notes that a V-tail is more susceptible to Dutch roll tendencies than a conventional tail.

Why swept wings are prone

Sweepback adds to both kinds of stability, but unequally. In a sideslip the advancing wing has less effective sweep, so it produces more lift and more drag. The extra lift is a strong dihedral effect, proportional to the wing's lift coefficient and to its sweep. The extra drag yaws the nose back, a stabilizing directional contribution that the FAA describes as relatively small compared with other components such as the fin (see swept wings).

Because the dihedral effect of sweep grows with lift coefficient, it is largest at low indicated airspeed. A swept-wing airplane is therefore most prone to Dutch roll when slow and at a high lift coefficient, and least prone at high IAS, where a spiral tendency may dominate instead. The FAA observes that in most modern airplanes, except high-speed swept-wing designs, these free directional oscillations usually die out in very few cycles unless the air stays gusty.

Altitude and speed effects

Altitude reduces the damping. A yawing motion damps itself because the fin, swinging sideways as the airplane yaws, meets the airflow at a changed angle of attack and generates a force that resists the yaw. How large that change is depends on the fin's sideways speed compared with the true airspeed.

A worked comparison shows the size of the effect. At a given indicated airspeed the true airspeed is roughly IAS ÷ √σ, where σ is the relative density. At FL400, where σ is about 0.25, the TAS is about twice the IAS. A given yaw rate swings the fin sideways at the same speed at either altitude, but against twice the airspeed it changes the fin's angle of attack only about half as much. The dynamic pressure is the same, because the IAS is the same, so the damping moment that the yaw rate produces is roughly halved: at the same IAS, a given yaw rate meets about half the resistance at FL400 that it meets near sea level.

High altitude also brings the low-speed side of the problem. FAA AC 61-107B notes that jets at high altitude and high Mach number may meet problems associated with slow-speed flight, Dutch roll among them, at the same time as compressibility effects, and that the reduced air density lowers aerodynamic damping. A swept-wing jet at cruise altitude flies at a low IAS and a high lift coefficient, which strengthens the dihedral effect of sweep, in air that damps it less. That combination is why yaw dampers matter most in the cruise, and why descending, which lowers the TAS, restores natural damping (see high-altitude operations).

Certification rules for Dutch roll

The certification code for large airplanes sets the standard. Under CS 25.181 and 14 CFR 25.181, any Dutch roll occurring between 1.13 VSR and the maximum allowable speed for the configuration must be positively damped with the controls free, and controllable with normal use of the primary controls without exceptional pilot skill.

Many swept-wing jets meet this only with their yaw damper working. AC 61-107B states that a stability augmentation system is required when the Dutch roll tendency is objectionable or adversely affects the control and stability requirements for certification. CS 25.672 and 14 CFR 25.672 then add conditions for any such system: a clearly distinguishable warning of a failure that could be unsafe if the crew did not notice it, and safe controllability after any single failure within the approved limitations. That is why many large transport aircraft carry two or three yaw damper channels, and why the minimum equipment list for an inoperative damper typically limits the altitude and may restrict speed or RVSM operations.

Yaw dampers

A yaw damper is a stability augmentation system that supplies the damping the airframe lacks. It senses yaw rate, with a rate gyro or from the inertial reference system, and makes small, rapid rudder movements against it, stopping the oscillation before it builds up. ATPL texts quote a typical authority of about 3° to 6° of rudder, enough to damp an oscillation that has not been allowed to grow.

Two refinements make it work. A Dutch roll filter, a narrow band-pass filter tuned to the Dutch roll frequency, keeps the damper from opposing a deliberate turn: in a steady turn the yaw rate is constant and the filter's output falls to zero. Phase advance brings the rudder correction forward so that it acts at the maximum yaw rate, not after the fin has begun to return the nose, when it would add to the next swing. On most transport aircraft the damper runs throughout the flight, whether or not the autopilot is engaged.

On the Boeing 737 NG either of the two yaw dampers provides Dutch roll prevention, gust damping and turn coordination, and their movements do not move the rudder pedals. On the A320 the ELACs compute the yaw damping orders and the two Flight Augmentation Computers execute them through the rudder; in yaw alternate law the remaining damping is limited to ±5° of rudder. The hardware, the filter and rudder limiting are covered in yaw dampers and rudder limiting.

Manual recovery

A yaw damper failure does not make the airplane uncontrollable, but at high altitude the Dutch roll may be poorly damped. The crew follow the checklist, and if an oscillation develops they damp it with small, well-timed aileron inputs against the roll. The rudder is not used.

The reason is the order of cause and effect seen in the cycle. A rudder input yaws the airplane first, the yaw creates a sideslip, and only then does the dihedral effect roll it, so roll lags the pedal. A pilot trying to stop a Dutch roll with the rudder reacts to a motion that is already changing, easily falls out of phase, and can turn the oscillation into a pilot-induced oscillation that diverges. Aileron acts on the roll directly. Descending to a lower altitude then lowers the TAS and restores natural damping; with a damper inoperative, the MEL typically limits the altitude for dispatch anyway.

The NTSB's investigation of American Airlines Flight 587, an Airbus A300-600 that lost its fin after a wake encounter in 2001, shows the same lag at work, although the accident was not a Dutch roll. The first officer made five alternating rudder inputs in about 7 seconds. Each built a larger sideslip; the roll, which follows the sideslip rather than the rudder, lagged behind the pedals, and the sideslip combined with the rudder deflections loaded the fin to about twice its certified limit load, beyond its ultimate design load. The Board found that if he had stopped the inputs at any time before the fin broke, the airplane's natural stability would have returned the sideslip to near zero. It discussed the sustained inputs as a possible adverse aircraft-pilot coupling.

Library articles are written for study and exam preparation. They do not replace your aircraft's approved documentation, your operator's procedures or the regulations themselves.