Leeham News and Analysis
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Leeham News and Analysis
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Bjorn’s Corner: Aircraft stability, Part 2
By Bjorn Fehrm.
April 20, 2018, ©. Leeham News: In the last Corner, we discussed how to stabilize an aircraft in pitch so it could fly stably straight ahead. For this, we needed a horizontal tail which had a negative lift.
This will buy us a short-term pitch stability, but not a long-term one. Why we will explain in this Corner.
Figure 1. The long-term pitch instability, Phugoid. Source: Leeham Co.
Aircraft long-term stability
Normally, stable aircraft (all commercial and private aircraft are of the stable type; only military fighters are allowed to use marginal stability to improve performance) have three modes of longer-term movement which are part of the aircraft’s natural way of flying.
These movements appear despite the aircraft at first flying stably straight ahead, perfectly trimmed in pitch, yaw and roll. One could say the three modes are part of the DNA of a flying aircraft. If one should suppress one of the movements, then the aircraft would feel awkward to fly for the pilot in normal maneuvers.
During design and flight-testing of an aircraft, the aircraft is tuned so it’s stable in the short-term and will react in a predictable manner for the longer-term movements. We start with the longer-term movement in pitch.
Phugoid
The first mode of oscillation is the most docile one. Those who have flown a private airplane on a long trip with a wings leveler autopilot (we come to why this is the most needed autopilot support) know what I’m talking about. With the wings leveler keeping the aircraft from dipping its wings, one trims the aircraft with the pitch trim to keep the altitude.
After careful pitch trimming (pitch trim adjusts the amount of downward lift of the horizontal tail) and flying hands-off, the aircraft flies straight for a while but then starts to cycle up and down in a slow mode, the Phugoid. When a tiny disturbance turns the nose down the slightest, the aircraft gains speed. As it gains speed, lift increases and after about half a minute it starts climbing, Figure 1. When climbing, it loses speed, so gradually the nose goes down again after another half minute. Then the cycle recommences with the aircraft gaining speed while dipping the nose followed by an up cycle.
The fact the nose goes down when the aircraft loses speed is an important aspect of a stable aircraft. It means most aircraft will get themselves out of trouble (trouble here is losing so much speed the air stream breaks down and we are in stall) if the pilot just lets go of the stick.
Spiral mode
In the description of the Phugoid, we presumed we had a wings leveler autopilot. If not, we would have suffered from a more troublesome mode than the Phugoid, the Spiral mode. The Spiral mode comes from the aircraft being stable in yaw. The vertical tail will make sure the aircraft returns in yaw to straight ahead after a disturbance. It has positive weathercock stability.
This weathercock stability will cause the aircraft to slowly start leaning over on one wing after the tiniest of disturbance. The leaning gets steeper and for most aircraft, it will take long to roll wings back to level; many will not roll back.
Spiral mode keeps the pilot the busiest. Take your mind off keeping the wings level for a few seconds and next time you check, you are hanging on a wing. If you are flying somewhere you have just steered off course.
Because of the Spiral mode, the first pilot aid one buys for a small aircraft is the wings-leveler. It’s a simple autopilot which uses the directional turn-rate gyro as the sensor (all aircraft have a turn-rate gyro, it’s one of the base instruments). The wings leveler makes sure we stay on course when flying. If we cycle a bit in altitude with the Phugoid in a private plane flying under visual conditions is often not bothersome. If it is, we need a pitch channel for the autopilot as well.
As an aircraft designer one can counter the spiral mode with more roll stiffness. To get more roll stiffness one increases the aircraft’s dihedral. This means we bend the wings up so any leaning followed by a sideslip mean the lower wing gets a longer horizontal part. It’s then more effective in producing lift and the roll is stopped.
But if we increase the roll stiffness of the aircraft too much we trigger the ugliest of the natural aircraft modes, the Dutch Roll.
Dutch Roll
The Dutch Roll is the most uncomfortable mode of aircraft movement for a naturally stable aircraft. It gets strong for an aircraft which is stiff in roll (with strong dihedral or wing sweep) and therefore has a weak spiral mode. The movement of the aircraft resembles the Dutch ice-skaters on their canals, therefore it came to be called Dutch Roll, Figure 2.
Figure 2. An aircraft starts a Dutch Roll movement. Source: Google images.
The sideslip and dipping of the wings are not too bothersome. But the wagging of the tail is. It’s a large problem for commercial aircraft as passengers in the rear of the aircraft get seasick from the movement.
Typically the low wing jet aircraft of today have wings which are angled upwards to make clearance for the engines, increasing roll stiffness. In addition, to lower transonic drag, the wings are swept and this increases roll stiffness further.
The result is an aircraft which is wagging the tail. To counter the wagging, all business and commercial aircraft have a yaw damper with a servo working on the rudder. By stopping the tail from wagging, the sideslip does not start and the Dutch Roll is stopped.
As we started talking about yaw dampers and some autopilot modes to make an aircraft fly stable, we will discuss autopilots a bit more in the next Corner.
You say all commercial aircraft are stable.
My father flew 707 and 727 types. I recall him telling me that without the yaw damper the 707’s dutch roll was controllable, but tricky, and the 727 would destroy itself in about a minute, and hence had two for redundancy. If allowed to progress, he said, dutch roll would remove the engines. 707 crews had to train to fly the aircraft without a yaw damper for this reason.
When I studied Aeronautical Engineering I came across data that the DC8 was stable in dutch roll – that it naturally died out (“deadbeat” was the term they used).
Also, for interests sake, starting dutch roll by means of giving the rudder pedal a small kick (small perturbation if you prefer) is called “Bonking”. It’s good to know there are two meanings (at least) to this word.
Hi Chris,
yes, there are certification rules mandating civil airliners shall not diverge (go totally unstable) in their bare non augmented state. This doesn’t mean there is no Dutch Roll. As long as it’s controllable by a pilot to an acceptable degree (like spiral mode and phugoid as well) it’s OK. This doesn’t mean people are not getting sick. Just the airplane is OK to land later on. I can’t believe the 727 was certified with a Dutch Roll which could remove the engines, despite pilot input.
The commentary says the 727 could fly with one YD operative but some flight restrictions but 2 YD inoperative meant no flight. Of course it had other major flight deficiencies combined with intial poor training
I’d be the first to admit the information was imparted to me, it’s not my own. However, two points;
– I was referring to the 707 losing its engines, not the 727. This certainly could be done on that aircraft – see https://aviation-safety.net/database/record.php?id=19591019-0 and also Wikipedia on BOAC flight 911 which crashed in Japan (nothing to do with Dutch Roll). I understand (again, imparted information) that the engines were designed to detach from the aircraft if imbalance loads got too big. Consequently excessive manoeuvre loads could, and did, cause engines to depart.
– Second, my father flew 707s on the British register; the UK CAA in its wisdom declared the 707’s weathercock longitudinal stability to be insufficient. Laughable as it is today to think that the British have a lick of sense, back in the day they prevailed upon Boeing to add a ventral fin and, I think, increase the height of the fin. As you point out in your piece, increasing weathercock stability can decrease dutch roll stability. Perhaps this was the case and it was a feature of British 707s. But note from the link that I gave above, those pilots who died in 1959 were being taught how to recover from dutch roll, and they failed. Rest In Peace.
From AOPA.ORG
The Boeing 727 was particularly in need of yaw dampers. These were so critical to flight safety that the 727 had two of them, one to operate the upper rudder and the other to operate the lower rudder. During Boeing 727 transition training, pilots were advised that a failure of both yaw dampers above FL 350 (such as would occur during a total electrical failure) would result in an irrecoverable loss of control (referred to by insurance carriers as a hull loss). There presumably was no way for a pilot to recover from the “three-holer’s” instability at high altitude without at least one operative yaw damper. Needless to say, many pilots would not operate a Boeing 727 above FL 350. (According to the operating limitations of the 727-100, for example, an immediate descent to FL 260 is required in the event of a single yaw damper failure.)”
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Thanks, Bjorn. A little OT, but do fighters have yaw dampers too? And, I assume all modern airliners have yaw damping “built in” digitally to a stability augmentation system? I’ve read older jets (“corporates” and airliners?) had a little red button on the yoke to disable the yaw damper during landings and takeoffs. Understand the need to disable the yaw damper during landings (“crabbed approaches”), but takeoffs too?
Hi MontanaOsprey,
fighters have yaw dampers as well and yes, the time of a separate subsystem for a yaw damper is over. The rudder servo executing for the yaw damper is also used for other purposes such as One Engine Inoperative (OEI) automatic compensation. It also does turn coordination on most airliners (ie kicks rudder to make aileron only turns clean. Amazing how pampered modern pilots are 🙂 ) I have flown the A350 and CS300 of the recent airliners and none of these have yaw damper off for landing or take-off. Neither A320 or MC-21 which I have flown in simulators. This might be something old or the disconnection of the yaw damping might be automatic for these FBW aircraft. I know business jets engage the yaw damper after take-off but haven’t seen it in an airliner check list.
Wow. What a great, concise summary note. Thanks, Bjorn. The only questions I’ve got left: 1) if you turn the autopilot “off” or to a standby mode (to “hand fly”), would you still have a “built in” yaw damper through a stability augmentation system; and 2) why would you (in olden days only?) have the yaw damper “off” until after takeoff? Thanks again.
Bjorn: Any idea if the (McDonnell-)Dougals NBs are somehow particularly susceptible to phugoid motion?
Last year sitting in a 717 I eventually noticed an ever-so-subtle pitch oscillation in cruise – it immediately recalled the phugoid demonstration I had been given almost a decade earlier in a piston-single. I kept wondering whether it really could be – I had to concentrate for a while to be sure I wasn’t imagining things and period seemed a tad short for a phugoid (somewhat shorter than the 30s you mention too – perhaps 10 to 15s, but memory might be playing tricks).
Also, it surprised me I would be able to feel it in an autopilot-controlled airliner in the “seat of my pants” (i.e. without instruments to watch) at all. But then I’m also the guy who noticed the Schlieren effect of a tiny shock on the engine nacelle of an E-190 against a background of cloud cover and took a photo of it. (It seemed to be caused by a minuscule excrescence where the bare aluminium inlet lip meets the nacelle proper and was only apparent at cruise Mach.)
Not many people pay that kind of obsessive attention I guess 😉