How controllable is the 737 in single-engine manual-reversion flight? Is it controllably landable (or go-around-able) in this condition?

The 737 is practically the only civilian jetliner still in production¹ to have provisions for flight-control manual reversion; in the event of a total failure of the A and B hydraulic systems, the 737’s elevators and ailerons are controlled by aerodynamic forces generated by servo tabs mechanically connected to the pilots’ control yokes (the input to these tabs is locked if hydraulic pressure is available in the A or B system; the locking mechanism requires hydraulic pressure, and disengages if pressure is lost in both systems, allowing the control tabs to be used to control the elevators and ailerons).

The 737’s rudder is a rather different beast. It has no control tabs, and has no significant manual-reversion capability;² on the other hand, in addition to the A and B hydraulic systems, the rudder is connected to the standby hydraulic system, which, although not normally pressurised, can be manually activated by the pilots if necessary (and automatically engages in the event of an A or B hydraulic system failure during critical portions of takeoff or landing). Nevertheless, a failure severe enough to disable both the A and B hydraulic systems (such as an uncontained engine failure, major wing fire, or rudder separation) would have a good chance of also taking out the standby hydraulic system, which powers several of the same components as the other two hydraulic systems (namely, the rudder, thrust reversers, and leading-edge high-lift devices), and, thus, would be vulnerable to being disabled by a failure that also ruptured the A and/or B hydraulic lines serving those same components.

Even in the event of a total hydraulic failure, though, the elevators’ and ailerons’ manual-reversion capability would still keep the aircraft perfectly (if tiringly) flyable, since the rudder stands idle in normal flight, being used in the air only for countering the large yawing moments produced by an engine failure (especially at low airspeed)⁷, and engine failures are very rare nowadays…

…except that a destructive engine failure, combined with the failure of the engine cowling to contain the resulting debris,⁸ could easily be the cause of a multiple-hydraulic-system failure. For instance, an uncontained turbine rotor burst in the #1 engine would almost certainly rupture at least some part of the A system’s engine-driven hydraulic pump, would likely breach both the A and standby lines in the #1 thrust reverser, and could easily penetrate the B and standby lines powering the left wing’s leading-edge high-lift devices, leaving the aircraft with one engine and no hydraulics.⁹

In single-engine manual-reversion flight, the only way possible to counter the yawing moment produced by the asymmetric-thrust condition is to bank the aircraft towards the operative engine; the positive bank/yaw coupling¹² resulting from the 737’s rear-mounted vertical tail produces a yawing moment in the direction of the bank, countering the yawing moment from the thrust asymmetry. This would likely require a fairly large bank angle¹³ to produce a sufficiently-powerful restorative yawing moment, and the ailerons would have to maintain this bank without the help of the spoilerons (which are inoperative in manual-reversion flight) and against the considerable rolling moment created by the asymmetric-thrust-induced sideslip angle and the positive slip/roll coupling¹⁴ resulting, in part, from the 737’s rearward-swept wings.

Even if the aircraft were controllable in manual-reversion flight with one engine out at high airspeed, it might not be controllable at lower airspeeds (such as one would normally use for landing), as the lateral (roll) control authority of ailerons decreases considerably at low airspeeds due to the higher angles of attack required to maintain flight at a slower airspeed (this is because a given aileron deflection increases the downgoing aileron’s lift coefficient less and less as the AoA of the wing as a whole – and, thus, the starting AoA of the aileron – increases towards the stall angle, causing the ailerons to produce a smaller and smaller proverse rolling moment as the wing’s attack angle increases, while the increase in the downgoing aileron’s drag coefficient for a given aileron deflection gets larger and larger as the wing’s AoA increases, causing the ailerons to produce a larger and larger adverse yawing moment at high attack angles¹⁵).¹⁶ This would be further aggravated by the unavailability, in manual-reversion flight, of the aircraft’s spoilerons and trailing-edge flaps – the former would assist the ailerons in rolling the aircraft, being especially useful at low speeds (as they are immune to the severe degradation in control authority experienced by ailerons at high attack angles, producing proverse rather than adverse yaw, in addition to proverse roll¹⁷), while the latter would increase the wing’s lift coefficient for a given angle of attack, allowing it to support the same weight at a lower AoA, shifting the wing into a more aileron-authority-friendly regime.

This would seem to require the aircraft to attempt a landing at very high speed while maintaining a fairly steep bank angle until just before touchdown, and I don’t see how it would be possible to go around without the increases in engine thrust and vehicle angle of attack causing a loss of lateral/directional control, or to avoid a high-speed excursion from the side of the runway immediately following touchdown.

The controllability issues in single-engine manual-reversion flight would presumably vary between different 737 models. All else being equal, one would expect that the variants with lower engine thrust would be easier to control than those with more powerful engines, due to the lesser thrust differential with one engine out (so an Original would be more controllable in this state than a Classic, which would itself be more controllable than an NG, which would still be more controllable than a MAX); that variants with higher wing loadings would be harder to control, due to their need to fly at higher attack angles (and, thus, in less-aileron-friendly regimes of flight); and that longer-bodied variants would be easier to control, due to the stronger bank-yaw coupling resulting from the vertical tail’s longer moment arm.

How controllable are the various 737s, actually, in manual-reversion flight with one engine out? Are any of them easily (or at all!) controllable attempting a landing or go-around in this condition? Are there other differences between the variants in this regard that I missed?

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¹: At least, if we overlook the (update: no-longer-) current pause in 737 production.

²: If you want to get really pedantically technical, a small amount of rudder deflection is attainable even without any hydraulic pressure, due to the design of the 737’s rudder system³; however, this requires the application of an extreme amount of force to the rudder pedals (approximately 300 pounds⁴ per inch of rudder pedal deflection after the first inch, in addition to the additional force required to push the rudder pedals the initial inch required to take up slack in the rudder control system), and the small amount of rudder deflection available isn’t enough to generally be useful.

³: The gory details, straight from one of the metaphorical horses’ mouths:

During normal operation of the rudder in flight, if a pilot applied between 9 and 70 pounds of force to a rudder pedal, the rudder would move in response until it reached its blowdown limit (when the aerodynamic forces acting on the rudder surface equal the hydraulic actuator force). According to Boeing engineers, if the pilot were to then apply additional force to the rudder pedal, the pedal would move about 1 inch farther, with no corresponding movement of the rudder, as the slack in the rudder linkage system is removed and the external input crank contacts the external stop. Any additional pilot application of force to the rudder pedal would result in rudder pedal movement of about 1 inch for each 300 pounds of rudder pedal force, which in turn would move the rudder surface slightly beyond the maximum deflection possible from the hydraulic actuator force. [NTSB AAR-99/01, page 26 (page 50 of the PDF file of the report), and NTSB AAR-01/01, pages 16-17 (34-35); the exact same text is present in both (these two AARs deal with a pair of very similar accidents). Although the quoted text describes the response of the rudder system to a sufficiently-forceful pedal input when the rudder is under full hydraulic power and at its aerodynamic blowdown limit, the same mechanism is applicable when the rudder is completely without hydraulics; the only difference is that the small directly-pilot-induced rudder deflection is relative to the rudder’s neutral position rather than its blowdown limit.⁵]

⁴: For reference, the maximum force that an average pilot is physically capable of applying to an aircraft’s rudder pedals is generally around 500 pounds (according to ergonomic studies cited by the NTSB in AAR-99/01 and AAR-01/01).

⁵: If you want to get really really pedantic, this deflection is still relative to the blowdown limit, even with fully-depressurised hydraulics; it’s just that, with no hydraulic pressure available, the rudder’s blowdown limit is 0° (the neutral position).⁶

⁶: Note that the calculation of the rudder’s blowdown limit takes into account only the rudder-deflection force provided by the rudder’s hydraulic actuators – the additional force available directly from the pilots’ feet if they press really hard on the rudder pedals (and the only force available for moving the rudder in the event of a total hydraulic failure) is not accounted for.

⁷: The rudder has three additional major functions in large aircraft (aligning the aircraft with the runway immediately following touchdown during a crosswind landing, to keep the tyres from being destroyed by the crab angle – sometimes quite large – that needs to be held until touchdown to keep the aircraft from being blown downwind of the runway; keeping the aircraft on the runway during a crosswind takeoff; and taking evasive action to avoid a collision at high speed during takeoff or landing roll), but these are purely ground phenomena.

⁸: Virtually guaranteed if the destructive engine failure takes the form of a full fan, compressor, or turbine rotor burst (due to the extreme amounts of kinetic energy released in these types of failures); less common for a simple blade-out (although even these can sometimes result in uncontained failures).

⁹: As for the other hydraulically-powered components on a 737, here’s a quick rundown of their statuses with the A and B systems both failed, or with the A and B systems plus the standby system all nonfunctional:

• Landing gear: Can be extended by means of gravity, but cannot be retracted.
• Nosewheel steering: Inoperative – the nosewheel casters freely.
• Wheelbrakes: Powered by the brake accumulator for six full applications or equivalent (which should be enough to get the aircraft stopped on the runway).¹⁰
• Spoilerons: Inoperative – lateral control is by ailerons alone.
• Thrust reversers: Both operative if standby hydraulic system functional; otherwise, both inoperative.
• Horizontal-stabiliser trim: Operative using the manual-pitch-trim wheel on the cockpit center console, but this may require an extreme amount of force at higher airspeeds and/or more-adverse longitudinal center-of-mass positions.¹¹
• Ground spoilers: Inoperative.
• Autopilots: Both inoperative.
• Trailing-edge flaps: Inoperative Operative at reduced rate using the backup electrical flap drive system.
• Leading-edge high-lift devices: Operative if standby system functional; otherwise inoperative.
• Autoslats: Inoperative.
• Yaw damper: Inoperative.

¹⁰: In theory, one could use differential braking (applying wheelbrakes only, or more strongly, on the side with the operative engine) to at least attempt to maintain directional control after touchdown; however, this would further increase the already-greatly-lengthened (due to the need to maintain a very high airspeed in order to maintain lateral/directional control before touchdown in single-engine manual-reversion flight, plus the inoperability of the spoilers and thrust reversers in the event of a total hydraulic failure) rollout distance needed, and would risk depleting the stored brake-accumulator pressure (as keeping the aircraft on the runway throughout rollout using differential braking alone would likely require at least a few changes in braking force, or even momentary brake reversals, which would quickly eat through the six full applications’ worth of pressure in the accumulator).

¹¹: The potential need to apply a very great deal of force to move the manual-pitch-trim wheel is especially severe on the 737 NG and MAX, which have a smaller manual-pitch-trim wheel (and, thus, provide the pilots with less of a mechanical advantage when trying to turn said wheel) than the 737 Original and Classic; for the NG and MAX at high airspeeds and/or adverse CoM locations, it may be physically impossible to trim the aircraft in pitch without the electrohydraulic trim system.

¹²: I.e., banking the aircraft to the right makes it want to yaw to the right, and vice versa.

¹³: Yes, I am aware that all non-centerline-thrust multiengine airplanes are required (at least in the U.S.) to demonstrate the ability to maintain lateral/directional control with one engine out without requiring a bank angle of greater than 15° away from the failed engine; however, this is with the rudder producing its own yawing moment to assist (quite potently) that produced by the aileron-induced bank. With the rudder down for the count, and the entire burden of resisting the asymmetric-thrust-induced yawing moment falling on the aircraft’s bank angle and bank/yaw coupling, the bank angle necessary to maintain lateral/directional control would be considerably greater.

¹⁴: I.e., placing the aircraft in a nose-right sideslip makes it want to roll to the right, and vice versa.

¹⁵: This is why aircraft have a crossover airspeed – a speed below which the rolling and yawing moment from a full-scale rudder deflection cannot be countered using the aircraft’s lateral controls alone.

¹⁶: More advanced aileron designs can reduce or even eliminate adverse yaw, mostly by generating enough extra drag on the upgoing aileron to balance out the extra lift-induced drag on the downgoing aileron (such as the differential aileron, which deflects the upgoing aileron much more than the downgoing aileron, and the Frise aileron, which has the lower front edge of the upgoing aileron protrude into the airflow below the wing), but these are less and less effective at higher and higher angles of attack.

¹⁷: As a result, one would expect that aircraft rolled solely by spoilerons and completely lacking traditional ailerons (such as the B-52G/H or the MU-2) would be immune to the crossover-airspeed phenomenon, although my question to that effect has yet to attract a useful answer.