Monday, July 29, 2019

Movable Stabilizer

Swept-wing airplanes inevitably suffer from pitch-up near stall, due to the tendency for their wing tips to stall before the wing root. This same effect is compounded by compressibility effects when nearing stall at high altitude (which brings high Mach number into play).

The fuselage itself can contribute to pitch-up at high angles of attack. An example of that can be related to the 737MAX engine nacelles (or pods).

Gen. Chuck Yeager credited the trimmable stabilizer as the key technology for dealing with Mach Tuck, or shifting the lift aft with supersonic speeds causing a pitch down. While Mach Tuck is managed separately, the principal objective with a trimmable stabilizer is to minimize drag along with maximizing the elevator for whatever flight condition or center of gravity.

The following discussion is based largely on the writing of D. P. Davies, Handling the Big Jets, third edition. I have copied in some of his figures in the discussion. Anyone interested in these matters is highly encouraged to obtain and read his book, it is amazing.

Various regulatory factors are listed at the end.

The first jet Air Transport, the Comet, used a fixed stabilizer. All jet transport following used a trimmable/flyable stabilizer.

On the variable incidence tailplanes, from D. P. Davies:
The enormous power in a variable incidence tailplane can be a good servant when required but an impossible master when not required. If, in an extreme case, the tail is needed to assist in a manoeuvre it should be used slowly and carefully and its effect should be used only in short bursts, particularly at very high speeds, and the full effect should be appreciated before any tail change is made.
The 707/727/737 original design used an electric actuator for manual electric control and another electric actuator for autopilot trim control. Starting with the 737NG, a single actuator with separate control interfaces for manual electric and for autopilot was used. The loss of the 737NG/MAX single actuator relies entirely on manual wheel trim. All other aircraft have a fully redundant powered trim actuators, some with manual wheel trim as well.

Manual wheel trim involves direct mechanical control of the jackscrew. In one case, the mechanical control is of the hydraulic servo-valves, but all others use cables, drums, clutches, brakes, and a jackscrew.

The position of the horizontal stabilizer was evident in the high "T-Tail" position and the low "traditional" position. The T-Tail was helpful to accommodate tail-mounted engines.

The stabilizer angle of incidence, or the local Angle of Attack of the slipstream impinging upon the stabilizer, acts upon its lift as with any airfoil.

D. P. Davies, Handling the Big Jets, third edition

If the horizontal tail is producing an downwards balancing force, a more downwards incidence will increase the downwards force. A more upwards incidence or if in disturbed air, the downwards force will decrease. In summary, a more downwards incidence will cause airplane nose up pitching, and a more upwards incidence or disturbed air will cause airplane nose down pitching.

Disturbed air also can cause elevator "blanking", where the airflow over the control surface does not generate any force.

For certain aft c.g. conditions, it is possible that the horizontal tail will produce an upwards force.

If the horizontal tail is producing an upwards force, a more downwards incidence will increase the upwards force. A more upwards incidence or if in disturbed air, the upwards force will decrease. In summary, a more downwards incidence will cause airplane nose down pitching, and a more upwards incidence or disturbed air will cause airplane nose up pitching.

Flaps increases downward incidence, demanding a more stabilizer leading edge upwards orientation than when the flaps are up. For this reason, the stabilizer may operate more stabilizer leading edge up to produce the same balancing force, flaps down Vs flaps up.

Airplane attitude changes the incidence angle at the same time the airflow incidence angle changes. The balancing force change must be accounted with the overall airplane wing changes too.
From a trim condition, if the airplane pitches up in upset, the net effect is to pitch down towards the trim point. Similarly, if the airplane pitches down in upset, the net effect is to pitch up towards the trim point.

In the figure below, the coefficient of Lift Cand the Pitching Moment Care plotted against incidence angle (AoA) for a particular airplane. The area of interest is where the Cm is zero at about 12 degrees AoA. If the airplane is pitched up, AoA increases, and Cm goes negative, commanding a pitch down in response. If the airplane is pitched down, AoA decreases, Cm goes positive, commanding a pitch up in response. This is stable in longitude.

Stick force (elevator) must oppose the airplane pitching moment when operating away from the trim point if pitch is to be controlled. If the airplane operates at a higher AoA than trimmed, it will want to pitch down. The stick must pull back to oppose the airplane native tendency. It takes increasing stick force to oppose the increasing pitch down moment as AoA increases.

If the airplane operates at a lower AoA than trimmed, it will want to pitch up. The stick must be pushed to oppose the native tendency. It takes more forward stick force to push the nose down as AoA goes lower and lower from the trim point, and the airplane opposes with more and more pitch up.

The handling qualities rely on consistent stick forces. If the airplane pitching moment lessen or reverse, the stick forces will similarly lessen or reverse.

Mack tuck presents such a situation.

For the example below, from the trim point of about Mach 0.79, as the airspeed increases, the airplane will want to climb, so the stick is pushed forward to maintain level flight. At about Mach 0.86, the airplane begins to pitch down, requiring the stick forces to switch from pushing to pulling as speed continues to rise. This pitch down is unacceptable.

D. P. Davies, Handling the Big Jets, third edition

A Mach trimmer will apply nose up pitching moment (thru elevator or stabilizer command) to offset the airplane Mach tuck and to smooth out the stick force so that it is an increasing push force with speed.

D. P. Davies, Handling the Big Jets, third edition

The B-47 made heavy use of vortex generators to put energy into the boundary layers at the wing tip to stave off airflow separation to stave off Mach tuck, a method still used widely today.

Wing sweep is used to delay the onset of supersonic flow. A shock wave forms (compressibility effects) on the leading edge, shifting the lift rearwards (by virtue of loss of lift on the leading surfaces). This is what causes the Mach tuck.

A simple geometry shows how the free stream (AB) is made up of normal component (AC) and spanwise component (CB). It turns out, the normal component is all that the "chord-wise" lift depends on. Effectively the airspeed the wing sees relating to lift is slowed by cos(sweep angle) factor.

D. P. Davies, Handling the Big Jets, third edition

Sweep angle is no panacea. The taper ratio and sweep angle are optimized for many factors, but one that is profound is the wing loading. The wing tip suffers from high wing loading, the most likely to develop shock waves, higher boundary layers due to spanswise flow, and other effects that ultimately lead to it stalling before the wing root. Wing twist can be used to counter the trend.

D. P. Davies, Handling the Big Jets, third edition

Shortal and Maggin found a relationship between aspect ration, sweepback angle, and longitudinal stability.  The figure below shows the trends for pitching moment in the two regions.

Quest for Performance, NASA

If the wing tip stalls first, the center of Lift moves forward, causing a pitch up. This pitch up due to wingtip stalling has been evident from the beginning.

Looking chord-wise, the center of pressure moves forward slightly as AoA increases until stall at which point it reduces rapidly and shifts rearward, providing a native pitch down.

D. P. Davies, Handling the Big Jets, third edition

A low tail airplane encounters wing-wake in the approach to stall. In this context, the tail is providing a downwards-force.

As the airplane incidence increases, the wing wake goes above the horizontal tail, effectively shifting the incidence more upwards onto the leading edge of the stabilizer, decreasing the downwards force and pitching the airplane nose down.

An unstable case may be encountered if the horizontal tail is producing an upwards force. The upwards incidence will reduce the upwards force, causing the airplane to pitch nose up.

D. P. Davies, Handling the Big Jets, third edition

While the ultimate stall may display a healthy nose-down pitching moment, the slight tendency for the nose-down pitching slope to flatten or slightly reverse can be disqualifying.

From D.P. Davies:
While the subsequent true stall can be an immaculate nose down pitch (the wing tips never stalling), the initial pitch up tendency is nevertheless quite unacceptable in principle because it represents longitudinal instability and leads to a tendency for the aircraft to self-stall from speed below which the pitch up starts. Where this occurs it is sometimes necessary to fit a stability augmenter to operate just before the stall. This is not in any way a stick pusher and cannot strictly have any effect on pitch up, with is a function only of pitching moment/incidence and total tail angle (stabilizer and elevator) to stall, if the pilot insists on stalling the aircraft. This stability augmenter introduces only a small force into the elevator circuit which imposes positive stick free stability and removes the otherwise self-stalling tendency. the augmenter having been mentioned it should also be stated that, as its input is som small, all the runaway cases are completely innocuous.
The T-Tail has a better and worse situation. In the approach to stall, the wing wake falls well below the tail, leaving the elevator in full control. However, as the incidence increases, the wing wake can impinge upon the tail, rendering the elevator ineffective.

As mentioned already, the approach to stall can encounter pitch up at high incidence angles due to lift peaking, due to wing tip stalling or compressibility effects, and due to forward fuselage lift.  A super stall, or deep stall can be encountered if the airplane pitches up as AoA increases and elevator does not have sufficient authority to command airplane nose down.

D. P. Davies, Handling the Big Jets, third edition

The BAE 1-11 was the first airplane to suffer a deep stall from its T-tail design. The following figure offers an example of the effect.

As the airplane incidence increases above the trim point, the airplane increasingly wants to pitch down. At about 18 degrees, the pitch-up effects emerge swinging the airplane moment from pitching down to pitching up through the stall. The stall introduces significant loss of lift, shifting the airplane path downwards, which increases the local angle of incidence on the wing, worsening the stall situation. Without control authority, the airplane can get locked in with little forward motion, descending almost straight down at a relatively flat attitude.

D. P. Davies, Handling the Big Jets, third edition

D. P. Davies, Handling the Big Jets, third edition

The aircraft designer will want to ensure elevator authority is available to pitch down in this situation. Here, the resultant pitching moment with full downwards elevator is plotted showing that it should still be able to recover from a deep stall.

D. P. Davies, Handling the Big Jets, third edition

Taking advantage of the good control performance of a T-tail approaching stall, stick-pushers emerged to command the airplane to pitch down and avoid a stall altogether - stall protection. The original stick pusher used two AoA vanes, one to trigger stick shaker and to arm the stick pusher, the second AoA vane to trigger the stick pusher.

Aircraft drag is a combination of profile and induced drag. The total drag arrives at a minimum drag point, here plotted as a function of equivalent airspeed (EAS). Speeds above minimum drag are considered front side: drag increases as speed increases. Speeds below the minimum drag are back side: drag increases as speed decreases.

Back side speed control can be difficult if thrust or pitch are not applied quickly to avoid a significant deceleration.

D. P. Davies, Handling the Big Jets, third edition

While the chart above portrays the full range of drag, zooming into the range between the stall speed and minimum drag reveals how flat the drag rise is. This flatness in drag degradees speed stability, the a whole speed can be operated with about the same level of thrust.  Speed trim applies stabilizer to artificially improve the stability and feel forces.

D. P. Davies, Handling the Big Jets, third edition

An aircraft must pull "g's" to maintain level flight in a turn, as the lift vector is normal to the bank angle.  The lift equation follows the square of airspeed. A 60 degree bank turn requires 2 g's, which raises the stall speed from 1g level flight by a factor of 1.41.  A 63 degree bank turn yeilds a 1.50 factor on stall speed.

D. P. Davies, Handling the Big Jets, third edition

A stall necessarily results in the aircraft descending, which itself increases the AoA. A recovery entails pitching the airplane nose down to recover lift and then carefully pulling the airplane out of its descent. The aircraft pull out entails more than one g, and is easily a factor in a subsequent accelerated stall if the pull out is too aggressive.  In particular, the rate of change in pitch can create momentum, for example a rapid pitch up to pull out of dive, that can cause the airplane to persist (coast) in pitch rate without command.

The probability of encountering a stall has been modeled as about 1 in 100,000. Here you can see a plot of speed to probability of encounter. This probability may provide relief in the reliability of any stall warning and prevention equipment.

D. P. Davies, Handling the Big Jets, third edition
On the subject of stabilizer mistrim, from D. P. Davies:
A stalled stabilizer drive can occur on some types where it is possible, with a very high elevator hinge moment, to apply a load on the tailplane so high that the drive mechanism is completely defeated and fails to produce any movement. It is unlikely that this will ever occur with the aeroplane in trim since a pilot is most unlikely ever to require a manoeuvre invoving such large elevator angles and high stick forces. In an upset of some kind, however, where the stabilizer has achieved a gross out-of-trim condition, this position can arise. In turbulence, for example, a pilot might have run the stabilizer rather a long way away from the trimmed condition, a large and rapid change in speed could produce a very high stick force or the autopilot...could have run the stabilizer a long way. All these could result in a grossly out-of-trim stabilizer setting with the immediate need of very high stick force  to keep control of the flight path.
...Just sitting there and pulling a very high load, while it is the instinctive reaction in order to produce the required flight path, only compounds the difficulty. The stabilizer will not run until the hinge moment is relieved....slowly ease off the stick force...the stabilizer will run when the force is relieved sufficiently.
On a runaway stabilizer, from D. P. Davies:
A runaway stabilizer must be stopped as soon as possible. If the runaway is not arrested life is going to get very difficult....If this should occur at high speed the airplane is bound to be in severe trouble, the only hope is to get the speed off. The design of aeroplanes is such that the possibility of this failure (to stop the runaway) occurring is extremely remote... 

14 CFR § 25.203 - Stall characteristics.

(a) It must be possible to produce and to correct roll and yaw by unreversed use of the aileron and rudder controls, up to the time the airplane is stalled. No abnormal nose-up pitching may occur. The longitudinal control force must be positive up to and throughout the stall. In addition, it must be possible to promptly prevent stalling and to recover from a stall by normal use of the controls.
(b) For level wing stalls, the roll occurring between the stall and the completion of the recovery may not exceed approximately 20 degrees.
(c) For turning flight stalls, the action of the airplane after the stall may not be so violent or extreme as to make it difficult, with normal piloting skill, to effect a prompt recovery and to regain control of the airplane. The maximum bank angle that occurs during the recovery may not exceed -
(1) Approximately 60 degrees in the original direction of the turn, or 30 degrees in the opposite direction, for deceleration rates up to 1 knot per second; and
(2) Approximately 90 degrees in the original direction of the turn, or 60 degrees in the opposite direction, for deceleration rates in excess of 1 knot per second.

FAA Presentation

The §25.255 regulation and guidance were originally created as a direct response to a series of accidents in the 1960’s involving transport category jets where a combination of nose down trim commanded by the flight crew in the presence of severe atmospheric disturbances, plus the onset of force reversals or force lightening, induced unrecoverable
high speed dives. While in the high speed dive the flight crews found there was not enough elevator power to overcome the horizontal stabilizer mistrim condition to initiate a recovery. Additionally, attempts to re-trim the stabilizer surface were also unsuccessful since the stabilizer actuation stalled under those high aerodynamic loads. 
Therefore, §25.255 was envisioned to assure that Part 25 aircraft would retain adequate
controllability (in terms of force reversal or force lightening) and maneuverability (in terms of minimum recovery load factor capability) when induced to a high speed dive by any reason (e.g. wind gusts) even when combined with some amount of mistrim (e.g. a three second movement of the longitudinal trim surface for conventional trim systems). 
Additionally, if trim surface movement is required in order to achieve that minimum
recovery load factor, it must be shown that the system is capable of operating at the critical aerodynamic loads associated with that scenario. 
(3) For airplanes with a longitudinal trim function where the pilot does not directly adjust the longitudinal trim surface position and the trim surface is controlled by an automatic function, the maximum mistrim must include any position that the longitudinal trim surface could achieve during expected atmospheric disturbances and normal maneuvering while in high speed cruising conditions.

14 CFR § 25.255 Out-of-trim characteristics.

(a) From an initial condition with the airplane trimmed at cruise speeds up to VMO/MMO, the airplane must have satisfactory maneuvering stability and controllability with the degree of out-of-trim in both the airplane nose-up and nose-down directions, which results from the greater of -
(1) A three-second movement of the longitudinal trim system at its normal rate for the particular flight condition with no aerodynamic load (or an equivalent degree of trim for airplanes that do not have a power-operated trim system), except as limited by stops in the trim system, including those required by § 25.655(b) for adjustable stabilizers; or
(2) The maximum mistrim that can be sustained by the autopilot while maintaining level flight in the high speed cruising condition.
(b) In the out-of-trim condition specified in paragraph (a) of this section, when the normal acceleration is varied from + 1 g to the positive and negative values specified in paragraph (c) of this section -
(1) The stick force vs. g curve must have a positive slope at any speed up to and including VFC/MFC; and
(2) At speeds between VFC/MFC and VDF/MDF the direction of the primary longitudinal control force may not reverse.
(c) Except as provided in paragraphs (d) and (e) of this section, compliance with the provisions of paragraph (a) of this section must be demonstrated in flight over the acceleration range -
(1) −1 g to + 2.5 g; or
(2) 0 g to 2.0 g, and extrapolating by an acceptable method to −1 g and + 2.5 g.
(d) If the procedure set forth in paragraph (c)(2) of this section is used to demonstrate compliance and marginal conditions exist during flight test with regard to reversal of primary longitudinal control force, flight tests must be accomplished from the normal acceleration at which a marginal condition is found to exist to the applicable limit specified in paragraph (b)(1) of this section.
(e) During flight tests required by paragraph (a) of this section, the limit maneuvering load factors prescribed in §§ 25.333(b) and 25.337, and the maneuvering load factors associated with probable inadvertent excursions beyond the boundaries of the buffet onset envelopes determined under § 25.251(e), need not be exceeded. In addition, the entry speeds for flight test demonstrations at normal acceleration values less than 1 g must be limited to the extent necessary to accomplish a recovery without exceeding VDF/MDF.
(f) In the out-of-trim condition specified in paragraph (a) of this section, it must be possible from an overspeed condition at VDF/MDF to produce at least 1.5 g for recovery by applying not more than 125 pounds of longitudinal control force using either the primary longitudinal control alone or the primary longitudinal control and the longitudinal trim system. If the longitudinal trim is used to assist in producing the required load factor, it must be shown at VDF/MDF that the longitudinal trim can be actuated in the airplane nose-up direction with the primary surface loaded to correspond to the least of the following airplane nose-up control forces:
(1) The maximum control forces expected in service as specified in §§ 25.301 and 25.397.
(2) The control force required to produce 1.5 g.
(3) The control force corresponding to buffeting or other phenomena of such intensity that it is a strong deterrent to further application of primary longitudinal control force.

14 CFR  25.655 — Installation

(b) If an adjustable stabilizer is used, it must have stops that will limit its range of travel to the maximum for which the airplane is shown to meet the trim requirements of §25.161.

14 CFR § 25.161 - Trim

(a)General. Each airplane must meet the trim requirements of this section after being trimmed, and without further pressure upon, or movement of, either the primary controls or their corresponding trim controls by the pilot or the automatic pilot.
(c)Longitudinal trim. The airplane must maintain longitudinal trim during -
(1) A climb with maximum continuous power at a speed not more than 1.3 VSR1, with the landing gear retracted, and the flaps (i) retracted and (ii) in the takeoff position;
(2) Either a glide with power off at a speed not more than 1.3 VSR1, or an approach within the normal range of approach speeds appropriate to the weight and configuration with power settings corresponding to a 3 degree glidepath, whichever is the most severe, with the landing gear extended, the wing flaps (i) retracted and (ii) extended, and with the most unfavorable combination of center of gravity position and weight approved for landing; and
(3) Level flight at any speed from 1.3 VSR1, to VMO/MMO, with the landing gear and flaps retracted, and from 1.3 VSR1 to VLE with the landing gear extended.
(d)Longitudinal, directional, and lateral trim. The airplane must maintain longitudinal, directional, and lateral trim (and for the lateral trim, the angle of bank may not exceed five degrees) at 1.3 VSR1 during climbing flight with -
(1) The critical engine inoperative;
(2) The remaining engines at maximum continuous power; and
(3) The landing gear and flaps retracted.
(e)Airplanes with four or more engines. Each airplane with four or more engines must also maintain trim in rectilinear flight with the most unfavorable center of gravity and at the climb speed, configuration, and power required by § 25.123(a) for the purpose of establishing the en route flight paths with two engines inoperative.


8.1.5 Stall Characteristics—§ 25.203 During the approach to the stall, the longitudinal control pull force should increase continuously as speed is reduced from the trimmed speed to the onset of stall warning. Below that speed some reduction in longitudinal control force is acceptable, provided it is not sudden or excessive. Stall characteristics should be investigated with any systems or devices that may alter the stalling behavior of the airplane in their normal functioning mode. Unless the design of the airplane’s automatic flight control system precludes its ability to operate beyond the stall warning angle-of-attack, stall characteristics and the adequacy of stall warning should be evaluated when the airplane is stalled under the control of the automatic flight control system
10.3 Out-of-Trim Characteristics—§ 25.255.
10.3.1 Explanation.
Certain early, trimmable stabilizer equipped jet transports experienced “jet upsets” that resulted in high speed dives. When the airplane was mistrimmed in the nose-down direction and allowed to accelerate to a high airspeed, it was found that there was insufficient elevator power to recover. Also, the stabilizer could not be trimmed in the nose-up direction, because the stabilizer motor stalled due to excessive airloads imposed on the horizontal stabilizer. As a result, a special condition was developed and applied to most part 25 airplanes with trimmable stabilizers. With certain substantive changes, it was adopted as § 25.255, effective with amendment 25-2. While these earlier problems seem to be generally associated with airplanes having trimmable stabilizers, it is clear from the preamble discussions to amendment 25-42 that § 25.255 applies “regardless of the type of trim system used in the airplane.” Section 25.255 is structured to give protection against the following unsatisfactory characteristics during mistrimmed flight in the higher speed regimes: Changes in maneuvering stability leading to over controlling in pitch. Inability to achieve at least 1.5 g for recovery from upset due to excessive control forces. Inability of the flightcrew to apply the control forces necessary to achieve recovery. Inability of the pitch-trim system to provide necessary control force relief when high control force inputs are present.

Peter Lemme

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Peter Lemme has been a leader in avionics engineering for 38 years. He offers independent consulting services largely focused on avionics and L, Ku, and Ka band satellite communications to aircraft. Peter chaired the SAE-ITC AEEC Ku/Ka-band satcom subcommittee for more than ten years, developing ARINC 791 and 792 characteristics, and continues as a member. He contributes to the Network Infrastructure and Interfaces (NIS) subcommittee developing Project Paper 848, standard for Media Independent Secure Offboard Network.

Peter was Boeing avionics supervisor for 767 and 747-400 data link recording, data link reporting, and satellite communications. He was an FAA designated engineering representative (DER) for ACARS, satellite communications, DFDAU, DFDR, ACMS and printers. Peter was lead engineer for Thrust Management System (757, 767, 747-400), also supervisor for satellite communications for 777, and was manager of terminal-area projects (GLS, MLS, enhanced vision).

An instrument-rated private pilot, single engine land and sea, Peter has enjoyed perspectives from both operating and designing airplanes. Hundreds of hours of flight test analysis and thousands of hours in simulators have given him an appreciation for the many aspects that drive aviation; whether tandem complexity, policy, human, or technical; and the difficulties and challenges to achieving success. 


  1. Great source of credible information and well put together as to what is ' required "

    IMHO this SLF questions re how to apply the " 125 pound " equivalent control force in a ' manual ' mode via the awkward to use trim wheel even with step down gearing which means many many revolutions in ??? time.
    And it seems to me the problem exists on both the MAX and NG and never properly addressed or tested in a few decades ?

  2. Please help me with the probability graph. According to the graph, probability of encountering a stall increases with increasing speed. What do I get wrong? I think, this plot must be labeled "inverted probability..."
    Or do I misread it completely?
    Thanks if you could find time to explain this