![](media/image1.wmf){width="5.997222222222222in" height="0.9625in"}

Simulation Test Plan to Develop Transport Aircraft Rudder Control System
Requirements

Phase 1 - Determine Simulator Motion Requirements

(Rev 1 NASA Ames VMS Simulator Test)

HAI Technical Report 1137-1

Roger H. Hoh

January 5, 2007

This work was performed for the FAA under contract DTFACT-05-C-00025

Table of Contents

[1 INTRODUCTION 2](#introduction)

[2 OBJECTIVES 3](#objectives)

[3 SIMULATOR REQUIREMENTS 4](#simulator-requirements)

[3.1 Visual 4](#visual)

[3.2 Motion 4](#motion)

[3.3 Cockpit 4](#cockpit)

[3.4 Feel System 4](#feel-system)

[3.5 Math Model 5](#math-model)

[4 TEST PROTOCOL 5](#test-protocol)

[4.1 Piloting tasks 5](#piloting-tasks)

[4.2 Test subjects 7](#test-subjects)

[4.3 Feel System Definitions 7](#feel-system-definitions)

[4.4 Configurations 8](#configurations)

[4.5 Test Conditions 11](#test-conditions)

[4.5.1 Configurations 12](#configurations-1)

[4.5.2 Estimated Simulator Time Requirements
13](#estimated-simulator-time-requirements)

[5 DATA REDUCTION AND ANALYSIS 16](#data-reduction-and-analysis)

[5.1 Qualitative Pilot Ratings 16](#qualitative-pilot-ratings)

[5.2 Quantitative Data 16](#quantitative-data)

[5.3 Proposed Metrics for Pass-Fail Criteria
18](#proposed-metrics-for-pass-fail-criteria)

[5.4 Data Reduction 20](#data-reduction)

[5.5 Data Analysis 20](#data-analysis)

[APPENDIX A --GENERIC RUDDER SYSTEMS **Error! Bookmark not
defined.**](#__RefHeading___Toc141168421)

[A-1 Variable-Gearing **Error! Bookmark not
defined.**](#__RefHeading___Toc141168422)

[A2. Variable-stop **Error! Bookmark not
defined.**](#__RefHeading___Toc141168423)

[A3. Force-limit **Error! Bookmark not
defined.**](#__RefHeading___Toc141168424)

[APPENDIX B -- MATH MODEL FOR GENERIC YAW DAMPERS **Error! Bookmark not
defined.**](#__RefHeading___Toc141168425)

[APPENDIX C -- PILOT RATING SCALES AND QUESTIONNAIRES
21](#appendix-c-pilot-rating-scales-and-questionnaires)

[APPENDIX D -- LINEARITY INDEX PARAMETER
37](#appendix-d-linearity-index-parameter)

[APPENDIX E -- EQUATIONS OF MOTION FOR PHASE 1 SIMULATION
39](#appendix-e-equations-of-motion-for-phase-1-simulation)

[REFERENCES 40](#references)

# INTRODUCTION

This test plan describes the first phase of testing to develop handling
qualities criteria for rudder flight control systems for large transport
aircraft. The three phases of planned testing to accomplish the
objectives are summarized as follows.

Phase 1 Determine the required lateral motion of the simulator necessary
to obtain valid pilot opinion for aggressive rudder control, and obtain
initial results for variable-gearing, variable-stop, and force-limit
rudder control system designs. Piloting tasks for this phase of testing
are designed to guarantee aggressive use of rudder.

Phase 2 Using a simulator that meets the requirements defined in Phase
1, conduct detailed experiments to determine criteria for transport
aircraft rudder control systems. Piloting tasks for this phase are
designed to guarantee aggressive use of rudder. Analyze the results to
formulate tentative criteria for rudder flight control systems in
transport aircraft.

Phase 3 Validate the Phase 2 results using more realistic piloting tasks
where rudder use is based on pilot judgment and technique. Results used
to validate, and if necessary refine the criteria developed in Phase 2.

The Phase 2 and Phase 3 Test Plans are given in References 1 and 2. This
test plan applies to Phase 1

# OBJECTIVES

The primary objective of Phase 1 is to determine the level of lateral
motion required to obtain valid results when aggressive rudder control
is used by the pilot. This determination will be made by noting if there
is a significant change in pilot opinion and rudder activity for full
motion and limited motion. The implicit assumption is that the "full
motion" that can be produced by the simulator in Phase 1 is
representative of the actual aircraft.

The secondary objective of Phase 1 is to obtain preliminary results for:

-   Variable-stop rudder systems

-   Variable-gearing rudder systems

-   Force-limit rudder systems

-   Effect of breakout

-   Effect of yaw damper implementation

# SIMULATOR REQUIREMENTS

## Visual

The outside visual scene is an important cue for pilot use of rudder.
Therefore, only simulators with a high quality outside visual scene, or
an in-flight variable stability aircraft are deemed as adequate for this
experiment. The primary requirement for the visual scene is that it must
have adequate bandwidth so that ratcheting is not apparent at aircraft
angular rates up to 15 deg/sec in the pitch and roll axes, and 7 deg/sec
in the pitch axis. This is based on time histories of aggressive
lateral-directional tracking maneuvers as well as a review of the AA 587
accident data.

The outside visual scene must support a realistic environment for
up-and-away maneuvering at altitudes between 1000 ft and 3000 ft a.g.l.

## Motion

The motion system or in-flight simulator must be capable of producing
lateral accelerations of at least 0.25g, and 0.4g would be highly
desirable, based on time histories from the AA 587 accident. It would
also be desirable to be able to sustain that level of lateral
acceleration for at least 2 to 3 seconds. A hexapod motion system is not
acceptable for this phase, because it cannot produce the required level
of lateral acceleration without using large bank angles that must be
washed out. The motion cueing during such rapid washouts would be
questionable.

## Cockpit

Only rudimentary cockpit displays are necessary. There should be at
least a conventional set of cockpit flight instruments. Conventional
"steam gauges" or a PFD are both acceptable. There must be a good
display of lateral acceleration that is easily readable by the pilot
such as a sideslip ball. This phase of testing is not designed to
evaluate the display of sideslip/lateral-acceleration. Therefore any
easily readable display with all the usual good human factors
characteristics (e.g., minimum tendency to reverse control) is
considered as adequate. The sideslip ball is considered as a good
candidate because it is well understood by all pilots.

## Feel System

The longitudinal and lateral controller can be a standard wheel, stick,
or even a sidestick. It should have a reasonable amount of fidelity, to
allow adequate control of pitch and roll attitudes.

The pedal feel system is the crucial element of this experiment and
shall have the following characteristics to accurately emulate transport
type aircraft.

-   Capability to program force gradient with deflection to achieve
    load-feel characteristics as shown in Figure 3 in Section 4.3.

-   Capability to set maximum deflection between 0.5 and 4 inches

-   Capability to set breakout between 0 lbs and 25 lbs

-   Capability to control friction

For this Phase 1 experiment, it is not necessary to program the maximum
pedal and/or rudder deflection as a function of airspeed.

## Math Model

The Phase 1 experiment will be accomplished at a single up-and-away
flight condition of 250 KCAS and altitude of 2,000 ft. If a variable
stability aircraft is used, it may be flown at any airspeed, as long as
the simulated dynamics are correct for 250 kts.

The longitudinal and lateral equations of motion shall be representative
of a transport category jet aircraft.

The detailed representations of the rudder flight control systems to be
modeled are provided in Appendix A and the models of the yaw damper are
given in Appendix B.

Appendix E provides guidance regarding the equations of motion necessary
to accomplish the objectives of this Phase 1 simulation.

# TEST PROTOCOL

## Piloting tasks

These semi-realistic tasks are designed to require aggressive use of
rudder. This testing is in recognition is that pilots of transport
aircraft are currently trained to only use rudder for crosswind landings
and engine out procedures. However, if in a critical situation and the
pilot does use rudder aggressively, the aircraft response should be
predictable, and there should be no tendency for overcontrol, PIO, or
reversals that could overstress the vertical stabilizer. The following
tasks are designed to expose deficiencies in aircraft handling qualities
in the directional axis.

**[Experiment #1]{.underline}**

-   Task is to null the lateral acceleration in the presence of a
    sum-of-sines lateral gust disturbance as shown in Figure 1.

> ![](media/image2.wmf)

Figure 1 Pilot-in-the-Loop Representation of Experiment #1

-   Tailor disturbance bandwidth and magnitude to induce desired
    frequency and magnitudes of pilot activity. If a variable stability
    aircraft is used, the structural limits of the sideforce generators
    under static and oscillatory loads are a safety consideration.

```{=html}
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```
-   Use realistic aircraft directional dynamics (Cn, Cy vs
    ![](media/image3.wmf) and ![](media/image4.wmf)), but remove
    coupling into lateral axis (e.g., ![](media/image5.wmf)) to create
    an essentially single axis task.

**[Experiment #2]{.underline}**

-   The task is to maintain zero bank angle in the presence of rolling
    gusts. Maintain zero bank-angle as primary task and coordinate
    sideslip as secondary task as shown in Figure 2.

> ![](media/image6.wmf)
>
> Figure 2 Pilot-in-the-Loop Representation of Experiment #2

-   Tailor rolling gusts to simulate a wake-vortex encounter. The
    initial rolling gusts may need to exceed the roll control authority
    to allow the bank angle to build to larger values. Tailor the roll
    gusts during the simulation set-up runs.

-   Aircraft dynamics in yaw require turn coordination with to keep
    sideslip near zero (i.e., force the pilot to use pedals). Make
    ![](media/image7.wmf) large (typical of swept wing transports) so
    lack of aileron-rudder coordination degrades performance in roll
    tracking task. (Similar to AA 587 scenario).

-   A variable stability aircraft must be equipped with side-force
    generators to allow tailoring of lateral acceleration with sideslip,
    rudder deflection, and pilot location.

The details of how the sum of sinewaves was mechanized on the VMS is
given in Appendix F.

Conduct the above tests with full lateral motion, and with reduced
motion consistent with a hexapod motion-system using washed-out bank
angle to produce lateral acceleration at the pilot station. The NASA
Ames Vertical Motion Simulator has a generic set of motion gains to
simulate a hexapod, and these will be used in this experiment.

If results show that the limited lateral motion produces significantly
different pilot opinion and rudder usage when compared to full motion,
it will be necessary to accomplish all testing on a large-motion
simulator, such as the VMS or a variable stability aircraft with
sideforce capability (e.g. Calspan TIFS).

## Test subjects

At least 3 test subjects will be used. Preferably these subject pilots
will have test pilot experience and will also have some experience with
transport category aircraft.

## Feel System Definitions

The rudder pedal feel system described below will be used for all of the
configurations

The nonlinear characteristics of a rudder system with a linear load-feel
curve are shown in Figure 3 below. A linear load-feel curve is used in
this illustration to isolate the effects of breakout, and friction.

![](media/image8.wmf)

Figure 3 Typical Nonlinear Rudder Flight Control System

For the purpose of simulation the following definitions will apply.

**Feel Spring Breakout (Fbofs)** -- A constant force in a direction to
return the rudder control to trim regardless of displacement. This is
simulated with a large spring gradient over a small deflection, with the
force held constant once that deflection is exceeded (e.g., see bottom
of Figure A-1).

**Coloumb Friction (Fcf)** -- A constant force that is independent of
displacement and in a direction opposite to the motion of the pedals -
Fcf.

**Breakout Force (Fbo)** -- The force required to initiate pedal motion.
This is the sum of the feel spring breakout and Coulomb friction: Fbo =
Fbofs + Fcf. In this work, it is important to make a distinction between
breakout of the feel spring (Fbosp) and total breakout force, Fbo.

**Load-Feel Curve** -- Pedal force as a function of pedal displacement
-- may be linear or nonlinear as shown later in Figure 4. The slope of
the linear load-feel curve in Figure 3 is Kped (lb/in). A nonlinear
load-feel gradient is typically used to provide good force cues for
small pedal deflections in variable stop systems without requiring
excessive forces to achieve large rudder deflections during engine out
or crosswind landing operations. Load feel curves are typically achieved
with one or more centering springs and, where necessary, cams to achieve
the nonlinear gradient. Both linear and nonlinear load-feel curves will
be studied in this experiment.

**Viscous Friction (Fvf)** -- Force that is proportional to pedal
velocity in a direction to resist pedal motion, and sets the feel system
damping. The work in Reference 3 did not indicate a strong sensitivity
in pilot opinion. The subject pilots in that experiment found that the
response was satisfactory without improvement (Cooper Harper Handling
Qualities (HQRs) ratings equal to or less than 3.5) for feel system
damping rations greater than 0.3. Tests with damping ratio of zero
resulting in HQRs of no worse than 4.2 (i.e., still acceptable). In this
experiment, the damping ratio will be held at approximately 0.6.

**Stop** -- A force that simulates the mechanical limit of travel. The
stop is a constant for variable gearing systems and variable with
airspeed in variable stop systems.

**Fmax** -- The pedal force necessary to move the pedals from trim to
the stop.

The pilot must input a force greater than the breakout force plus the
Coulomb friction force (Fbo + Fcf) before the rudder pedals move. The
force required to keep the rudder pedals from returning to center is
equal to or greater than (Fbo -- Fcf). These parameters have been
studied in Reference 3 and are discussed in more detail in Section
5.1.3.

## Configurations

The variations in rudder system configurations to be tested are defined
as follows.

-   Variations in load-feel (rudder force vs. pedal deflection).

-   Low breakout and high breakout. (Figure 4)

-   Variable-stop with airspeed

-   Variable rudder-to-pedal gearing with airspeed

-   Force-limit system that limits the amount of rudder hinge-moment
    that can be commanded by the pilot

Block diagrams and detailed descriptions of each of the rudder system
configurations planned for testing are given in Appendix A.

The variations in load-feel systems between rudder system designs is
significant. For example, the load feel curves for three different
aircraft are shown in Figure 4.

![](media/image9.wmf){width="5.9944444444444445in"
height="3.1819444444444445in"}

Figure 4 Load-feel Curves for Existing Aircraft[^1]

The load-feel curves shown in Figure 4 include the effect of breakout.
They represent three different approaches to rudder system design as
summarized below.

-   The A300-600 is a variable stop design, and employs a high level of
    breakout and a nearly linear variation in pedal force vs.
    deflection. This linear variation results in relatively low levels
    of pedal force for maximum rudder as the stop is decreased with
    increasing airspeed. For example, at 250 kts, the pedal stop is at
    1.2 inches, resulting in a force of only 32 lbs to achieve maximum
    rudder deflection.

-   The MD-80 employs the same variable stop design as the A300-600
    except that the breakout is more moderate and the load-feel curve is
    highly nonlinear. This non-linear variation results in significantly
    higher levels of pedal force for maximum rudder as the stop is
    decreased with increasing airspeed. For example, at 250 kts, the
    pedal stop is at 1.1 inches, resulting in a force of 60 lbs to
    achieve maximum rudder deflection.

-   The 737 NG employs a force limit system, and a nonlinear load-feel
    curve as shown in Figure 4. The force-limit system also results in a
    variable pedal stop with airspeed. At 250 kts, the pedal stop is 1.5
    inches, resulting in 52 lbs of force.

-   The B747 employs a variable gearing system. The load-feel curve is
    linear and very similar to the A300-600.

Variable-stop systems have been designed with linear and nonlinear
load-feel curves[^2]. Based on the available data from the NTSB report,
it appears that Airbus has employed an essentially linear load-feel
curve for the variable-stop systems, whereas Boeing/Douglas tended to
use a nonlinear load-feel curve for their variable-stop designs.

The Boeing 727, 737, DC-10, and MD-11 aircraft employ the force-limit
design. Figure 4 indicates that the 737 utilizes a nonlinear load-feel
curve and this is taken as representative of this type of system. That
is because a nonlinear load-feel is the only way to achieve high rudder
pedal forces at small pedal deflections without excessive forces for
maximum rudder at low airspeeds. Note that mechanical implementations of
the variable force design require variable pedal stops, very similar to
the variable stop design (see Appendix A).

Variable-gearing systems have been employed by Boeing on the 747 through
777 series aircraft as well as the Airbus A300B2/B4. The B747 has an
essentially linear load feel curve, and it is assumed that this is
representative of variable gearing systems. That is because such systems
do not require significant nonlinearities to achieve high pedal forces
at limit rudder deflections. That function is accomplished by reducing
the pedal-to-rudder gearing.

The linear and Nonlinear generic load-feel curves used in Phase 1
testing on the VMS are shown in Figure 5.

![](media/image10.wmf){width="5.999305555555556in"
height="3.3381944444444445in"}

Figure 5 Generic Load-Feel Curves for Phase 1 Testing

These load-feel curves are representative of current designs as
illustrated in Figure 4.

For this experiment, the nonlinear load-feel curves are the same for the
Variable-stop and Variable-gearing designs. This is done to isolate the
effect of varying the stop or the gearing. Because there is precedent
for a linear load-feel curve in some Airbus aircraft with variable stop
rudder designs, such a linear load-feel curve is included in the
experimental matrix for the variable stop design.

The effect of breakout is expected to be important, especially for the
linear load-feel design, because with that design the maximum force is
not much greater than the breakout force. To isolate this effect, a low
and high breakout version of each design is included in the tests.
Breakout is calculated separately, and therefore is not included in the
load-feel curves in Figure 5 (e.g. see Figure A-1 in Appendix A).

Breakout is defined herein as the force required to initiate motion of
the rudder pedals, and this is the convention that was used in the
Reference 8 NTSB report. Using this definition, Fbo is defined as the
sum of the feel spring breakout plus Coulomb (static) friction. The feel
spring breakout results from cable stretch. Since the spring does not
move until the breakout force is applied, there is a deadband in the
load feel curves, which is calculated as follows:
![](media/image11.wmf). In this experiment, the cable stretch
coefficient (K~CS~) was set to .005 in/lb.

Two levels of Fbo were used -- 10 lbs and 22 lbs. These were taken as
representative of the low and high values of breakout found on existing
transport aircraft. The values of feel spring breakout (Fbosp) static
friction (Fsf), and cable stretch (![](media/image12.wmf)) used to
represent the low and high breakout cases are given below.

  -------------------------- ----------------------- -----------------------
                             Low Breakout            High Breakout

  Fbo -- lbs                 10                      22

  Fbosp - lb                 6                       12

  ![](media/image13.wmf) -   0.030                   0.060
  inches                                             

  Fcf - lb                   4                       10
  -------------------------- ----------------------- -----------------------

## Test Conditions 

### Configurations {#configurations-1 .unnumbered}

The cases tested during the VMS Phase I effort are given in Table 1.

  ------ --------- ----------- ---------- ---------- ---------- ------- ----------- --------
  Case   Maximum   Load Feel   Breakout   Coloumb    Feel       Kped    Rudder      Yaw
         Pedal     curve shape lbs        Friction   Spring             Control     Damper
         Travel                           Fcf lbs    Breakout           System      
         in.                                         Fbosp lbs                      

  1      1.2       Linear      Low        4          6          7.5     Variable    A
                                                                        Stop        

  2      1.2       Nonlinear   Low        4          6          7.5     Variable    A
                                                                        Stop        

  3      1.2       Linear      High       10         12         7.5     Variable    A
                                                                        Stop        

  4      1.2       Nonlinear   High       10         12         7.5     Variable    A
                                                                        Stop        

  5      4.0       Nonlinear   Low        4          6          Fig A-3 Variable\   A
                                                                        Gearing     

  6      4.0       Nonlinear   High       10         12         Fig A-3 Variable    A
                                                                        Gearing     

  7      1.2       Nonlinear   Low        4          6          7.5     Force Limit A

  8      1.2       Linear      Low        4          6          7.5     Variable    B
                                                                        Stop        

  9      1.2       Nonlinear   Low        4          6          7.5     Variable    B
                                                                        Stop        

  10     1.2       Linear      High       10         12         7.5     Variable    B
                                                                        Stop        

  11     1.2       Nonlinear   High       10         12         7.5     Variable    B
                                                                        Stop        
  ------ --------- ----------- ---------- ---------- ---------- ------- ----------- --------

Table 1 Test Matrix for Phase 1

Cases 1 through 4 are intended to investigate the variable-stop design
with low and high breakout and linear and nonlinear load-feel. The
linear load-feel results in a significantly decreased maximum force when
the pedal throw is limited to 1.2 inches at 250 kts (see Figure 5
above).

Cases 5 and 6 represent the variable-gearing design with low and high
breakout and a nonlinear load-feel.

Case 7 is included to investigate the force-limit design for comparison
with the variable-stop design in Case 2. A review of the configurations
in Appendix A shows that the force-limit and variable-stop designs are
similar except that the force-limit design has about 0.7 inches of pedal
motion with no rudder motion before reaching the stop at 1.2 inches.
Note that this results in the maximum rudder deflection at only 0.5
inches of pedal motion. The force-limit design results in variations in
the maximum pedal travel depending on sideslip (see Appendix A), whereas
the variable-stop system does not.

Case 3 represents the A300-600 variable-stop design, which incorporates
an essentially linear load-feel curve. Case 1 represents that design
with decreased breakout. Cases 2 and 4 investigate the variable-stop
design with nonlinear load-feel curve (i.e. the approach taken by
Douglas Aircraft Co.) combined with low and high breakout forces. Case 8
is case 3 with an improved yaw damper design and case 9 is case 3 with
the improved yaw damper and reduced breakout.

Cases 1 through 7 represent cases where the yaw damper output to the
rudder can be limited when pilot pedal inputs are large (Version A), and
cases 8 through 11 investigate the alternative yaw damper design where
such limiting does not occur (Version B). The two yaw damper designs are
discussed in detail in Appendix B.

The primary objective of this program is to determine the motion system
requirements for more extensive Phase 2 and Phase 3 testing. In theory
this could be accomplished with only two configurations, and that is the
basis for setting the Priority 1 configurations as #3 and #5: cases 3
and 5 represent the extreme ends of the spectrum. Case 3 represents the
AA-587 accident aircraft system (1.2 inches pedal travel, max force = 35
lbs, 22 lbs breakout), and Case 5 is a variable-gearing system (4 inches
pedal travel, max force = 60 lbs, 10 lb breakout). Cases 1, 2, and 4 are
listed as Priority 2 because they should yield results that provide
insight into the effect of breakout for variable stop systems, which is
expected to be important. Case 6 provides insight into the effect of
breakout for a variable-gearing system and case 7 allows a first look at
a force-limit system. These are assigned Priority 3. The priority 4
cases all investigate the effect of yaw damper implementation.

Once the simulation is checked out, the project pilot(s) will accomplish
preliminary evaluations to judge whether the configurations and tasks
will meet the Phase 1 objectives. There shall be time allotted to make
adjustments to the configurations and tasks to ensure that the
objectives will be met, and that configurations that do not show
significant effects are eliminated.

### Estimated Simulator Time Requirements

The following estimates are made to provide a basis for estimating cost
to accomplish this program. Priorities have been established to allow
the Phase 1 testing to be downsized to accommodate an available budget.

If each data run requires 1 minute and each evaluation pilot is required
to make three repeat runs for each configuration the time required to
evaluate each configuration in Table 1 for a single pilot is as follows.

> Evaluation time for one pilot = 1 min/run X 3 runs +7 min to set up
> and to rate = 10 min/config/pilot/task

Each configuration will be evaluated for two tasks and for limited
motion and full motion with 3 pilots -- therefore:

> Evaluation Time/config = 10 min/config/pilot/task X 2 tasks X 2 motion
> systems X 3 pilots = 2 hrs/config.

If a variable stability aircraft is used, add 0.5 hrs for takeoff and
landing and transition to and from the test area.

The checkout hours include basic checkout of the motion gains as well as
providing time for the project pilot to refine the configurations as
necessary.

With these assumptions, the following table applies.

  ----------- ----------- ----------- ------------ ----------- -----------
  Priority    Configs     Sorties     Evaluation   Checkout    Total
                                      Hours        Hours       flight
                                                               hours

  1           2           2           5.0          4           9

  1,2         5           5           13           5           18

  1,2,3       7           7           18           6           24

  1,2,3, and  11          10          27           7           34
  4                                                            
  ----------- ----------- ----------- ------------ ----------- -----------

Table 2 Flight Time Required if Use In-Flight Simulator

If a motion-base simulator is used, the time for takeoff and landing can
be eliminated, but add .25 hours for every evaluation hour to allow the
cab to be docked and undocked to change pilots. Further assume that it
will take four days to develop and finalize the motion gains for each of
the two tasks, as well as to allow time for the project pilot to
finalize the configurations.

  -------------- -------------- -------------- -------------- --------------
  Priority       Configs        Evaluation     Motion-Base    Total
                                Hours          Checkout Hours motion-base
                                                              hours

  1              2              5.0            32             38

  1,2            5              13             32             45

  1,2,3          7              18             32             50

  1,2,3, and 4   11             27             32             59
  -------------- -------------- -------------- -------------- --------------

Table 3 Motion-Base Simulator Time

It is estimated that approximately one month of setup, and fixed-base
simulation time will be required to get the in-flight or ground-based
simulator ready for checkout flights. This will of course be less if
only the higher priority configurations are tested.

# DATA REDUCTION AND ANALYSIS

The data will consist of pilot ratings and commentary as well as
quantitative data such as time histories. For this Phase 1 effort, the
primary objective of the data analysis will be to determine the motion
requirements to obtain valid results using ground-based simulators. The
secondary objective of the data analysis will be to obtain initial
results for the most common types of rudder flight control systems used
on transport aircraft.

## Qualitative Pilot Ratings

Experience has shown that when systematically varying aircraft handling
qualities, care must be taken to provide the necessary adaptation time
to achieve a valid evaluation following a change in configuration. For
example, after flying a series of runs with a good configuration, the
pilot may initially have problems flying a new equally good
configuration. That is because the pilot must adapt his or her control
strategy to be compatible with the new configuration. Normally, full
adaptation occurs in three runs[^3]. For that reason, the pilot ratings
and commentary should only be taken after three or more runs have been
accomplished.

Pilots will be asked to rate the handling qualities to accomplish the
tasks in Section 4.1 using the standard Cooper-Harper Handling Qualities
Rating (HQR) scale from Reference 4, and to estimate workload using the
workload rating scale from Reference 5. These pilot rating scales are
given in Appendix C. Since the tasks have been designed to require
aggressive use of rudder, it is expected that any deficiencies in the
directional axis will be reflected in the ratings.

In addition to pilot ratings, the pilots will be asked to answer the
questionnaire in Appendix C.

## Quantitative Data

Time histories will be recorded for the following parameters.

-   Pitch, roll, and heading (deg)

-   Pitch, roll, and yaw rates (deg/sec)

-   Angle-of-attack and sideslip angle (deg)

-   Airspeed and altitude (kts and ft/sec)

-   Sideslip input to model (![](media/image14.wmf)) -- sum of sinewaves
    (deg)

-   Lateral acceleration at the c.g. and pilot station (g's)

-   ![](media/image15.wmf)at pilot station

-   Rudder position data

    -   Limited and unlimited pilot input to rudder (deg)

    -   Limited and unlimited yaw damper output to rudder (deg)

    -   pedal position (in)

    -   rudder angle (deg)

-   Pedal force (lb)

-   Longitudinal column (in) and lateral wheel (deg)

-   Calculated load on vertical stabilizer

-   Rudder hinge-moment

The following statistical data shall be obtained for each run.

-   RMS sideslip angle (deg) -- measure of goodness of tracking
    performance with rudder

-   RMS pedal deflection (in)

-   RMS pedal force (lb)

-   Percentage of time that pedal is on the stop

-   RMS lateral acceleration at pilot station (g's)

-   RMS vertical stabilizer load (lb)

-   Calculate mean and standard deviation of peak load on vertical
    stabilizer

An approximation to the loads on the vertical stabilizer will be
calculated based on the fact that the lateral force on the vertical
stabilizer is a result of sideslip and rudder deflection.

![](media/image16.wmf) 1

This expression assumes that all of the sideforce due to sideslip is due
to the vertical stabilizer. This is a reasonable approximation for the
purpose of this study.

For the purpose of this study, generic values of the aircraft
derivatives that are representative of large transport aircraft will
provide the needed data. Using representative values of the pertinent
derivatives and a representative wing area (S) results in:

![](media/image17.wmf) 2

![](media/image18.wmf) 3

Where sideslip and rudder deflection are in degrees and airspeed is in
ft/sec, ![](media/image19.wmf) is in lbs, and sideslip is positive with
wind from the right, and rudder deflection is positive trailing edge
left (standard NASA sign conventions).

This expression will not provide exact values for any single aircraft,
but does give the correct proportions of force due to sideslip and force
due to rudder deflection for a typical transport aircraft. By using this
same expression for all the tested configurations, it will be possible
to compare the forces on the vertical stabilizer that result from
different rudder flight control system mechanizations.

As a sanity check, the sideslip (10 deg) and rudder deflection (-6 deg)
for AA 587 at the time of failure at 250 kts, were input to equation 3,
resulting in a force of 71,400 lbs force on the vertical stabilizer. At
a near maximum takeoff weight for our generic aircraft of 175,000 lbs,
this results in a lateral acceleration of 0.41g. The NTSB data indicated
a lateral acceleration of 0.38g, indicating that equation 3 is a good
estimate of sideforce due to sideslip and rudder deflection.

Positive rudder deflection produces left yawing and positive sideslip.
Note that this causes the terms in equation 3 to subtract. The only way
that sideslip and rudder deflection can be additive in Equation 3, is
for the pilot to get out of phase with the aircraft (rudder deflection
of opposite sign from sideslip). This, in fact, was the scenario for
AA-587.

## Proposed Metrics for Pass-Fail Criteria

In the end, the objective of this work is to develop limits that may be
used by the FAA to develop certification guidelines for transport
aircraft rudder flight control systems. This is best done by developing
quantitative criteria. The objective of the criteria is to set limits
that if met will minimize or eliminate any tendency to overcontrol or
PIO in the directional axis. It is important to ensure that meeting
these criteria does not compromise the handling qualities for normal
rudder tasks, such as recovery from engine-out, or crosswind landings.
However, there is no intention to develop criteria to optimize the
rudder handling qualities in this project.

It has been hypothesized that the rudder overcontrol that occurred in
the AA 587 A-300 accident was related to the fact that Fmax was not much
greater than Fbo. It is not difficult to imagine that such a scenario
would result in overcontrol. That is because it deprives the pilot of
the ability to use pedal force to close the loop on sideslip, i.e.,
there is only a small region of pedal force between zero and maximum
rudder deflection.

Metrics designed to set limits on the amount of force differential that
is available to travel from zero rudder deflection to maximum rudder
deflection are discussed below.

[M1 = Fbo/Fmax]{.underline} -- Simply specifying a limit on the maximum
breakout as a function of the maximum pedal force is probably sufficient
to define limits on overcontrol tendency. F~MAX~ is defined as the force
required to reach the maximum rudder deflection, and Fbo is defined as
the sum of the feel spring breakout force and Coulomb friction as
defined in Section 4.3. M1 is suggested as a metric in Table 5 of the
Reference 8 NTSB report. Note that if Fbo = Fmax, the effect is that of
an on-off relay (all or nothing). Such systems are known to limit cycle
at best, and are unstable with any additional lag. Values of the M1
parameter are given for the aircraft reviewed by the NTSB in Table 2.

It is notable that the Airbus variable-stop designs have much larger
values of Fbo/Fmax than all other aircraft reviewed in this table. The
large value of Fbo/Fmax is a result of using the variable stop design
along with an almost linear force-feel gradient.

Note from Table 2 that the Douglas/Boeing variable stop designs have an
Fbo/Fmax that is consistent with the variable gearing and force limit
configurations. This is a result of using a highly nonlinear load-feel
curve.

![](media/image20.wmf){width="3.8159722222222223in"
height="3.6493055555555554in"}

Table 2 Values of Parameters from Reference 8 NTSB Report

![](media/image21.wmf)- This parameter is also suggested by the NTSB in
Table 5 of their report. Large values of M2 imply that it takes
relatively little additional force above breakout to achieve the maximum
rudder displacement. F~MAX~ is defined as the force required to reach
the maximum rudder deflection, ![](media/image22.wmf). The rationale
here is similar to M1 = Fbo/Fmax in that there should be a substantial
difference between the maximum force and the breakout force. The
difference is that this parameter accounts for rudder deflection
explicitly. The M2 parameter is shown for the aircraft reviewed by the
NTSB in Table 2. As with metric M1, the Airbus variable-stop designs
stand out with higher values than the rest. It is not clear that it is
important to include rudder deflection, as long as the maximum rudder
deflection occurs at Fmax (i.e., Fbo/Fmax might be good enough).

![](media/image23.wmf) - This parameter accounts for the available
control power as measured by the sideslip angle that can be produced
with full rudder. The sideslip angle that can be produced is a measure
of the achievable loads on the vertical stabilizer. The value of
![](media/image24.wmf) that can be achieved statically may be somewhat
less than dynamically if the yaw damper does not produce a deadbeat
response.

Hess developed a "Linearity Index", LI, (Reference 7) that is proposed
as a measure of the linearity of the load-feel curve. In its current
form, this parameter is not proposed as a metric for the reasons given
in Appendix D.

## Data Reduction

The data reduction will consist of the following.

1\. Plot data from pilot rating scales for each evaluated system for
full and for limited motion in such a way that it is easy to compare the
HQRs for each tested configuration with full motion and with limited
motion.

2\. Summarize pilot commentary for each evaluated system in a table in
such a way that it is easy to compare the key comments for each tested
system with full and limited motion.

3\. Plot HQR and workload ratings against proposed metrics (Section 5.3)
to determine if trends can be identified.

4\. Fast Fourier Transform of ![](media/image25.wmf)to obtain
quasi-linear describing function for the pilot.

## Data Analysis

The primary objective of this Phase 1 simulation is to determine how
much lateral motion is required to obtain valid results. In particular
it is necessary to determine if it is possible to accomplish the
majority of the rudder research on a limited authority motion system
such as found on most training simulators (e.g., hexapod).

The test procedure will be to conduct the evaluations on a simulation
that is capable of large lateral motion, first with full motion, and
then with limited motion. A comparison of results should indicate if
limited motion is adequate. The yes/no decision on limited motion will
be based on the following criteria.

A limited motion simulator is acceptable if a comparison between full
and limited motion shows that:

1\. There is no consistent difference in the mean handling qualities and
workload pilot ratings from the scales in Appendix C.

2\. There is no consistent difference in variability of the inter-pilot
and intra-pilot handling qualities and workload pilot ratings.
(Variability is just as important as the average ratings. For example,
if one pilot rates a system much worse than the others, it may be that
his or her technique has exposed a deficiency, not seen by the other
pilots. If such a trend were seen with full motion but not with limited
motion, full motion would be required for Phases 2 and 3.)

3\. The pilot commentary do not show parallel trends for large and
limited motion. (For example, if the pilots all comment negatively on
one type of rudder system for full motion, but not for limited motion,
it would indicate that full motion is necessary for valid results. It is
quite common to see more of such a trend in the commentary than in the
numerical ratings.)

4\. The correlations of HQRs with the proposed handling qualities
metrics (e.g., Fbo/Fmax) are similar for large and for limited motion.

5\. The quasi-linear describing function for the pilot
(![](media/image26.wmf)) shows similar crossover frequency and lead
generation for full motion and for limited motion.

6\. RMS values of sideslip angle, pedal position, pedal force, and
vertical stabilizer load are similar for full motion and for limited
motion.

7\. The maximum value of pedal deflection and load on the vertical
stabilizer are similar for full motion and for limited motion.

#### APPENDIX A --GENERIC RUDDER SYSTEMS

Generic versions of the three types of rudder flight control systems to
be studied are given in this section. It is intended that these
representations of rudder systems will be used for all three phases of
testing.

The generic rudder flight control systems provided below do not include
the effects of structural compliance. If the pilot applies a force of
approximately 50 lbs to the pedal on a typical transport rudder flight
control system, structural compliance accounts for approximately 2% of
the total pedal travel, which is judged to be insignificant for the
purposes of this experiment.

##### A-1 Variable-Gearing {#a-1-variable-gearing .unnumbered}

The block diagram to simulate a generic variable-gearing system is shown
in Figure A-1 below.

![](media/image27.wmf)

Figure A-1 Generic Variable-gearing Rudder System

The force command to the control loader actuator (Fcom) is the sum of
the viscous friction, Coulomb friction, load-feel spring, and breakout
of the load-feel spring. Pedal motion occurs when the pilot force is not
equal to Fcom.

The pedal stops are achieved within the control loaders by increasing
the spring force to a very large value. This is constant for the
variable gearing system, but is a calculated variable in the variable
stop (Figure A-4) and force limit systems (Figure A-6).

The force command to the control loader actuator (Fcom) is the sum of
the viscous friction, Coulomb friction, load-feel spring, and breakout
of the load-feel spring. Pedal motion occurs when the pilot force is not
equal to Fcom.

The pedal stops are achieved within the control loaders by increasing
the spring force to a very large value. This is constant for the
variable gearing system, but is a calculated variable in the variable
stop (Figure A-4) and force limit systems (Figure A-6).

Note that because Kbofs is a large number (100 lb/in), the feel spring
breakout is a constant (Fbofs) for pedal deflections above approximately
0.10 to 0.20 inches (![](media/image28.wmf)), and has the sign of the
pedal deflection. This could also be modeled without the limiter as
![](media/image29.wmf).

Cable stretch is accounted for as a result of the sum of the feel spring
and feel spring breakout forces. This assumes that the rudder feel
spring is located at the aft end of the aircraft near the rudder.
![](media/image30.wmf) is the "effective pedal travel", which is defined
as the pedal travel that contributes to moving the rudder. It is always
slightly less than the actual pedal travel due to cable stretch.

A provision for rudder trim is included in the model, to show where it
will be included in later testing. For the pilot tasks used in this
experiment (Figures 1 and 2), there is no need for rudder trim, so it
may be excluded.

The load-feel curves in Figures 5 and 6 include breakout. When
incorporating the load-feel curves in the simulator model, it will be
necessary to subtract the value of breakout, so the curves pass through
the origin. This is necessary because breakout and static friction are
accounted for separately in the simulation models in this appendix.

Variable-gearing systems reduce the rudder control gearing (Kped = ratio
of rudder travel to pedal travel) as a function of airspeed or dynamic
pressure. As a result, the total pedal travel does not change, but the
gradient of rudder surface deflection-to-pedal travel decreases as
airspeed increases.

Note that the rudder is not mechanically limited, its maximum travel
being "limited" solely by the reduced gearing between pedal and rudder.
The variable gearing is usually accomplished by means of a mechanical
ratio changer (e.g., a variable lever arm). Since the yaw damper is
always in series with the pedals (i.e., yaw damper does not cause pedals
to move), the yaw damper servo effectively sums with the output of the
ratio changer. As a consequence of this, the sum of the yaw damper input
and pilot pedal motion can cause the rudder to momentarily exceed its
theoretical limit. The advantage of this is that the yaw damper
continues to perform its function regardless of the magnitude of the
pilot input. The disadvantage of such a system is that a hardover
failure could cause the rudder to move full travel (30 degrees) at any
airspeed. As noted in Reference 8 (section 1.6.2.2), the motivation for
Airbus to change from a variable gearing system in the A300B2/B4 to a
variable stop system in the A300-600 was that "it was less complex and
had less severe failure modes".

The rudder pedal limits for the variable gearing system are fixed at
![](media/image31.wmf)4 inches. Rudder limiting is achieved by reducing
Kped as a function of airspeed as shown. The schedule of Kped vs.
calibrated airspeed is made such that the rudder deflection at full
pedal is identical to the variable-stop system at full pedal, at the
same calibrated airspeed. The difference between the systems for this
experiment is that full pedal will be 4.0 inches for the
variable-gearing system, and 1.2 inches for the variable-stop and
force-limit systems.

The variation of maximum rudder deflection as a function of airspeed is
typically inversely proportional to the square of calibrated airspeed.
i.e., dynamic pressure. The generic curve in Figure A-2 reflects this
relationship with minor adjustments based on a review of available data
for (Douglas/Boeing and Airbus).

![](media/image32.wmf){width="3.182638888888889in"
height="2.077777777777778in"}

Figure A-2 Limit on Rudder Travel (![](media/image33.wmf)) as Function
of Calibrated Airspeed -- Variable Gearing

The pedal deflection at airspeeds below 135 kts is based on a
pedal-to-rudder gearing of Kped = 7.5 deg/in. This gearing is calculated
to produce 30 deg of rudder deflection when the pedal is deflected 4.0
inches (i.e., ![](media/image34.wmf)). At calibrated airspeeds above 135
kts, ![](media/image35.wmf) is reduced (Figure A-2), and the resulting
variation in Kped with airspeed is shown in Figure A-3.

![](media/image36.wmf){width="2.9291666666666667in"
height="1.9201388888888888in"}

Figure A-3 Variation of Kped with Airspeed -- Variable Gearing

In this Phase 1 experiment airspeed is nominally constant at 250 kts.
Nonetheless, the nonlinear ratio changer is necessary to account for the
effect of changes in the pedal-to-rudder gearing with airspeed changes
during the run.

##### A2. Variable-stop {#a2.-variable-stop .unnumbered}

In this design, the rudder pedals and rudder surface are mechanically
limited as a function of airspeed. The control gearing between rudder
surface and rudder pedal (Kped) remains constant.

The block diagram to simulate a generic variable-stop system is shown in
Figure A-4 below.

![](media/image37.wmf)

Figure A-4 Generic Variable-Stop Rudder Control System

The pedal stop is a calculated variable in this mechanization. The
A-300-600 variable stop function is achieved by means of a mechanical
limit on rudder travel that is varied as a function of airspeed. The
commanded rudder position (![](media/image38.wmf)) is determined by the
sum of the pilot's rudder pedal input (![](media/image39.wmf)) and yaw
damper command (![](media/image40.wmf)). Since ![](media/image41.wmf),
the only way for ![](media/image42.wmf) to exceed the rudder limit is
via yaw damper inputs that occur simultaneously with a large pedal
input. According to Reference 8, yaw damper inputs that cause the rudder
limit to be exceeded result in the pedal being pushed aft while the
rudder position remains constant on the limit. This is simulated by the
![](media/image43.wmf) input to the control loader in Figure A-4. This
is not shown as a force input to denote that it cannot be resisted by
the pilot because the hydraulic system forces are very high.

The variation of maximum rudder deflection with airspeed is identical to
that used for the variable gearing system. The variation of pedal
deflection limit with calibrated airspeed was achieved by dividing the
rudder deflection by the constant Kped = 7.5 deg/in to achieve the
result shown in Figure A-5.

![](media/image44.wmf){width="2.932638888888889in"
height="1.9131944444444444in"}

Figure A-5 Reduction in Pedal and Rudder Deflection with Airspeed --
Variable Stop

The maximum rudder deflection plot shown in Figures A-2 and A-5 was
adjusted slightly to achieve a maximum pedal of 1.2 inches at 250 kts
for the variable stop system (value common to A300-600, A300B2/B4, A310,
A330-300). The maximum pedal deflection of the MD-80 and MD-90 at 250
kts is 1.1 inches.

In the Phase 1 and 2 experiments, airspeed will vary about an initial
condition of 250 kts.

##### A3. Force-limit {#a3.-force-limit .unnumbered}

The force-limit rudder system is intended to prevent excessive loads on
the vertical stabilizer and rudder. This is typically done by limiting
the rudder hinge moment, which is assumed to be proportional to the
loads on the vertical stabilizer and rudder. The rudder hinge moment is
given as:[^4]

![](media/image45.wmf)![](media/image46.wmf) A-1

Where S = rudder area,![](media/image47.wmf)= m.a.c. of rudder,
![](media/image48.wmf)= sea level air density = .00238 slug-ft^2^,
V~CAS~ is the calibrated airspeed, and C~Hr~ is the rudder hinge moment
coefficient which is a function of rudder deflection and sideslip angle.
It is important to note that ![](media/image49.wmf)is the aerodynamic
sideslip angle, i.e.,

![](media/image50.wmf)

The force-limit system usually operates by providing a method to bypass
hydraulic fluid around or through the actuator piston, such as by
drilling an orifice in the piston. This bypass is set so that the
actuator will stall at some level of reactive force (i.e., rudder hinge
moment divided by lever arm). Once the actuator stalls, the pilot can
move the control valve by increasing pedal deflection until the control
valve bottoms. However, when the actuator is stalled, the inflow of
hydraulic fluid is equal to the flow through the orifice, and therefore
the actuator piston does not move, and hence the rudder does not move.
Inherent in this design is the fact that the rudder pedal must move
through some stroke, ![](media/image51.wmf), (typically about 0.7
inches) before the control valve bottoms. The rudder surface does not
move during that interval. Once the control valve bottoms, additional
force on the pedals is transmitted directly to the rudder surface. The
aerodynamic loads are sufficiently high, that this is equivalent to a
hard stop.

Simulation of a generic force-limit rudder flight control system is
accomplished with the block diagram shown below in Figure A-6

![](media/image52.wmf){width="5.998611111111111in" height="3.7875in"}

Figure A-6 Generic Force-limit Rudder Control System

The pedal stops are variable in this mechanization, and are a function
of rudder hinge moment as described below. Note that if the aircraft is
accelerated with a large rudder deflection, the effect should be to
backdrive the pedals (as the value of the pedal limiter is reduced).
This should be verified during simulator checkout.

The commanded rudder is the sum of the pilot pedal input and yaw damper.
A combination of large pedal input and yaw damper activity could cause
hinge moment limiting, and render the yaw damper ineffective. For
mechanical implementations of this system, it would not be practical to
sum the yaw damper input downstream of the rudder limiter. However, for
a fly-by-wire implementation it would be possible to set limits only on
the portion of the input due to pedal, leaving the yaw damper to operate
independent of pedal input. This is discussed further in Appendix B.

As long as the rudder hinge moment (HMr) is equal to or less than the
maximum specified hinge moment (HMr~max~), the rudder deflection is
proportional to the pedal input according to the control gearing, Kped.
When the rudder hinge moment increases above HM~max~, the rudder
actuator stalls resulting in a effective rudder deflection limit,
![](media/image53.wmf). The calculation of the rudder limit is derived
below. The pedal stop limiter is set to allow the pedal travel required
to reach the rudder limit, and then to bottom the servo valve,
![](media/image54.wmf). Therefore, the pedal limiter is set as follows.

![](media/image55.wmf) A-2

For this series of experiments the rudder travel to bottom the control
valve (![](media/image56.wmf)) shall be set to 0.7 inches.

The rudder limit (![](media/image57.wmf)) is set by calculating the
rudder deflection that results in HMr~max~ as follows. The rudder hinge
moment coefficient corresponding to HMr~max~ is:

![](media/image58.wmf) A-3

S = area of rudder and ![](media/image59.wmf)= mearn aerodynamic chord
of rudder

The rudder hinge moment characteristics to be used in this simulation
are a generic representation of large transport aircraft rudders. The
variation of hinge moment with sideslip tends to be highly nonlinear as
shown in Figure A-7.

![](media/image60.png){width="3.4784722222222224in"
height="2.609027777777778in"}

Figure A-7 Generic Variation of Rudder Hinge Moment With Sideslip

The plus signs in Figure A-7 indicate the results of a 5^th^ order
polynomial fit to the solid line as follows.

![](media/image61.wmf)

eq A-4

Where ![](media/image62.wmf)is in degrees. The variation of the hinge
moment with rudder deflection is well represented as a linear function
for rudder deflection angles less than 20 degrees as follows.

![](media/image63.wmf) A-5

The total hinge moment is:

![](media/image64.wmf) A-6

The maximum hinge moment occurs when the rudder is on its limit:

![](media/image65.wmf) A-7

Finally, solving for the rudder limit:

![](media/image66.wmf)![](media/image67.wmf) (V~CAS~ in ft/sec and
![](media/image68.wmf)in deg.) A-8 Where ![](media/image69.wmf) is
calculated from the fifth order polynomial in Equation A-4. Recall that
the pedal deflection when the rudder is at the limit is calculated from
Equation A-2.

The value of the rudder hinge-moment limit (HM~max~) is set to 3508
ft-lbs so that the rudder limit is nominally 8 deg (at zero sideslip),
to be consistent with the variable gearing and variable stop
configurations at 250 KCAS. Kr = .27 lb sec^2^/ft for the generic rudder
configuration used in this experiment.

Recall from Equation A-2 that the rudder reaches its limit at 0.7 inches
of pedal (![](media/image70.wmf)) before the pedal reaches its limit. At
the 250 KIAS used in this experiment, the rudder limits at 1.2 inches of
pedal travel, and the pedal continues to move an additional 0.7 inches.
As a result, the final 35% of pedal travel occurs with no response from
the rudder ("unproductive pedal travel" = 0.7 inches). Comparison with
the variable-stop configuration with the same pedal travel (compare
Cases 7 and 2) will determine if this is good, bad, or not important.

Unproductive pedal travel will be further investigated as discussed in
Section 4.3.2.

Equation A-8 shows that for the force-limit system, the rudder limit
depends on the hinge moment limit and aerodynamic sideslip angle. So for
example, if the pilot applies and holds a positive (left) rudder-pedal
input, a positive sideslip results. From Figure A-7 this results in a
positive hinge-moment coefficient, which from equation A-8 causes a
higher value of rudder limit (![](media/image71.wmf)is negative) than
would occur with a variable-stop system, i.e., more control authority.
However, if there is a positive sideslip (tending to cause a left roll
rate), and the pilot uses negative (right) rudder to decrease the
sideslip and thereby reduce the left roll response, the sideslip term in
Equation A-8 subtracts from the HM~max~ term, resulting in a decreased
rudder limit compared to the variable-stop system. This scenario was
what existed at the time of structural failure of the vertical
stabilizer in the AA 587 accident, so it is possible that a force-limit
system would have prevented the failure. This is especially true because
the combination of positive sideslip and negative rudder deflection is
additive in terms of aerodynamic load on the vertical stabilizer and
rudder.

#### APPENDIX B -- MATH MODEL FOR GENERIC YAW DAMPERS

All large aircraft utilize a yaw damper. A generic yaw damper that is
representative of large aircraft is required to investigate the
interaction between the pilot's use of rudder and the yaw damper. Since
the primary purpose of a yaw damper is to damp the dutch roll mode, and
to enhance turn coordination, they all have similar dynamic response
characteristics. Therefore a single generic yaw-damper that accomplishes
that function is adequate for this study. Such a yaw damper is given in
the block diagram in Figure B-1.

![](media/image72.wmf)

Figure B-1 Generic Yaw Damper

This commonly used yaw damper design is essentially a feedback of
sideslip rate to rudder, where sideslip rate is calculated as:

![](media/image73.wmf)

where V~T~ = true airspeed and ![](media/image74.wmf). Lx is the
distance from the inertial reference system to the aircraft center of
gravity.

As shown in the Appendix A block diagrams, the yaw damper authority is
limited for each of the rudder system designs. This limit is usually
inversely proportional to airspeed above some reference airspeed. For
example, Reference 8 notes that the A300-600 is limited to
![](media/image75.wmf)10 deg at and below 165 kts, and to
![](media/image76.wmf) at airspeeds above 165 kts. This works out to 3.4
deg at 250 kts. By comparison, the Boeing 737NG limits the yaw damper
travel to ![](media/image77.wmf)3 deg at 250 kts. For the Phase 1 and 2
testing at 250 kts, the yaw damper limit will be fixed at
![](media/image78.wmf)3 deg.

Two implementations of the yaw damper in Figure B-1 will be
investigated.

-   Version A Yaw Damper -- This is illustrated in Figure B-2.

-   Version B Yaw Damper -- This is illustrated in Figure B-3

![](media/image79.wmf)

Figure B-2 Version A Yaw Damper

With the Version A implementation, it is possible for the yaw damper to
be rendered ineffective when the pilot rudder pedal input is large. That
is because the rudder limiter limits the sum of the yaw damper and pilot
input. Recall from Appendix A, that the rudder is mechanically limited
by variable stop and force limit designs, but not by the variable
gearing design. Therefore this limitation on yaw damper operation only
applies to the variable stop and force limit systems. One possible
workaround for these systems would be to implement the yaw damper
downstream of the rudder limiter as shown below in Figure B-3.

![](media/image80.wmf)

Figure B-3 Version B Yaw Damper

With this implementation, the yaw damper input to the rudder is
unaffected by the size of the pilot input. It will be useful to
investigate the Version B yaw damper implementation for the variable
stop system to determine if improved yaw damper operation can actually
be achieved with Version B, and if this improvement results in increased
loads on the vertical stabilizer.

The Version A and B yaw damper implementations are incorporated into the
variable stop and force-limit rudder flight control system designs as
shown in Figures B-4 and B-5 below.

**[Variable-Stop]{.underline}**

![](media/image81.wmf)

Figure B-4 Variable-stop System with Version A and B Yaw Dampers

With this mechanization, there is the possibility that the pilot's
rudder command could saturate the rudder limiter so that the Version A
yaw damper becomes ineffective. For that reason, the test matrix
includes the Version A and Version B yaw dampers for each of the
variable-stop system configurations (see Table 1).

**[Force-Limit]{.underline}**

![](media/image82.wmf)

Figure B-5 Force-Limit System with Version A and B Yaw Dampers r

For a mechanical implementation of the force-limit system, Version A is
the only realizable mechanization. That is because the hydraulic
actuator has no way of reacting to the proportion of the commanded
rudder that is due to the yaw damper. Since the purpose of the
force-limit system is to protect the vertical stabilizer from overload
due to rudder inputs, it makes sense to limit the total rudder command
(pilot plus yaw damper) as in Version A, and that is what is done in
current systems.

It would be possible to achieve the Version B yaw damper with a
fly-by-wire system wherein the rudder limiting is done in software. The
effect of moving the yaw damper input downstream of the rudder limiter
is adequately tested with the variable stop system (Figures A-4 and
B-4). For that reason, this will not be tested with the variable force
mechanization unless the experimental results show a compelling reason
to do so.

#### 

#### APPENDIX C -- PILOT RATING SCALES AND QUESTIONNAIRES

The qualitative pilot rating scales to be used to evaluate each
configuration for Experiments 1 and 2 are given in this appendix.

![](media/image83.wmf)

Figure C-1 Cooper-Harper Handling Qualities Rating (HQR) Scale from
Reference 4

![](media/image84.wmf)

Figure C-2 Modified Cooper-Harper Workload Rating Scale From Reference
5.

Groundrules for using the scales.

-   Always start at the lower-left and work up and to the right.

-   The major decisions on both scales do not allow half ratings. That
    is, ratings of 3.5, 6.5, and 9.5 cannot be assigned. It is otherwise
    okay to assign half ratings, e.g., a rating of 2.5 is acceptable.

-   When using the Cooper-Harper Handling Qualities scale, emphasize
    workload over performance. For example, if desired performance is
    achieved, but considerable compensation was required it is okay to
    give an HQR of 5. Be sure to note that is what you are doing in your
    commentary.

-   It is not okay to assign an HQR that is not warranted by your
    performance. For example, if it is not possible to achieve desired
    performance, the rating must be 5 or worse. If workload is low, and
    desired performance is not achieved, the correct procedure is to
    re-fly the task and increase aggressiveness in an attempt to achieve
    desired performance. The desired and acceptable performance levels
    are intended to set the level of aggressiveness for the task.

-   Always fly the task at least three times before assigning a rating.
    If in doubt, it is acceptable to fly additional trials.

PILOT QUESTIONNAIRE FOR FAA RUDDER SIMULATION

Were aircraft responses to rudder pedal inputs predictable?

2\. Describe rudder pedal characteristics:

-   Control forces desirable, too light, or too heavy?

-   Aircraft response to pedal inputs acceptable, too sensitive, or too
    sluggish?

-   Any comments relative to breakout, friction, or deadband?

-   Did you notice any rudder pedal backdrive? If so, was it
    objectionable?

3\. Did undesirable oscillations occur?

4\. Did you feel that your inputs were large enough to potentially
overstress the rudder or vertical stabilizer?

5\. Any tendency to reverse control (use the wrong rudder)?

6\. Assign HQR. Then answer one of the following questions.

-   [If HQR]{.underline} ![](media/image85.wmf)[3]{.underline}, briefly
    describe enhancing features of the aircraft response.

-   [If HQR is greater than 3]{.underline}, briefly summarize the
    deficiencies that make this configuration unsuitable for normal
    accomplishment of this task. Specifically note whether or not the
    deficiency is related to the aircraft response to rudder inputs.

7 Assign a workload rating from the Modified Cooper-Harper Scale

#### APPENDIX D -- LINEARITY INDEX PARAMETER

Hess, in Reference 6 has developed a "Linearity Index", LI. The
linearity index is proposed as a measure of the linearity of the
load-feel curve. Referring to Figure D-1a (copied from Reference 6), LI
is defined by constructing a line DB from the origin to the point on the
graph farthest from the origin. Then LI is defined as:

![](media/image86.wmf) D-1

If LI = 1.0, the force/feel system is said to be "completely linear". If
LI=0, it is highly nonlinear. There are a few issues regarding this
parameter that must be resolved. First, the load-feel curve is often, by
design, highly nonlinear (e.g., see Figures 4 and 5). Second the curve
in Figure D-1a, implicitly assumes that the control system breakout is
equal to the static friction (Fsf). Based on the definitions presented
in Section 4.3, point A in Figure D-1a is equal to (Fbofs + Fcf) and
point E is equal to (Fbofs -- Fcf). Note that point E is not part of the
definition of the linearity index. The only way for the curve to return
to the origin (point D), is if Fbofs = Fcf. In all practical designs the
breakout is designed to be greater than the static friction (Fbo \> Fsf)
to provide positive centering. This is shown in Figure D-1b.

Many rudder flight control system designs employ a highly nonlinear
load-feel curve as illustrated in Figure D-1c.

![](media/image87.wmf)

Figure D-1 Application of Linearity Index to Load-Feel Curves

The application of equation D-1 becomes somewhat problematic for the
more realistic load-feel curves in Figures D-1b and D-1c. In fact the
areas DABD and DBCD have no physical significance for realizable
systems.

It may be possible to redefine the linearity index to provide more
meaningful results for more practical systems, and that should be done
before applying it to the data from this experiment. However, there
seems no reason to do that if the proposed parameters in Section 5.1.3
successfully distinguish between satisfactory and unsatisfactory
configurations.

As shown in Figure D1(c), significant nonlinearities are intentionally
built into some rudder flight control systems. It is not so much the
magnitude of the nonlinearity that is important, but rather the nature
of it. For example, cases with point A near point E are expected to have
poor flying qualities because of high values of Fbo/Fmax. It is expected
that this will be captured by the parameters proposed in Section 5.1.3.

#### APPENDIX E -- EQUATIONS OF MOTION FOR PHASE 1 SIMULATION

The equations of motion to be used can take a variety of formats
depending on what is available for the selected simulator. Some factors
to consider are:

-   The lateral directional equations should include nonlinear effects
    with sideslip and rudder hinge moment (for example Cy vs
    ![](media/image88.wmf)). However, most other nonlinear effects such
    as with airspeed, angle-of-attack, and aileron hinge moment are not
    necessary

-   A representative set of aerodynamic data will be used throughout the
    Phase 1 experiment. By keeping the aero data constant, it is
    possible to isolate the effect of different motion system
    capabilities and different rudder flight control system.

-   Suggest using the rudder hinge moment coefficient data from Figure
    A-7 or some equivalent.

-   A rudimentary set of longitudinal equations is acceptable. Even
    linear transfer functions are acceptable because the experiment
    takes place at one flight condition.

#### APPENDIX F -- SUM OF SINES DISTURBANCE FUNCTIONS

Tasks 1 and 2 in the test plan call for Sum of sines (SOS) as
disturbance functions. This memo describes the SOS inputs for the VMS
experiment.

The governing equation is:

![](media/image89.wmf)

set n = 7 and incorporate the values given in Table 1 for Task 1 and
Task 2.

K~SF~ is a scale factor to allow adjustment of all amplitude values
together. Based on trial and error during checkout, the scale factors
used on the VMS were as follows.

![](media/image90.wmf)

![](media/image91.wmf)is the initial phase angle and was changed for
each run to cause the disturbances to look more random to the pilots.
The initial phase angle was changed by 60 deg for each run for three
runs. It was set back to zero on the fourth run. Since the pilots flew
three runs for each case, this procedure resulted in the same three
disturbance profiles being flown for every evaluation. This ensured that
the pilots were rating the rudder systems independent of the disturbance
profiles (i.e., every system got the same disturbance inputs). If a
pilot chose to run more than three runs to evaluate a case, the fourth
run resulted in repeating the ![](media/image92.wmf)= 0 case. The
initial phase angle was always set to zero for the first run on each
case -- again to ensure the same disturbance sequence for every case.
None of the pilots noted that they "learned" the disturbance profiles.

The task is to be set up to last 74.25 seconds. The first 5 seconds was
for warm-up (non-scored time). Data was taken during the following 63
seconds, and the disturbance inputs terminated 1.25 seconds later. A
light in the cockpit informed the pilot when the task was started and
terminated.

As a side note, the frequencies in Table 1 are calculated as a function
of the number of cycles (![](media/image93.wmf)), and the scoring time
(![](media/image94.wmf)= 63 sec) - ![](media/image95.wmf)

Table 1 SOS Command Signals for yaw and roll.

+-----+---------+---------+---------+---------+---------+---------+
| S   | Yaw     |         |         | Roll    |         |         |
| ine | Axis    |         |         | Axis    |         |         |
| w   | (side   |         |         | (roll   |         |         |
| ave | gust    |         |         | gust    |         |         |
| No. | inputs) |         |         | inputs) |         |         |
+-----+---------+---------+---------+---------+---------+---------+
|     | Ai      | No.     | !       | Ai      | No.     | !       |
|     | (v      | Cycles  | [](medi | (p      | Cycles  | [](medi |
|     | ~gust~) |         | a/image | ~gust~) |         | a/image |
|     | ft/sec  |         | 96.wmf) | deg/sec |         | 97.wmf) |
|     |         |         |         |         |         |         |
|     |         |         | rad/sec |         |         | rad/sec |
+-----+---------+---------+---------+---------+---------+---------+
| 1   | -35     | 2       | 0.19947 | -9      | 3       | 0.2992  |
+-----+---------+---------+---------+---------+---------+---------+
| 2   | 35      | 5       | 0.49867 | -9      | 4       | 0.39893 |
+-----+---------+---------+---------+---------+---------+---------+
| 3   | 35      | 9       | 0.8976  | 9       | 7       | 0.69813 |
+-----+---------+---------+---------+---------+---------+---------+
| 4   | 17.5    | 14      | 1.39626 | 4.5     | 18      | 1.79519 |
+-----+---------+---------+---------+---------+---------+---------+
| 5   | -7      | 24      | 2.39359 | -1.8    | 30      | 2.99199 |
+-----+---------+---------+---------+---------+---------+---------+
| 6   | 7       | 42      | 4.18879 | -1.8    | 40      | 3.98932 |
+-----+---------+---------+---------+---------+---------+---------+
| 7   | 2.8     | 90      | 8.97597 | 0.72    | 70      | 6.98131 |
+-----+---------+---------+---------+---------+---------+---------+

Task 1 is a rudder tracking task and the input is a lateral gust
(![](media/image98.wmf)). Task 2 is a roll tracking task and the input
is a rolling gust (![](media/image99.wmf)).

#### REFERENCES

1\. Hoh, Roger H., "Simulation Test Plan to Develop Transport Aircraft
Rudder Control System Requirements -- Phase 2 - Criteria Development",
DOT/FAA/RD/XXX, July, 2006

2\. Hoh, Roger H. "Simulation Test Plan to Develop Transport Aircraft
Rudder Control System Requirements -- Phase 3 -- Validation of Criteria"
DOT/FAA/RD/XXX, July, 2006

3\. Lee, B, and V. Rodchenko, et. al., Effect of Pedal Feel System
Characteristics on Aircraft HQ, Proceedings of AIAA Atmospheric Flight
Mechanics Conference, 15--18 August, 2005, San Francisco, CA, AIAA
2005-6034

4\. Cooper, Gorge E. and Robert P. Harper., "The Use of Pilot Rating in
the Evaluation of Aircraft Handling Qualities", NASA TN D-5153, April
1969.

5\. Wierwille, Walter E., and John G. Casili, "A Validated Rating Scale
for Global Mental Workload Measurement Applications," Proceedings of the
Human Factors Society -- 27^th^ Annual Meeting, 1983, pp 129-133.

6\. Hess, Ronald A, "Handling Qualities and Flight Safety Implications
of Rudder Control Strategies and Systems in Transport Aircraft",
Proceedings of AIAA Atmospheric Flight Mechanics Conference, 15--19
August, 2004, Providence, RI, AIAA 2004-4701

7\. Hess, Ronald A, "Handling Qualities and Flight Safety Implications
of Rudder Control Strategies and Systems in Transport Aircraft",
Proceedings of AIAA Atmospheric Flight Mechanics Conference, 15--19
August, 2004, Providence, RI, AIAA 2004-4701

8 Anon, In-flight Separation of Vertical Stabilizer American Airlines
Flight 587 Airbus Industrie A300-605R, N14053 Belle Harbor, New York
November 12, 2001, NTSB/AAR-0404, PB2004-910404, Notation 7439B, October
12, 2004

[^1]: The industry standard is to plot pedal deflection on the x-axis
    and pedal force on the y-axis. This is an unusual convention since
    the input to the system is force and the output is position.
    Nonetheless we have elected to illustrate the load-feel curves
    "backwards" to be consistent with industry practice. This should be
    kept in mind when using the block diagrams in Appendix A.

[^2]: The load-feel curves in Figure 1 are estimates based on limited
    data from the Reference 1 NTSB report (3 points - breakout, pedal
    deflection and force at 135 kts and 250 kts).

[^3]: This of course depends on the length and nature of the task. For
    shorter tasks (say less than one minute), three runs are necessary.
    For longer tasks, it may be possible to adapt in one or two runs.

[^4]: The total force on the vertical fin is a result of rudder
    deflection and sideslip. Limiting the rudder hinge moment to a value
    that limits rudder deflections that would exceed the allowable loads
    on the rudder mitigates the chances of exceeding the limit loads.
    However, the rudder hinge moment is an indirect measure of load on
    the vertical stabilizer, and it may be possible to exceed the
    allowable load due to certain combinations of sideslip and rudder
    deflection, with an operational force-limit system.