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A NONLINEAR AIRCRAFT SIMULATION OF ICE CONTAMINATED TAILPLANE STALL
DISSERTATION
Presented in Partial Fulfillment of the Requirements for
the Degree of Doctor of Philosophy in the Graduate
School of The Ohio State University
By
Dale W. Hiltner, B.S., M.S
*****
The Ohio State University 1998
Dissertation Committee: Approved by Professor Gerald M. Gregorek, Adviser
Professor Rama. K. Yedavalli
Professor Hayrani Oz i ‘ Advise] Aeronautical and Astronautical Engineering Graduate Program UMI Number: 99 00844
Copyright 19 9 8 by Hiltner, Dale William
All rights reserved.
UMI Microform 9900844 Copyright 1998, by UMI Company. All rights reserved.
This microform edition is protected against unauthorized copying under Title 17, United States Code.
UMI 300 North Zeeb Road Ann Arbor, MI 48103 Copyright by Dale W. Hiltner 1 9 9 8 ABSTRACT
The effects of tailplane icing on the flight dynamics of the NASA Lewis Research Center DHC-6 Twin Otter research aircraft have been analyzed using a specialized nonlinear simulation program. The program performed the integration of standard aircraft equations of motion with aircraft characteristics determined from tables and functions. For this research, a specialized database based on flight test and wind tunnel test data was developed. Unique methods were used to separate the tailplane contribution from the aircraft characteristics to create this database and separately model the wing/body and tailplane aerodynamic characteristics of the DHC-6 Twin Otter aircraft. A pilot model and a reversible control system model tailored for this research were effective in assessing the effects of tailplane icing.
Tailplane angle-of-attack showed trends of decreasing with decreasing airspeed and decreasing pitch rate during pushover maneuvers. At trim flight conditions, tailplane angle-of-attack was shown to decrease with increasing airspeed and increasing flap deflection. All of the pushover maneuvers to zero g load factor with non-zero flap
11 deflections and the iced tailplane model showed a tendency for control difficulties. The simulation responses were shown to be slightly conservative in predicting tailplane stall flight conditions compared to flight test data.
The simulation program responses suggest that a discriminator of susceptibility to ice contaminated tailplane stall for the DHC-6 Twin Otter is a pushover maneuver through a load factor of nz=0. 5g with no significant stick force lightening, no tendency for a divergent load factor or pitch rate, and positive control of the maneuver. The responses showed that tailplane icing causes two distinct stability and control problems; inadequate flying qualities if the tailplane angle-of-attack exceeds that of the hinge moment break, and reduced stability when the tailplane is near the stalling angle-of-attack. A novel V-n diagram limited by tailplane stall angle-of-attack was useful in quantifying these maneuvering limitations caused by tailplane icing across the flight envelope.
Ill Dedication
To all those pilots and passengers flying into dark and stormy winter skies.
IV ACKNOWLEDGMENTS
I wish to chank the NASA Lewis Research Center Icing
Technology Branch for providing the funding to support this effort. I also wish to thank all those friends and acquaintances who have put up with my unique personality during the course of this effort. Especially Dr. Michael J.
Flanagan and his wife Stephanie, without whose support and advice I would not have finished this endeavor. VITA
April 17, 1956 ...... Born - Dover, Ohio
1978 ...... B.S. Aeronautical and Astronautical Engineering, The Ohio State University
1983 ...... M.S. Aeronautics and Astronautics, M.I.T.
1978-1991 ...... Engineer McDonnell Aircraft Co. St. Louis, MO
1991-1996 ...... Graduate Research Assistant, Department of Aeronautical and Astronautical Engineering, The Ohio State University Columbus, Ohio
19 96-Present ...... Engineer, Aerodynamics Stability and Control Boeing Seattle, WA
FIELDS OF STUDY
Major Field: Aeronautical and Astronautical Engineering
VI TABLE OF CONTENTS
A b s t r a c t ...... ii
D e d i c a t i o n ...... iii
Acknowledgments...... iv
V i t a ...... V
LIST OF TABLES ...... ix
LIST OF FIGURES ...... x
LIST OF SYMBOLS ...... xv
1. INTRODUCTION AND BACKGROUND ...... 1 1.2 Ice Contaminated Tailplane Stall Background . 2 1.3 Research Approach ...... 7
2 . PRIOR STUDIES OF TAILPLANE I C I N G ...... 13 2.1 Wind Tunnel and Flight Test Results ...... 13 2.2 Simplified Longitudinal Simulation Analysis 16 2.3 Analysis of the Zero G Pushover Maneuver . . 18 2.4 Summary of Prior S t u d i e s ...... 22
3. DEVELOPMENT OF THE DHC-6 TWIN OTTER DATABASE . . . 23 3.1 NASA Lewis Stability and Control Flight T e s t i n g ...... 23 3.2 Twin Otter Tailplane Airfoil Wind Tunnel T e s t ...... 28 3.2.1 Discussion of Wind Tunnel Test R e s u l t s ...... 3 6 3.3 Creation of Tailplane Aerodynamic Coefficients ...... 46 3.4 Development of the Complete Aircraft Model D a t a b a s e ...... 51
4. LINEAR DYNAMICAL SYSTEMS ANALYSIS ...... 62
5 . OSU/AARL FLIGHT PATH SIMULATION PROGRAM, TAILSIM 74 5.1 Program O v e r v i e w ...... 74 5.2 Program Structure ...... 7 6 5.4 Implementation of Reversible Elevator Control M o d e l ...... 8 3
vii 5.5 Implementation of the Pilot M o d e l ...... 88
6. SIMULATION ANALYSIS ...... 93 6.1 Comparison with Flight Test Parameter Estimation M a n e u v e r s ...... 94 6.2 Trim Flight Conditions ...... 99 6.3 Pushover Maneuvers, Uniced Tailplane .... 103 6.4 Pushover Maneuvers with the Iced Tailplane . 114 6.5 Pushover Maneuvers with the Pilot Model . . . 132 6.6 Discussion and Definition of an Alternate Pushover Maneuver ...... 14 9
7 . COMPARISON OF FLIGHT TEST AND SIMULATION RESPONSES ...... 156
8. TAILPLANE STALL LIMITED MANEUVER CAPABILITY DIAGRAM ...... 163
9. SUMMARY AND DISCUSSION ...... 170
10. CONCLUSIONS AND RECOMMENDATIONS ...... 176
LIST OF REFERENCES ...... 182
APPENDIX A. DHC-6 TWIN OTTER FLIGHT TEST COEFFICIENTS AND DERIVATIVES ...... 185
APPENDIX B. DHC-6 TWIN OTTER AIRCRAFT MODEL DATABASE COEFFICIENTS AND DERIVATIVES ...... 192
APPENDIX C. DHC-6 TWIN OTTER TAILPLANE DATABASE COEFFICIENTS ...... 215
APPENDIX D. AIRFOIL TO TAILPLANE CORRECTION CONSTANTS ...... 222
APPENDIX E. DOWNWASH CALCULATION...... 224
APPENDIX F. EQUATIONS OF MOTION, OUTPUTS, AND RUNGE- KUTTA INTEGRATION ...... 230
Vlll LIST OF TABLES
Table 3.1 NASA LeRC DHC-6 Twin Otter Aircraft Specifications ...... 27
IX LIST OF FIGURES
Figure 1-1 Key Aircraft Parameters at Cruise and ApproachG Figure 3.2 OSU 7X10 Wind T u n n e l ...... 31 Figure 3.3 Baseline Installation, 0„=-26.6° (Wake Probe in Foreground) ...... 32 Figure 3.4 LEWICE Ice Shape Installation (View from Upstream) ...... 33 Figure 3.5 Section 1 (Baseline) and Section 2 Airfoil Sections ...... 34 Figure 3.6 Ice Shape Sections ...... 3 5 Figure 3.7 Lift Characteristics, V=100 kts, 6,=0.0 41 Figure 3.8 Hinge Moment Characteristics, V=100 kts, a.= 0 . 0 ...... 41 Figure 3.9 Lift Characteristics, Large Deflections . . 42 Figure 3.10 Hinge Moment Characteristics, Large Deflections ...... 42 Figure 3.11 Velocity Effects, Baseline, Lift Characteristics ...... 43 Figure 3.12 Velocity Effects, LEWICE Ice Shape, Lift Characteristics ...... 43 Figure 3.13 Velocity Effects, Baseline, Hinge Moment Characteristics ...... 44 Figure 3.14 Velocity Effects, LEWICE Ice Shape, Hinge Moment Characteristics...... 44 Figure 3.15 Section 2 Lift Characteristics Comparison...... 4 5 Figure 3.16 Section 2 Hinge Moment Comparison .... 45 Figure 3.17 Effects of Elevator Horn on Hinge Moment Coefficient (Reprinted from Ref. 1 7 ) ...... 50 Figure 4.1 Linear Model Second Order Step Response . . 70 Figure 4.2 Linear Analysis Pushover Maneuver, Load F a c t o r ...... 70 Figure 4.3 Linear Analysis Pushover Maneuver, Steady State A G A ...... 71 Figure 4.4 Linear Analysis Pushover Maneuver, Minimum Peak A G A ...... 71 Figure 4.5 Linear Analysis Pushover Maneuver, Steady State Pitch R a t e ...... 72 Figure 4.6 Linear Analysis Pushover Maneuver, Minimum Peak Pitch R a t e ...... 72 Figure 4.7 Linear Analysis Pushover Maneuver, Steady State Tailplane A G A ...... 73 Figure 4.8 Linear Analysis Pushover Maneuver, Minimum Peak Tailplane A O A ...... 7 3 Figure 5.1 TAILSIM Program Flow Block Diagram .... 80 Figure 5.2 Reversible Control System Schematic .... 87 Figure 6.1 Example Maneuver Elevator Deflection Comparison...... 96 Figure 6.2 Example Maneuver Airspeed Comparison . . . 96 Figure 6.3 Example Maneuver Angle-of-Attack Comparison...... 97 Figure 6.4 Excimple Maneuver Pitch Angle Comparison . . 97 Figure 6.5 Example Maneuver Pitch Rate Comparison . . 98 Figure 6.6 Example Maneuver Normal Acceleration Comparison...... 98 Figure 6.7 Simulation Trim Characteristics, Tailplane Angle-of-Attack ...... 101 Figure 6.8 Simulation Trim Characteristics, Elevator Deflection...... 101 Figure 6.9 Simulation Tailplane Trim and Stall Characteristics ...... 102 Figure 6.10 Simulation Trim Characteristics, Angle-of- A t t a c k ...... 102 Figure 6,11 Example Simulation Pushover Maneuver Time History, 0^=0°, Uniced Tailplane ...... 108 Figure 6.12 Pushover Maneuvers, G Level Attained . . . 10 9 Figure 6.13 Pushover Maneuvers, Pitch Rate Functionality ...... 109 Figure 6.14 Pushover Maneuvers, Incremental Effect of Pitch R a t e ...... 110 Figure 6.15 Pushover Maneuvers, Airspeed Functionality ...... 110 Figure 6.16 Pushover Maneuvers, Airspeed/Pitch Rate Functionality ...... Ill Figure 6.17 Pushover Maneuvers, Angle-of-Attack A t t a i n e d ...... Ill Figure 6.18 Pushover Maneuvers, Elevator Deflection R e q u i r e d ...... 112 Figure 6.19 Pushover Maneuvers, Effect of Input Ramp T i m e ...... 112 Figure 6.20 Pushover Maneuver Comparison, Airspeed Functionality ...... 113 Figure 6.21 Pushover Maneuver Comparison, Pitch Rate Functionality ...... 113 Figure 6.22 Push Over Maneuver, Iced Tailplane, Approach Airspeed, 6^ Command, 5f = 0 ° ...... 12 0 Figrure 6.23 Push Over Maneuver, Iced Tailplane, Approach Airspeed, Ô, Command, 0^=10° 121 Figure 6.24 Push Over Maneuver, Iced Tailplane, Minimum Airspeed, Ô, Command, ô j =10° ...... 122 Figure 6.25 Push Over Maneuver, Iced Tailplane, Approach Airspeed, Ô, Command, 0f=20° 123
XI Figure 6.26 Push Over Maneuver, Uniced Tailplane, Approach Airspeed, Ô, Command, 0^=20° ...... 124 Figure 6.27 Slow Push Over Maneuver, Iced Tailplane, Approach Airspeed, Ô, Command, 6f=2 0° ...... 125 Figure 6.28 Push Over Maneuver, Iced Tailplane, Approach Airspeed, F, Command, 0^=0° ...... 126 Figure 6.2 9 Push Over Maneuver, Uniced Tailplane, Approach Airspeed, F, Command, 0f=10° 127 Figure 6.3 0 Push Over Maneuver, Iced Tailplane, Approach Airspeed, F, Command, 0^=10° 128 Figure 6.31 Push Over Maneuver, Uniced Tailplane, Approach Airspeed, F, Command, 0g=20° 129 Figure 6.32 Push Over Maneuver, Iced Tailplane, Approach Airspeed, F, Command, 6^=20° ...... 130 Figure 6.33 Push Over Maneuver, n=0.4g. Iced Tailplane, Approach Airspeed, Ô, Command, ôf=20° 131 Figure 6.34 Push Over Maneuver, Iced Tailplane, Approach Airspeed, Pilot Model Command, 6^=0° . . 137 Figure 6.35 Push Over Maneuver, Uniced Tailplane, Approach Airspeed, Pilot Model Command, 5f=lG° 138 Figure 6.3 6 Push Over Maneuver, Minimum Airspeed, Uniced Tailplane, Pilot Model Command, 0^=10° . . 139 Figure 6.37 Push Over Maneuver, Approach Airspeed, Uniced Tailplane, Pilot Model Command, 0^=20° . . 140 Figure 6.38 Push Over Maneuver, Iced Tailplane, Approach Airspeed, Pilot Model Command, 0^=10° 141 Figure 6.3 9 Push Over Maneuver, Iced Tailplane, Minimum Airspeed, Pilot Model Command, 5^=10° . . 142 Figure 6.40 Slow Push Over Maneuver, Iced Tailplane, Minimum Airspeed, Pilot Model Command, 5^=10° . . 143 Figure 6.41 Push Over Maneuver, Iced Tailplane, Approach Airspeed, Pilot Model Command, 0^=20° 144 Figure 6.42 Push Over Maneuver, 0.4 G, Iced Tailplane, Approach Airspeed, Pilot Model Command, 6^=2 0° 145 Figure 6.43 Pitch Doublets Maneuver, Approach Airspeed, Uniced Tailplane, Pilot Model Command, 6f=40' 146 Figure 6.44 Pitch Doublets Maneuver, Iced Tailplane, Approach Airspeed, Pilot Model Command, 0^=40° 147 Figure 6.45 Vickers Viscount Accident Flight Recorder Data (reprinted from Ref. 1) . . . . 148 Figure 6.46 Alternate Pushover Maneuver, 6f=1 0 ° 154 Figure 6 47 Alternate Pushover Maneuver, 5f=20° 155 Figure 7 1 Pushover Maneuver n^ Comparison 159 Figure 7 2 Pushover Maneuver Airspeed Comparison 159 Figure 7 3 Pushover Maneuver Stick Force Comparison 160 Figure 7.4 Pushover Maneuver Elevator Deflection Comparison . . . 160 Figure 7.5 Pushover Maneuver AOA Time History Comparison .... 161
Xll Figure 7 .6 Pushover Maneuver Tailplane AOA Comparison...... 161 Figure 7.7 Pushover Maneuver Pitch Angle Comparison 162 Figure 7.8 Pushover Maneuver Pitch Rate Comparison . 162 Figrure 8.1 Tailplane Stall Maneuver Capability, Effect of Power, Iced Tailplane ...... 168 Figure 8.2 Tailplane Stall Maneuver Capability, Effect of Flaps, Iced T a i l p l a n e ...... 168 Figure 8.3 Tailplane Stall and Hinge Moment Break Maneuver Capability, Effect of Flaps, Iced T a i l p l a n e ...... 169 Figrure 8.4 TAILSIM Tailplane Trim and Stall Characteristics ...... 16 9 Figrure A. 1 C^q, All Flight Test Configurations . . 186 Figure A. 2 Cj„, All Flight Test Configurations . . . .18 6 Figure A. 3 C^^,, All Flight Test Configfurations . . 18 7 Figure A.4 C^^, All Flight Test Configurations .... 187 Figure A. 5 C^q, All Flight Test Configurations . . 188 Figure A.6 C^, All Flight Test Configurations .... 188 Figure A. 7 All Flight Test Configurations . 189 Figure A. 8 All Flight Test Configurations . . . .18 9 Figure A. 9 C^^, All Flight Test Configurations . 190 Figure A. 10 C^j^, All Flight Test Configurations .... 190 Figure A. 11 C^^, All Flight Test Configurations .... 191 Figure B.l C^g, Cy=0.0, ...... 193 Figure B.2 C^,, C.j=0.Q7 193 Figure B.3 €^,= 0.14 194 Figure B.4 Cj„ ...... 194 Figure B.5 195 Figrure B.6 C^q ...... 195 Figure B.7 Drag Polar, C^sO. 0 196 Figure B.8 Cg, Drag Polar, Cq.=0.07 196 Figure B.9 Cj,, Drag Polar, Cq.= 0.14 197 Figure B.IO C^o Calculation, C^^^ Term ...... 197 Figure B.ll Cqq Calculation Terms ...... 198 Figure B.12 C^^ 198 Figure B.13 C ^ g , ...... 199 Figure B.14 C^., C^=0.0 199 Figure B.15 C^, Ct=0.07 200 Figure B.16 C^., Ct=0.14 200 Figure B.17 C^j,, C^=0.0 201 Figure B.18 C^g,, C^=0.07 201 Figure B.19 C^g., C^=0.14 202 Figure B. 20 C^q, C^=0 . 0 202 Figure B.21 C^, C^=0.07 203 Figure B.22 C^, C,.=0.14 203 Figure B. 23 Ô, C^= 0.0, Uniced Tailplane ...... 204 Figure B. 24 5, C,= 0 . 07, Uniced Tailplane ...... 2 04 Figrure B.25 0^=0.14, Uniced Tailplane ...... 205 Figure B.26 C^= 0.0, Iced Tailplane ...... 205 Figure B. 27 C^= 0.07, Iced Tailplane ...... 206
Xlll Figure B.28 ô, tria' Ct=0.14, Iced Tailplane ...... 206 Figure B.29 Vf Ct,-0 .0 ...... 207 Figure B.30 V^> C^-0.07 ...... 207 Figure B.31 7r.' C^-0.14 ...... 208 Figure B.32 ^Zqt, 0^.-0.0 ...... 208 Figure B.33 , C,-0.07 ...... 209 Figure B.34 Czqr, C^-0.14 ...... 209 Figure B.35 Cxqr, Ct-0.0 ...... 2 1 0 Figure B.36 Cxqr, Ct.-0.07 ...... 2 1 0 Figure B.37 Cxqr, Ct,-0.14 ...... 2 1 1 Figure B.38 CMcr, Ct,-0.0 ...... 2 1 1 Figure B.39 , Ct.-0.07 ...... 2 1 2 Figure B.40 , C^-0.14 ...... 2 1 2 Figure B.41 , Ct.-0.0 ...... 213 Figure B.42 Cxqt, Ct.-0.07 ...... 213 Figure B.43 Cxqt, C^-0.14 ...... 214 Figure C.l Cjt' üniced ...... 216 Figure C.2 Cjt ' Iced ...... 216 Figure C.3 ^Xt' üniced ...... 217 Figure C.4 ^Xt' Iced ...... 217 Figure C.5 Ct.r' üniced ...... 218 Figure C.6 Ct.r' Iced ...... 218 Figure C.7 ^Dt' üniced ...... 219 Figure C.8 ^Dt ' Iced ...... 219 Figure C.9 ^MC' üniced ...... 2 2 0 Figure C.IO I c e d ...... 2 2 0 Figure C.ll ^Ht ' üniced ...... 2 2 1 Figure C.12 Iced ...... 2 2 1
XIV LIST OF SYMBOLS
Regular Symbols, General
Ar Aspect ratio
A Area
AOA Angle-of-attack
a. Tailplane lift curve slope
b Wing span
C Centigrade
c chord length
Drag coefficient
C-_ Induced drag coefficient
C- Trimmed drag coefficient
Elevator hinge moment coefficient
Variation of elevator hinge moment coefficient with angle-of-attack
Ch> Variation of elevator hinge moment coefficient with elevator deflection
Section elevator hinge moment coefficient
C._ Lift coefficient
Lift curve slope
Trimmed lift coefficient
C- Section lift coefficient
XV C-^ Section lift curve slope
C- Rolling moment coefficient
Variation of rolling moment coefficient with sideslip
C.„ Variation of rolling moment coefficient with roll rate
C . Variation of rolling moment coefficient with yaw rate
Variation of rolling moment coefficient with aileron deflection
C.Variation of rolling moment coefficient with rudder deflection
Cv Moment coefficient
C„^ Variation of moment coefficient with angle-of- attack
Cm, Variation of moment coefficient with pitch rate
Cm. Trimmed moment coefficient
C_ Section moment coefficient
C_ Yawing moment coefficient
C__. Variation of yawing moment coefficient with sideslip
C_c Variation of yawing moment coefficient with roll rate
C„, Variation of yawing moment coefficient with yaw rate
C_:a Variation of yawing moment coefficient with aileron deflection
C,,_ Variation of yawing moment coefficient with rudder deflection
Cg Pressure coefficient
C- Thrust coefficient
XV i c. Section force coefficient in Z-direction
Cv Axial force coefficient
Cy^ Variation of axial force coefficient with angle-of-attack
Variation of axial force coefficient with angle-of-attack squared
Cy, Variation of axial force coefficient with pitch rate
Cy- Trimmed axial force coefficient
C., Section axial force coefficient
C., Side force coefficient
C._ Variation of side force coefficient with sideslip
C,_ Variation of side force coefficient with roll rate
C,,, Variation of side force coefficient with yaw rate
C.,,^ Variation of side force coefficient with aileron deflection
C,., Variation of side force coefficient with rudder deflection
Cy Force coefficient in Z-direction
Cy, Variation of force coefficient in Z-direction with angle-of-attack
Cy, Variation of force coefficient in Z-direction with pitch rate
Cy; Trimmed force coefficient in Z-direction
D Propeller diameter g Acceleration of gravity g Grams
H., Hinge moment of elevator
xvii Moment of inertia about X axis
I.„, Moment of inertia about Y axis
1.. Moment of inertia about Z axis
1.... Product of inertia in XY axes
Product of inertia in XZ axes
1.... Product of inertia in YZ axes i, Tailplane incidence angle
K., K;, K',K' Scale factors used in drag correction k Reduced frequency k. Scale factor in second order system response
1 Length
1, Arm length, CG to tailplane 1/4 chord
L' Primed dimensional rolling moment, L' = (L+(I,=/I^)N)/(l-(I,=V(IxxI==)) Mj Variation of dimensional pitching moment parameter with angle-of-attack
M> Variation of dimensional pitching moment parameter with elevator deflection
M; Area moment of elevator about hinge line, excluding elevator horn. From Ref. 17
M. ... Area moment of the elevator horn about the hinge line. From Ref. 17
M, Variation of dimensional pitching moment parameter with pitch rate
M._, Variation of dimensional pitching moment parameter with vertical velocity m Mass n Load factor n Propeller revolutions per second
xviii n. Normal acceleration, z-direction
N' Primed dimensional yawing moment, N' = (N+ (!_/!_) L) / (I- (I_V(IxxI==) ) q Pitch rate q^ Dynamic pressure
Reynolds Number
S Wing area s Transfer function frequency variable
T Time constant t Time
V Velocity
V._. Tail volume
W Weight w Vertical velocity
X Distance along x-axis
Z,., Variation of dimensional force parameter in z direction with vertical velocity
Z. Variation of dimensional force parameter in z direction with angle-of-attack
Z, Variation of dimensional force parameter in z direction with elevator deflection
Greek Symbols, General
O', Angle-of-attack of aircraft reference line
Of, Induced angle-of-attack
Ofggczior Angle-of-attack of an airfoil section a. Tailplane angle-of-attack
xix a.q Angle-of-attack at the tailplane due to pitch rate
а,; Angle-of-attack at the tailplane at zero tailplane lift
/3 Angle-of-sideslip
T], Dynamic pressure ratio, tailplane to freestream
Ô Deflection angle
6j Aileron deflection angle
Elevator deflection angle
Ô.- Flap deflection angle
б, Rudder deflection angle
e Downwash angle
£; Lagged downwash angle
e. Downwash angle at zero lift
* Phase angle
0 Bank angle y Flight path angle fi Micro, xlO"
7T Pi
6 Pitch attitude angle p Air density
(7 Attenuation, a =
T Time constant
ÙJ, Damped natural frequency cuu Undamped natural frequency
XX \P Heading angle f Damping ratio
Subscript Symbols a Aileron e Elevator f Flap
FRL Fuselage reference line g Gust i Induced i Implies any appropriate axis max Maximum min Minimum
0 Defines the condition at zero lift or zero angle-of-attack, or bias value r Rudder ref Reference s Stick or control column ss Steady state t Tailplane
Reversible Elevator Control Model Symbols
Length of control stick pivot point to elevator control cable
XXI Length of elevator control arm
bg Length of control stick
Elevator damping coefficient
Cg Control stick damping coefficient
E Modulus of elasticity
F- Stick force due to cable force
Eg Stick force commanded by pilot
Elevator gearing ratio
Moment of inertia of elevator
I, Moment of inertia of control stick
K. Elevator control cable spring constant
1 Elevator control cable length
Angular rate of elevator deflection
W3 Angular rate of stick deflection
e Elastic strain
(5. Elastic strain length due to cable force
a Elastic stress
Pilot Model Symbols
K, Transfer function gain n. Commanded load factor
Lead time constant
T; Lag time constant
X., X- State variables of controllable canonical form model
XXI 1 Pilot model elevator command
Time constant for pilot reaction delay
XXX XI CHAPTER 1
INTRODUCTION AND BACKGROUND
1.1 Introduction
In 1977, a Vickers Viscount, a 4-engine turbopropeller aircraft with a 58,000 lb. gross weight, was on approach to
Bromma airport in Stockholm, Sweden. Shortly after applying full flaps, the aircraft pitched over to a load factor of n=-1.4g and crashed. In 1973 an Iljushin 11-18, a 110,000 lb gross weight 4-engine turbopropeller aircraft, was on approach to Sheremetovo airport in Moscow. While making a glide path correction the elevator abruptly moved to a full nose down position. This position was unrecoverable and caused the aircraft to pitch over and crash. On another approach to a Swedish airport prior to 1985, a Piper
Cherokee, a single piston engine 4 seat aircraft, pitched over uncontrollably when the pilot applied the last "notch" of flap deflection. Only the accidental reversing of this full flap deflection allowed the pilot to regain controlled flight and complete the landing.
These and other accidents and incidents are reported in
References 1, 2 and 3. In all cases icing conditions were present. In all cases, the primary cause is surmised to be the phenomenon of Ice Contaminated Tailplane Stall (ICTS).
1.2 Ice Contaminated Tailplane Stall Background
Icing is one of the most insidious problems of aircraft operations. Ice contamination of aircraft surfaces can have a dramatic impact on an aircraft's flight characteristics.
Typically, when discussing icing, the wing is most often considered. Historically pilots have checked for ice on the wings as the most critical indication of icing conditions.
This is understandable, since changes in wing characteristics have the greatest impact on the performance of an aircraft.
However, there is a potentially more serious icing scenario; ice contamination of the tailplane, with or without ice contamination of the wing. This tailplane icing may result in an ICTS event, which occurs when the local angle-of-attack (AOA) at the tailplane exceeds the stalling
AOA. It most commonly occurs when an aircraft is on approach and has flaps extended. The result can be an uncontrollable nose down pitching motion and accompanying dive from which the aircraft may be too low to recover. An ICTS event is often accompanied by nose down elevator lock, a condition in which the differential pressure on the elevator of the stalled tailplane may cause the elevator to be forced into a nose down position. The resulting elevator hinge moment may be strong enough to pull the yoke from the pilots hands, and prevent recovery to a nose up control position.
The key aerodynamic parameters that describe the conditions of an ICTS event are illustrated in Figure 1.1.
This figure shows a cruise condition and an approach condition. At cruise, the higher speed requires a low angle- of-attack, ot, and a low wing lift coefficient and circulation. The low wing circulation causes a small downwash angle resulting in a small, but typically negative, tailplane angle of attack, At approach airspeed with approach flaps extended, the angle-of-attack may be the same but due to the lower airspeed, the wing lift coefficient and circulation are larger. This larger circulation causes a larger down wash angle resulting in a much more negative tailplane angle-of-attack. The effect of a positive, or nose down, pitch rate about the aircraft center-of-gravity causes the tailplane angle of attack to become more negative simply by the airflow induced at the tailplane moment arm.
Over the past 18 years, ICTS has been responsible or is suspected in 16 accidents with 139 fatalities [4] . Due to their flight at lower altitudes where icing is most common and their simple reversible control systems, commuter class aircraft are most commonly affected. In response to this problem, the Federal Aviation Administration (FAA) has conducted workshops on the ICTS phenomenon and conducted a study to identify aircraft susceptible to ICTS. As a result of this effort, more knowledge of ICTS has been presented to the pilot community [1,2,3,5,6,8] and a greater understanding of ICTS is developing. While this current understanding is significant, there is still a lack of accurate, quantified knowledge of the aerodynamics and flight dynamics of the ICTS phenomenon. To meet this need, the FAA and NASA, in cooperation with The Ohio State University, have instituted a project to more fully investigate the ICTS phenomenon.
The tailplane icing phenomenon has been studied using the methods of flight tests [1,7], wind tunnel tests of typical tailplane airfoils [5,6], and analysis of aircraft dynamics [8,9]. Most of the previous efforts attempted to define the effects of tailplane icing on local tailplane airfoil characteristics or overall aircraft dynamic characteristics. Reference 8 included nonlinear tailplane data in a simplified longitudinal flight path simulation analysis. Reference 9 attempted to quantify tailplane lift requirements during dynamic pushover maneuvers.
Currently, a pushover to zero load factor, or the Zero
G maneuver, and steady heading sideslips are the only known flight test methods to indicate susceptibility to ICTS [10] .
The effect of the Zero G maneuver is to increase the negative angle-of-attack at the tailplane. The intent is to create larger negative tailplane AOA than would normally occur during a typical flight. As defined in Reference 10, the maneuver is expected to be performed over a complete range of flap deflections and airspeeds, with representative tailplane ice shapes attached to the tail. If tailplane stall occurs, as indicated by a stick force reversal, the aircraft is considered to be susceptible to ICTS.
The effect of a steady heading sideslip on the aerodynamics at the tailplane is less clear. There is also less analysis available to quantify this phenomenon. Two factors that would seem to be dominant in determining the local tailplane flow angles in sideslip are; a shift in downwash due to the change in tailplane location relative to the wing/flap vortices, and blanking or other cross flow effects caused by the fuselage and vertical tail. Lift *
Downforce
Cruise Configuration
(+) Approach Configuration Figure 1.1 Key Aircraft Parameters at Cruise and Approach 1.3 Research Approach The Zero G maneuver will increase the negative AOA at the tailplane, and the analysis of Reference 9 shows a good correlation with known aircraft susceptibility. However, no attempt at comparing such analysis to flight test data has been made. In addition, the accuracy and repeatability of the flown maneuver is questionable, as it is largely dependent on the quality of the pilot input. Additionally, Reference 8 shows effects of tailplane icing on aircraft responses, but these results are considered to be qualitative. These and other results of prior studies are discussed in Chapter 2, and indicated that there is a need to quantify more completely the aerodynamic and dynamic phenomenon of pushover maneuvers. The joint FAA, NASA, and OSU ICTS analysis project was formed to provide a more complete understanding of the accepted ICTS susceptibility flight maneuvers. As part of this project, the research described herein accomplished flight dynamics analysis and provided modeling methods to support the flight testing of pushover maneuvers. Specific to this study, data would be obtained from a flight test aircraft and be compared to that from the analysis. Because of this, the analysis method had to be as close to the "real world" as possible. The area of interest in analyzing the ICTS phenomenon is the tailplane stall, which is by nature a nonlinear characteristic. The goal of this research is to represent the tailplane stall characteristics and their effect on aircraft dynamics as accurately as possible. As such, linear methods that rely on aircraft coefficients linearized about a point flight condition would not be effective. The only available methods to provide the desired fidelity in describing the stall aerodynamics and aircraft dynamics is a numerical nonlinear simulation program. This would allow the aircraft to be "flown" similarly to the flight test aircraft, and so would provide responses to compare to and support those of the test aircraft. The ability of the simulation to provide the response of any desired parameter would allow the parameters describing the tailplane aerodynamic characteristics to be monitored during a maneuver. In this way, the desired result of this research of quantifying the effect of tailplane stall characteristics on aircraft dynamics could be accomplished. Nonlinear simulations consist of aircraft coefficients contained in tables that are used to determine the forces and moments acting on an aircraft. These forces and moments are then used in the nonlinear aircraft equations of motion (EOM) to determine the accelerations on the aircraft. These accelerations are then integrated to determine the aircraft's motion. A benefit of this analysis method is that the tables can be used to describe any parameter to a high level of fidelity. For example, tailplane stall characteristics can 8 be readily implemented by creating a table of lift coefficient versus angle-of-attack. The nonlinear simulation was chosen for this research because it can provide the level of fidelity desired. Another advantage is that different characteristics can be implemented readily by changing the data in the tables. Additionally, the pushover maneuvers performed for this research are not small perturbation maneuvers and so would fall outside the scope of linear methods. Choosing a nonlinear simulation as the method to analyze the ICTS phenomenon dictated the remaining effort for this research. To use a nonlinear simulation, a database of aircraft coefficients is required. This was available from prior testing of the NASA Lewis Research Center's DHC-6 Twin Otter and is described in Section 3.1. The emphasis on this study is on the tailplane, though, so a database of tailplane aerodynamic characteristics was required. Hinge moment characteristics were of special interest, since very little information was available describing their characteristics, and they directly impact pilot control forces. It was desired to utilize as much "real world" data as possible during the course of this research, so a wind tunnel test of the tailplane was a logical choice to acquire data on tailplane characteristics. The available wind tunnels could support testing of tailplane airfoil sections, which are described in Section 3.2. This 2-D section data does not represent the tailplane, so 3-D tailplane characteristics had to be estimated. This effort is described in Section 3.3. This research required using the tailplane database to represent the tailplane characteristics during the simulation maneuvers. This dictated separating the tailplane contribution from the available aircraft database which already included the tailplane effects in its coefficients. Considering the wing/body and tailplane characteristics separately is typically not done for simulation analysis, so this effort is considered to be a novel aspect of this research. Specific method were required to accomplish this, using the standard aircraft/tailplane interface parameters, downwash angle and tailplane dynamic pressure ratio. This effort is described in Section 3.4. Implementation of a simulation program is relatively straightforward and is described in Chapter 5. Because of its emphasis on the effects of the tailplane, the simulation developed for this research has been named TAILSIM. The use of separate tailplane characteristics requires tailoring the simulation so that the airflow at the tailplane is modeled correctly. This results in functions specific to TAILSIM which are described in Chapter 5. Because the ICTS phenomenon is typically accompanied by tailplane hinge moment and, therefore, stick force variations, it was required to model the reversible control system. As noted above, analyzing the impact of hinge moment 10 characteristics on aircraft responses was a requirement of this research. It was clear during the course of this research that some control of the aircraft responses was required, to realistically determine the aircraft response to tailplane hinge moment variations. A pilot model was chosen for this control, as it would duplicate typical responses and generate information on handling qualities. Both of these simulation functions are specific to TAILSIM and are described in Sections 5.4 and 5.5. TAILSIM was created to represent the DHC-6 Twin Otter aircraft. To determine its success in doing so, comparisons to flight test maneuvers were required and are described in Section 6.1 and Chapter 7. These comparisons were favorable, so TAILSIM was considered to be a valid research tool for use in analyzing the ICTS phenomenon. This ICTS analysis effort was is described in Chapter 6. Using TAILSIM, pushover maneuvers were first "flown" with an uniced tailplane. The effectiveness of the maneuvers in generating tailplane angle-of-attack were noted. Parameters, such as load factor, stick input rate, and elevator deflection were noted relative to the tailplane AOA and resulting aircraft response. This analysis then provided information that was used to prepare for the flight testing of pushover maneuvers with ice shapes on the tailplane. The primary method to evaluate pushover maneuvers with an uniced tailplane was to use a direct elevator input. In 11 addition to this input, reversible control system dynamics and a pilot model were also available. These were used on select runs to more effectively illustrate the effect of iced tailplane hinge moment characteristics on the stability and control of the aircraft. The pilot model was especially useful in simulating representative ICTS events. While the accuracy of linear analysis was not expected to be high, as noted above, linear dynamical systems analysis was performed to provide information on the trends of key parameters. This analysis provided insight for quantifying the impact of key parameters on aircraft responses. It also gave a "first look" at pushover maneuvers, which was useful as trend information in evaluating the first pushover maneuvers generated by the newly developed simulation program. This effort is described in Chapter 4. In the course of this research, it became apparent that, while the simulation responses provided much insight into the ICTS phenomenon during specific maneuvers, the impact on the aircraft flight envelope was not well defined. To fill this void, a specialized, novel V-n diagram was developed to provide a description of the impact of tailplane stall on the maneuvering flight envelope. This diagram showed negative load factor limited by tailplane stall angle-of-attack. It supported the pushover maneuver analysis of Chapter 6, and is described in Chapter 8. 12 CHAPTER 2 PRIOR STUDIES OF TAILPLANE ICING The current understanding of the ICTS phenomenon is based on References 1,5,6,7,8,9. These efforts involved flight test, wind tunnel tests, and theoretical analysis. Their analyses and results will now be briefly discussed. 2.1 Wind Tunnel and Flight Test Results References 1,5, and 6 form a three part series investigating icing effects on aircraft. Wind tunnel studies of icing effects on scale model tailplanes of Swedish aircraft are presented in Reference 6. Two tailplanes were used for this testing. One had a 44° leading edge sweep and a NACA 64A-009 airfoil section. The other was swept 18° and had a NACA 0009 airfoil section. This tailplane was modified with a NACA 0012 leading edge to simulate the tailplane airfoil of the Vickers Viscount aircraft. Both tailplanes were tested as half-span models in the low speed tunnel at the Aeronautical Research Institute of Sweden (FFA). The ice shapes used were generated from molds taken from actual ice accretion on half span models tested in the icing research tunnel of the Ministry of Civil Aviation, USSR. 13 Results of lift and hinge moment for the 44° sweep model showed little effect due to any ice shape. This was also the result for the unmodified 18° sweep model. This was judged to be caused by separation occurring at low values for the thin airfoils of these models. The low efficiency of these inverted tailplanes could be seen in their maximum negative lift coefficients with 5^=0° of C^=-0.85 and C^=-0.7, respectively. In contrast, the modified 18° sweep tailplane showed a significant effect of icing. Lift, with 6^=0°, was reduced from -1.25 to - 0 . 8 , or 35%. Angle-of-attack at C-Ta:.: was also reduced from o;staii=-2 5° to ofs^a, , = -18°. A significant hinge moment break occurred at stall also. Hinge moment, with 6^ = 0°, changed from C„,- = 0.04 to C„;. = 0.14 over a 4° change in angle-of-attack. This change was equivalent to that for an elevator deflection change of Aôg=10°. Clearly, this higher lift airfoil section suffered a greater flow degradation due to icing. The main results of Reference 1 were obtained from flight test pushover maneuvers performed with step elevator deflections with actual icing on the aircraft. For this testing, aircraft were flown in icing conditions with anti icing systems turned off until the desired amount of ice accretion was achieved. The pushover maneuvers were then performed in clear air. The primary parameters noted during the maneuvers were stick force per g and elevator deflection. 14 A broad range of aircraft were flown including medium and large size turbopropeller and jet transport aircraft. All but one of the jet aircraft were configured with T-tails. The results for all aircraft were similar. A significant reduction in push force to obtain a specified load factor was shown for the iced aircraft. In some cases, this resulted in a reduction in Dc„t:/dô^ and a gradual change, with decreasing load factor, to a change in sign of Dcu^/d<5g or a stick force gradient reversal. In other cases, no significant change in slope was noted, but the change in sign of DCuVdô^ occurred abruptly. In all cases, increasing flap deflection and negative trim tailplane incidence angle caused the slope reversal to occur at a higher load factor, closer to n=1.0g. Basic trimmed stability was not significantly affected, and trim elevator deflections were only slightly changed. That only moderate changes in basic stability and control are seen at low flap deflections with tailplane icing is verified by Reference 7. This flight test effort was performed on the DeHavilland DHC-6 Twin Otter aircraft. Parameter estimation maneuvers were flown with no ice and artificial moderate glaze ice shapes on the horizontal tail and vertical tail leading edges. The entire n=1.0g trim flight envelope was tested with three power settings. With iced empennage surfaces, a 10% reduction in static longitudinal stability and elevator and rudder effectiveness 15 was seen. Directional stability was reduced by 20% with zero thrust but was otherwise unaffected. Pitch damping was reduced only in powered flight. Yaw damping was unaffected. 2.2 Simplified Longitudinal Simulation Analysis Reference 8 describes a simulation analysis of the longitudinal dynamics of a small transport aircraft with tailplane icing. Simplified longitudinal equations of motion were chosen. Representative constant coefficients and derivatives were used, except for the tailplane lift coefficient. The tailplane lift was separated into a linear term, representative of an uniced tailplane, and a nonlinear correction term, to simulate an iced tailplane. These terms were determined by matching the available wind tunnel data of [6] . Elevator effectiveness was assumed to be constant. Downwash was determined by a constant de/do; value. Flap deflection was simulated by choosing a. ...,^=-16°, and adjusting a and airspeed accordingly. Responses to gusts, elevator inputs, and action of a simple autopilot during random gusts were the chosen analysis methods. Single pulse gusts were simulated by applying a step input change in a. These showed that a single down gust of Ofg=-5' caused a reversal in initial pitch response, compared to the uniced tailplane, due to the stalling of the iced tailplane. Recovery did occur, but with very low 16 damping and more altitude loss. For a gust of a^=-6°\ the response indicated a diverging departure. A sinusoidal down-up gust was also used as an input to the simulation. This showed that minimum a. occurred during the upward part of the gust due to the interaction of pitch rate with a.. It was noted that pilot input to recover from the initial down gust could aggravate this minimum of,. For similar reasons, a down-up elevator input showed the most under damped responses. In this case, however, the initial elevator input caused the tailplane to stall. Random gusts were simulated by applying a discrete vertical velocity with a typical spectrum used in the modeling of turbulence. The autopilot used a simple proportional plus derivative control law applied to the altitude deviation from the glide path. The responses with an iced tailplane diverged when control law gains that would be acceptable for an uniced tailplane were used. Successful control was achieved when the gains were reduced by roughly 60%, indicating that pilot control inputs should be significantly reduced when the tailplane is contaminated with ice . Of significance in these simulations was the initial setting of a. .,,^=-15°. This value was chosen because it equaled a.,scaii Eor zero elevator deflection. Poor pitch responses were seen only when a. was at or near tailplane stall. Otherwise, the reduction in elevator effectiveness 17 with an iced tailplane was offset by a reduction in pitch damping. This analysis provided valuable insight into the dynamics of aircraft with iced tailplanes. It also showed that numerical simulations can be effective analysis tools. However, due to the many simplifications chosen for the analysis, the results are considered to be primarily qualitative. Additionally, while hinge moment effects on the pilot control of the elevator were mentioned, they were not developed further. 2.3 Analysis of the Zero G Pushover Maneuver Reference 9 discusses an investigation employing a linear analysis of the Zero G maneuver for determining susceptibility to ICTS. The approach taken was to survey more than thirty commuter class aircraft for which some indications of susceptibility were available. These indications were obtained from FAA records of incidents or results of Zero G maneuver testing. The end result was the development of a "tailplane stall margin". This margin was the difference between the required tailplane lift coefficient at the specific steady state condition and the maximum available lift coefficient of the tailplane. As detailed engineering information on the aircraft was generally not available, other available information sources were used to determine required aircraft characteristics. 18 Aircraft geometry and operating capabilities were provided by manufacturers, or, in a few cases, obtained from aircraft flight manuals (AFM) and sources such as Jane's All the World's Aircraft book series. These sources provided the information to define each aircraft configuration. As noted above the analysis focused on defining tailplane lift coefficient in the Zero G maneuver. No references were listed in [9] , but. References such as 11,12, and 13 are typically used to define the given equations and estimated coefficients. The tailplane lift coefficient at Zero G was determined by considering a moment balance of the wing, tail, and fuselage. Wing and tailplane lift curve slopes were obtained from available or estimated section lift curve slopes modified by standard wing theory. The incremental lift coefficient with flap deflection was obtained from the change in stall speed at a given weight as noted in the AFM. Basic wing lift was considered to act at 25% MAC, with incremental flap lift acting at 50% MAC. An effect of elevator deflection was determined by applying a dûî/dô terra. Wing downwash was determined from the standard inviscid flow value for fully rolled up vortices. Ci^^ax was taken as 0 . 9*C,^ax - Tailplane AOA was defined as. û!tq - e 19 with a . q = 53.85 ( l,(n-l)/V^ ) , the induced tailplane AOA due to pitch rate. Close inspection of the equations used in the analysis determined that the "tailplane stall margin" was defined by, AC.. = - C- — _ + (Of> - Of. - ) a. where a.; = tailplane ot at zero lift, a^ = tailplane lift curve slope, and represents Cr.cmax the tailplane because of its inverted installation. Note that a positive "tailplane stall margin" represents a safe flight condition, while a negative margin means more downforce is required on the tailplane than is available. Since there is no elevator influence on the "tailplane stall margin", this equation can also be restated as, àC-_ = [ -(%: aca:: + (CK. - Of;. ) ] a. So, the "tailplane stall margin" can also be thought of as a representation of the margin between actual and stall tailplane AOA. A key contribution of the analysis was the determination of an estimated for tailplanes with ice contamination. Most of the tailplane airfoils used on the aircraft being evaluated were NACA series airfoils. This allowed the C^^^x 20 with standard roughness data of Reference 14 to be used to represent the effect of surface contamination due to ice. The results of this analysis showed good agreement with the available information on the set of commuter aircraft. The susceptibility ranking, from most susceptible to least susceptible, correlated well with known accident and incident histories. The "tailplane stall margin" discriminator clearly identified aircraft that were very susceptible and those that were marginally susceptible. The effectiveness of this simplified analysis method is of interest. Results of the tailplane airfoil section test of the Twin Otter, discussed in Section 3, showed a = and a AC:.„,. = 1.0 difference between full negative and positive elevator deflection. Not properly accounting for elevator deflection would seem to be a potential source of error. Also, since zero load factor is obtained at zero lift, some of the flaps down configurations required an unusually low level of negative in the range of . In addition, no consideration of the ability of the aircraft to generate enough elevator control to be able to maneuver to zero load factor was taken into account. Finally, no power effects, tailplane location effects, or specific flap effects on the downwash were considered. Clearly, the analysis approach was sound and provided a useful screening tool. However, the many assumptions required suggested that a 21 more in depth analysis of pushover maneuvers could yield new and useful insight. 2.4 Summary of Prior Studies The above analysis methods offer good insight into the ICTS phenomenon. However, neither represents a complete dynamic model and aircraft configuration. It is clear that a more complete dynamic simulation which incorporates the effects of elevator hinge moment has the potential to provide additional insight into the effect of tailplane icing on a variety of flight safety parameters. The goal of this research is to extend the above analysis concepts using a specialized aircraft and tailplane model, and a specialized nonlinear aircraft dynamics analysis program. 22 CHAPTER 3 DEVELOPMENT OF THE DHC-6 TWIN OTTER DATABASE A goal of this research was to use all available test data to create a nonlinear database of aircraft coefficients and stability and control derivatives for use in the nonlinear simulation program. Test data for the Twin Otter was available from flight testing of the aircraft and wind tunnel testing of the tailplane airfoil. Various methods were used to incorporate the data from these different sources into a single database, and to extend the database to the required range of angle-of-attack. Empirical methods from well known sources were only used when test data was not available to define required parameters suoh as downwash angle. 3.1 NASA Lewis Stability and Control Flight Testing As part of the ongoing objective of the NASA Lewis Research Center's (LeRc) icing research program, a stability and control data set was experimentally determined for the DeHavilland DHC-6 Twin Otter test aircraft in 1992 [7] . This aircraft represented a smaller payload commuter class 23 configuration and had advantages of low operating cost and simplicity (Figure 3.1, Table 3.1) . The aircraft was powered by two 550 SHP Pratt and Whitney PT6A-20A turbine engines driving three-bladed Hartzell propellers. The flight control surfaces were operated through reversible mechanical cable systems. The flight test program was conducted using iced and uniced horizontal tail and vertical tail surfaces. The ice shapes were representative of typical inflight icing accretion, as well as results of analytical methods. The ice shapes were formed in styrofoam which did not duplicate typical surface irregularities. Flight testing was performed with wing flaps at 0p=Q° and 6^=10'. Three power settings were used and represented by thrust coefficients of C.r=0.0, 0.07, and 0.14. The propellers were kept at a constant 1800 RPM for all powered test points and were feathered for the power off test points. To maintain trim at all flight conditions shallow climbs and descents were flown as required. Doublet maneuvers about all axes were flown with the fully instrumented aircraft. The parameter estimation technique known as Modified Stepwise Regression (reference included in Ref. 7} was then used to determine the stability and control derivatives. The models used in the estimation were those typical of standard aircraft dynamics analysis. The longitudinal model equations were, 24 Cy = Cy, + Cy„*ûf + Cyq* { / 2V ) + Ô ^ Cz = Cz. + Cz^*a + C^*(qc/2V) + Czg^*ôg C;< = Cv: + C;,^*q; + Cz„2*a^ + (q*c/2V) + Note that since all test points started from trimmed flight, Cy; = 0 . 0 . The lateral/directional model equations were, C, = C:,*|g + C,p*(pb/2V) + C,,*(rb/2V) + C, = + Qp*(pb/2V) + C,,*(rb/2V) + + C^ar*6r C, = C.,/jg + C,^*(pb/2V) + Cy,*(rb/2V) + CyAa*5^ + Note that bias terms are not shown as all testpoints were started from a trimmed flight condition. To produce a usable database for the simulation program the flight test data set was curve fit to a standard set of AOA breakpoints. Because the AOA range of each data set was not the same, some extrapolation was required. This influenced the choice of order of the least squares fits. The final curve fits used third order for all C,o coefficients, and second order for all other coefficients. Additionally, some fairing of the coefficients was accomplished based on engineering judgement. Appendix A shows plots of the available flight test data. Appendix B contains plots of the complete aircraft model database which is discussed in Section 3.4. 25 Since all flight test maneuvers were started from a trimmed flight condition there was no Cj,g term. This is acceptable for linearized force and moment equations. However, a C„t- term was calculated for the simulation program and is discussed in Section 3.4 26 Table 3.1 NASA LeRC DHC-6 Twin Otter Aircraft Specifications CHARACTERISTICS LOW HIGH Weight, lb 9943 10957 INERTIA: I., Ib-ft- 6 2 1 , 4 7 7 6 3 2 , 6 3 0 I.. Ib-ft- 793,990 822,229 I., Ib-fc' 1, 1 3 7 , 1 2 0 1 , 2 2 5 , 6 3 1 I..., Ib-ft^ 35,357 3 7,018 WING: Area, f f ‘ 420 Aspect Ratio 10 .06 Span, ft 65 .00 Mean Geometric Chord, ft 6.5 Airfoil Section (17V thickness) "DeHavilland High Lift" HORIZONTAL TAIL: Area, ft" 97 .95 Aspect Ratio 4 .35 Span, ft 20 .67 Mean Geometric Chord, ft 4 .75 Airfoil Section (inverted) NACA 63A213 27 3.2 Twin Otter Tailplane Airfoil Wind Tunnel Test As noted in the introduction, a low speed wind tunnel test was conducted to determine the section characteristics of the Twin Otter tailplane [15] . These tests were performed in the Ohio State University Aeronautical and Astronautical Research Laboratory Low-Speed Wind Tunnel Facility (OSU LSWT) at airspeeds of V=60 kts (Rg=2.7xl0®) and V=100 kts (R„=4 . 8x10"^ ) . Highlights will be presented here. The OSU LSWT is a closed-loop circuit with a 7x10 ft. high-speed test section and a 14x16 ft. low-speed test section. A 2000 Hp electric motor driving a 6-bladed propeller provides dynamic pressures up to 65 psf in the 7x10 ft. section (Figure 3.2) . A sting balance mount allows models to be tested at AOA ranging from -15° to +45°, while the rotating tunnel floor has a range of -90° to +270°. Testing of two-dimensional airfoils is conducted by installing a 7 ft. span model vertically in the high speed test section. The model is attached to the floor mounting table, which is then rotated to provide a specific AOA. Surface taps on the model are used to acquire pressure distributions which are integrated to obtain model forces and moments. To determine drag, wake survey probes are installed downstream of the model. By sweeping these probes across the test section, the model wake can be measured. For the Twin Otter tailplane airfoil section testing pressure data from surface taps and belt taps were integrated 28 to obtain lift, drag, pitching moment, and hinge moment coefficients. The belt taps consisted of precise holes punched into each tube of a series of strip-a-tube belts wrapped around the airfoil section. Belt taps were included in che testing to provide a correlation to belt taps installed on the aircraft during flight testing. Tap locations were chosen to provide high resolution where pressure gradients were large and low resolution elsewhere to maximize through-put. Tests were conducted on the clean, or uniced, airfoil as well as the airfoil with two representative ice shapes. Testing was accomplished over a full range of AOA, from large negative to beyond stall, and the aircraft's full range of elevator deflection. Reynolds number effects were obtained by testing at two velocities, V=60 and 100 kts. As shown in Figure 3.1, the DHC-6 Twin Otter tailplane is composed of two separate airfoil sections. Basic data for the clean secondary airfoil section were also acquired. In addition, data were taken from a Five-Hole Probe mounted on the airfoil leading edge. This probe data was used for the calibration of similar probes used in flight testing. Figure 3.3 and 3.4 show the model installation in the wind tunnel. The two ice shapes tested were called S&C and LEWIC E . The S&C ice shape has been used in several stability and control programs on the DHC-6 Twin Otter. This ice shape was determined using a combination of in-flight photographs of 29 icing on the DHC-6 Twin Otter tailplane and Reference 16. The LEWICE ice shape was predicted using the LEWICE 1.3 computer program. Specific input conditions were : V=120 kts, liquid water content=0.5 g/m\ median volumetric diameter=20ptm, icing time=45 min, AOA=0°, static temperature = -4" C . The ice shape was determined in five equal time steps. Each step consisted of a 9 minute accretion time, a redefining of the iced airfoil geometry, and a recalculation of the airflow over the new geometry. The 45 minute accretion time was chosen to be conservative while aligning with the FAA requirement of demonstrating capability with 45 minute accretion time on an unprotected surface. The two airfoil sections are shown in Figure 3.5. Drawings of the two ice shapes are shown in Figure 3.6. Both ice shapes show the typical two horned formation. The ice shapes were created from machineable plastic, with machine cuts along the span creating ridges. No other roughness was applied to the ice shapes. 30 6 BLADE FAN - 20 FT. DIA. 40 FT FLOW 7 X 10 FT 16 X 14 FT ■test section SCREEN TEST SECTION I"h - H L 1 5 F T______BUILDING WALLS 15 FT 154 FT - 6 IN Figure 3.2 OSU 7X10 Wind Tunnel 31 Figure 3.3 Baseline Installation, ô,=-26.6‘ (Wake Probe in Foreground) 32 Figure 33 Section 1 (Baseline) Section 2 Figure 3 .5 Section 1 (Baseline) and Section 2 Airfoil Sections 34 Figure 3.6 Ice Shape Sections 35 3.2.1 Discussion of Wind Tunnel Test Results The lift characteristics with zero elevator deflection are shown in Figure 3.7. Note that the sign convention is that of the aircraft and a downward lifting tailplane will provide negative lift coefficients. The significant increase in and increase in a^scaii due to the ice shapes is clearly seen. Specifically, is increased from C-.^,„ = -1.3 for the Baseline airfoil to C;.^,„=-0.64 for the S&C ice shape and to - 0 . 60 for the LEWICE ice shape. Also, Of. is increased from the Baseline's (%= -18 .6° to approximately 0'=-8 .2° for either ice shape. Hinge moment characteristics are shown in Figure 3.8. These clearly show the ice shapes causing an approximate AC^[=0 .02 increase at stall. Note that, for the LEWICE ice shape, the transition is not as abrupt as for the S&C ice shape. This 52% decrease in downward lift is larger than the 35% noted for the NACA 0012 tailplane in Section 2.1. The decrease in negative stall angle-of-attack of the section is also larger at Aa. 3_^:; = 10 . 2^ versus 8°, and would be expected to remain approximately the same for the tailplane. It is suspected that this larger degradation is mainly due to the larger clean of the Twin Otter airfoil, in addition to variations caused by the different ice shapes tested. The change in hinge moment is not as large, ACh. = 0 .02 versus ACu-=0-10. However, both of these changes in hinge moment 36 coefficient are approximately equivalent to an elevator deflection change of A0^=10° as noted in Section 2.1. The effects of the ice shapes on elevator effectiveness are shown in Figures 3.9. Only the LEWICE ice shape data is shown, as there is little difference in the results with either ice shape. A noticeable effect of elevator deflection is that a. seal: is increased for negative elevator deflections and decreased for positive elevator deflections. This can be seen at the negative deflection of 0^=-20^ where C,^^_=-l. 21 at a=-4.32^. These stall angle-of-attack and effects of flow separation with elevator deflection are also seen in the hinge moment shown in Figures 3.10. At ô^=-20°, there is a significant AC^.=0 .0 2 increase, starting at a negative angle- of -attack below stall of Q! = -2.3°. The positive increase in hinge moment is greater for positive deflection. At 5„=14.2° the hinge moment for the LEWICE Ice shape shows a peak increase from the uniced data of ACv,- = 0.05 at Q!=-14.0°. For other deflections, the C^.^ for the LEWICE ice shape shows similar trends to that for the uniced airfoil. The test data shows that, while C^-c, of the Baseline airfoil is negative and relatively constant, C^.cc for the LEWICE ice shape shows a trend of negatively increasing with increasing positive or negative elevator deflection. These results match well with observed tailplane stall phenomenon. During approach, the elevator would most likely 37 be at a negative deflection. Tailplane stall could more readily occur, since the angle-of-attack at which stall would occur would be lowered. If the stall did occur, the angle- of -attack would become more negative due to the nose down pitching dynamics. With a negative the trailing edge down (positive) hinge moment would increase, pushing the elevator to a trailing edge down position. The elevator would continue its trailing edge down tendency until it reached a position limit or the angle-of-attack stabilized. Also, in general, the trend in is decreasing with increasing positive elevator deflection. This would support the typically observed stick force lightening phenomenon. However, the trend in C..^, at the maximum positive elevator deflections and largest negative angle-of-attack is significantly increasing, causing a tendency for the elevator deflection to stabilize. This suggests that any stick force lightening would be dependent on the specific AOA and elevator deflection of the maneuvering aircraft. Representative velocity effects are shown in Figures 3.11 through 3.14 for the Baseline and LEWICE configurations. Figure 3.11 indicates that, for 5^=0. O'", there is a Aq!.=2° increase in a. at V=60 kts (Re = 2.7xlO®) compared to the V=100 kts (Re=4.8xl0®) data. There is also an earlier stall break at positive angle-of-attack for the +6^ case. In general, there is a decrease in lift at the higher speed. At 5^=-20° with V=60 kts, there is a noticeable increase in 38 at about q;^ = -4.0°, which is most likely caused by increased flow separation at this deflection. These results are consistent with typical Reynolds number effects. Figure 3.13 shows an indication of the earlier stall break at V=60 kts for the 5^=0.0° case in the hinge moment data. Some slight increase in hinge moment is seen for the lower speed, but this is nominally in the repeatability range and so is not considered to be significant. The LEWICE ice shape data of Figures 3 .12 and 3 .14 show little differences due to the speed variation. Except for some noticeable larger differences at the most positive angle-of-attack, such differences that are seen are within nominal repeatability. The Section 2 airfoil was tested at V=60 kts with 5^ = 0. O'", 14.2°, and -20.0°. No other deflections or ice shapes were tested due to time limitations. Lift and hinge moment comparison plots are shown in Figures 3.15 and 3.16. The most distinctive characteristics of the Section 2 airfoil in comparison to the Baseline, are its lower C;^„^„=-1.36 with 5^=0.0°, approximately Ao:.=2.0° higher 0!c,scaii ' and the sharpness of the stall break. Section 2 has a longer chord for the main element, significantly smaller gap, and no extension of the elevator leading edge. All of these configuration differences contribute to this higher The hinge moment behaves as expected, with a larger , 39 caused by the lack of the moment balancing elevator extension as on the Baseline elevator. 40 Figure 3.7 Lift Characteristics, V=100 kts, 0^=0.0 Figure 3.8 Hinge Moment Characteristics, V=100 kts, 6^=0.0 41 Figure 3.9 Lift Characteristics, Large Deflections Figure 3.10 Hinge Moment Characteristics, Large Deflections 42 Figure 3.11 Velocity Effects, Baseline, Lift Characteristics Figure 3.12 Velocity Effects, LEWICE Ice Shape, Lift Characteristics 43 Figure 3,13 Velocity Effects, Baseline, Hinge Moment Characteristics Figure 3.14 Velocity Effects, LEWICE Ice Shape, Hinge Moment Characteristics 44 ▲ A A - m m i » m 1 M • T ■ m - # - m . " * " » * #' * Figure 3.15 Section 2 Lift Characteristics Comparison Figure 3.16 Section 2 Hinge Moment Comparison 45 3.3 Creation of Tailplane Aerodynamic Coefficients Plots of the estimated tailplane coefficients are shown in Appendix C. Section airfoil C,_ was corrected based on the standard two-dimensional to three-dimensional lift curve slope correction. The slope correction was interpreted as being applied to the at a given angle-of-attack. It was assumed that a., was the same for the airfoil and tailplane data. This results in the airfoil data being scaled by the ratio of three-dimensional to two-dimensional slope. This scaling was done to all data points except those at and near C-T.:- - was scaled by the factor of 0.9 [13] . Angle-of- attack at was determined using the methods of [13] . This required determining an appropriate a.n. For the purposes of this calculation, a,, was determined by assuming the two-dimensional slope was applied to the angle-of-attack at The three-dimensional slope was then applied to and this a.- to determine the final tailplane AOA at . Finally, additional adjustments as defined in [13] were applied to this angle-of-attack value. This method of determining angle-of-attack at was chosen for consistency, as the airfoil slope changed with AOA. Because of this, a least squares fit was applied to a limited, linear, range of angle-of-attack to determine the two-dimensional slopes. These values and the range of angle- of -attack used are indicated in Appendix D. 46 The scaling factor for was different than the scaling factor based on the slopes. Angle-of-attack was also decreased by the decrease in three-dimensional angle-of- attack at This required fairing some of the data points near . This v/as accomplished straightforwardly, by picking a starting angle-of-attack, and decreasing this value and C^. linearly to smoothly match the angle-of-attack at C . The starting values for performing this fairing are indicated in Appendix D. To determine the effect of the reduced elevator chord section, the appropriate wind tunnel test data at V=60 kts were compared to those at V=100 kts. Scaling factors for both slope and were then determined assuming the small chord elevator was active on 30% of the tailplane area. These scaling factors are also shown in Appendix D. No correction was applied to account for the elevator horn, as its effect on the tailplane span loading was assumed to be small. Typical correction methods for hinge moment assume that C;_.. can be written as, Ch, = + CHcàe*<5.3 This implies that the three-dimensional corrections shift the data by applying a scaling factor to the Ô effects and then rotate the data by applying a scaling factor to the angle-of- 47 attack effects. This describes how the corrections were applied using the methods of [13] . The correction scale factors were applied to the values between data points of each deflection. The correction scaling factors were then applied to the delta values from the resulting at a. = 0‘-. Because of the loss of hinge moment effectiveness at some deflections, these scaling factors were limited to a minimum of Chc=0-35 and 0^4 = 0.55. The method of [13] requires a which was the same as those used in the corrections. Also required are C,>j, and values. 0^.^ was determined by the delta values between a;, = 0= and 4^. and were determined by averaging the delta values for successive deflections at a.=0° and 4". Appendix D lists these correction constants. The small chord elevator and elevator horn were accounted for by applying a correction scaling factor to the final and values based on the area forward and aft of the hinge line. This correction is described in a plot from Reference 17 which is duplicated in Figure 3.17. The scale factors to correct the nominal and Qca were determined by assuming that was obtained with the nominal elevator across the full tailplane span. Then, M^orn was found by determining the difference between this area and that of the actual tailplane configuration. The ratio of the coefficients obtained from the plot using this Mhom, and 48 those with .0 , determined the final scale factors indicated in Appendix D. Drag was corrected by applying the standard induced drag term to the at section- This o;^,section was found by “t.sect.cn = CK. - O'., , with Û!., = C^/(rAr) Then Cnt = + Qc:, with Coe, = C , V ( 2 TTAr) The previously calculated described above was used for this value. No specific correction for pitching moment was found in either [13] or any of the stability and control references. However, [13] does contain a correction for . For wings with zero sweep, this correction is simply = C_. ,Ar/ (Ar+2 . 0 ) As the tailplane C„ term is a only a small component of the total aircraft C.,., this correction was applied to all data. 49 '' ^horn Centroid of horn area If Hinge line ^ — Centroid of flop area 0.002 - 0.002 « -0.006 -0 010 0 0.2 0.4 0.6 0.8 1.0 ^ horn flap ^hoTn — ^horn ^ ~ ^flap ^ h' Figure 3.17 Effects of Elevator Horn on Hinge Moment Coefficient (Reprinted from Ref. 17) 50 3.4 Development of the Complete Aircraft Model Database A significant task of this research effort was to use the available aircraft and wind tunnel data to create a database for the DHC-6 Twin Otter aircraft that would allow the tailplane aerodynamic coefficients to be tracked during a dynamic maneuver. The aircraft database contained only total aircraft coefficients and derivatives, while the tailplane database contained only tailplane coefficient estimates. For an investigation of the local tailplane flowfield these two sets of data needed to be merged. The interface between the two is typically the downwash angle and the ratio of local tailplane dynamic pressure to aircraft dynamic pressure [11] . Estimating the value of these parameters would define the tailplane aerodynamic flow field. This would allow the tailplane components of the total aircraft coefficients and derivatives to be determined. Subtracting these components from their respective total aircraft values would result in coefficients for the wing- body only. The tailplane could then be added back in by directly accessing the tailplane database coefficients. Using these concepts, an initial database was developed using all the available DHC-6 Twin Otter stability and control data supplied by NASA and the wind tunnel data generated by OSU. Implementation was as direct as indicated above. The available DHC-6 Twin Otter data was valid for a range of approximately a=-2° to +12°, and for flap deflections 51 of 6; = 0^ and 10°. Simple extrapolation of the last two data points of the tables was used for all values outside of this range. Comparison runs with flight test parameter estimation maneuvers showed good agreement with the simulation. This provided confidence in the method and the simulation responses. Simulation results were useful in helping to prepare for the flight testing of Zero G maneuvers with the uniced tailplane. However, during this Zero G maneuver flight testing, accomplished in fall 1995, it soon became apparent that the simulation did not agree well with the preliminary flight test data. Minimum tailplane angle-of-attack did not agree as well as desired for 0^ = 10° and 20°, although the proper trends were indicated. Of more concern, the pitch rates and attainable load factors differed significantly for flap deflections greater than 5^=20°. A portion of these errors were attributed to use of a simplified downwash calculation instead of the full analysis of [13] . However, database extrapolation was judged to be the most significant cause of the errors, since the angle-of-attack of interest at zero load factor was a=-6° to -10°. Therefore, a more accurate database that did not require extrapolation was desired. It was never the intent of this research to create a database for the DHC-6 Twin Otter from scratch. Therefore, it was decided to attempt to extend the existing aircraft data to the range of interest using standard first order 52 methods and engineering judgement. The available curve fit flight test data provided the basis for this extrapolation. To estimate the stall characteristics of the Twin Otter the available data was extrapolated and integrated. The resulting was compared to the existing 0% and shifted to match the C. in its valid range. This had the effect of producing a smooth stall break. The accuracy of this break is questionable, however it was considered to be acceptable since it achieved the main goal of a limit on the maximum lift. To further refine the lift curves stall speeds from the aircraft flight manual (AFM), assumed to be for C~=0.14, were used to determine - All curves were then shifted to match this It was judged to be important to estimate the negative AGA lift and stall characteristics due to the possible limit on load factor capability this would cause. No method was found to estimate the negative stall characteristics of a wing with a positive flap deflection. However, in looking at the lift curves in [14] it was noted that the effect of camber could be approximated by a simple upward shift of the lift curve. This implies that the incremental effect of camber is similar at both positive and negative AGA. Using this concept, the lift curve at negative AGA can be created by negatively mirror imaging the positive AGA data about q;=0“. This concept was assumed to be applicable to the flap deflection data, so that the increments on ^.t negative 53 AOA were the same as those at positive AO A, and that increments on were also the same. This resulted in creating the negative AOA lift curve with flap deflection by negatively mirror imaging the positive AOA data about q;=Aq'3.3-. 4.-. While these methods are not typical, they are considered to be a reasonable first order assessment. These methods were implemented using the aircraft and a.^=0”, or Q!=-2.5° for 0, = 0°. For 5^ = 10°, o;=-4.0° was used. Additionally, the lift curves were made more linear near zero AOA to insure a linear and constant lift curve slope for these values. Data was created for o;=-20° to +20°. This method produced the desired results of less magnitude change for than for C^^ax and more magnitude change of negative - than positive These are considered to be acceptable first order effects. To obtain data for higher flap deflections the 0^=0° and 10° data were extrapolated based on matching C^^ax obtained from the AFM stall speeds. This resulted in the desired characteristics up to stall, as well as the increasing typically seen with flaps. As noted earlier, the post stall breaks were probably inaccurate, but were not of prime importance for this effort. There are more methods available in the literature for estimating drag and [18] contains a well organized first order method. Drag polars were created for the 0f=0° and 10° data from the existing aircraft data and the latest estimated 54 C._ data. Co was Chen fit with second order polynomials in C^- These values were Chen adjusted to match two flight test trim conditions, one each at 0, = 0° and 10°. This resulted in typical drag polar characteristics at both positive and negative AOA. The second order equation was matched to the form of the equation in [18] to provide flexibility in determining minimum coefficients. Second Order Fit Cg = Cgg + K,Cg + KjCg' Standard form [18] Cg = Cg„,„ + K'Qy + K" (Cg-Cg^^^) , Therefore, C=: = Cg,.:, + K, = -2K"Cg,,,^ K- = K" + K' From these equations, Cg„,„, K', and K" could be determined. No method was indicated to extrapolate these constants so the 5. = 10° constants were used for all flap deflections. Reference 18 does have methods for estimating Cg^..^ and Cg^,, which were used to develop ratios to apply to the 6, = 10° data. The above drag data was for C?=0 only. As a first step in applying Cg effects, increments were obtained for the 6,=0° and 10° data and plotted versus Cg. It was found that the Cg=0.0 7 and 0.14 data fell into two groups of approximately linear lines. This allowed the ACg due to to be implemented as a linear function of Cg. However, propeller 55 characteristics are more typically a function of [19] , and the linear variation implied a linear variation in 1/qp since the data was obtained about a trimmed condition. That is, W=C:_ so 1 - 0/qp=C[.,crim/(W/S) . Therefore, delta due to C- was implemented as a simple linear equation in 1/qp, ACp = -1 . 086C^(W/S)/qp This implementation allowed thrust effects to be calculated separately from drag effects. Additionally, as a constant weight was used for all simulation responses in this study, a constant scale factor could be used. Downwash was built up using the methods of [13] . A wing is required for the method. This was determined from the aircraft C,_ by correcting for fuselage and propeller normal force, as well as . As a first order estimate it was judged that using a 17. = 1.0 was adequate for this calculation. Reference 13 was used to estimate linear fuselage lift and [13,17] were used to estimate propeller normal force. An iteration program was then used to find the downwash over the desired angle-of-attack range of a=+/-16° degrees. This range was chosen to avoid stall effects since the method is not valid in the post stall range. The downwash for flap deflection was determined using a similar iteration method to determine the increment of wing due to flap deflection and applied with an equation in [13]. Thrust, or power, effects 56 on downwash were also determined by the methods of [13] . These power effects are a function of velocity. Typically, all aircraft model coefficients and derivatives were calculated about a trim condition, with trim velocity determined based on aircraft lift coefficient and the atmospheric conditions at 6000 feet. These flight conditions approximated those used during the parameter estimation flight testing. Additionally, these equations were programmed into the simulation program, and continuously calculated during any maneuvers. All downwash calculations are completely described in Appendix E. To determine the qp,.aii' it was judged that the from aircraft flight test data should match that from the differentiated tailplane coefficient database. This required extrapolating the flight test based values to the desired range of the database. It was noted that for both 0,=0° and 10' the values were roughly constant at 0^=0. However, at C-=0.07 and 0.14, the variation in was fairly linear with C._. Therefore, was judged to be a function of l.O/q^ as above for the ACg due to C^. Additionally, as the typical maximum airspeed for this work is 100 kts, data for trim flight above this airspeed was smoothed. the 0^=0° and 10' data was extrapolated as a function of 1/qp. No method was available for determining Cy^e for varying flap deflection so the 6^ = 10° data was assumed to be valid for all higher flap deflections. To determine the tailplane dynamic 57 pressure ratio, t]^, was ratioed Co the local 00^^/d^g obtained from the tailplane database. This was accomplished for both the uniced and iced configurations, resulting in a factor of 1.2 being applied to the uniced t]^ values to create the iced 17. values. The resulting values behaved as expected, in general, and also provided a direct fit between the aircraft and tailplane data. To extrapolate the to the larger negative and positive range of AOA, the effects of the wing and tailplane were considered. Reference 13 states that for slotted flaps the average Cp is at 44%, so delta lift due to flap should act at this location. A program was set up to calculate 0%* using the current C^, downwash, and 17^, with estimates for fuselage and propeller effects. The results showed fairly good agreement with the aircraft Cy,^ at low AOA but were much more nonlinear at other AOA. Therefore, only the trends of these results were used to extrapolate the existing 0%* coefficients. The primary driver of is the tail contribution, which is. ' M . g c X a c ^ 2/2 58 This was found to be fairly constant with airspeed when calculations were made. Some nonlinearities were seen, primarily as a function of the local de/da, but these were judged to be too inaccurate to use. Therefore, the C„q at low q; was held constant to o;=-16°. It was desired to maintain the nonlinearities at the higher AOA for 0^ = 0° and 10°, which were assumed to be real nonlinearities. The variation of C^q with larger flap deflections was estimated by using the previously mentioned tailplane only calculation of C„q and scaling the average, constant value for 0^^^ at 0^=10°. As noted above, the available data was used to create the extended database. The flight test based data was in the form of coefficients and stability derivatives. The tailplane database was in the form of coefficients only. Derivatives of the tailplane data were found by assuming a trimmed flight condition and then finding the desired local slopes. Typically, for AOA slopes, àa^ = + /~ 0.5° was used. For elevator slopes, Aô^=+/- 5.0° was used. Both deltas are 1/2 of the corresponding breakpoint increments of the database. These deltas smoothed the sparse data by averaging the slopes between breakpoints. Additionally, some further smoothing and simplifying of the aircraft data from that mentioned in Section 3.1 was accomplished based on engineering judgement. No method to estimate trim elevator position was found, so the data for 5.-=0° and 10° were simply extrapolated for the other flap 59 deflections. was assumed to be a function of angle-of- attack and flap deflection only, and the 0^=10° data was used for all other flap deflections. and were assumed to be zero, due to their small values. C^ie was not extrapolated beyond ô.= 10‘^ or a=-2^ to +12^. was assumed to be a function of angle-of-attack. As noted earlier, the aircraft was considered to be in a trim condition for all data points. This required creating a Cy. bias term by accessing the tailplane coefficients at 5^ for each AOA, <5.-, and C.r of the database. This term is used only in the trimming routine of the simulation program, and allows a trim elevator deflection to be calculated for any flight condition. The final force and moment summation equations maintained the flight test aircraft derivatives and the tailplane derivatives in separate tables. This allowed easy variation of these derivatives for parametric studies, if desired. The equations are shown below. The longitudinal buildup equations were, + r[(CmrC*^)Aa] + (CmrCw^)(qc/2V) + C? = Cjc " ^zot + (Czq-Czq[) (qc/2V) + = C y: " Cy:t + ( Cyq - Cyq. ) (qC/2V) + Cyr The longitudinal moment equation used in the trim process was, 60 Cx — Cxc J + ( Cxq (-Xq, ) (C5C/2V) + Cx- Not0 : CxQ = ~^yto The lateral/directional buildup equations were unchanged from those determined from flight test data, C, = + C,p(pb/2V) + C,,(pr/2V) + + 0,^,6, C, = + Cp*(pb/2V) + C,Xpr/2V) + Cy = C_jg + C.yp(pb/2V) + C .jpr/2V ) + CyAa^a + Cy^.Ô, It should be noted that these equations are common and can be used to represent almost any aircraft. A contribution of this research is considered to be the specific methods used to develop the coefficients for the DHC-6 Twin Otter aircraft using all of the available test data. Specifically, the separation of tailplane effects from total aircraft effects is considered to be somewhat novel. 61 CHAPTER 4 LINEAR DYNAMICAL SYSTEMS ANALYSIS While the main analysis method of this effort was considered to be the simulation program, TAILSIM, linear dynamical systems analysis was also found to be useful. The methods and results discussed in this section helped to provide insight into the TAILSIM responses. They also supported the quantification of these responses and gave insight on the effect of various derivatives on the aircraft responses . Second order short period dynamics analysis was performed using the aircraft database. Elevator deflection inputs from a trim AOA and velocity were used to drive these dynamics. Tailplane angle-of-attack was determined by a simple calculation similar to that of Section 2 . Peak and steady state AOA, pitch rate, q, and were noted. The standard small perturbation, linear, second order, short period transfer functions for angle-of-attack and pitch rate, as defined in [1 1 ,1 2 ,2 1 ,2 2 ], are. 62 Assuming a step Ô input and noting that VM.^ = a n d VZ.^ Z^, the steady state values are, 0^55 _ -Mgy-ZgMg For most aircraft, Z.M. << MjV Z*M^ << Z^Mt so the steady state equations can be simplified to. 63 Q'ss __ --^=^5 Converting the dimensional derivatives to non-dimensional derivatives we have, ^ s s ~ _ 2 V p p S c C ^ ^ 4rnCf_j^ Steady state q is produced by load factor and velocity, as defined by, q^. = (n-l)g/V Since load factor is a function of V' at a constant a., steady state q depends on V, as seen. Cm* is a direct multiplying factor as expected. Since all derivatives are negative, the terms in the denominator are additive. Therefore, an increase in pitch resistance, by an increase in or C„q, will result in a decrease in the magnitude of both steady 64 State values. An increase in C z a will result in a decrease in steady state AOA and a decrease in steady state pitch rate. The implicit assumption in the linear equations above is that the maneuver starts from a n=1 .0g trim condition at a specific velocity. The elevator deflection in the above equations is therefore an available value or, available ~ '^emax ~ '^e.crim From [17], we have, defining trends from some starting airspeed and trim elevator deflection, <5^^, Then, . . _ ^ X ^ e,available ^emax Since x/c is negative for a stable aircraft, 5g.available increases with decreasing airspeed as becomes more negative. The functional variation of the steady state values with airspeed including available elevator deflection 65 are 1/V- for and 1/V for . This variation with airspeed is of interest, since airspeed is a key control parameter in any aircraft operations. To determine an value the downwash was determined as in section 3.4 by, de/da = 0.31 = 2C^/(n-Ar) Then, O'. = a. + { 1-de/do; )a + l . q / V Using standard linear analysis the above transfer functions result in time functions of the form. a - = Ofgs + K^e'^'sin (w^t + <î>) Peak values were found by setting the first derivative to zero, resulting in = ( tan - (Wj/c) - * )/W] These equations are readily programmed and, using a database access program, values for many flight conditions were easily obtained. A typical linear response is shown in Figure 4.1. Note the large overshoot in pitch rate and smaller overshoot in AOA. Also of note is that the peak pitch rate occurs well before the peak AOA, and, therefore, 66 the peak load factor. The peak in or. occurs slightly before AOA peaks. As this response is for a full elevator deflection, the pitch rates and AOA values are very negative. Peak and steady state values versus trim airspeed for the pitch rate corresponding to zero, or the maximum available, load factor are shown in Figures 4.2-4.7. These are for the uniced aircraft at C~=0.14, which results in the minimum a. values. All coefficients used are those of the trim condition which is the starting flight condition for the maneuver. Note, from Figure 4.2, that zero load factor could not be attained at any airspeed for flap deflections of ôj = 20° to 40°, and at low airspeeds with ôj=10°. This is due to the more positive 5^ required and the flattening of the lift curve slope with flap deflection at moderate angle-of-attack. This makes the responses more limited and assessment of the results less clear. As expected, the a and q values are very negative and well beyond normal small perturbation excursions. Therefore, these plots should be used as trend indicators only. Generally, when zero load factor is attainable, there is a decrease in a and q with decreasing airspeed. This is especially noticeable in cx at the lower airspeeds where the functionality approximates 1/V\ as predicted. Peak a is only a few degrees lower than steady state cx, as was seen in the response plot. Steady state pitch rate is limited at the 67 higher flap deflections. Significant overshoot in q is seen at the lower airspeeds. Values of a. are shown in Figures 4.7-4.9. Note that, O', values calculated using peak a and q are pseudo peak values as these individual peaks do not occur at the same time. A general trend of decreasing with decreasing airspeed is seen, as predicted. Also seen is that flap deflection provides an approximate step decrease in when zero load factor is attainable. Minimum is obtained at maximum flap deflection and minimum airspeed, at which minimum pitch rate also occurs, even though this corresponds to a load factor of only n=0.65 g. These minimums would be lower if zero load factor was attainable. For the iced tailplane = -1 1 . 5^, approximately, so a potential for an ICTS event exists for all configurations. The absolute magnitudes of parameters obtained from this linear analysis do not match those of the simulation or flight test data, as will be discussed in Section 6 . This is judged to be because of typical characteristics of linearization. A response that ranges from n=lg to zero g can not be considered a small perturbation maneuver, and so exceeds the valid range of the linearized EOM. Additionally, due to the nonlinear nature of the database, differences in the linearized coefficients at high and low airspeed will contribute to differences in the responses. However, the 68 indicated trends with airspeed and configuration are considered to be representative. 69 Figure 4.1 Linear Model Second Order Step Response Figure 4,2 Linear Analysis Pushover Maneuver, Load Factor 70 Figure 4.3 Linear Analysis Pushover Maneuver, Steady State AOA Figure 4.4 Linear Analysis Pushover Maneuver, Minimum Peak AOA 71 Figure 4.5 Linear Analysis Pushover Maneuver, Steady State Pitch Rate Figure 4.6 Linear Analysis Pushover Maneuver, Minimum Peak Pitch Rate 72 Figure 4.7 Linear Analysis Pushover Maneuver, Steady State Tailplane AOA Figure 4.8 Linear Analysis Pushover Maneuver, Minimum Peak Tailplane AOA 73 CHAPTER 5 OSU/AARL FLIGHT PATH SIMULATION PROGRAM, TAILSIM This section describes the TAILSIM program, so named because of its emphasis on the effects of tailplane aerodynamics. Only a brief overview of the program function and operation is given, as the concepts are well known. Factors that are important for complete analysis of the dynamics of pushover maneuvers are described more fully. The reversible elevator control system model and pilot models are described fully, as they provide an important function in this research. 5.1 Program Overview The ICTS phenomenon is highly non-linear, so a six degree-of - freedom nonlinear flight path program was required for quantitative analysis. It was also required to be able to output local tailplane AOA and tailplane aerodynamic characteristics during a time history maneuver. As has been described in Section 3.4, a specific set of stability and control derivatives to be used in a specific set of build-up equations were developed for the DHC-6 Twin Otter. Due to 74 these specific requirements and the desire to maintain flexibility in program development, an in-house program was created. The TAILSIM program is typical of many dynamics programs. It uses a 4'^^ order Runge-Kutta method to integrate the standard aircraft equations-of-motion (EOM). This integration method is popular because of its ease of use and its good convergence properties. Evidence of this was noted during this study as the simulation program could generate good responses with time steps as high as At = 0.1 seconds. More complete convergence was seen for time steps of At=0.01 and 0.02 seconds, which showed negligible differences in time history response parameters when compared. A time step of At = 0.02 seconds, or 50 Hz, was chosen for most of the time histories, as it offered a good compromise between accuracy and calculation time. Also, the short period frequency of commuter class aircraft is typically below cOgp=3.0 rad/sec or 1/2 Hz, and cable dynamics caused elevator oscillations on the order of 3 Hz, so the 50 Hz integration rate was considered to be quite adequate. Single precision was used for all calculations, as it was judged to result in responses within the overall accuracy of the simulation, and allowed faster through-put. Additionally, most time histories were short, 2 0 seconds or less, which kept any accumulating numerical errors from building to noticeable levels. Finally, as will be presented in Section 6.1, the overall 75 accuracy of the simulation was determined to be acceptable by comparison to flight test responses. Forces and moments that drive the EOM were provided by buildup equations as discussed in Chapter 3. The derivatives and command inputs for these buildup equations were obtained by linear interpolation, and extrapolation if desired, of tables in the database. These program features were generic and can accommodate many aircraft. Additionally, the programming of TAILSIM was chosen to be straightforward to allow the flexibility to make modifications to fit Che specific characteristics of any aircraft. Other features of TAILSIM included trim to a fixed power setting or to n=1 .0g level flight, incorporation of a standard atmosphere into the flight condition calculations, modeling of the cable dynamics of the reversible elevator control system, a simple pilot model, and immediate post-run plot page displays of key response parameters. 5.2 Program Structure The functional program structure overview is shown in the program flow block diagram of Figure 5.1. Here INIT represents the initialization actions of the program. The main action of the initialization subroutine is to trim the aircraft to the input flight condition. Other supporting actions include reading in the aircraft geometry and flight condition data and input and output file names. The database 76 initialization program is also accessed in this subroutine and reads in all database tables and stores the data into a single variable array. Multiple options exist for trimming the aircraft. In all options, Mach number and altitude are inputs. These are used with the standard atmosphere calculations to determine the true and calibrated airspeeds. Angle-of-attack is always a variable and is set to match the required load factor. If thrust coefficient is an input, the trim function will vary the flight path angle to provide unaccelerated flight. If thrust coefficient is not an input, the trim will be to the input flight path angle and thrust will be varied. If maximum or minimum thrust levels would be exceeded, the flight path angle is again allowed to vary to trim. A bank angle can also be input to perform a trim to the required load factor in a coordinated turn. The main line on the block diagram defines the Runge- Kutta integration loop. This loop starts with the determination of the current flight condition, as noted by the FC block. The PCS block represents the calculation of the control surfaces from command inputs. Command inputs are read in directly from tables and can vary depending on the command input option chosen. The command inputs can be direct elevator deflection, stick force to drive the reversible control stick dynamics, or load factor, which drives the pilot model which then commands a stick force. 77 With the flight condition and surface inputs known, the forces and moments acting on the aircraft may be determined. The FM block represents this program action. In this program section the table lookup program is used to access the required tables and determine the stability and control derivatives. These are then used in the buildup equations to determine total derivatives which are then used at the known flight condition to calculate the total forces and moments. These equations were described in Section 3.4. Most terms of the buildup equations are determined on each of the 4 passes of the Runge-Kutta integration, as their derivatives are secant derivatives. The a derivatives, however, are tangential derivatives. To provide a more correct usage of these derivatives and enhance the accuracy of the longitudinal motion, these terms were summed prior to their usage in the Runge-Kutta loop. Inside the R-K loop, a Aa is then applied to the derivative and added to the summed terms. The total forces and moments are input into the EOM (EOM block). This program section defines the standard body axis accelerations and includes the Euler axes rates and their transformation equations. The EOM equations output accelerations which are then integrated. Concurrently the required integrations for the pilot model and stick dynamics are accomplished (INT block). The integration subroutine keeps track of past values and properly scales them to calculate the values for the next pass of the R-K loop. An 78 important feature of the program is that all integrations are performed in this separate subroutine. This allows the integration of parameters from other subroutines to be kept in sync, maintaining the "vector" nature of the EOM, and contributes to the good convergence qualities of the program. All of the above equations are shown in Appendix F. Finally, the OUT block indicates the saving of output parameters into individual arrays. The location of this saving action in the R-K loop was chosen to provide a direct comparison of sate and control parameters to EOM accelerations. Not shown in the block diagram is the plotting subroutine. This subroutine may be accessed after the completion of a time history run, and displays multiple plot pages of the saved parameters. These plots may be screen dumped to provide a hard copy of the time history. The output arrays may also be saved for later plotting or analysis. 79 INIT OUT FC PCS FM EOM INT ► Figure 5.1 TAILSIM Program Flow Block Diagram 80 5 • 3 Implementation of Aerodynamic Lag TAILSIM is typical of many aircraft simulation programs in that it obtains its derivatives from table look-ups, primarily based on AOA. An implicit assumption is that the derivatives change instantaneously with AOA. For typical aircraft maneuvers that do not approach high pitch rates or dcx/dt values, this is a reasonable assumption. Reference 23, however, describes a study for a fighter aircraft in which the instantaneous derivative assumption failed. In that study it was found that applying a first order lag to the AOA used in accessing the database resulted in a much improved response. Reference 24 provides a definition of the methodology to incorporate unsteady aerodynamic effects in a simulation such as TAILSIM. This methodology develops a linear filter transfer function for the Kussner function found in aeroelasticiy analysis [25,26] . This was attempted in this study, with no significant change in the agreement with flight test responses. Reference 11 suggests a limit on the reduced frequency of da/dt, defined by, k = c(da/dt)/(2V) < 0.04 for the instantaneous derivative assumption to be valid. Time history responses showed a peak value of da/dt=0.02 which is well within the above limit. Additionally, da/dt will slow to a much lower level immediately after reaching a 81 peak due to aircraft pitch damping. Reference 27, however, shows significant changes in 0 ,^^% an oscillating airfoil at a constant reduced frequency of k=0 .0 2 2 , although at a much higher absolute frequency. The applicability of these results to tailplane lift characteristics is not considered to be direct, due to the constant frequency of the oscillation, and the factor of 10 difference in frequency. Therefore, these effects were not included in the TAILSIM program. However, most aircraft dynamics references such as [11,12], note that the tailplane AOA can be assumed to lag the wing AOA due to the time it takes airflow to travel the distance between the wing and the tailplane. This fact is used to derive an adjustment to the downwash angle which is then applied as da/dt derivatives. In this study, however, the tailplane AOA was used independently of the aircraft AOA, so the described lag was applied directly to the calculation of the downwash. This lag was implemented by applying a Pade filter to the downwash angle determined by aircraft AOA to create a lagged downwash value, The Pade transfer function form of this downwash angle is. 82 with the time constant defined by, r = l./V This was implemented as, d e . / d t = 1/ t ( e - rde/dt - e, ) with de/dt = (de/do:) (da/dt) The derivative de/da was calculated continuously in the coefficient table lookup subroutine and da/dt was an output in the EOM subroutine. This lag had a minimal effect on aircraft responses, but was judged important to keep for completeness. 5.4 Implementation of Reversible Elevator Control Model As noted in the introduction, the commuter aircraft of interest in this study have reversible control systems. These systems typically use cables to directly connect the stick, or control column, to the elevator. Due to the length of the cables, cable stretch can be considerable. This stretch can cause the actual surface position to be different than that expected from the stick position. 83 It was desirable to model elevator cable dynamics, both to generate the correct elevator position, and to provide a correct definition of the reversibility of the control system so that the effect of a hinge moment reversal on the stick and elevator position could be represented. A simple control system description was chosen and is defined in Figure 5.2. The cable was modeled as a spring driven by pilot stick force and elevator hinge moment. Both the stick and the elevator were assumed to have mass and inertia. Reference 28 was useful in developing these dynamical equations. The final dynamic equations used were, dWg/dt = -C3W3 + as/IgFc + Fgbg/Ig dWg/dt = -C^w^ + a^/IgPT + H,/I^ dFVdt = -K^a^Wg - K^a^w^ The implementation in TAILSIM was done in the flight control subroutine. The following values were measured on the DHC-6 Twin Otter, Gg = 0.07 lbs./in. lb. - elevator gearing du/ôg = 2.0 - elevator to stick deflection ratio Other physical measurements of the control system components were not available, so they were estimated based on the size of the aircraft. It was estimated that a^ = 3.0 inches, which 84 resulted in 3.3 = 6.0 inches and bg=28.6 inches using the above values. The elevator weight was estimated to be 50 lb, one- half of the total tailplane weight, with a radius of gyration of 10 inches, giving an inertia of Ig=1.08 Ib-ft^. The stick inertia was estimated to be 1^ = 0.44 Ib-ft^, that of a 12 lb weight with a radius of gyration of 13 inches. Cable length was estimated to be 1=500 in. The cable spring constant, K^, wasdetermined by assuming two steel cables of 1/4 in. diameter, giving A=0.098 in.^. Using basic strength of materials we have, E = 30.0 X 10'’ - modulus of elasticity for steel a = eE = Eô,/1 = F/A Therefore, F = AEÔ,/1 = so K, = 5890 lb/in No static "breakout" friction was assumed, but dynamic friction of the cable system and normal pilot control operation were assumed to provide damping. To simulate this effect, values of damping, Cg and Cg, were chosen by trial and error to give a response that matched the general characteristics seen in the DHC-6 Twin Otter elevator deflection time histories. The final values were Cg=-20.0 and CL=-4.0. 85 These damping coefficient values were not considered to be unique, but achieved the goal of providing the desired response characteristics when compared to flight test data. Other values could be as effective in achieving the same response. It would have been desirable to have measured values for all terms in the model, however, all such information was not available. The specific values of the model were not considered to be critical to this analysis, but a representation of the dominant effects were required to provide a higher fidelity simulation of the impact of elevator hinge moment on pilot model response. The pilot model is discussed in the next section. 86 ♦H, gySt©®^ SC trol Reversible = » Figure 81 5.5 Implementation of the Pilot Model The aircraft response to a commanded elevator input is useful in generating consistent responses and showing the changes in hinge moment on the elevator. However, the lack of any response to those changes in hinge moment is not valid in the "real world". The reversible elevator control dynamics respond to changes in hinge moment but can result in uncontrolled, stick-free, responses. This is useful in showing the potential for control problems caused by changes in hinge moment. However, to provide the proper aircraft response to any variation in hinge moment while still maintaining a desired load factor, a pilot model is needed. This is especially important for this simulation effort, because pilot response is a significant factor in the outcome of any ICTS event. When a pilot model is used a simulation becomes a closed loop system, so the pilot model has the role of a feedback compensator. The proper form of this compensator has been developed over many years of research with human pilots. References 11, 12 and 22 provide descriptions of classical pilot models. In classical form a pilot model is a transfer function that consists of some combination of a pure gain, delay term, lead term, and one or more lag terms. The delay term represents a reaction time delay while one lag term corresponds to a neuromuscular lag. These terms are not adjustable by the pilot. Human pilots are very adaptable, 88 however, and may vary their performance to match the desired response. This is represented by a lead and lag term with adjustable time constants in the pilot model. Reference 11 suggests that it is acceptable to combine all lag terms. The form of the pilot model is, then, using a Pade filter to represent the delay term, _ Kp{\-xj2s) ( 1 + r^ s ) (1+t ^/2s ) (1 + r^s) The reaction delay was chosen to be the average of the ranges given in [11,12], r, = 0.12 sec. The value of the lead time constant was chosen to be T^ = 0.4 sec, which is a conservative value based on [11] , which suggests that 0.5 sec is a maximum reasonable value for this term. The above values were chosen independently of choice of command and feedback parameters of the model. The pilot gain and the lag term are dependent on this choice. It was desired to command load factor, so that a zero load factor command could be used to drive the response. This was readily implemented through a pitch rate command system by, qc = ( n^ - 1 ) /V with, q^rrcr ~ qc " q 89 The pilot model and q/ô^ transfer function is a Type 0 system so, to eliminate any error in q, an integrator is needed. This was accomplished by simply using the integrated pitch rate error to drive the pilot model. The pilot gain, ô^/q^rrcr ot Kp, was then determined by inverting the steady state value of the q/ô^ transfer function defined in Section 4 and was continuously calculated in the TAILSIM program. The output of the pilot model was then a 5p elevator command, however, the reversible control system is driven by a stick force command. To determine the correct stick force, the elevator hinge moment was continuously calculated by accessing the uniced tailplane hinge moment table, and the required stick force determined by multiplying this value by the stick gain. The lag time constant was then determined by trial and error, within the limits suggested in [11] , resulting in T- = 0.5 sec. The pilot model transfer function is a second order system, which was implemented in controllable canonical form as, 0 1 0 X - ( T ^ + T / 2 ) + Kp a TVc/2 T\T/2 .^^2. T,x/2_ .^2. 90 1 + - ^ Tr-x/2 + ^ {T,+x/2) L Tr .^2. ^ I These equations were straightforwardly programmed into the flight control system subroutine of TAILSIM. This pilot model implementation resulted in smooth, well controlled response during pushover maneuver simulations with the uniced tailplane at approach speeds with flaps set at ô.- = 10° and 20°. This was the desired result for determining the lag time constant, and verifying that the pilot model function was acceptable. Additionally, in a typical ICTS scenario, the pilot is "caught off guard" by the changes in aircraft stability and control characteristics. This implies that the pilot does not have time to adapt to the unexpected change in stick force characteristics. To simulate this, neither the pilot model gains, nor the elevator hinge moment used in the pilot model, were changed when the iced tailplane model was used. The definition of this pilot and aircraft closed loop system in terms of more standard control system analysis terms of frequency, damping, and phase or gain margin could add further insight into the impact of the pilot model, including the stick force dynamics, on the closed loop system response. This was not accomplished in this study, in keeping with the goal of working with the nonlinear 91 characteristics as determined by simulation responses as the primary source of system information. A concern that the numeric implementation of the pilot model/stick force system would cause excessive lag was addressed by running a simulation without the stick force dynamics, applying the output of the pilot model directly to the elevator. No significant differences in response were seen. Some more noticeable differences might be expected in some of the more active responses described in the next section, however, such differences were expected to be within the overall accuracy of the simulation. Therefore, the main goal of the pilot model in determining representative responses to iced tailplane characteristics could be achieved, and are described in the next section. 92 CHAPTER 6 SIMULATION ANALYSIS TAILSIM was considered to be a research tool, and was used as such. The general approach was to provide command inputs that would result in pushover maneuvers that met the criteria defined in [10] for the Zero G maneuver. These inputs were elevator deflection, stick force, or pilot model commands. At zero load factor, or the minimum attainable load factor, the resulting tailplane AOA, load factor, pitch rate, angle-of-attack, pitch angle, and other parameters were noted. Using these outputs, qualitative and quantitative assessment of the aircraft capability and the effectiveness of the Zero G maneuver were determined. The results presented in this section represent the important results obtained over many simulation responses. The specific inputs used to achieve the Zero G maneuver criteria were obtained by trial and error for each configuration tested. Variations on these inputs could also achieve zero load factor, but, the inputs presented showed the most consistent capacity for achieving the desired criteria. 93 6.1 Comparison with Flight Test Parameter Estimation Maneuvers During the development of the TAILSIM program and database time history comparisons were made for three different flight test maneuvers. The maneuvers selected from the 1992 flight test program were; uniced tailplane, flap deflection of 5^=0°, 0^=0.07 ; uniced tailplane, 6,=10°, C-=0.07; and iced tailplane, 6^=10°, C~=0.14 . Comparison plots for the first maneuver are shown in Figures 6.1-6.6. The overall match of these responses is representative for all three cases considered. The first plot. Figure 6.1, shows the elevator deflection which was used to drive the maneuver. There is a slight disagreement between the initial trim value, which is indicative of the accuracy of the database. Initial trim airspeed is an input, so the match at time t = 0 .0 seconds is exact. However, as is seen in Figure 6.2, the flight test trim was not perfect. No attempt to "fudge" this slight mismatch was made or considered necessary, as the TAILSIM response showed similar characteristics to the flight test response. The TAILSIM response does tend to slow down more quickly than the flight test response, most likely due to the more simplified drag characteristics of the database. The angle-of-attack comparison of Figure 6.3 shows excellent agreement, with trim values within hot=0.2°, peak values within Aa=0.5° and At=0.1 seconds, and even closer 94 post-input steady state values. In Figure 6.4, pitch angle shows similar agreement until the end of the maneuver, where increased pitch attitude is caused by the lower airspeed noted above. The pitch rate response of TAILSIM in Figure 6.5 shows very good agreement except for the second negative peak which is low by Aq=2.5 degrees/second. Normal force also shows excellent agreement, except for the positive peaks which are high by An^=0.1g, Figure 6.6. These comparison plots show, overall, a very good agreement between the responses of TAILSIM and those of the aircraft. Such mismatches that do exist are considered to be typical for the chosen level of development of the database, and are judged to be acceptable for use of the program as an analysis tool. 95 Figure 6.1 Example Maneuver Elevator Deflection Comparison Figure 6.2 Example Maneuver Airspeed Comparison 96 T, '■ L '■ : '1 " I j T Figure 6.3 Example Maneuver Angle-of-Attack Comparison Figure 6.4 Example Maneuver Pitch Angle Comparison 97 • A Figure 6.5 Example Maneuver Pitch Rate Comparison Figure 6.6 Example Maneuver Normal Acceleration Comparison 98 6.2 Trim Flight Conditions All simulation maneuvers started from a n=1.0g trim flight condition at 7,000 feet, standard day, low gross weight, and required for level flight. Plots of the important trim parameters are shown in Figures 6.7-6.10. The iced tailplane is used here for later reference, however, there is little difference from the uniced tailplane. Trim conditions are of interest because they define the available capability for any maneuver. Specifically of interest are available elevator deflection and margin in a. versus seal:- These trim conditions should be kept in mind in the following simulation analysis. The trim elevator deflection plots show the decrease in elevator deflection with decreasing airspeed of a stable aircraft. This results in more available elevator deflection for pushover maneuvers at lower airspeeds. The effect is to somewhat equalize the loss of dynamic pressure on pushover capability. Note that flap deflection causes a relatively constant shift in all terms at all airspeeds. Trim a. shows a decrease with increasing airspeed. Therefore, higher speeds result in less margin to scaii' which is shown in Figure 6.9 for the iced tailplane. With 5.=40°, the tailplane is almost at Q!c with a Aa=l° margin, and is definitely in the nonlinear range of the tailplane lift curve. The a. at which the hinge moment break occurs for the iced tailplane is also indicated and is higher than 99 some values. This suggests that control difficulties may occur just trying to maintain trim flight above V=60 KCAS with ô.- = 30“, and above V=55 KCAS for 0^=40°. It is also noted that relatively high angle-of-attack is required to trim at the lower airspeeds, as shown in Figure 6.10. The high values may be due to the method of extrapolation used in the database, which may not accurately match the aircraft at these flight conditions. 100 Figure 6 .7 Simulation Trim Characteristics, Tailplane Angle-of-Attack Fiçrure 6.8 Simulation Trim Characteristics, Elevator Deflection 101 Figure 6.9 Simulation Tailplane Trim and Stall Characteristics Figure 6.10 Simulation Trim Characteristics, Angle-of- Attack 102 6.3 Pushover Maneuvers, Uniced Tailplane A pushover maneuver consisted of first trimming the aircraft to n=1.0g level flight at a given airspeed and altitude with a, 0^, and varying as required. Elevator deflections from an input table were then used to drive the maneuver. The proper inputs were determined by trial and error. The standard input ramp time used was At=0.5 seconds which corresponded to the minimum seen during flight test. The maneuver was started with a pushover to approximately n=0.8g, followed by a pitch up to a pitch attitude of approximately 0=20°, followed by the maximum pushover to zero load factor, and then recovery. The maximum pushover 5^ deflection was held for 1 to 2 seconds before initiating a recovery. Success criteria were to reach zero load factor with pitch angle within 0=+/-lO° of horizontal. In some cases flap speed limits were exceeded, indicating the severity of these types of maneuvers. Figure 6.11 shows a sample output plot page. As indicated in Figure 6.12, zero load factor was not attained for flap deflections of 5j=40°, which was similar to preliminary flight test results. Note that some scatter in the data is due to the nonlinear nature of the maneuvers. Figure 6.13 shows a. versus pitch rate. There is a consistent trend of decreasing 0;^ for decreasing pitch rate, for all flap deflections. The rate of change is consistent at all flap deflections, and is Aq!. = 0.2° to 0.4° per deg/sec 103 of pitch rate. The shift in a. due to flap deflection is clearly seen. The strength of the pitch rate functionality is shown in Figure 6.14. This plot shows the incremental change in from a. versus pitch rate. The data falls within a reasonably linear range with pitch rate, as might be expected from the term. However, this linear characteristic is considered to be somewhat surprising as there are many nonlinearities in downwash and de/da for the different flap deflections and trim power settings used in the different flight conditions of these maneuvers. Trends with decreasing airspeed also show decreasing a^, Figure 6.15. The decrease ranges from Aa^=-1° with 0f=0’, to Aa. = -3- with ô.- = 40^. These trends are expected based on the analysis of section 4.0, however, they are not as strong a function of 1/V" as suggested in Section 4.0. The trend for an inverse variation of pitch rate with airspeed described in Section 4.0 is verified by the Figure 6.16, while Figure 6.17 shows that angle-of-attack is relatively constant at the constant zero load factor. This dependency on airspeed differs from that of Section 4.0, indicating further that the linear analysis could not maintain as valid a relationship between a, q, and n for these highly dynamic, large amplitude, pushover maneuvers. The maximum elevator deflection required in the pushover to attain the above results is shown in Figure 6.18. The 104 positive elevator position limit of 0^=14.2° is reached for the 5j=40^ flap deflection maneuvers, which contributed to preventing zero load factor from being reached. Elevator deflection is close to the limit when 5^=20° is used and remains within A5^=l° to 3°. A wider deflection margin is shown for the 0^=10° responses. Implications of these deflection margins will be shown in later Sections. In order to verify the effectiveness of the input ramp time of At=0.5 seconds, other ramp times were used. A representative configuration of 0j = 20° at V=70 KCAS was chosen. Zero G maneuvers were run for ramp times up to 5 seconds. Figure 6.19 shows that there was no significant difference in the resulting a, at zero load factor. It should be noted, however, that the longer ramp time maneuvers required more extreme flight attitudes and elevator deflections to produce a level pitch attitude at zero load factor. Figures 6.20 and 6.21 show how these results compare to the preliminary flight test data for 0^=20° with 0^=0.07 and 0.14. Tailplane angle-of-attack was used as the comparison parameter. The agreement is good until below an airspeed of V=60 KCAS and pitch rate of q=-15 deg/sec. Below these flight conditions the flight test results show a strong decrease in a,, while the simulation results seem to be limited to a. = -15°. This would suggest inaccuracies in the database, most probably in the lift curves and downwash 105 calculations. However, it should be noted that these preliminary flight test results were obtained using Five-Hole Probe calibrations that were suspect at extreme values. The full range calibration based results were not available at this time, but, in general, showed that more correction was needed at higher tailplane angle-of-attack. It is, therefore, suggested that some of the differences are attributable to not using valid Five-Hole Probe calibrations. The higher accuracy of the nonlinear simulation is clearly seen when compared to the results of the linear analysis of Section 4. Most significantly, for all non-zero flap deflections, the attainable load factors of the linear analysis were much closer to n=1.0g than shown by the nonlinear simulation and preliminary flight test data. Additionally, tailplane angle-of-attack differences of as much as Aa. = -5° were noted. This is of special concern given the higher load factors. Comparing the flight test data noted above for 5.- = 20° and C~=0.14 to that of the linear analysis, it was found that tailplane angle-of-attack differed by àa^ = -3° to -4° at all airspeeds. This poor agreement of the linear analysis further verifies the necessity to use nonlinear methods in this research. Of interest is that the preliminary flight test results do not show a consistent, strong, effect of thrust coefficient (Figure 6.20 and 6.21). Thrust coefficient is apparent in the at trim flight conditions, but the zero 106 lift condition required at zero load factor tends to negate these differences. Note that much of the differences between thrust coefficients are considered to be typical scatter due to differences in maneuver performance. 107 Figure 6.11 Example Simulation Pushover Maneuver Time History, 6f=0°, Uniced Tailplane 108 Figure 6.12 Pushover Maneuvers, G Level Attained Figure 6.13 Pushover Maneuvers, Pitch Rate Functionality 109 Figure 6.14 Pushover Maneuvers, Incremental Effect of Pitch Rate Figure 6.15 Pushover Maneuvers, Airspeed Functionality 110 Figure 6.16 Pushover Maneuvers, Airspeed/Pitch Rate Functionality Figure 6.17 Pushover Maneuvers, Angle-of-Attack Attained 111 Figure 6.18 Pushover Maneuvers, Elevator Deflection Required Figure 6.19 Pushover Maneuvers, Effect of Input Ramp Time 112 Figure 6.20 Pushover Maneuver Comparison, Airspeed Functionality Figure 6.21 Pushover Maneuver Comparison, Pitch Rate Functionality 113 6.4 Pushover Maneuvers with the Iced Tailplane From Figure 6.9 it can be determined that the data for Che iced tailplane shows = -11.5°, approximately. Additionally, this figure shows that the hinge moment break occurs at approximately û^=-8° for positive elevator deflection. Figure 6.15 shows that the stall angle-of-attack would be exceeded in Zero G maneuvers for flap deflections greater than 0,=10°. The hinge moment break angle-of-attack is exceeded at all flap deflections. The effect of these angle-of-attack characteristics on flight characteristics will now be investigated using simulation responses with the iced tailplane database. Note that the responses shown below are a small subset of those generated in the course of this research, and were chosen to illustrate the most significant characteristics discovered. A Zero G pushover maneuver with zero flap deflection and the iced tailplane is shown in Figure 6.22. This elevator driven maneuver is well controlled and shows no signs of any abrupt changes in tailplane hinge moment. Since the tailplane angle-of-attack remains above the stall and hinge moment break values, this is expected. At an approach airspeed of V=80 KCAS with 6^ = 10°, Figure 6.15 shows a. above stall angle-of-attack with an iced tailplane. A Zero G pushover maneuver at this airspeed with iced tailplane driven by elevator deflection is shown in Figure 6.23. While there is a reduction in hinge moment 114 during the extended four second positive elevator deflection, the response is stable. Typical of all responses, including those in Section 4.0, is that a. reaches a minimum after the minimum in q but before the minimum in o:. At the lowest airspeed indicated inFigure 6.15 with 0j = lO=, a. just reaches ac.scau- A pushover at this airspeed is shown in Figure 6.24. The response is stable and well controlled. There is a tendency for increasing pitch rate and decreasing a, a;,, and n, due to the airspeed increase at the constant elevator position of the pushover. This was commonly seen in all stable responses. The slow stall break of the iced tailplane prevents any noticeable divergence even though is reached just prior to the recovery elevator input. Figure 6.25 shows a Zero G maneuver driven by elevator deflection with 0^=20° at an approach airspeed. In this case, the maneuver is controlled. However, at t=10.5 seconds there is a significant reduction in hinge moment, at approximately a. = -9", and a significant decrease in . In fact, after slowing down initially, the rate of change of is seen to be sharply decreasing at t=12 seconds. This decrease occurs at approximately c^ = -11.5° when the tailplane is fully stalled. As decreases further, hinge moment almost reaches Hg=0 .0 but does not reverse. Compared to a similar Zero G pushover maneuver with uniced tailplane. Figure 6.26, the tendency for divergence when a^ = -11.5° is clear. This 115 tendency for divergence contributes to why zero load factor is exceeded for the maneuver with the iced tailplane. Had recovery elevator not been input upon reaching zero load factor, this divergence may have resulted in departure from controlled flight. The reduction in hinge moment at the onset of the pushover seen in Figure 6.25 appears at first glance to be a hinge moment gradient reversal. That is, hinge moment increases with decreasing instead of steadily decreasing. However, it is more accurately described as an induced effect. This effect, which was also seen for uniced tailplane responses, occurred when the maximum elevator position preceded most of the excursion. The negative slope of Chcc then caused a reduction in hinge moment as a.^ decreased. This effect was most noticeable for abrupt elevator inputs. Figure 6.27 shows a more definite hinge moment gradient reversal. With a slower elevator input, the hinge moment starts to decrease at t=l2 seconds, slightly before the maximum elevator position is reached. This is clearly associated with the tailplane angle-of-attack reaching approximately o!^=-10°'. However, the change in hinge moment gradient starts at approximately t=9.5 seconds, when ck'. = -8°, at the hinge moment break. Changes in hinge moment at maneuver onset should not be confused with these significant changes in hinge moment seen at large negative a.^ values. 116 Note that in none of these responses was there a full hinge moment reversal, as never became positive. However, responses with non-zero flap deflection showed significant reductions in stick force gradient and elevator hinge moment gradient. These were clearly associated with the tailplane hinge moment break and stall, and caused the divergent responses. In order to investigate more fully the effect of hinge moment slope reversal, pushover maneuvers were run using the reversible elevator control model. For these responses, stick force was used to drive the elevator control model and command an elevator position. This allowed the elevator to float to maintain the hinge moment required to balance the input stick force. As with the elevator driven input, using stick force to drive a Zero G maneuver with zero flap deflection and the iced tailplane results in no noticeable control difficulties. This is shown in Figure 6.28. The response is well controlled. The cable dynamics of the reversible control model are noticeable during the abrupt stick force inputs, but, these do not effect the response characteristics. When stick force is used in a maneuver at approach airspeed with the uniced tailplane and 6, = 10°, Figure 6.29, the response is very similar to those using the elevator command. The cable dynamics are noticeable, but are too small to show clearly in the other response parameters. The 117 tailplane angle-of-attack does reach ck^ = -10°, which is beyond the hinge moment break of the iced tailplane. The response of Figure 6.30, at a slower airspeed, shows that reaching the hinge moment break causes the elevator to be driven sharply to its position limit. This drives the response to overshoot to n=-0.5g. The response is stopped at t=14 seconds because simple step stick force commands could not control it. Clearly, the hinge moment has a more significant impact at this lower airspeed than indicated by using fixed elevator inputs. A pushover with uniced tailplane and 0f=20° is shown in Figure 6.31. The stick force required to reach zero load factor was Fs=-16.5 lb. Here it is seen that the elevator floats to the maximum deflection limit of 0^=14.2° while the nose down stick force is held constant, primarily due to the decreasing airspeed. Hinge moment does not vary significantly while this occurs, so the balance with stick force is verified. The response does not reach a steady state condition as quickly as when using abrupt elevator deflection inputs, but is otherwise stable. The response is divergent when the same stick force input is used with the iced tailplane. Figure 6.32. As in an earlier iced tailplane maneuver the stick force input drives the tailplane angle-of-attack beyond ot^=-8°. Then the hinge moment break drives the elevator sharply to its positive limit. This causes the divergence, which is greater than 118 that for the fixed elevator input responses and, for these specific stick force inputs, would be unrecoverable. However, the divergence occurs more slowly than for the above ô,=10^ response. A contributing factor to this is the smaller elevator deflection margin to the positive maximum limit, discussed in Section 6.3 and shown in Figure 6.18. This results in less nose down elevator deflection available to drive the response below zero load factor. Additionally, less negative lift is generated with 5f=20°, than with 0,=10° (Appendix B, Figures B.l to B.3) . Therefore, as the airplane diverges and angle-of-attack becomes more negative, load factor does not become as negative. For a lower pushover stick force input used in the response of Figure 6.33, Fg=-14.0 lb, the pushover is recoverable. This amount of stick force input does not drive a. to the level of the hinge moment break initially. This results in a slower rate of floating elevator increase. The response would, most likely, diverge if the recovery stick force was delayed, but is otherwise controllable. Note that n=0.4g was the lowest load factor at this airspeed that did not result in a divergent response. 119 Figure 6.22 Push Over Maneuver, Iced Tailplane, Approach Airspeed, Ô, Command, 6^ = 0° 120 Figure 6.23 Push Over Maneuver, Iced Tailplane, Approach Airspeed, 5, Command, 5f=10° 121 Figure 6.24 Push Over Maneuver, Iced Tailplane, Minimum Airspeed, Ô, Command, 5^=10' 122 Figure 6.25 Push Over Maneuver, Iced Tailplane, Approach Airspeed, Ô, Command, 0^=2 0° 123 Figure 6.26 Push Over Maneuver, Uniced Tailplane, Approach Airspeed, Ô, Command, 0^=20° 124 Figure 6.27 Slow Push Over Maneuver, Iced Tailplane, Approach Airspeed, 5, Command, 0^=20° 125 Figure 6.28 Push Over Maneuver, Iced Tailplane, Approach Airspeed, F, Command, 0^ = 0° 126 Figure 6.29 Push Over Maneuver, Uniced Tailplane, Approach Airspeed, F, Command, 0f=10° 127 Figure 6.30 Push Over Maneuver, Iced Tailplane, Approach Airspeed, F, Command, 0f=10° 128 Figure 6.31 Push Over Maneuver, Uniced Tailplane, Approach Airspeed, F, Command, 0^=20° 129 Figure 6.32 Push Over Maneuver, Iced Tailplane, Approach Airspeed, F, Command, 6^=20° 130 Figure 6.33 Push Over Maneuver, n=0.4g. Iced Tailplane, Approach Airspeed, Ô, Command, 6j=20° 131 6.5 Pushover Maneuvers with the Pilot Model Section 6.4 showed that control problems exist if the tailplane angle-of-attack exceeds the hinge moment break and stall values. To investigate these results further, the pilot model as described in Section 5.5 was used to command pushover maneuvers for various aircraft configurations and flight conditions. To illustrate the most important results, responses for the aircraft configurations used in Section 6.4, as well as supporting responses, are presented. The Zero G maneuver response with an iced tailplane and zero flap deflection is shown in Figure 6.34. As for all the zero flap deflection responses, the maneuver is stable and well controlled. The pitch rate error compensation of the pilot model is clearly seen, and approximates a typical second order response. A minimum load factor command of n^=- 0.2g was used to compensate for the slowness in the response of the pilot model as the target load factor was reached. This allowed zero load factor to be reached at a time consistent with previous responses. Similar command inputs were used on all runs for consistency. As noted in 5.5, the constant pilot model gains were chosen by trial and error to give acceptable control over all flight configurations and conditions with the uniced tailplane. Additionally, stick force was calculated based on elevator hinge moment with the uniced tailplane. To account for a pilot being "caught off 132 guard" in an ICTS event, these gains and calculations were not changed for the iced tailplane responses. Figures 6.3 5-6.37 show responses for the uniced tailplane at non-zero flap deflections. As is seen, all responses are stable. Also visible is the reaction delay of the pilot model. Only the response at the minimum airspeed flight condition with ô.=10° shows some difficulty in maintaining the desired load factor. The higher control activity indicates that the pilot model dynamics may be too fast for this flight configuration and airspeed. Additionally, the aircraft angle-of-attack reaches the stall range in this response, above o;=10°, making control difficult for the pilot model. Pushover maneuver responses with the iced tailplane are shown in Figures 6.38-6.42. The first noticeable characteristic of these responses is that all show signs of tailplane stall, and all show that recovery is possible. In Figure 5.38, with ô.-=10°, the divergence seems to start at approximately t = 11.5 seconds when a^=-d°. Prior to this time, the response showed a tendency to be stabilizing. The elevator deflection diverges into the full nose down position at approximately t=12 seconds as passes through a^=-10°. The aircraft divergence escalates at this time, reaching a minimum of n=-0.8g, before the recovery command is generated. Stick force magnitude is, approximately, 84% of the magnitude of the hinge moment, neglecting cable dynamics, and so does 133 not exceed Pg = 70 lb of pull during the recovery. This is within a typical pilot's capability. There are some extreme oscillations after this, but the response eventually stabilizes. The lower airspeed response with 5f=10° is similar but, with slightly less overshoot in load factor, slightly higher stick forces of approximately Fg=85 lb, and slightly fewer oscillations (Figure 6.39). The abruptness of the input command caused the pilot model to drive the elevator to its position limit at the start of this maneuver. To avoid this elevator deflection overshoot, a slower load factor command input was applied, as seen in Figure 6.40. The response shows similar divergence and recovery characteristics. This suggests that tuning of the pilot model gains is not required to give consistent response characteristics to an ICTS event. Note that in each of these responses the pilot model recovery commands were initiated at approximately the same time as the commanded load factor was reached. The peak overshoot in load factor occurred after the recovery command was initiated, when the undesired pitch rate overshoot was finally reversed. This is representative of a typical piloted aircraft response. The response at approach airspeed with ô,=20°. Figure 6.41, appears to start diverging at t=10.5 seconds, when is just below O!^=-10°. The elevator then quickly diverges to the positive limit of 5g=14.2° at t=ll seconds. The target 134 of n„=-0.2g is exceeded at t=12 seconds, and the pilot model responds after an approximate delay of 0.2 5 seconds. The pilot model is effective in stabilizing the response and holds the overshoot in load factor to n=-0.5g. The resulting recovery is then much smoother than for the previous responses and requires only moderate stick forces. As noted in Section 6.4, pushovers with 0^=20° departed unless load factor was greater than n=0.4g. Figure 6.42 shows no divergence tendencies for a pushover to a commanded load factor of n^= 0.4g. All of the above pushover maneuvers showed a tendency for control difficulties that lead to divergence when the angle-of-attack of the tailplane hinge moment break was exceeded. Figures 6.7 and 6.9 showed that, for approach airspeeds with 5^=40°, this value of is exceeded in a trim flight condition, but is not exceeded. It was, therefore, desired to investigate a pushover maneuver at this higher flap deflection, to verify the above results. Figure 6.43 shows the response for a slow, symmetric, pitch doublet command of An^=0.05g, with the uniced tailplane. The response is stable and well controlled, although there is an increase in airspeed due to the initial reduction in flight path angle caused by the initial pushover. The response with the iced tailplane is very different, as shown in Figure 6.44. While the aircraft can fly in a trimmed condition, the small n^ command causes the response 135 to slowly build up to a slightly unstable, nearly limit cycle oscillation. Because of the flat stall characteristics of the iced tailplane (Appendix C, Figure C.6), the stability contribution of the tailplane is lost causing the aircraft to become slightly unstable. Clearly, this is too much instability for the pilot model to control. Additionally, it is easy to see that alternate n^ inputs could readily cause a divergence. Because of these stability characteristics, no aggressive pushover maneuvers were attempted with 5^=40°. This limit cycle type response is judged to be qualitatively similar to oscillations seen in the Vickers Viscount accident discussed in the introduction. A time history of this accident is shown in Figure 6.45, reprinted from [1] . At 120 seconds before impact, 0f = 32° flaps were selected. Oscillations in the flight path then started, and control difficulties were noted by the crew. Full flaps were selected 20 seconds before impact. The aircraft diverged and departed from controlled flight some 10 seconds later. The above analysis suggests that tailplane icing may have reduced the aircraft's stability and precipitated the final loss of control which caused the crash. 136 Figure 6.34 Push Over Maneuver, Iced Tailplane, Approach Airspeed, Pilot Model Command, ôf=0° 137 Figure 6.35 Push Over Maneuver, Uniced Tailplane, Approach Airspeed, Pilot Model Command, ôf=10® 138 Figure 6.36 Push Over Maneuver, Minimum Airspeed, Uniced Tailplane, Pilot Model Command, 6^=10° 139 Figure 6.37 Push Over Maneuver, Approach Airspeed, Uniced Tailplane, Pilot Model Command, 0^ = 20° 140 Figure 6.38 Push Over Maneuver, Iced Tailplane, Approach Airspeed, Pilot Model Command, 6f=10* 141 Figure 6.39 Push Over Maneuver, Iced Tailplane, Minimum Airspeed, Pilot Model Command, 6f=10° 142 Figure 6.40 Slow Push Over Maneuver, Iced Tailplane, Minimum Airspeed, Pilot Model Command, ôf=10° 143 Figure 6.41 Push Over Maneuver, Iced Tailplane, Approach Airspeed, Pilot Model Command, 5^=20° 144 Figure 6.42 Push Over Maneuver, 0.4 G, Iced Tailplane, Approach Airspeed, Pilot Model Command, 0^=20° 145 Figure 6.43 Pitch Doublets Maneuver, Approach Airspeed, Uniced Tailplane, Pilot Model Command, 0^=40° 146 Figure 6.44 Pitch Doublets Maneuver, Iced Tailplane, Approach Airspeed, Pilot Model Command, 0f=40° 147 Alt Al cicude :t -2000 Hdg degr - 1 40 Heading (degr -1000 - U O - 120 L 0 T ------1------1------1------1------1------1 I ~ 1 T I I 1 - i - r - r i 1^0 ’ 05 90 75 60 45 30 24 18 12 6 0 seconds before impact 200 V. knots -180 -160 - 140 Ll20 T 1' f I ' I I r I 90 60 seconds before impact Figure 6.45 Vickers Viscount Accident Flight Recorder Data (reprinted from Ref. 1) 148 6.6 Discussion, and Definition of an Alternate Pushover Maneuver The previous analysis of Zero G pushover maneuvers with the iced tailplane showed that, if the tailplane angle-of- attack at the elevator hinge moment break was exceeded, control of the aircraft response was difficult and contributed to a tendency for divergence. If the maneuver was such that 0% was exceeded, there was a strong tendency for a divergent response. This could occur by the controlled aircraft motion or by the elevator position diverging to its maximum positive limit when the a, at the hinge moment break was exceeded, driving the motion to exceed Qt-.sca::- Additionally, it was shown that elevator control capability was always available to prevent departed flight but required proper elevator control input. While significant stick force lightening and the effects of tailplane stall were seen, no full stick force reversals were noted. A potential for false stick force reversal indications was shown for abrupt direct elevator inputs. When the reversible elevator control system was used, the elevator would diverge to its maximum nose down position when the hinge moment break was exceeded during a Zero G pushover. When this occurred, no extremely large stick forces were required to recover it from this position during any maneuver attempted. However, timely recovery inputs were required to prevent departures. 149 Greater flap deflection allowed the aircraft to fly at lower velocities and increased the downwash angle at the tailplane. These factors contributed to the more negative pitch rates and lower values seen during pushover maneuvers started at lower airspeeds. For a given flap deflection, a Aa^ = -2° to -3° decrease was seen when comparing the highest to lowest airspeed Zero G maneuvers. The variation in a. was relatively linear with pitch rate for a given flap deflection. The rate of change ranged from Aa.=0.2° to 0.4° per deg/sec of pitch rate. The incremental change in a. from correlated well with pitch rate. Pitch rate was near or below q=-10°/sec for all Zero G maneuvers. Additionally, it is clear that negative aircraft angle- of-attack and negative pitch rate effectively decrease the tailplane angle-of-attack of any given aircraft configuration and flight condition. Other maneuvers were attempted during the course of this research, but no other maneuver was as effective at accomplishing this as was a pushover maneuver. The specific requirement of the Zero G maneuver of reaching the target load factor at zero pitch attitude does not appear to be critical in generating similar tailplane angle-of- attack. The more critical parameters are airspeed and pitch rate. This suggests that the focus of pushover maneuvers be at the low speed, high power end of the flight envelope. 150 The current operational history of the DHC-6 Twin Otter suggests that flight with a flap deflection of 0^=10° does not show a tendency for ICTS and shows no control difficulties. The Zero G maneuver simulation analysis suggests that the DHC-6 Twin Otter has control difficulties with 5^=10° and, therefore, is susceptible to ICTS at this and all higher flap deflections. This differs with the ICTS susceptibility criteria of the Zero G maneuver, which is indicated by a stick force reversal. These factors suggest that the Zero G maneuver criteria of a stick force reversal is not sensitive enough, and that the criteria of reaching Zero G is overly aggressive. It would be desirable to define a maneuver that did not drive the tailplane angle-of-attack beyond that of the hinge moment break with §£=10°. The analysis of Section 6.5 suggested that load factors greater than n=0.4g would cause this to occur at approach airspeeds with 0j = 20°. The above discussion notes that lower airspeeds result in lower values. Using these factors, pushover maneuvers to n^=0.3g were performed at This was judged to be the lowest practical maneuvering airspeed. A lower airspeed is also desirable to prevent excessive build up of airspeed during the maneuver recovery. The resulting responses are shown in Figures 6.46 and 6.47. With ôf=10°, the response was stable and well controlled. Hinge moment shows no significant reduction 151 during the maneuver, so stick force gradients would remain relatively constant. A load factor of n=0.3g was reached just before the recovery command input. Pitch rate reached approximately q=-10 deg/sec at a load factor of n=0.5g. Tailplane angle-of-attack just reached o^=-8.0°, at the hinge moment break, at n=0.3g. The response shows a divergent tendency when the flap deflection of 6j=20° is used. The divergence starts when load factor goes below n=0.6g and Q!. = -10.5°, below the hinge moment break, which causes the elevator deflection to overshoot and the stick force gradient to be reduced. This occurs as pitch rate exceeds q=-10 deg/sec, which then diverges to q=-19 deg/sec as load factor overshoots the commanded value and reaches n=O.Og. While the maneuver is controlled due to the action of the pilot model, the reduction in hinge moment and the significant overshoots in tailplane angle-of-attack, load factor, and pitch rate, clearly indicate susceptibility to ICTS. The above responses suggest that an ICTS discriminator that distinguishes between 6.=10° and 20° for the DHC-6 Twin Otter is a pushover through n=0.5g at q=-10 deg/sec, with a primary requirement of no significant stick force lightening. Also required are no tendency for a divergent load factor or pitch rate, and positive control of the maneuver. The target airspeed for the maneuver is a low practical maneuvering airspeed of 1. n/scaii- These are more sensitive criteria than the Zero G maneuver. However, they are considered to be 152 necessary to provide an accurate indication of the initial onset of separated tailplane airflow that could lead to an ICTS event. 153 Figure 6.46 Alternate Pushover Maneuver, ôg=10' 154 Figure 6.47 Alternate Pushover Maneuver, ôf=20‘ 155 CHAPTER 7 COMPARISON OF FLIGHT TEST AND SIMULATION RESPONSES Section 6.1 showed time history comparisons used to develop the DHC-6 Twin Otter database. Section 6.2 showed preliminary trim data from flight testing accomplished in September 1995. The maneuver presented in this chapter is from flight testing accomplished in October 1997 in which pushover maneuvers were performed with an iced tailplane. It was chosen because it shows a near tailplane stall. Therefore, the ability of TAILSIM to perform its goal of predicting a tailplane stall can be analyzed. For this maneuver the DHC-6 Twin Otter aircraft was configured with a flap deflection of 6f=20^ and the S&C ice shape on the tailplane. This configuration was shown during flight testing to allow aggressive pushover maneuvers to be performed without causing a full tailplane stall. In order to obtain a good match with flight test, an n^ command profile was generated that resulted in a good match in airspeed as well as ng. This required some "tuning" of the n„ command input, including an approximate 1 second lead. The riz and airspeed comparison time histories are shown in 156 Figures 7.1 through 7.8. Note that flight test data is shown as circles so that dropouts in the data, including the flight test airspeed, do not confuse the plot presentation. The n% and airspeed responses show reasonably good agreement except where a tailplane stall is reached in TAILSIM, which results in an overshoot response. Stick force shows some of the recovery peaks that are seen in the flight test data, but they are delayed. This is because the pilot model reacts to the n^ command error caused by tailplane stall and so cannot provide any lead for the recovery. Qualitatively, however, both the stick force and elevator deflection match do not show good agreement. The other parameters of interest show good agreement, except where the responses show an overshoot. Angle-of- attack shows qualitatively good agreement remaining within Aa=l'. Pitch angle and tailplane angle-of-attack show, qualitatively, very good agreement, maintaining their respective trim mismatches. Note that these trim mismatches may be evidence of possible inaccuracies in the basic lift curve data. Pitch rate shows excellent agreement, except for the overshoot at both positive and negative peaks. Overall, the TAILSIM program agreement with flight test is mixed. Qualitatively, TAILSIM shows overall good agreement with flight test data. The physics of the program seem correct, as represented by the good n^ versus pitch rate comparison. The attitude parameters show good accuracy 157 qualitatively but are not as quantitatively accurate as desired. The evidence presented here suggests that there may be inaccuracies in the basic lift, drag, and moment data of the database. These inaccuracies would contribute to errors in downwash angle, which are also caused by a calculation method that has only first order effects. Additionally, it is clear that the stick, pilot model, and elevator deflection dynamics are not quantitatively as accurate as desired. The match of these parameters can only be described as fair. The more significant question, though, is how well the current TAILSIM program predicts a tailplane stall condition for the aircraft. Flight test notes indicate that control force lightening occurred on this pushover maneuver. The TAILSIM response clearly shows a tailplane hinge moment break and stall break causing an overshoot. Therefore, the TAILSIM prediction is considered to be good but conservative. 158 \ Figure 7.1 Pushover Maneuver n^ Comparison V Figure 7.2 Pushover Maneuver Airspeed Comparison 159 Figure 7.3 Pushover Maneuver Stick Force Comparison Figure 7.4 Pushover Maneuver Elevator Deflection Comparison 160 il Figure 7.5 Pushover Maneuver AOA Time History Comparison Figure 7•6 Pushover Maneuver Tailplane AOA Comparison 161 ^ Figure 7.7 Pushover Maneuver Pitch Angle Comparison % % 3 Figure 7.8 Pushover Maneuver Pitch Rate Comparison 162 CHAPTER 8 TAILPLANE STALL LIMITED MANEUVER CAPABILITY DIAGRAM In the previous work on tailplane stall discussed in the references and earlier chapters, the limits of an aircraft with an ice contaminated tailplane have generally been expressed in terms of a dynamic maneuver. The emphasis has been on defining the specific flight condition of a tailplane stall. However, the analysis presented in previous chapters has shown that an ice contaminated tailplane can cause control problems across a wide range of flight conditions. A way to present the effect of an ice contaminated tailplane across the flight envelope is shown in Figures 8.1 through 8.3. These plots quantify the maneuver margin to tailplane stall by showing the n% at which tailplane stall angle-of-attack is reached. Essentially, this diagram represents the lower left section of a V-n diagram. However, instead of being limited by a this diagram shows the limits caused by an ice contaminated tailplane. To generate the available n^, the TAILSIM trim routine was used to zero the pitching moment with varying pitch rate until <%. stall was reached. To further compare these results 163 CO previous work, available Co Cailplane hinge momenc break angle-of-atCack was also deCermined and is shown in Figure 8.3. Tailplane sCall angle-of-aCCack and hinge momenC break were Che same as shown in Seccion 6.2 and are repeaCed in Figure 8.4. NoCe ChaC, for Che n=lg Crims shown in Chis figure, C-r was noC consCanC buC varied as required up to a maximum value of C.r=0.18. Since n^ varies wich piCch raCe and airspeed, lines of constant pitch rate are also shown. The results show some interesting trends. Figure 8.1 shows the effect of at constant flap setting of 0p.=20°. (Note that all data is for GW=10,000 lbs, at altitude = 7000 ft., for a standard day atmosphere.) With 0^=0.0, the maneuver capability is relatively constant across the airspeed range, while for 0^=0.14 and 0.28 the maneuver capability is shown to decrease with lowering airspeed. The reduction in maneuver capability with increasing power setting is clear. This agrees with the general assessment that lower airspeed and higher power settings are worst case. However, it disagrees with the concept that higher airspeeds do not have as much tailplane stall margin. For this b~=20° configuration, there is enough difference between n=lg trim and stall tailplane angle-of-attack to reach, approximately, a relatively low level of ng=0.3 at high airspeeds. This large maneuver margin can only be reduced by the effects of lower airspeed; increasing downwash and larger decrease in tailplane angle-of-attack due to pitch rate. Additionally, 164 with no power effects, it is seen that there is little change in maneuvering capability across the airspeed range. With no power, downwash effects are not as strong at low airspeeds. Also, this configuration is pitch control power limited and so falls short of tailplane stall angle-of-attack at low airspeeds by as much as àa^=0.6°. Other nonlinearities also contribute to this result, such as, lower lift and less tailplane dynamic pressure from thrust effects. Figure 8.2 shows the effect of flaps at a constant thrust coefficient of 0^=0.14. It is clearly seen that at ôp=40° only marginal maneuvering capability exists at any airspeed. Some margin is available at lower airspeeds, due to an increasing margin in n=lg trim tailplane angle-of- attack, while a small increase in margin is available at higher airspeeds due to the decrease in n=lg trim tailplane stall angle-of-attack. Figure 8.4. The other flap deflections clearly show the dominant effect of increasing downwash with increasing flap deflection. As noted above, the TAILSIM study of Chapter 6 showed that with 0p=20° at nz=0.4 evidence of tailplane stall was noted. Figure 8.1 shows that this level is reached at lower airspeeds. Therefore, this analysis agrees, in general, with the TAILSIM dynamic responses. Control difficulties were also noted in Chapter 6 when the tailplane angle-of-attack of the hinge moment break was exceeded. The maneuvering capability to both of these tailplane angle-of- 165 attack values is shown in Figure 8.3. It is clearly seen that the maneuvering capability to the hinge moment break is different. This is the effect of not having any margin at the higher airspeeds. In this case, the effect of increasing n=lg trim tailplane angle-of-attack margin result in more maneuver margin at lower airspeed. It was noted in Chapter 6 that if tailplane angle-of- attack went below the hinge moment break angle-of-attack, control anomalies were seen. It is clear from Figure 8.3 that almost any pushover with 5j,=20° has the possibility of control anomalies. Also shown in Figure 8.3 are data for ôp=10'. For this configuration, the tailplane stall angle-of- attack is incorrectly indicated as being reached at greater than zero g only at very low airspeeds. Below 8 0 KCAS, the ability to generate negative load factor is limited by the elevator effectiveness, and so tailplane stall angle-of- attack is not reached. However, the hinge moment break is reached and exceeded for any pushover to below, roughly, n2=0.3g. This agrees with the Chapter 6 results that indicated a potential for control difficulties for any non zero flap configurations during Zero G pushovers. This diagram has revealed some useful concepts for the tailplane stall margin considerations of the DHC-6 Twin Otter. If a large tailplane stall margin exists at higher airspeed, it will, most likely, be reduced at lower airspeed. If limited maneuvering capability exists at higher airspeed, 166 it may be increased at lower airspeeds. This means that if tailplane icing is suspected, but no tailplane stall characteristics are noted, going slow is not necessarily safer. If tailplane stall characteristics are seen, going slow may be safer. This maneuvering capability presentation has another benefit. As in a V-n diagram, if an n^ limit is known, it can be applied directly to this plot. This plot presentation will then clearly show the maximum flap and power setting to prevent tailplane stall, and also for a pitch rate limit if set at a given airspeed. This is, in fact, suggested as a method for determining a useable tailplane stall margin with the limits defined based on operational requirements. It is also suggested that maneuver capability characteristics determined from a dynamic analysis be used, and supplemented with this available n, analysis. These results show higher load factor levels than have been shown by TAILSIM or flight test pushover maneuvers, due to the overshoot capability of the dynamic maneuvers. So, while the available n^ can show the limits, a dynamic TAILSIM maneuver can show if these limits can be exceeded. 167 t • ■ • * Figure 8.1 Tailplane Stall Maneuver Capability, Effect of Power, Iced Tailplane Figure 8.2 Tailplane Stall Maneuver Capability, Effect of Flaps, Iced Tailplane 168 Figure 8.3 Tailplane Stall and Hinge Moment Break Maneuver Capability, Effect of Flaps, Iced Tailplane Figure 8.4 TAILSIM Tailplane Trim and Stall Characteristics 169 CHAPTER 9 SUMMARY AND DISCUSSION A method for analyzing the flight dynamics of the DHC-6 Twin Otter aircraft primarily using a specialized nonlinear simulation program has been presented. The primary focus of this analysis has been to determine the effect of an iced tailplane on the response of this aircraft when performing pushover maneuvers. A specialized database based on flight test and wind tunnel test data has been developed to model the aircraft's aerodynamic characteristics. A pilot model and a reversible control system model tailored for this research played critical roles in assessing the effects of tailplane icing. Using the simulation program, pushover maneuvers were performed and the values of key parameters and their effect on the resulting responses have been analyzed. Based on this analysis, an alternate pushover maneuver has been suggested as an Ice Contaminated Tailplane Stall discriminator for the DHC-6 Twin Otter aircraft. Additionally, presenting the effect of tailplane stall on maneuvering capability in the 170 form of a V-n diagram has been shown to help clarify the results of the dynamic analysis. Simplified linear simulation analysis was also performed and provided trends in the effect of some parameters on the aircraft's response. However, simulated pushover maneuvers showed incorrect magnitudes of key parameters. Most of the load factor, tailplane angle-of-attack, and aircraft angle- of-attack values did not agree well with those shown by preliminary flight test data and the nonlinear simulation. The inability of the simplified linear analysis to match the response of the aircraft emphasized the necessity to use nonlinear methods in this research. The nonlinear simulation program developed for this research consisted of a order Runge-Kutta integration of the rigid aircraft equations of motion. The program "core" is generic to any aircraft and only needs to be "driven" by forces and moments determined by a buildup of database coefficient tables. This was accomplished for the DHC-6 Twin Otter aircraft using a specific database and buildup equations that allowed the tailplane to be considered separately. Direct elevator deflection, a reversible elevator control system model, and a pilot model which drove the elevator control system model were used as command inputs to drive the elevator. Modeling methods were developed to incorporate tailplane wind tunnel test data, aircraft flight test data, and empirical estimates into the aircraft 171 database. Other methods were developed to extend this data to a useful angle-of-attack range, beyond that available from flight test. During the course of the database development, specific functions were determined to provide typical thrust/airspeed effects on drag and elevator effectiveness. Zero G pushover maneuvers with the uniced tailplane were performed for all flap deflections. A comparison of preliminary flight test data with 0^=20° showed good agreement. For each flap deflection, ot^ at zero load factor showed similar trends in decreasing with decreasing airspeed and decreasing pitch rate. The incremental change in a. from Of. correlated well with pitch rate. Therefore, at the lowest airspeeds, a. was closer to resulting in less maneuvering capability. This reduced maneuvering capability was also shown in a V-n diagram when the attainable negative load factor was limited by gtaii - Additionally, at trim flight conditions, was shown to decrease with increasing airspeed. Therefore, higher airspeeds resulted in less steady state margin to CK^.staii- This suggests that at all airspeeds, flying the DHC-6 Twin Otter smoothly and with minimum control input is highly desirable. Pushover maneuvers at approach airspeeds and below with the iced tailplane were performed with flap deflections of (5.- = 0°, 10°, 20° and 40°. Use of fixed elevator inputs showed a tendency for divergence with 0^=20° but also showed good control capability. Use of fixed stick force inputs driving 172 Che reversible elevator control model showed that improper use of commanded stick force could cause the aircraft to depart with 0^=10° and above. All of the Zero G pushover maneuvers with non-zero flap deflection showed a tendency for control difficulties when the pilot model was used. The pilot model specifically showed that control was degraded if the angle-of-attack of the tailplane hinge moment break was exceeded. In all cases, a strong tendency for a divergent response resulted if the tailplane stall angle-of-attack was exceeded. In an example illustration of these effects, use of the pilot model resulted in the aircraft being judged to be unflyable with ôf=40°- In this case, the response to small changes in commanded load factor showed slightly unstable, nearly limit cycle, oscillations, which were judged to have qualitatively similar characteristics to those seen in the 1977 Vickers Viscount accident. This was judged to be a significant result that added validity to the chosen method of analysis. These simulation responses suggest that the DHC-6 Twin Otter has control difficulties and is susceptible to ICTS at all non-zero flap deflections. However, no stick force reversal was seen during any Zero G maneuver, only stick force lightening. This differs with the ICTS susceptibility criteria of the Zero G maneuver which is indicated by a stick force reversal. Because the current operational assessment 173 of the DHC-6 Twin Otter suggests that flight with a flap deflection of 5f=10° does not show a tendency for ICTS, and also shows no control difficulties, an alternate pushover maneuver was suggested. Simulation responses with the pilot model were used to define a pushover maneuver that resulted in responses with ô.=10^ not indicating a susceptibility to ICTS. This alternate pushover maneuver was defined by a pushover through a load factor of n=0.5g at q=-10 deg/sec pitch rate and an airspeed of 1. . The primary success criteria was no significant stick force lightening. Also required were no tendency for a divergent load factor or pitch rate, and positive control of the maneuver. This is a more qualitative and conservative criteria than the current Zero G pushover maneuver, requiring more pilot sensitivity to control force, and suggesting that any stick force lightening is cause for concern. A comparison of TAILSIM and flight test responses showed that TAILSIM compared favorably but was conservative in predicting tailplane stall during a pushover maneuver. More comparisons are desirable, however, this comparison with the S&C ice shape on the tailplane suggests that the TAILSIM analysis of this research effort has merit. While the simulation results and alternate pushover maneuver may be more sensitive, it appears that the Zero G pushover maneuver is too aggressive. Further time history comparisons and an 174 assessment of the accuracy of the TAILSIM database would help to quantify this assessment. It should also be noted, that, this research suggests that ICTS is composed of two distinct stability and control problems. One is inadequate flying qualities if the tailplane angle-of-attack exceeds that of the hinge moment break, due to the rapidly varying elevator hinge moment characteristics. The other is inadequate stability or an unstable aircraft, when the tailplane is near stalling angle- of-attack, due to the reduction in CLca- The DHC-6 Twin Otter data showed these characteristics separately due to the approximately Aa^=2° difference between them. As tailplane characteristics are different on different aircraft, the responses leading to an ICTS event will vary. Clearly, if more exists, there will be an earlier indication of a problem. If less or no Aoc^ exists, an ICTS event could occur with little warning to the pilot and quickly become unrecoverable. 175 C H A P T E R 1 0 CONCLUSIONS AND RECOMMENDATIONS The significant conclusions from this study of the flight dynamics and aerodynamics of the DHC-6 Twin Otter with an ice contaminated tailplane are as follows; - Two distinct stability and control problems were noted by this research; inadequate flying qualities if the tailplane angle-of-attack exceeds that of the hinge moment break, which causes significant changes in stick force gradients, and reduced stability when the tailplane angle-of- attack is near the stall angle-of-attack. - For the DHC-6 Twin Otter, the Zero G maneuver was found to be unnecessarily aggressive, and using the indication of a stick force reversal as the primary susceptibility criteria could occur too late to prevent a divergence due to a tailplane stall. - A better discriminator of susceptibility to ICTS for the DHC-6 Twin Otter aircraft was determined to be a low speed, pushover to n=0.5g at q=-10 deg/sec with success criteria of no significant stick force lightening. 176 Additionally, no tendency for a divergent load factor or pitch rate, and positive control of the maneuver, were required. - The most negative tailplane angle-of-attack occurred during pushover maneuvers at the lowest airspeeds, highest power settings, and largest flap deflections. The most negative trim tailplane angle-of-attack occurred at the highest airspeeds and largest flap deflections. The most important pilot actions if an ice contaminated tailplane is suspected are to not lower the flaps and fly smoothly with minimal load factor excursions. - Use of the nonlinear simulation program, TAILSIM, as a research tool provided improved fidelity and greater insight into key issues of the ICTS phenomenon. TAILSIM was shown to be close but, conservative in determining the flight conditions at which a tailplane stall would occur during a pushover maneuver. The pilot model and reversible control system model provided important contributions to the insight provided by this research. - A database generated from flight test and wind tunnel test data with separate wing/body and tailplane data is required to analyze ICTS and contributed to the good results generated by this study. The development and use of this database is considered to be a novel result of this research. 177 - The use of a V-n diagram limited by tailplane stall was shown to provide a clear presentation of the maneuvering limitations/capability caused by tailplane stall, supported the simulation analysis, and is considered to be a novel result of this research. The pilot model used in this research is of a standard form. However, pilot gains can vary, and could alter the resulting recovery response to an ICTS event. It is clear that a reversible elevator control model and pilot model are required to simulate the control problems associated with typical hinge moment variations with an iced tailplane. Further study of pilot models oriented to the control of highly dynamic maneuvering flight is warranted to determine how pilot responses to the stick force lightening seen in this research can affect the assessment of sensitivity to ICTS. In conjunction with this study, a sensitivity analysis of the angle-of-attack of the hinge moment and stall breaks, as well as the strengths of each break, should be accomplished. A goal of this effort might be to determine a maximum change in stick force gradient and stall break that could be adequately controlled by a typical pilot. Results of this effort might also be used to determine tailplane design parameters. The analysis methods developed for this research are judged to be effective. However, for continuation of this 178 study, improvements are desired. The nonlinear aircraft simulation program developed for this research is judged to accurately implement the aircraft equations of motion. The program showed good convergence properties and matched example flight test time histories well. However, any numerical integration is always an approximation, and a rigorous assessment of the program accuracy was not accomplished. The 4th order Runge-Kutta integration method was implemented straightforwardly in single precision, as it was considered to provide acceptable accuracy. For further use of this simulation program, a sensitivity study on the integration scheme would be desirable. Implementation of double precision and an advanced predictor-corrector integration method are suggested to determine if the simulation accuracy can be improved. This would be especially important if longer time histories, such as for a piloted simulation, were desired. The numerical integration accuracy is a consideration in the overall program accuracy, however, it is judged that the most significant factor in the accuracy of the simulation is the database and force and moment build-up equations. The important results of this research are dependent on the specific characteristics of the database. Limitations to the available data prevented the database from being as accurate as desired. Additionally, the comparison pushover maneuvers suggest that the database may contain inaccuracies in the 179 basic aircraft coefficients. It would be desirable to have a complete aircraft database obtained from wind tunnel testing over the range of angle-of-attack seen during Zero G pushover maneuvers. A critical requirement of this testing would be the determination of power effects on downwash angle and other aircraft characteristics. A sensitivity study on the terms of the database with simulation comparison to flight test is suggested to provide a focus on the accuracy requirements of the database. The unused terms of the parameter estimation coefficient equations could also be included to determine if their effect was, indeed, not significant. This database study would also support results of the numeric study by showing the relative importance of the numerical integration accuracy versus the database accuracy. Presentation of the aircraft and pilot control system characteristics in terms of typical control system parameters was not accomplished in order to emphasize the use of the nonlinear simulation program. This would be desirable for further use of the simulation to provide an assessment of the aircraft and pilot control system in terms of more quantifiable parameters. It would also provide insight on pilot control characteristics. An extension of this study should include further study of aerodynamic lift and hysteresis during dynamic maneuvers to more accurately quantify divergent responses. Finally, 180 there are many other studies that could be suggested. While this research effort has improved the understanding of the aerodynamics and aircraft dynamics of the ice contaminated tailplane stall, the TAILSIM program has the flexibility to continue to generate insights into a variety of issues related to the ICTS phenomenon. 181 LIST OF REFERENCES 1. Trunov, O.K., and Ingleman-Sundberg, M. , "On the Problem of Horizontal Tail Stall Due to Ice", Report No. JR-3, The Swedish-Soviet Working Group on Scientific-Technical Cooperation in the Field of Flight Safety, 1985. 2. Manningham, , "Tails of Woe", Business and Commercial Aviation, January, 1993. 3. Horne, T.A., "Tailplane Icing," AGFA Pilot, March, 1994. 4. NASA/FAA/OSU Tailplane Icing Program Planning Meeting, May 2-3, 1994. 5. Trunov, O.K., Ivaniko, A., and Ingleman-Sundberg, M . , "Methods for Prediction of the Influence of Ice on Aircraft Flying Characteristics", Report No. JR-1, The Swedish-Soviet Working Group on Scientific-Technical Cooperation in the Field of Flight Safety, 1977. 6 . Trunov, O.K., and Ingleman-Sundberg, M. , "Wind Tunnel Investigation of the Hazardous Tail Stall Due to Icing", Report No. JR-2, The Swedish-Soviet Working Group on Scientific-Technical Cooperation in the Field of Flight Safety, 1979. 7. Ratvasky, T. P. and Ranaudo, R. J ., "Icing Effects on Aircraft Stability and Control Determined from Flight Data," AIAA-93-0398, 31st Aerospace Sciences Meeting and Exhibit, January 11-14, 1993. 8 . Karlsen, L.K. and Solberg, A., "Digital Simulation of Aircraft Longitudinal Motions with Tailplane Icing", KTH Aero Report 55, Royal Institute of Technology, Stockholm, Sweden, Department of Aeronautics, December 20, 1983. 9. Hellsten, Pete, "Aerodynamic Analysis of Susceptibility to Ice-Induced Tailplane Stall," International Tailplane Icing Workshop II, April 21-23, 1993. 10. Federal Aviation Administration Memorandum, From: Manager, Transport Airplane Directorate, Aircraft 182 Certification Service, ANM-100, Subject: Recommended Method of Identification, Susceptibility to Ice Contaminated Tailplane Stall. 11. Roskam, Jan, Airplane Flight Dynamics and Automatic Flight Controls, Roskam Aviation and Engineering Corporation, 1979. 12. Etkin, Bernard, Dynamics of Atmospheric Flight, John Wiley Sc Sons, Inc., 1972. 13. Hoak, D. E. and Ellison, D. E. et al,, "USAF Stability and Control Datcom," 1968 Edition, Flight Control Division, Air Force Flight Dynamics Laboratory, Wright Patterson Air Force Base, Ohio. 14. Abott, I. H. and VonDoenhoff, A. E . , Theory of Wing Sections, Dover Publications, Inc., 1949. 15. Hiltner, D. and La Noe, K. et al., "DHC-6 Twin Otter Tailplane Airfoil Section Testing in The Ohio State University 7X10 Wind Tunnel," unpublished. 16. ADS-4 report "Engineering Summary of Airframe Icing Technical Data", General Dynamics/Convair. 17. Dommasch, D . , Sherby S., and Connolloy, T., Airplane Aerodynamics, Fourth Edition, Pitman Publishing Corporation, 1967. 18. Nicolai, Leland M . , Fundamentals of Aircraft Design, 1975 . 19. Perkins, Courtland. D ., and Hage, Robert. E ., Airplane Performance Stability and Control, John Wiley and Sons, Inc., 1949 . 20. Decker, James L ., "Prediction of Downwash at Various Angles-of-Attack for Arbitrary Tail Locations," Aeronautical Engineering Review, August, 1956. 21. McRuer, Duane, Ashkenas, Irving and Graham, Dunstan, Aircraft Dynamics and Automatic Control, Princeton University Press, 1973. 22. McLean, Donald, Automatic Flight Control Systems, Prentice Hall, 1990. 23. Thomas, R. W. "An Investigation of the Impact of Aerodynamic Lags on Dynamic Flight Characteristics," AIAA-81- 183 1892, August 21, 1981, AIAA Atmospheric Flight Mechanics Conference. 24. Van der Vart, J. C . , "Effects of Aerodynamic Lags on Aircraft Responses," AGARD CP-386, 1985 pp. 33-1-33-11. 25. Bisplinghoff, Raymond L. and Ashley, Holt, Principles of Aeroelasticity, Dover Publications, Inc., 1962. 26. Dowell, Earl H. , Curtiss, Howard C. Jr., Scanlan, Robert H. and Sisto Fernando, A Modern Course in Aeroelasticity, Kluwer Academic Publishers, 1989. 27. Montgomerie B ., "Dynamic Stall Model Called Simple," Report Number ECN-C-- 95 - 060, Commission of the European Communities. 28. MacFarlane, A.G.J., Dynamic System Models, George G . Harrap & Co. LTD, 1970. 184 APPENDIX A. DHC-6 TWIN OTTER FLIGHT TEST COEFFICIENTS AND DERIVATIVES 185 ♦ ♦ » T ■ â •• r • Figure À.l Cjq, All Flight Test Configurations • t • ♦ ■ ^ *•** Figure A.2 Cz„, All Flight Test Configurations 186 ... t " - ♦ *. Figure A. 3 0^^,, All Flight Test Configurations ♦ T M 4 * T . • Figure A. 4 C^q, All Flight Test Configurations 187 A Figure A. 5 C^q, All Flight Test Configurations A ■ Figure A. 6 Cy^, All Flight Test Configurations 188 V : Figure A.7 C^ 2 > All Flight Test Configurations #- -♦ • *7 :#* • - V%. - .* V ▼ ' % ▼ T Figure A. 8 Cx^,, All Flight Test Configurations 189 ♦ Figure A. 9 C^a/ All Flight Test Configurations -t- * J." Figure A. 10 0^6,, All Flight Test Configurations 190 •t O T ^ ^ \ ♦* Figure A.11 C^, Ail Flight Test Configurations 191 APPENDIX B. DHC-6 TWIN OTTER AIRCRAFT MODEL DATABASE COEFFICIENTS AND DERIVATIVES 192 Figure B.l Cn,, 0^=0 . 0, Figure B.2 C^o, 0^= 0.07 193 Figure B.3 C^o/ 0^=0 .14 - Figure B . 4 194 ri- Figure B.5 CZfie Figure B.6 CZq 195 Figure B.7 Cg, Drag Polar, 0^=0.0 r Figure B.8 Cg, Drag Polar, 0^=0.07 196 -I: Figure B.9 Cg, Drag Polar, 0^=0.14 Figure B.IO Calculation, Term 197 Figure B.ll Cdq Calculation Terms .SB Figure B.12 Cj, 198 Figure B.13 CX àe f Figure B.14 C^, C^=0.0 199 a ■ t f. f. Figure B.15 C ^ , C^=0.07 Figure B.16 Cwa, C,= 0 .14 200 K -& O' O' ô -O Q. -O -O" O0OOOOÔOOÔO€ Figure B.17 C^aa, 0^=0 . 0 >- O O G- O 0---Ô' 0- 0- o- Figure B.18 C^s^, 0^=0 . 07 201 - Q — 4^ _e 43- Figure B.19 0^^»' 0^=0 .14 Figure B.2 0 C„q, 0^=0 .0 202 -£• -3- -3- -5- Figure B.21 Cj^, 0^=0 . 07 Figure B.22 C^q, 0^=0.14 203 ». o Ô ^ S r - & V » Figure B.23 6*,trim/ Ct=0.0, Uniced Tailplane Figure B.24 6,,trim/ 0^=0.07, Uniced Tailplane 204 Figure B.25 6,,„im/ 0^=0.14, Uniced Tailplane ► Ô Ô '^*4. , - : .- T Figure B.2 6 6,,crim/ 0^=0.0, Iced Tailplane 205 Figure B.27 0^=0.07, Iced Tailplane f ^ 5['»‘ * - » 'S, Figure B.2 8 ôe.trim/ Ct=0.14, Iced Tailplane 206 ë -e-‘ 9- e- * Figure B.2 9 17^/ 0^=0.0 Figure B.3 0 17^/ 0^=0.07 207 3 -U: * à i * Figure B.31 r]^, 0^=0 .14 Figure B.32 C^„t' 0^=0 . 0 208 _ : ■ ■ ■ ■ i- ■ Figure B.3 3 t/ 0^=0 . 07 f!-?-* a.a Figure B.34 Cj 0^=0 .14 209 Figure B.35 C^-t/ 0^=0 . 0 Figure B.36 C^qt# Ct=0.07 2 1 0 Figure B.37 C^^t/ Cy=0 .14 % I - T ■;/ Figure B.3 8 0^^^' Ct=0.0 2 1 1 t 'T : Figure B.3 9 0^=0 . 07 r - ï~- ■ ■■ ■ ■ Figure B.40 C^t' 0^=0.14 2 1 2 <• • Figure B.41 C^t/ ^^=0 . 0 Figure B.42 Cj^t/ 0^=0 .07 213 ■ a ■ Figure B.43 C^t' Ct=0.14 214 APPENDIX C. DHC-6 TWIN OTTER TAILPLANE DATABASE COEFFICIENTS 215 Figure C.l 0%%, Uniced Figure C.2 Iced 216 *• * f ^ . Figure C.3 0%%, Uniced Figure C.4 0%%, Iced 217 :r-‘ Figure C.5 Uniced Figure C.6 0%%, Iced 218 r t y T -r y > T . " -'T:- Figure C.7 Coe Uniced A AO * Figure C.8 Cg», Iced 219 Figure C.9 Cut/ Uniced Figure C.IO C„t/ Iced 2 2 0 * fiTï f f Y - Figure C.ll Cgc, Uniced r r T ! r Figure C.12 Cgt, Iced 2 2 1 APPENDIX D. AIRFOIL TO TAILPLANE CORRECTION CONSTANTS Baseline Lift Correction. Constants 5 *Cr^Lcmax a Range OfRange Linear Fairing -26 . 6 0.0527 1 . 10 1 . 00 -12/4 4/8 -20 . 0 0.0547 1 . 10 1 . 00 -12/8 -4/8 -10.0 0.0621 1.10 1 . 00 -15/4 -8/4 0 . 0 0.0797 1 . 04 1.03 -15/4 -8/0 10 . 0 0.0960 0 . 99 1.00 -12/4 -8/0 14 . 2 0.0917 0 . 99 1.00 -12/4 -8/0 LEWICE Lift Correction Constants 5 Cic. *c^Ltmax a Range a Range Linear Fairing -26 . 6 0.0618 1 . 10 1.00 -2/4 0/4 -20 . 0 0.0673 1 . 10 1.00 -2/8 0/4 -10.0 0.0767 1 . 10 1 . 00 -4/4 -3/0 0 . 0 0 . 0831 1 . 04 1 . 03 -6/4 -4/0 10 . 0 0.0916 0 . 99 1 .00 -8/0 -4/-4 14 . 2 0.0877 0 . 99 1 .00 -8/0 -4/-4 Notes : 1 . Cica is 1/deg. 2 . *(],._ and *Crrmax are correction scale factors to account for the small chord flap effects. 3 . a Range Linear gives the lower and upper a (deg) used to determine the lift curve slope a Range Fairing gives the minimum and maximum a (deg) beyond which the data was fared to the C^cmax point. Aa at Cr = 1.0 (Reference 13 correction) 2 2 2 àce at C^tmax = -0.6 (short chord elevator correction) e = G . 9 Baseline Hinge Moment Correction Constants •26.6 -0.00352 -0.00442 0.0531 20.0 -0.00280 -0.00476 0.0449 10.0 -0.00334 -0.00089 0.0529 0.0 -0.00278 -0.00656 0.0097 10.0 -0.00232 -0.00408 0.0613 14.2 -0.00162 -0.00127 0.0659 LEWICE Hinge Moment Correction Constants ^ ^hca ^ht6 26.6 -0.00211 -0.00427 0.0473 20.0 -0.00535 -0.00462 0.0427 10.0 -0.01200 -0.00292 0.0517 0.0 -0.00936 -0.00442 0.0161 10.0 -0.00230 -0.00392 0.0518 14.2 -0.00378 -0.00285 0.0643 Notes: 1. Scaling factors for forward/aft hinge line area consideration, 0.89*C^^, 0.93*C^^. 2. Other Required Constants = 0.01 = 0.0145 Bj = 1.16 = Kj = 1.0 223 APPENDIX E. DOWNWASH CALCULATION To estimate downwash, References 13, 17, 18, 19, and 20 were consulted. Method 1 from [13] is taken from [18] which also provides additional guidance for performing the method properly. For this method, wing characteristics are required. The complete aircraft lift coefficient described in Section 3.4 was the best source to use in determining wing lift. This lift coefficient was available for all required angle-of-attack and flap deflections. This aircraft was corrected for fuselage and propeller normal force, as well as tailplane C, . As a first order estimate, it was judged that using a 17, = 1.0 was adequate. Reference [13] was used to estimate linear fuselage lift, and [13,17,35] were used to estimate propeller C„p. The values calculated were. Fuselage = 0.396*a (1/rad) Propeller C^p = 0 . 1 0 * q; (1/rad) These first order effects were considered to be the most consistent to apply to the complete aircraft lift. Method 1 of [13] is straight forward and is also described by an example which is tabulated on page 4.4.1-15 224 of [13] . This reference should be consulted for a description of the parameters. The required parameters and the equations used are as follows; A = = 10.0 b = bgff = 65 . 0 1. = 20.37 ft le,f = 25.30 h^ = 2.68 \ = 1.0 Ac,. 4 = 0.0 r = 3.0°, wing dihedral = 0.085 (1/deg) e = 0.9, T = 0.225 Using these parameter values and the information from Section 4.4.1 of [13] , the following calculated parameters are found, (de/da)* = 0.31 = 2.0*57.3*C^/(nA) (de/da)., = 0.3 8 Downwash is then calculate by determining de/do; and integrating over the a range, starting at • This requires the following equations, with trailing edge separation assumed, 225 de/da = ( 1/( 1 + (2a/b^)“ )*(de/do!)^ with a = h„ - leff* ( 01 ~ 0.41*C^^^/(nA) ) - beff/2 , 0*tanr K = - ( beff - b ^ )*( 2 . (b^^) b.,^ = ( 0.78 + 0.1* ( -0.41) ) *b^ff ^ru = 0.56*A/Cl To determine the required coefficients, only two Figures in [13] needed to be accessed. Agjf/A and b^f^/b was obtained from Figure 4.4.1-66. Because the Twin Otter has no sweep or taper, these ratios were taken to be unity. This greatly simplified the calculations, as further access of this Figure was unnecessary. Another important parameter, (de/da)V/ was obtained from Figure 4.4.1-67. The aspect ratio of 10 of the Twin Otter was at the limit of the plots. Fortunately, the (de/da) ^ = 0.31, obtained from the wing characteristics, was seen to be the proper value at this plot limit. Also, because Agff=A, this figure needed to be accessed only once, again greatly simplifying the process. With the required equations and calculations defined, a program was then used to iterate on Cl„ to find the AOA at zero wing lift. A process was then programmed to increment a from this value, and then iteratively determine downwash and C^w. This was done to build up downwash in the positive and negative directions. The range chosen for this data was 226 QL=+/- 16"^ as the method is not valid in the post stall range. The increment in downwash angle for deflected flaps is also calculated from [13] using Section 4.4.1. The method is strictly empirical and based on Figure 4.4.1-72 of [13]. A slotted flap is assumed. The increment is found by, 6 = 22.3ACl/( A( bf/(b/2.0) ) ) or e = 5.18* The factor of 22.3 is the output of the plot of Figure 4.4.1- 72. The other required parameter values were as follows, A = 10.0 b = 65.0 ft hf = 14.0 ft, flap 1/2 span h„ = 2.68 ft, tailplane height above root chord plane For this calculation Cl„ with zero flap deflection was calculated as noted above. A similar iterative process was then programmed to determine and downwash angle with flap deflection using the above equations. The incremental downwash angle due to power effects were determined from [13] Section 4.6.3. The method used is empirical and based on Figure 4.6.3-15 of [13] . To implement 227 this figure, the curve as a function of 6po„er off versus S„T'c/(8Rp“) , per engine, was implemented in a table. The output of the table ranged from 0 to 1 .0 , so the e for flaps 0° could be determined by multiplying this output by one value obtained from the 2^^/ (2Rp) input to the Figure. That is, with (SEDPWR) the table output, fp.flaps 0 = (SEDPWR) *9.9, A sightly different scaling and equation was needed for the non-zero flaps cases. This resulted in, E p. flaps none = (SEDPWR) * 8 . 78 - 0.88 This equation became active at flaps 10° and varied linearly from the flaps 0° value. This table and equation implementation was necessary for programming the calculations, as £power off varied with a and flap deflection. To use the aircraft thrust coefficients, a conversion factor was necessary. The aircraft database uses, C, = T/ (pn^D") while [13] uses, T\ = T/(qSJ 228 Using these coefficients at matching thrust, gives, S.„T',7 (8Rp") = n^D^C^/V^ = 65025C7V^ The density factor has been removed, but a velocity factor remains. Other required parameters are, with the assumption that the thrust line is parallel to the fuselage x-axis reference line, S„ = 420 ft^ n = 30 rev/sec D = 8.5 ft, propeller diameter Rp = 4.2 5 ft z.„.^ = 0.88 ft This table and set of equations was programmed directly into the simulation program and any program used to calculate coefficients. Due to this dependence on velocity, care must be taken when examining coefficients in detail. 229 APPENDIX F. EQUATIONS OF MOTION, OUTPUTS, AND RUNGE-KUTTA INTEGRATION Longitudinal Equations of Motion Ü = -qw + rv - gsiniQ) + X{x,ô) w = -pv + qu + geos(0) cos (4)) + Z{x,à) q = pr {I„ - I^^)/Iyy + Mix.b) Lateral/Directional Equations of Motion p = P'J^^xx ^ xy* ^ zz^ -rgz ( ^zz ^xz'l L ' [ X Ô) ^xx^zz ~ ^xz f = ^ xz~^ ^ XX ^xx^yy^ ^ xx^ ^yy ^ zz ^xx^ N'{X Ô ) ^ xx ^ zz ~ ^ X X V = -ru + p w + geos (6 )sin((t)) + Y{x,b) 230 Euler Angle Races (j) = p + p s i /7 ((j)) can (0) + rcos ((J)) Can (0) 0 = pcos(4)) - rsin((j)) = ( qsiniQ) + rcos(^) )/cos(0) Euler Angle Trans forma cions X - ucos ((J))cos((j;) + v( sin(cj))sin(0 )cos(il;) -cos (({)) si n (ij;) ) + w{ c o s {({)) sin (0 ) cos (ij;)+sin ((})) s i n (v|;) ) ÿ = ucos (4>) sin(ij;) + v{ sin(#)sin(0 ) sin(^)-cos (^)soc(^) ) ^ w{ cos (<|)) cos (0 ) sin(i|;)-sin((J)) co s (i|f) ) z = -usinid) + vsin((j)) cos (0 ) + wcos(^) cos (0 ) 231 Auxiliary Relacions a = can'^ ( w/ u) (3 = sin'- ( v/ V) Y = s i n ' i { x / V^) = ( -w + gu - p v + geos ((})) c o s (0 ) ) /g = { Ù -rv + g v + gsin {vCheCa) ) /g = ( V - pw + ru - gcosiQ) s i n ((J)) ) /g a = wcos (a) - L/sin (a) Vcos(P) o ^ V - sin(P) [ ÙCOS (P) cos (g) - vsin ( P ) + wcos(P)sin(a) ] V c o s (p) 232 4""^ Order Runge-Kutta Integration With, dy/dt = f(y,t) then, y.., = y, + dt [ l/6f(y,,tj + 1/3 E 1/2, + ]L/3E , ti.1/2) + l/6 E(y\^i,ti,J ] where, y\-:/2 = Yi + dt/ 2 E ( y , , t j y'%.:/2 = Y: + dt/2E(y\.,/2,t,.,/2] 233 IMAGE EVALUATION TEST TARGET (Q A -3 ) // A % 1.0 im u lài 2.2 Ï: c 2.0 1.1 1.8 1.25 1.4 1.6 150mm V cP7 /APPLIED A IM7IGE . 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