NASA Contractor Report 145281
Expansion of Flight Simulator Capability for Study and Solution of Aircraft Directional Control Problems on Runways — Appendixes
J. A. McGowan McDonnell Douglas Corporation Douglas Aircraft Company
CONTRACT NAS1-13981 JANUARY 1978
NASA National Aeronautics and Space Administration
Langley Research Center Hampton, Virginia 23665 NASA CR-145281 EXPANSION OF FLIGHT SIMULATOR CAPABILITY FOR STUDY AND SOLUTION OF AIRCRAFT DIRECTIONAL CONTROL PROBLEMS ON RUNWAYS
APPENDIXES
20 JANUARY 1978
PREPARED UNDER CONTRACT NO. NAST-13981
FOR
NASA
LANGLEY RESEARCH CENTER NATIONAL AERONAUTICS AND SPACE ADMINISTRATION LANGLEY STATION, HAMPTON, VIRGINIA
MCDONNELL DOUGLAS CORPORATION DOUGLAS AIRCRAFT COMPANY LONG BEACH, CALIFORNIA o
\
o TABLE OF CONTENTS
PAGE
CONVERSION FACTORS ~"iv"
INTRODUCTION 1
APPENDIX A - Aircraft Simulation 2
Section 1 - Basic Airframe Equations of Motion 7 Section 2 - Aerodynamic and Control System Models 23 Section 3 - Engine Model 75 Section 4 _ Environmental Models 79 Section 5 - Struts Subroutine Implementation Notes 85 Section 6 - Auxiliary Equations Ill
APPENDIX B - Software Antiskid 122
APPENDIX C - Analog/Hardware Antiskid 125
Section 1 - Introduction , 125 - Section 2 - Model Derivation 127 Section 3 - Program 156 Section 4 - Hardware 161 Section 5 - Analog Antiskid Simulator Validation 203
APPENDIX D - Cockpit Simulator 209
APPENDIX E - Programming Considerations 216
REFERENCES 219
iii CONVERSION FACTORS
The following table gives conversion factors from the English system to SI units for those quantities used in this report.
The sign and first two digits of each numerical entry represent a power of 10.
TO CONVERT FROM TO MULTIPLY BY
Fahrenheit (temperature) Celsius tc- (5/9) (tf-32) Foot Meter -01 3.048 Inch Meter -02 2.54 Knot (international) Meter/Second -01 5.144 444 Mile (U.S. Statue) Meter +03 1.609 344 Mile (U.S. Nautical) Meter +03 1.852 Pound Force (Ibf avoirdupois) Newton +00 4.448 222 Slug Kilograms +01 1.459 390 Foot/Second2 Meter/Second2 -01 3.048 Free Fall, Standard (g's) Meter/Second2 +00 9.806 65 Foot2 Meter2 -02 9.290 304 Ibf/Foot2 Newton/Meter2 +01 4.788 026 psi(lbf/Inch2) Newton/Meter2 +03 6.894 757 Foot/second Meter/Second -01 3.048
The foregoing values were taken from Reference 11. Some of the values were rounded to six digits after the decimal point.
iv INTRODUCTION
The intention of this report is to present the models used implementing the
DC-9-10 aircraft simulation for the Runway Direction Control study. The study was done on the Douglas Aircraft six-degree-of-freedom motion simulator at
Long Beach.
The approach taken in documenting the models has been to describe them in algebraic form, to the extent possible. Furthermore, the effort has been directed toward presenting what was actually done rather than general forms.
The following Douglas personnel contributed to this report: P. L. Jernigan and R. E. Adams of the Systems Simulation group; G. W. Kibbee, R. A. Storley and R. P. Schiltz of Hydro-Mechanical group; and E. F. Admiral of Avionics group. APPENDIX A AIRCRAFT SIMULATION
The DC-9-10 aircraft was simulated using math models derived from information supplied by Aero Stability and Control, Power Plant and Hydro-Mechanical Controls groups. The supplied data was combined with classical kinematic and transformation equations to form the airframe model. The calculation flow of the airframe model is shown in Figure 1.
In developing the model it was assumed that the flight envelope would be in the low speed (mach 0-.3) and low altitude (0-500 feet) region. Also, since the runs were to be short (i.e., approach, landing and roll out), the aircraft weight was assumed to be constant and the C.G. position fixed at 25% MAC.
Three basic axes systems are used to represent the relative motions and orientations of the aircraft. The inertial system (called earth axes) has its origin at the "touchdown" point of the runway (see Figure 2). For the ground handling simulation the touchdown point was choosen to be 1000 feet in from the threshold. Another axes system called the Aircraft Body Axes System has its origin at the C.G. of the aircraft. (See Figure 3.) The sign conventions for these axes systems are as follows:
X body axis velocity positive forward X earth axis velocity positive toward runway and position positive beyond touchdown point Y body axis velocity positive to right Y earth axis velocity positive to the right and position positive to the right Z body axis velocity positive down (negative up) Z earth axis velocity negative up and position negative above ground.
A third axes system used is called the Stability Axes. This system is closely related to the body axes system but is aligned with the longitudinal wind vector rather than the body of the aircraft. The stability axes are used in defining most of the aerodynamic data. Validation of the aircraft simulation was accomplished in three phases. First, the individual sections (aero, engine, etc.) were checked to see that they were statically correct. Secondly, to the extent possible, the various models were checked dynamically using inputs which produce transient responses. These responses, recorded as time histories, were then compared with expected responses. Where direct time histories were not available comparative parameters such as frequency and time to damp were used.
The third phase of validation was to have test pilots familiar with the DC-9-10 aircraft "fly" the simulator through various maneuvers. Their comments were used to adjust some parameters to improve the "feel" of the simulation.
The data collected during some of the validation runs and the associated comparative data is part of the file of rolled charts and is labeled Validation Data.
For convenience the description of the aircraft simulation has been divided into six sections. Sections 1 and 2 cover aerodynamics and equations of motion; Section 3 describes the engine model used; Section 4 explains the environmental model (winds, and runway conditions); Section 5 covers the landing gear but does not include the antiskid system which is described in Appendices B and C; and Section 6 picks up other programs such as instrument drives, motion drives, visual system drives, etc. s-- o
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6 . Section 1 Basic Airframe Equations of Motion
The calculations covered in the Equations of Motion (EOM) are those which form the six independent variables of the airframe system and preform the appropriate axes transformations between the three axes systems used. Basically these equations are those needed to describe the motions of any rigid body. The derivations of these equations are covered in almost any text on aerodynamics or rigid body dynamics. Looking at Figure 1, this section covers all the boxes enclosed by the dashed line.
The associated equations for the EOM boxes are shown in Figures 1.1 - 1.9. Table 1.1 has descriptions of all the symbols used.
The EOM used for the Ground Handling Simulation are essentially the same for any aircraft using the same axes systems. The documentation of the equations should be fairly self sufficient, however, there are a few things that might be mentioned.
The 57.3 and 1/57.3 factors show up because it was desired to have the angular state variables in units of degrees rather than radians. The method employed is to assume the angles to be in degrees and convert them back to radians for summation into the force and moment equations. The results of the summations are then converted back to degrees!
In Figure 1.4 the 1/1.69 factor in the Ve equation is the ratio of knots to feet per sec. It is more convenient to have Ve in units of knots.
The fact that weight and C.G. position were constant in this simulation meant that mass, moments of inertia, and the lever arms only had to be calculated once at initialization and remained constant during real time runs. These EOM are designed to handle winds and wind shears, i.e., time-rate-of-change of wind speed and/or direction. This is accomplished by first defining the wind profile in the inertial (earth) axes system. The steady state part of the wind components are then summed directly onto the inertial velocities. The time-rate- of -change parts are transformed to the body axes and summed directly into the force equations. (See Figures 1.1 and 1.7). This method allows a very versatile representation of 'the wind conditions without sacrificing the true inertial effects of a changing wind vector on the aircraft dynamics.
It should be noted that although a transformation matrix (direction cosines) is defined, and its elements are mentioned, the EOM program uses no matrix type operations. Using the individual matrix elements streamlines the calculations by eliminating any operation where the result would be zero anyway, e.g., the gravity vector transformation into the body axes.
Validation of the EGM program consisted mainly of checking to see that the proper parameters were entered for the DC-9-10. Further tests and check runs were not made on the EQM themselves for two reasons. First, this program has been used, in almost the same form, for numerous other transport type airframe simulations. Since the changes to the EOM for the DC-9-10 were minor it was felt that any more extensive checking would not be productive. Second, and foremost, the EOM are an integral part of the whole dynamic airframe simulation. For this reason it was felt that it would be more cost effective to validate the system as a whole and only do a detailed check if it was indicated. (Which, as it turned out, it was not.) •
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22 ' Section 2 Aerodynamic and Control System Jlodels
This section contains descriptions of the Pilot Controls and Aero Forces and Moments algorithms. The information is presented in two parts. The first part is called Pilot Control Inputs to Aero Equations and the second is called Aerodynamic Equations.
The primary source for the data and algorithms used in this section is the Douglas Aircraft Estimated Data for Stability and Control. (Reference 6),
The references cited in the equations are to/this document.
The aerodynamic equations were developed using the assumptions of low mach number and no weight change as stated. Aero elasticity terms were, however, included eventhough their value for this study is questionable.
23 PILOT CONTROL INPUTS TO AERO EQUATIONS
Along with the inputs from the EOM the aero force equations require eight pilot control inputs. These eight inputs are generated from seven pilot operated controls in the cockpit as follows:
Elevator Input: y- Where: is the (?.(* posit ion as a ratio of MAC. is the position of the control column in inches and has a dead band of .25 inch. is elevator deflection in degrees and is limited to the range of 15° trailing edge down to 25° trailing edge up.
Aileron Input: - • 2.5 Where: -i-o & Rudder Input: -f- Where: to^p is rudder pedal deflection in inches with stops at 4.78 inches left and right and a dead band of .25 inch. is rudder deflection in degrees limited to 30 degrees trailing edge left and right. is rudder deflection due to yaw damper. This input is limited to approximately +1.6 degrees. (See Section 6 YAW DAMPER.) 24 PILOT CONTROL INPUTS TO AERO EQUATIONS Spoiler Input On the DC-9-10 the spoiler surfaces are used for three areas of flight, 1) speed brakes, all spoilers go up at once as commanded by speed brake control, 2) ground spoilers, all spoilers go full up (60 degrees) automatically if armed and main gear spin up, and 3) lateral control spoilers, spoilers are deployed one side at a time to aid the ailerons in the rolling maneuver. In this simulation both the speed brake function and the ground spoiler function (symmetric spoiler deployment) are referred to as speed brakes. Lateral Control Spoiler Input Where: 0 is spoiler deflection in degrees, positive for right wing down and negative for left wing down. 1 is control wheel deflection (same as drives the ailerons). is defined by the following table: 0 0 3 0 10 .8 20 2.5 30 5.0 40 6.7 50 7.9 60 9.3 70 12.0 75 14.2 80 17.5 90 28.7 113 60.0 25 PILOT CONTROL INPUTS TO AERO EQUATIONS The table is entered using absolute value of wheel deflection. The direction of the wheel deflection is tested and the function value is returned with a positive value for right wing down and a negative value for left wing down. This accounts for the differential nature of roll control. Speed Brakes/Ground Spoilers It should be noted that all of the control surfaces mentioned above have some associated lags in the actual aircraft system. These lags are of the order of .1 to .3 of a second. These lags were not implemented in the ground handling simulation. It is felt that this omission does not significantly alter the overall fidelity of the simulation. Horizontal Stabilizer Input f • ' Ct4 is the angle of incidence of the horizontal stabilizer in degrees. (-H is limited to the range of 12 degrees trailing edge up and 1.5 degrees trailing edge down. * For the ground handling simulation ty was controlled by a thumb switch on the left side of the wheel. Pushing the switch down caused Lrf to move trailing edge up and pushing the switch up caused it to move in the opposite direction. The rate of Ly. movement was 1/3 of a degree per second in both directions. The maximum displacewe^t- of ty was limited to 12 degrees trailing edge up and 1.5 degrees trailing edge down represented as -12 and +1.5 degrees. 26 : PILOT CONTROL INPUTS TO AERO EQUATIONS Flap Input &$• is the flap angle in degrees. ds, is limited to the range of 0 to 50 degrees trailing edge down. 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(\ 66 u f r* xQ vr* I u_ ul Of o fX Q K s N t - V O t ^ ^ § 0 O 0 O O ^ ^ K 0 O o O V 67 fO ^ 0 § o o . o o xj CQ 0 o V \i o O 0 O o s V tXs 0 i 0 I 68 k: 0_ -si CO o o| o Q Oo ^ ^ V Q c\ 0 § ^ 8 1 5 ! 1 69 o K: ex 2 I > § 0 i 1 I* 1 *1 ! X 70 XO Q vS I rv) S u UJ vi, ^N] v § 18 \ xo I -t- Q 5 8 irt • It I l & 71 />* Vr- \j o 00 ro 0 -1- o 0 O | * + VJ» ^ \ CO -i. oo vj O I vj o o § Qi o O '* Q> o 0 § k § u\ \ Iu\ 72 . o rl : V X o §X I M. e- -.. o 1 i i s i 1 11 \ \ k \l i! \ I 0 o- 1 '4. 1 O V 73 iv o >x Vo x S i L \ Q t 1 V a Vi » J <0 v! cr * ««. o 3- \ \J -\r ! 8 r V) 11, L '{ ! I o " 1 I«-^ " NC 74 Section 3 Engine Model The simulation model for the JT8D DC-9 engine was developed from static and dynamic data provided by Pratt § Whitney and Douglas Flight Test. The static data for forward and reverse thrust were formed into a table with mach number and E.P.R. as arguments. (See Table 5.1) Likewise, a table of E.P.R. versus cross shaft angle was formed. (See Table 3.2) Table 32was taken directly from the published engine performance data for the sea level static case. The values of E.P.R. were taken from the 59 degree F curve with the exception that the reverse E.P.R. 's were made negative to facilitate entry into the thrust vs. E.P.R./mach no. table, Table 3.1.The dynamic data (consisting of typical engine acceleration and deceleration time histories) was used to estimate a representative time constant. The engine model was configured as shown in Figure 3.LThe sensor on the cockpit throttle pedestal provides a positive signal for the position of the main throttle handles and a negative signal for the position of the reverse thrust levers. When this plus/minus signal reaches the computer it is biased and scaled to represent cross shaft angle (XS) which has a range of 2.5 to 90 degrees. A cross shaft angle between 2.5 and 20 degrees indicates reverse thrust and an XS angle between 45 and 90 degrees indicates forward thrust. The idle position is 38.4 degrees of XS. The past value of XS is subtracted from the current XS value to form a differential. After limiting the differential is integrated to form a new current value of XS angle. This process results in a first order lag which approximates the engine dynamics. The lagged XS position is then used as an argument in Table 3.2to find E.P.R. and E.P.R. along with mach number is used to find thrust from Table 3.1 The absolute value of E.P.R. is limited and sent to the E.P.R. instrument in the cockpit and thrust is made available to the equations of motion for force calculations. With the main throttle handles in the idle position, "reverse thrust" is commanded by pulling the reverse thrust levers up to a detent. At the detent the amber "UNLOCK" light is lit and a logic signal is sent to the engine program which starts a 2 second timer. After 2 seconds the computer returns a logic signal which causes the green "REVERSE THRUST1 light to be lit and at the same time causes the detent to be retracted allowing the levers to move on up, thus increasing reverse thrust. IS Returning the reverse thrust levers to the stowed position turns out the amber light and causes the computer to turn out the green light and reset the detent. The engine model was validated by first comparing E.P.R. and thrust values for various cross shaft angles with supplied data. Secondly, the dynamic response of the engine model was adjusted using pilot comments and comparisons to supplied data. NOTE: The actual engine acceleration and deceleration responses are not simple lags as used in the model. The deceleration of the engine is fairly close to a first order lag while the acceleration is more akin to a second order type response. Never- theless, it has been found in past simulations, that a first order lag gives a very acceptable representation of engine dynamics. The data indicated a time constant of about 3 seconds, however, pilots seemed to prefer something a little less than 2 seconds. A time constant of 2 seconds was used in the simulation. 76 . ^Of \i> > ^ - JC -K_ X J k N ! 00 kk -J xx n > k ^ * ^ 1 •(. V "^ Q '< t v X > K t ' " ^ I X? iN -J ^ <; 8 j t K > 1 t 77 ENGINE NDDEL FUNCTION TABLES TABLE 3.1 THRUST VS. EPR AND MACH NO. -2.2 -1.8 -1.4 -1 -.6 EPR 1. 1.3 1.6 1.9 2.2 EPR -7150. -4360. -1920. -100. 0. M = 0. 0. 5250. 9520. 13200. 16400. M = 0 -9200. -6230. -3400. -820. 0. M = .1 0. 4750. 8750. 12320. 15400. M = .1 11920. -8510. -5130. -1880. 0. M = .2 90. 4400. 8240. 11780. 14890. M = .2 15200. -11400. -7600. -3740. 0. M = .3 200. 4300. 8000. 11470. 14700. M = .3 TABLE 3.2 EPR VS. CROSS SHAFT ANGLE 2.5 10. 15. 20. 35. 36. XS 45. 55. 73.5 90. XS -2.13 -1.60 -1.27 -1.03 -1.03 1.03 EPR 1.03 1.03 1.70 2.16 EPR 78 Section 4 Environmental Models This section covers the runway condition models (crown, roughness and friction), the wind model and the turbulence model. The crown, roughness and friction models are fully described in MCAIR report - titled "DC-9 Landing Gear Math Model for Directional Control On Runway Flight Simulation", by Harry Passmore, Reference 4. The crown model is the same as that in the report and the roughness and friction models are essentially the same except for the following changes: 1) The runway roughness table used was the same as the table 7-1 of the Passmore report except that all the bump heights were multiplied by 2. Also, the starting point of the table was set 500 feet "in" from the threshold to allow a "smooth" area for trimming the airframe simulation on the ground. 2) The DC-9 Nose Tire Cornering Coefficient (see figure 7-4 of the Passmore report) was multiplied by a factor of 5/7. This was done to reduce nose wheel steering sensitivity but did not take the resulting cornering force outside of an acceptable range. The main gear curves were the same as in the report. 3) The patchy runway condition profiles used in the study were essentially the same as cases 3 and 4 of figure 7-3 of the Passmore report. The exception is that in case 4, the patchy asymmetric profile, the "ICE" 79 segments were replaced with "WET" or "FLOODED" segments (see figure 4.1 below). Turbulence Model: The air turbulence model used for the ground handling study was developed from the Dryden* spectra (as opposed to the von Karman spectra). The independent longitudinal, lateral and vertical gust components are generated by filtering Gaussian random signals with the following three filters: / Longitudinal /^^ {£) — Lateral Vertical ^~kr where: G^ &Y, (jZr = RMS gust intensities. These sigma values are a function of altitude. ALT . (fa AND 20 .65 0 75 1.63 .15 150 3.61 .25 300 4.75 .31 450 .5 .09 600 .25 .06 *See, for example, Reference 7. 80 PATCHY RUNWAY CONDITION PROFILES RUNWAY DISTANCE, PATCHY SYMMETRIC PATCHY UN SYMMETRIC FT LMG NG RMG LMG NG RMG 0-500 WET WET - WET A I WET WFT WFT 500-1000 WET WET WET 4 WET WET WET 1000-1500 WET WET WET & -» WET - WET WET 1500-2000 WET WET WFT 0 L| WFT WFT WFT 2000-2500 WET WET WET € <> WET WET WET Q 2500-3000 WET WET- • WET ? <. WET WET WET q. 3000-3500 WET WET WET £ . • ~> WET WET WET 3500-4000 WET WET WET U * WET WET WET 4000-4500 FLOODFD Fi nnnFn Fi nnnpn f 1 n nnnpn WFT WFT 4500-5000 WFT WFT WFT f ' • ,. WFT WFT pRy 5000-5050 FLOODED Fi nnnpn Fi nnnpn \L . DRY DRY WFT 5050-5100 WFT UFT UFT L, ,v WFT WFT F| nnpFP 5100-5150 FLOODFD FLOODFD FI nnnFn M 15 DRY DRY WFT NOTE: Patchy symmetrical same as Case #3 used 1n McAir simulator runs FIGURE. 4.1.' = scale lengths. These are normally functions of altitude, however, for the ground handling study they were held constant. \/ = the true airspeed of the aircraft. For this study the used for the filters was held constant at 100 f.p.s. o = the Laplace transform variable. The turbulence model was activated by using a numerical Gaussian random number generator to supply the inputs to the filters. The outputs of the filters are then considered to be the X, Y and Z gust components. where: gust velocity components in feet per second. (/ ) f three Gaussian random numbers which range from zero to +1 and are generated in series from a common seed. the three £ilters shown above- 82 The actual digital algorithm was patterned after that in a NASA-Ames Program Specification, titled "Wind," by R. E. McFarland. (Reference 8). The algorithm used in the ground handling simulation did not include the rotational terms and had /(/£, less gain than the "Wind" algorithm. Wind Model : The wind model allowed for the specification of the wind components in the earth axes system. The X, Y and Z wind components could be specified as constants or functions of either range or altitude. Several of these tables of winds could be stored and the particular table desired could be called up before a run. Actually the tables for the gust paraemters , were also handled by the wind routine making it the complete definer of the wind conditions. After calculating the various 'elements these elements were summed to form the total wind component for each axes. y- y- These wind components are then differentiated to form the wind acceleration components, The six wind velocities and accelerations are picked up in the ECM where the velocity components are added to the inertial velocity components and the acceleration components are transformed to the body axis where they are added to the body axis force equations. See Figures 1.1, 1.2 and 1.7 of the EOM section. The ground handling study only required a constant side wind and turbulence so that all terms except STEADYy and the three GUST terms were zero. Note that was zero below 20 feet so that GUSTz was zero on the ground. See description of turbulence model above. 84 ; Section 5 Struts Subroutine Implementation Notes The STRUTS subroutine, written in FORTRAN, is an implementation of the mathe- matical model defined in Ref. 4, "DC-9 Landing Gear Math Model for Directional Control on Runway Flight Simulation." Most of the FORTRAN names defined in that report are used in STRUTS. The basic structure of STRUTS is similar to the subroutine LNDGR mentioned in the above report. Figure El is a general flow chart of STRUTS with line number references to the listing of STRUTS. The differences between STRUTS and LNDGR occur in the implementation of coordinate transformations, strut dynamic model and antiskid model. Most of the changes were made to decrease compute time. An examination of the numerous coordinate transformations required in the gear model indicates that many of the transformation matrices are sparce. (They have several elements which are zero.) Therefore, compute time can be saved by coding the transform equations directly rather than using a general matrix multiply subroutine. Compute time is saved by eliminating the overhead required for a subroutine linkage. Simulation of the strut dynamics (strut plus wheel mass dynamics) as defined in the above report consumes a lot of compute time. The natural frequency of that mass suspended between the tire spring and the strut spring is 15-20 Hz. Therefore, these equations must be solved approximately 200 times each second. In the RDC simulation, STRUTS was called 20 times each second and these high frequency equations were solved 7 times for each pass through STRUTS. Satisfactory results were obtained with this solution rate of 140 times a second. Compute time can be substantially reduced by minimizing the number of operations performed in the iterative loop used to solve for the strut dynamics. This was accomplished in STRUTS by expanding the dynamic equations and collecting all terms which are constant. All constant terms were moved outside the iterative loop and computed once for each pass through STRUTS to initialize the iterative loop. Included in this initialization are calculations designed to minimize the step inputs to the strut dynamics. If the aircraft lands with a vertical velocity of 10 FPS and the simulation is solved 20 times a second, the step input to the landing 85 gear can be 6 inches. This is a large step when compared to the total tire and strut movement. Therefore, the step change in height input to STRUTS is divided by the number of passes through the strut dynamics. This makes each step into the strut dynamics less than 1 inch. No investigation was made of the efficacy of this technique. It is recommended that elimination of the strut dynamics be investigated in future RDC programs. Adequate results can probably be obtained by allowing the aircraft mass to land on a non linear spring with a combined characteristic of the strut and tire. The savings in coding complexity and, therefore, compute time in the strut routine would be substantial. See Appendix B for a detailed description of the software antiskid system. A great deal of time was spent developing the low speed taxiing characteristics of the simulation. During checkout, the pilots had the sensation of skidding too much at low speeds. Also, after coming to a complete halt, an oscillation would occur which was very unreal. Adjustments of tire and strut damping did not affect the oscillation. Since the very low speed regime was not considered important in this program, speed logic and simple geometric relations were added to remedy these irregularities. The following equations were added to the equations of motion (see subroutine EOM, lines 135-39 § 196-201). VE * SQKT (VIX*vTX+vTY*vTY) = /VTX2+VTY2 RDLLG - YAWG = 0.0 FYG = XMASS*(UB*RB*DTR - QSM*CYB - 32.2*AT(2,3)) RB * VE*INS* .0229 PB » -PHI ANY = VE*RB*.000542 86 VE is the ground velocity of the aircraft in feet per second. When VE is less than 20 these simplified equations are used. The roll and yaw moments due to the gear are zeroed. The lateral force due to the gear, FYG, is set to a value that balances the aircraft side force equation. Body yaw rate, KB, is computed as simple circular motion based on the nose wheel steering angle, ENS, and VE. See Figure E2 for a derivation of the simplified RB equation. Body roll rate, PB, is set equal to negative roll angle to washout any roll angle that exists when the low speed logic is entered. Lateral acceleration, ANY, is also computed based on simple circular motion. 87 Of • Es, lU Oont*et) fiUUUX>r » UIX. DATA funos. 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Z-AX/S FT 110 Section 6 Auxiliary Equations This section contains descriptions of the models for the ILS and marker beacons; the instrument drive algorithms; and the yaw damper model. Also included are short descriptions of the interfaces to the motion base and the visual system. ILS (Instrument Landing System) : The ILS consists of a glide slope beam (G/S) and a localizer beam (LOG). The G/S provides a descending path to the runway touch-down point which is about 1000' in from the threshold. Typically this path is about 3 degrees. The LOG provides lateral guidance by defining a path down the center of the runway. The origins of the LOG beam is at the far end of the runway. The ILS model essentially does two things: 1) establish the position of the ILS receivers, on the aircraft, with respect to the transmitters on the ground, and 2) calculates the angular errors from the fixed beams. The positions of the ILS sensors are transformed to the earth axes by the following equations: G/S *GI "X I * ^GsVl * ^GS^,! ZGI = ZI * ^GS^.S * ZBGSA3,3 + ^ALT LOG XLI = *I * ^L^,! + ZBLA3,1 YLI = Yi + *v*i.z + ZM/S.Z Where: ^BtS' ZB(S = the body axes coordinates of the G/S antenna.* XBL, Yg. = The body axes coordinates of the LOG antenna.* A. . = Elements of the body to earth transformation matrix x'^ (direction cosines). Y, Z = Earth axes coordinates of the aircraft. APALT = Airport altitude Zg, = Earth axes coordinates of the G/S antenna. YLI = Earth axes coordinates of the LOG antenna. NOTE: Body axes coordinates are based on a longitudinal C.G. position at the quarter chord and on the aircraft center line. Ill The earth axes positions of the ILS sensors on the aircraft are used to calculate the voltage errors as follows: EG/S = tG/S X " (Arc*311 GI/X^ ^ 57<31 *214 E LI/ LDC " Utoctan. XjJ-RWY'L) 57.3] .075 Where: G/S X = The fixed glide path angle defined by the glide slope transmitter. RWYL = The .length of the runway from the touch-down point to the far end (position of the localizer transmitter). 57.3 = Numbers of degrees in radian. Used here to convert from radians to degrees. .214 = Volts per degree of G/S error. .075 = Volts per degree of LOG error. EG/S 3 Glide slope error in volts. ELOTorG, = Localizer error in volts. The glide slope and localizer error signals are sent to the indicators in the ADI and HSI instruments. The ILS displays are scaled in "DOTS" where .075 volts equals one dot for both G/S and LOG. Marker Beacons: Two marker beacons were simulated for the RDC study. Typically airports will have 2 or 3 of these beacons spaced out along the runway approach. These beacons activate a beeper and lights in the cockpit. There is a light for each beacon. The simulation model consisted of using comparisons on longitudinal and lateral aircraft displacement to define two rectangles within which the beeper and appropriate light are activated. 112 For the RDC study the following dimensions were used: Outer Marker: -35856 Middle Marker: -4640 The rectangle sizes are the approximate size of the beacon radiation pattern if the aircraft were following a 3 degree glide slope. Instrument Drives: The six primary flight instruments were active at both the Captain's and First Officer's positions^ The Captain's instruments were DC-9 types and the First Officer's were DC-10 types. In addition the center panel contained two DC-9 type Engine Pressure Ratio (EPR) instruments. Both the DC-9 and DC-10 instruments were driven with the same parameters, for the most part. ADI (Attitude and Director Indicator) Artificial horizon - driven by pitch and roll (6 and <|>). ILS indicators - driven by the ILS parameters E and E . r/u/cO xAArTnrf The flight director bars, speed command bug and skid ball were not driven. HSI (Horizontal Situation Indicator) Ccmpas - driven by heading (ij>) ILS - same as ADI DME (Distance Measuring Equipment) indicator was not used. 113 BARD altimeter - driven by C.G. attitude (hc(,) Radio altimeter - The altitude of the radio altimeter antenna is found as follows: hRA = ~hRABIAS~(ZI * 3 Where: h_. • radio altimeter altitude = B*as SU("k ^at t*ie Ta(^-0 altimeter will read zero when the main gear just touch the ground and the aircraft pitch angle is 6 degrees. = earth axes Z component (-Iw) • = X ^°^ axes coraP°nent °^ radio altimeter antenna position.* = Z ^0(^ axes c011?50116^ °^ radio altimeter antenna position.* A. . a elements of body to earth transformation matrix. 1>j APALT = airport altitude *NOTE: Body axes coordinates are based on a longitudinal C.G. position at the quarter chord and on the aircraft center line. 114 In order to drive the radio altitude indicator h^. must be changed to a voltage. The h^ voltage relationship is non- linear as follows: VOLTS 0 .4 200 4.4 400 8.4 600 12.151 800 14.947 1000 17.130 1200 18.920 1400 20.438 1600 21. 756 1800 22.920 2000 23.962 2200 24.907 2400 25.769 2600 26.6 2800 32. * * This point is used to drive the DC- 10 tape instrument display out of sight. 115 VSI (Vertical Speed Indicator) The VSI instrument was driven with a first order lag as shown. • f VSI drive = I/yS+1 Where: Z, = aircraft vertical rate component in earth axes Y ° .5 second IAS (Indicated Air Speed) IAS was driven with equivalent airspeed (V ) as calculated by EOM. EPR (Engine Pressure Ratio) EPR indicators were driven with EPR as calculated in the engine algorithm (see Section 3). 116 Yaw Damper The DC-9 model used for the RDC study included a yaw damper. The yaw damper model used was optimized for the approach configuration. A block diagram of the yaw damper algorithm is shown in Figure 6.1. The body axes yaw rate (rg) is the primary damping loop while the body axes roll rate (Pg) provides some turn coordination. The limiter is used to limit the authority of the yaw damper. Kj is needed to change the commanded rudder deflection in hinge coordinates to stream coordinates. Stream coordinates are used in the computation of aero forces. Motion Base Drive The algorithms for the motion base drive have been taken from NASA report TN D-7350 (Reference 3). The only changes made by Douglas to the algorithms, other than those which relate to the geometry of the platform, were as follows: 1) The braking acceleration circuit was not used. 2) The lead compensation was applied directly to the jack signals and not to the centroid position as shown in the report. 3) The washout parameters used are very similar to those shown in Table 2 of a NASA paper presented at an AIAA conference (Reference 9). Table 6.1 below shows the actual values used for the Douglas motion base. 117 1 § u sA V UL 118 NOTION BASE WASHOUT PARAMETERS TABLE 6.1 VARIABLE UNITS VALUE MATH COMPUTER HIGH PASS FILTER Cl(3) - 0.8 ZET1(3) - 0.7 OM1(3) rad/sec 2.0 C2(3) - 1.0 Z,2 LOW PASS FILTER e,l Cl(l) - 0.5 ZET1(1) - 0.7 <*>n,9 CML(l) rad/sec 5.0 - Ke,2 C2(l) 0 Cl(2) • 0.05 ZET1(2) - 0.7 OML(2) rad/sec 5.0 C2(2) • 0 SIGNAL-SHAPING NETWORK K C3(l) per ft. 0.001 q,T,l K C3(l) sec 30.0 q,T,2 CS(1) per sec. 0.05 C3(2) per ft. -0.001 * KP,T,1 C4(2) sec 30.0 C5(2) per sec 0.05 KP,T,3 per ft. 0.004 Kr,l C3(3) 3.8 Kr,2 C4(3) sec C5(3) per sec. 0.05 Kr,3 * The minus value takes the place of the minus signs in the ^ equation. (See page 21 of NASA report.) 119 MOTION BASE WASHOUT PARAMETERS TABLE 6.1 (Cont'd) VARIABLE UNITS VALUE MATH COMPUTER SCALE AIRPLANE ANGULAR RATES Kp C6(l) - 0.7 Kq C6(2) - 0.5 Kr C6(3) - 0.2 TRANSLATIONAL WASHOUT a C7(l) rad/sec 1.414 a C7(2) rad/sec 2.1 a C7(3) rad/sec 2.1 b C8(l) rad/sec 1.0 b1 C8(2) rad/sec 2.25 b C8(3) rad/sec 2.25 120 Visual System Drive The visual system used during the RDC study was a T.V. viewed model type called a Visual Flight Attachment (VFA), made by Redifon of England. The VFA T.V. camera is mounted on a moving platform which can be moved over the model. The moving platform is driven by servos with the controlling signals originating in a "mini" digital computer. The drive algorithms, which were supplied by Redifon*, are calculated in the mini computer. The basic aircraft position, rate and orientation signals are calculated and transformed to the pilot's eye position in the main simulation computer. These signals are then transmitted to the mini over an analog link. The main simulation computer calculates the input signals for theWA at a frame rate of 20 per second. The mini does its calculations at a frame rate of 50 per second. It should be mentioned that the analog link is just that, the signals from the main computer are put through digital to analog converters (DAC's) and transmitted over analog trunk lines to the VFA area where they are re- digitized by an analog-to-digital converter (ADC) and sent to the mini. It also should be mentioned that it is generally felt that an analog link is probably not the best way to interface two digital computers! * See Reference 10. 121 APPENDIX B -SOFTWARE ANTISKID The software antiskid model defined in Ref. 4 , "DC-9 Landing Gear Math Model For Directional Control on Runway Flight Simulation", pages 36-38, was changed slightly to simplify the logic, decrease compute time and obtain the desired performance. This appendix will document those changes. The same notation is used here except the subscript, j, has been deleted in this appendix with the under- standing that the equations and diagrams apply to both right and left main gears. Figure Bl is a flow chart of the antiskid system as implemented in STRUTS, the Douglas subroutine implementation of the above report. Figure B2 is a typical time history of braking force with period Cp and duty C^. In the original model, when FBCQM > FBQ^ (see Figure Bl) antiskid cycling is started. In STRUTS, this decision point was made independent of Ct because at high speeds on wet runways Ct is small which makes FJJQN large and the antiskid did not cycle as desired. In STRUTS, FgQjYj is compared to the product of the effective coefficient of friction, UD, normal tire load, Fg, and a constant, 1.35, to determine the onset of antiskid cycling. FBCQM was a^so i11016356^ by changing the effective braking area from 5 to 8 square inches. In retrospect, this value of FBCQM was probably too high. However, since maximum performance stops were used on most test runs, the high command level was not obvious. The precise onset of antiskid cycling was not investigated. During checkout of the simulation, the antiskid system was evaluated by Douglas pilots and compared with the analog (hardware) antiskid system. The result of this check was a modification to the period and duty of the antiskid cycling. This change is illustrated in Figure B3. The period, Cp, was increased 0.8 seconds over the entire speed range and the duty, Ct, was increased for wet and flooded runway conditions. 122 Bl L COMPUTE. C tf C f T (£I6M i-oAD ON = /^/3CT/OAJ OF 123 cp- OF Pe&tOD ' OA/ (&UTY) 7.0 !•* 'f> •T 1.0 SO /Off 2.00 124! APPENDIX C ANALOG/HARDWARE ANTISKID Section If INTRODUCTION The analog/hardware antiskid simulator is a system that produces real time drag and cornering tire forces for the aircraft simulation. The system consists of an analog computer and actual aircraft hardware implemented as shown in Figure C-l. The analog computer receives inputs from the digital aircraft simulation and brake pressure from the hydraulics and calculates in real time the tire drag and cornering forces and wheel speed. The wheel speed is output to the antiskid control box and the forces are output to the aircraft simulation. The antiskid control box produces an antiskid control valve signal that controls brake pressure. 125 en O TJ IT3 <«- • C •O 0) 3 CO to M u in O) o u £ Q. S g s- o a. CO H- X U. 0 o HH Z mO JK; & s 2 a. a. n) o Qi CO co 01 •p- 0) cc (O 'to 4J «*- O) a> > CO CO J CO C CO (O aQ£ 0c) ••s- _O >J • i- a> i— : •— 4J uj f- -a (J . ' >— CO -r- CO 3 - -^ CO CO 126 Section 2. MODEL DERIVATION The math flow diagram of the model for one strut is shown in Figure C-2. Both strut mechanizations are identical. These equations are implemented on an analog computer because of the high frequencies involved. PRIMARY TIRE CORNERING AND DRAG FORCE Originally it was planned to generate tire cornering and drag forces similarly to the method developed in Exhibit A of Reference 2. However, the method gave excessive side loads in the unbraked condition. Figure C-3 illustrates this problem. A new empirical method was developed based on data from Reference 5. This new method is developed in Primary Tire Cornering and Drag Force Analysis. SECOND TIRE CORNERING AND DRAG FORCES. STRUT FORE-AFT AND TWIST RATES. BRAKE TORQUE, TIRE AND WHEEL SPEED, AND TIRE SLIP RATIO The remainder of the items shown in Figure C-3 are developed in the above named analysis. ' '•• . 127. , '.jK c >' ~ ; ~: '~L'3 128; 1 15x10° - 10 - -o to o V£2T\CAL LDAO- 23000 s (/) s_ MASA TM D-8332 8 12 T1re yaw angle, degrees FIGURE C-3 COMPARISON OF HYDRO AIRE'S TIRE CORNERING .THEORY WITH THAT OF NASA TR R-64 — WITHOUT BRAKING 129 J. 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I ... ..I- 1JT-« _r.- li—". - ~-—" - - «-T- • • A' --~ •••• • ^-*—r**'.- ""'*'" ~*"_7r7-T^'^' *-'^^"-^rT"!'' -— -- ^i; r^j.7 ''1TT" ~4 "TT '''' ^ ''-'-- t~*,'~'^~^L^~i"*^ - r r:t:i:^-n:^i- -i::rr:;ij::-"ri."1 ..r __,_.__ a • 8 -.: /.O De\/ei-of>*> TWs EQUATIONS t=o£- WHG.ec- COMPUTATION. 3 D \ 149 AXLE. Def=Lec.rion V To /5 sreur. Foee- To D sreor Foee-Arr OF Morton. Aee ) Auo ^> tv T/ye Moj>£i~. THS. £*Peesstorf Foe. 150 FucJ> TO sreor A/c ATST8OT £06 TO I L8 LoftO 6y e foe.ce - See F/6 2. /J 13 THE V, P/ygoro/4/c, COEFIT - AT STZuT DOG. To A / FT-i-S INITIAL 15Z TO Be OP TWO FojJCT/o/os T6 - 5 AW (- FOJOCTIOM u;jfH /5 AM UCT? ows . 153 To Foe. A IIM& D /3 PS* J. ( PB Foe. P.(o) OK. \ 3 - T6 .5 154 77/ B 1 7 F * T * -t 155 Section 3. PROGRAM ANALOG PROGRAM The analog computer program is shown in Figure C-4. The program was set up so that it could be used in either the stand alone or normal mode. This allowed the program to be developed independently of the total simulator. INTERFACE AND PROGRAMMING CONSIDERATIONS The simulation was interfaced with the digital simulation and hardware as illustrated in the Analog Antiskid Interface Description. Analog computer to Hardware Interface - Wheel speed from the computer drove voltage controlled oscillators. The oscillator outputs were impressed on the antiskid control box to simulate the signal from each tire. The frequency corresponded to 40 pulses per wheel revolution. The squat signal was 28 vdc when the nose gear was fully extended and zero when the gear compressed one and one half inches. The PMV servos drove the PMV in response to brake pedal position. Brake pressure was monitored by pressure transducers connected to amplifiers with appropriate gains for the analog circuit. Digital Computer to Analog Computer Interface - The signal from the digital computer was processed by a Digital-to-Analog converter. To take advantage 31 of the digital computer capabilities the product of normal load and maximum friction coefficient was formed in the digital computer. The unbraked cornering force and ^M were also calculated in the digital computer because of nature of the computations and the relatively slow changes experienced by these parameters. Aircraft axle velocities and aircraft acceleration were also input to the analog computer. Cornering and drag loads were impressed on analog-to-digital converters for communication with the digital computer. 156 I CD O eg < i—i o C9 157 8 : 1-4 CO a 1-4 i C9 O a 13 158. THE. 7//£ SIMULATION) C QMS TO OF THE -rue TO PILOTS TO & SOOAT SJ&UAL THAT A/ase (fr N02.MAL LoAO MOLT/ pLi &> BY FONC.TIOU 05 eo TO Reooce DJSAG FOSCE ftS A FUUC.TIOM OF T& To 159 ANTI SKID SIMULATION 160 Section 4. HARDWARE The hardware needed for this program is outlined in the Task Assignment Drawing Z7802765. Details of the hardware are given in Drawing 27935344, Equipment serial numbers used in the simulation were as follows: LH A/S Valve P/N 39-101 S/N 797C RH A/S Valve P/N 39-101 S/N 799C LH PMV P/N 7920966-5503 S/N 416309A RH PMV P/N 7920966-5503 S/N 416308A Control Box P/N 42-089-5 S/N 256 LH Brake P/N 9560788 S/N MAY66-8E RH Brake P/N 9560788 S/N NOV66-31 161 25-1821 (10-68) REVISIONS LTR DESCRIPTION DATE APPROVED » Xj 5£-€ &./£-£ ] Pp <££- e.,-0, /0-/4-77 £l>,^b. r ^ 7- SCHEDULE INFORMATION DATE DOUGLAS AIRCRAFT COMF>AIW TEST INITIATED **** *H**n"l_\«_5t LONO mmACH. CALIFO/tNIA FINAL REPORT SUBMITTAL TITUE ANTISKID SIMULATION - RUNWAY DIRECTIONAL DESIGN APPROVAL. DATE CONTROL SIMULATOR DC-9 SERIES 10 .AB TEST TASK ASSIGNMENT DRAWING STRENGTH SIZE PR ENGR r^cJ-^f^wi*^ 3/*j/7 GR ENGR 6 .10. Kiftpe*s TABLE OF CONTENTS 2 A B INTRODUCTION 3 PURPOSE 4 REQUIRED EQUIPMENT 5 B ' TEST REQUIREMENTS 6 /&LD WORK ITEMS 7 & • SCHEDULE .8 FIGURE 1 - 9 FIGURE 2 - 10 A % ' SIZE CODE (DENT NO. DOUGLAS A 88277 Z7802765 i REV LTR -B I SHEET 2. 163 FAD - CONTINUATION SHEET DAC 25-1979 (10-69) SYM INTRODUCTION This Task Assignment Drawing details the requirements for an analog/hardware antiskid simulation to be inter- faced with the motion-base flight simulator. Actual brake and antiskid system hardware will be used, operating in conjunction with an analog computer. SIZE T 7802765 CO/VffVi/VV EWO 164 I SHEET 3 FAD - CONTINUATION SHEET DAC 25-1979 (10-69) SYM PURPOSE The purpose of these tests 1s to extend existing flight simulator capability for the study and solution of aircraft directional control problems on runways. A man-1n-loop DC-9 aircraft ground handling simulator will be developed, correlated and then demonstrated to NASA personnel. A realistic simulation would be very useful In evaluating factors which Influence aircraft ground handling performance up to and beyond the operational limits of the aircraft without risk to equipment and pilot. SIZE A 7802765 165 COM f>AMY EWO- S.O. [SHEET 4 TAD - CONTINUATION SHEET DAC 25,1979 (10-69) ISYM B REQUIRED EQUIPMENT' » ^^M^MMMM^HV^H^MMH^^B^B^^^B^B^^^MM j 1. Hydro-Aire DC-9 Hydraulic Brake System Simulator 2. Hydraulic Power Supply (Skydrol, 3000 ps1, 15 GPM m1n.) 3. Brake Application Servo (two required) 4. Six Strain Gage Power Supplies 5. Six Channel Bridge Balance 6. Six Preston Model 8300 00 Amplifiers 7. Two Comcor C1-175 Analog Computers 8. DC-9 Transformer/Rectifier 9. Two VCO's (HP 3310A or equivalent) *10. Function Generator (HP 3300A), with "Offset" plug-In (HP 3304A) *11. Electronic Counter (HP 5512A or equivalent) *12. X-Y Plotter 13. Beckman Six Channel Recorder *14. Scope 15. Two Pressure Gages (0-5000 psl) 16. Six Pressure Transducers (0-5000 ps1) 17. Two Break-out Boards (Z7935344-13 and -15) 18. Connector Cables (Z7935344-17,-T9, -21, -23) 19. Six Amplifier Pressure Monitoring Board (No Identification) - Available on DC-10 Antiskid Simulator A general layout of the required equipment Is shown in Figure 1. *Not required full time SIZE A I 7802765 1 66 J^ [SHEET 5 - CONTINUATION SHEET DAC 25-1979 SYM TEST REQUIREMENTS The following tests will be conducted: 1. A predemonstratlon evaluation of the simulator will be made, utilizing a FAA and a Douglas pilot. Corrective action will be taken to resolve any problem areas. 2. The complete simulation will be evaluated by both a FAA and a Douglas pilot. This demonstration program will be designed to qualitatively evaluate: a. The benefits of using the antiskid simulation In conjunction with the aircraft simulator. b. The degree of correlation between the simulator and the pilot's experience and available DC-9 flight test data. SIZE T A 7802765 167 AU9CKAFT CO/tV/»>4/W EWO S.O. [SHEET 6 TAD - CONTINUATION SHEET DAC 2S-1979 (10-69) SYM B> F&LD WORK ITEMS , ' .u. 1. Obtain and Install Hydro-AIre DC-9 hydraulic brake system simulator. 2. Install hydraulic piping between hydraulic power supply and brake system simulator. 3. Develop and install brake application system. 4. Install pressure transducers and gages on brake system simulator (see Figure 2). 5. Operate hydraulic system as required. 6. Restore hydraulic brake system simulator to original condition and return to Hydro-Aire upon completion of test. 7. Obtain and install pressure instrumentation (strain gage power supplies, bridge balance, and Preston amplifiers) per drawing # Z7935344 (-501 rack assembly). 8. Fabricate two break-out boards per drawing # Z7935344 (-13 and -15 panel assemblies). 9. Fabricate and install connector cables. Fabricate per drawing # Z7935344-17, -19, -21, -23. Install per drawing I Z7935344. 10. Set up instrumentation rack per drawing # Z7935344 (-503 rack assembly). 11. Set up and maintain two Comcor C1-175 computers and the Beckman recorder (setup in enclosed platform adjacent to motion-base). 12. Obtain VCO's, function generators, electronic counter, X-Y plotter and scope. Place near Comcor computers. 13. Return all instruments to stockroom at completion of test. *Urite consignment purchase order and provide transportation. Unit will be available from 1 May 1977 until 29 July 1977. SIZE T A I 7802765 168; | SHEET 7 TAD - CONTINUATION SHEET DAC 25-1979 (10-69) ISYM SCHEDULE Set-up of the Comcor C1-175 computers 1s required by 22 April 1977 so that programming can be started. Fabrication and/or Installation of all other required equipment 1s to be complete by 6 May 1977. System Integration (with the flight simulator), checkout and demonstration will continue through 29 July 1977. SIZE T A 7802765 AtS9Ct9AFY SHEET 8 i £n FORM XA60-I3A2 (1-68) / / 7 7~ 1- § \ 1 ^. A SJ " *&3n$s32tet x 1 rvrvdv 93V29 ~~ Lt J I 8 SIZE CODE I DENT NO. 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ANALOG ANTISKID SIMULATOR VALIDATION The validation consisted of matching Langley test-track test data (NASA TN D-8332) on the antiskid simulator. The test conditions (speed, vertical load, maximum coefficient of friction, tire yaw angle, and commanded brake pressure) were set up on the simulator and runs were made. The drag loads decelerating the aircraft were adjusted to give the same deceleration and the torque gain was adjusted to give the same skid pressure level as on the test data. The brake characteristics utilized are shown in Figure C-5. Two of the Langley tests were selected for correlation. The time history for the first, in which the tire was unyawed, is shown in Figure C-6. The actual test conditions are denoted on the figure. Figure C-7 presents the simulator run for the same conditions. The degree of correlation between the simulator and test data can be seen by comparing these two figures. Note the similarity in skid depth and in the levels of the brake pressure, brake torque and drag coefficient of friction just prior to the skids. The . correlation between the simulator and test data is good, except that the pressure recovery immediately following a skid was quicker on the simulator. The time history of the second test, in which the tire was yawed 6°, is shown in Figure C-8 and the corresponding simulator run is shown in Figure C-9. Here, particularly note how well MS correlates, both unbraked and with 2000 psi applied (slip ratio = 10%). The comments made above about the degree of correlation for the other case apply here also for the initial skid. The subsequent shallow skids shown in the test data weren't duplicated *on the simulator. These deep skids on the simulator are probably due to the adjustments made to achieve rougher cockpit motion. 203 Brake torque = f, (Speed) x f2 (Pressure) 5 rotor brake (PD2231-22) 19T4 brake mix TOO stop energy level 1.0 •a 9) (U Q. to 0.5 0 2 x Speed, ft/sec 20x1Ov 10 V) to c, a. 0 1 2 3 x TO* :^s- sc-rCE^L:-s£3 ^SE Brake pressure, psi FIGURE C-5 BRAKE TORQUE/PRESSURE/SPEED RELATIONSHIP 204 20 - Wheel . . speed, 10 =— .^ _ ^ ' ' ' •-•-•• . • ' - rps" " i i. . \T i t • •• lOr- Skid signal, 5 volts ..•i ^ !^-^_ f ,0 3 20 r- -, 3xl0 ; Brake - 2 Brake -^ 1 -t" ; pressure, 1 0 ,^^~ pressure. /^^^ ~^~~ / *^ — i MPa J \J / psi 0 • \s . \s . \.' n 4 40 r- . - 3xl0 Brake - 2 Brake torque, 20 — -t —| torque, _j^f^^ ' l\ "»• T^^» i kN-m / \f~~* .\S~~~~- 1r ft-ibf — 1 1 ll : fitf^^ • - - • • L 1 1.0 '**• -5 • ... L : - • _••'..., 5 V -i 4xl04 ! Alining ; Alining torque, 0 / 0 torque, : kN-m ! _l .•-.4 - in-lbf -5L •1.0 - ' *''.'• ' . '• .-. 1 fl II Slip 5 ratio I V I - w i — •*-***( 1 0 2 4 6 8 10 12 Time, sec - - - Time histories for run 2; noriinal carriage speed, 44 knots;. vertical load, 59-6 kN (1? 400 Ibf); yaw anrle, -0°; surface condition, dry; tire condition, new; brake pressure, 14 MPa (2000 Ibf/in2). FIGURE C-6 TEST TIf€ HISTORY SELECTED FOR ANTISKID SIMULATOR VALIDATION -- UNYAWED._TIRE. _ _ .. ~ " ~ 205 100 Wheel Speed, rad/sec 0 10 A/S Valve VoTtage, Volts 0 2500 Brake Pressure, psi 25 000, f Brake torque, i ft-lb RJJ838igi$£jmRH!!fln!Min!8ifllili!n^ nilUUiiUHifllHWIilfllittfllili^ 0 1.0 iy«yiiHiaiiiiB«rdiuniUfflK^ Slip ratio _FI6URE_C-7_ANTISKID SIMUUTORJTIMEJilSTORY.- .UNY/WED TIRE 206 PAGE NQ 20 Wheel 10 rps 0 10 Skid signal, 5 volts 0 20 3xl0 Brake 2 Brake pressure, 10 pressure, MPa 0 40 3x10* Brake 2 Brake torque, 20 torque, KN-m 1 0 0 1..0 ,5 1.0 .5 r 4x1m ,0» Alining Alining torque, torque, kN-m -51- l.Or Slip I ' I ratio i ^—4i- — '\1L1___ _1 I >—__i -- LJ>-r — 'wLj r —^n ^^^i u ) .2 .10 12 Time, sec i- =.-.- -•-•_-•,.-. Time histories for run 36; nominal carriage speed, U6 knots; vertical load, 83.6 kN (18 800 Ibf); yaw angle, 6°; surface condition, dry; tire condition, new; brake pressure, 1^ MPa (2000 Ibf/in2). FIGURE C-8 TEST TIME HISTORY SELECTED FOR ANTISKID SIMULATOR VALIDATION YAWED TIRE --.-.. 207 _iU*. - —. 1 se. _.t_c 31HKt.UHUIHn LilElAllllU CHJHTOJl 1GRAPHI UAIIUlHlM.-.,IL..C CONTROLS CDHPQHflllQ. r-JL-^o-IL-N . BUFIF NO. 7BT 100 Wheel speed, rad/sec A/S valve voltage, volts Brake pressure, psi Brake torque, ft-lb Slip ratio FIGURE C-9 ANTISKID SIMULATOR TIME HISTORY ~ YAWED TIRE 208; APPENDIX D COCKPIT SIMULATOR The cockpit mounted on the motion base platform is sized and configured as a DC-10. This appendix outlines those changes that were made to the cockpit to more closely represent the DC-9 for the ground handling study. Flight Instruments DC-9 type instruments were installed on the Captain's side. These instruments were all types normally used in DC-9's except the vertical speed indicator which was a DC-10 type. The three DC-10 engine NI indicators were replaced with two DC-9 type EPR indicators. See Table Dl for list of instruments used. The First Officer's side remained in the DC-10 configuration. Pilot Controls The only changes made to the pilot controls were changes in the force gradients and the removal of the number three engine control lever. Figures Dl through D4 show the force versus position curves of the column, wheel, rudder pedals and toe brakes. The spring rates of the column and wheel were changed to more closely match the DC-9. The force gradient of the rudder pedals was left the same as the DC-10. The force gradient of the toe brakes was adjusted using test pilot's comments. The curve shown is the gradient actually used. As mentioned the number three (farthest right) engine control lever was removed leaving numbers one and two for independent twin engine control. A reverse thrust detent was added for the ground handling study. This addition is described in Appendix A Section 3 "Engine Model." Pitch trim was provided through a thumb activated switch on the left hand side of the Captain's wheel and the right hand side of the First Officer's wheel. 209- Pilot Controls (Continued) The speed brake and flap controls were DC-10 types but were active with the exception that the speed brake lever did not move with auto ground spoilers. the nose wheel steering side controller "tiller" was not active for this study. See Appendix A Section 2 "Aero and Control Systems" for additional descriptions of pilot controls. Outside Visual Scene The outside visual scene was provided by a Redifon Visual Flight Attachment (VFA). At the cockpit the VFA image is presented to the pilot by a T.V. monitor through large collimating lenses. The faces of the T.V. monitors are masked to provide the proper pilot eye cut off angle. For the DC-9 this angle is about 15.5° down from horizontal and was obtained in the DC-10 cockpit by moving the masks on the monitors up to a point where the cut off angle is correct^ provided the eye is in the designated position. (See Figure D5.) NOTE: It is very important for those "flying" the simulator (and the aircraft for that matter) to have their eyes in the proper position! TABLE Dl EQUIPMENT USED FOR DC-9 VENDOR PART NO. SERIAL NO. NAME VENDOR 2067635-0701 TYPE 1NA-51A 7526 RADIO ALTIMETER IND. BENDIX 522-3907-001 TYPE 329B-7M 666 ALTITUDE INDICATOR COLLINS (FLT DIR. INDICATOR) 522-3875-002 TYPE 33/A-6K E-5 HOR. SITUATION IND. COLLINS (COURSE INDICATOR) ASOD-10D KIT 4191 SIMULATED ALTIMETER AEROSONIC MS-45-ID KIT 8252 SIM. MACH/AIRSPD. IND. MIDWAY JG298H1 B-416 EPR INDICATOR HONEYWELL B-432 EPR INDICATOR HONEYWELL 2594468-902 2090895 VERTICAL SPD. IND. SPERRY 210 f. ' k-'-'. ! J 1 .v;:t 1-.1r:-'t^-:iir:-i.i:-- .t::--!:—^r'ir-i^iLTi:l;..-.l..ij).l... Jrl...,l,.,...;':. 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Q Qi-«°.° Uv. tf* >•• Ul &I— . uU.l t/y Ul QUCl UJ X < o. < OS cr> n n o UJ3 OS O 215 APPENDIX E PROGRAMMING CONSIDERATIONS This appendix covers some considerations in programming a digital computer to form a real-time solution to the airframe model. The term "real-time" in this context means that vehicle command inputs must be received and "next" airframe state variables calculated fast enough so that the various pilot displays can be updated with no perceptable "steps." The DC-9-10 airframe model was programmed on the Systems Simulation Sigma V digital computer. An extended version of Fortran was used extensively as the programming language. All of the algorithms associated with the airframe simulation were solved at least once every 50 milli seconds. The single exception was a section of the strut routine (STRUTS) which was solved 7 times faster. The execution of the program took almost 100% of the 50 milli second frame. When the simulation program was first assembled it took a few milli seconds longer than 50 to solve. This "overframing" condition was rectified by the following procedures: 1) All routines not specifically needed for RDC were taken out; 2) The beam noise was eliminated from the ILS model; 3) The turbulence filter parameters, which normally vary with speed and altitude, were calculated for a nominal speed and altitude and held constant during the real-time sequence. (See Sppendix A, Section 4 for description of the turbulence model); 4) The choice of 7 iterations per frame for a segment of the strut routine was due in part to timing considerations. (See Appendix A, Section 5); 5) Some other minor simplifications were made to the strut routine. (The statements preceded by an "X" in the Fortran listing of the STRUTS routine were left out). The above five items were specific things done to the RDC program to make it "fit" in the frame time. Some general techniques used by the Douglas Systems Simulation group to effect time saving are described below: o Simple Euler integration is used throughout the program with the only exception being some linear transfer funtions where finite difference equations are used. 216 o A special limited range arc tangent routine was implemented. This routine, which is good for resultant angles between +_20 degrees, was used for solving angle of attack, side slip angle and the ILS deviations. o No matrix arithmetic or general matrix subroutines are used for real- time calculations. o An attempt is made to minimize subroutine CALL'S. Fortran CALL statements invoke linkage routines which can be time consuming. 0 A careful check is made to be sure that all calculations of constants are done "outside" the real-time loop. Another point of interest to programmers is that in the solving of the X and Z axes moments of the aircraft a cross inertia term must be delt with. (See Appendix A, Section 1, Figure 1.2). For the RDC DC-9 model the P dot and r dot equations were solved using Cramer's rule to eliminate the "cross" terms. This technique seems to work quite well. However, in previous airframe simulations this same situation was handled by simply using the "past" value of one of the dot terms in the solution of current value of the other. This method also gave satisfactory results. An important aspect of simulating an aircraft is providing the capability to place the simulated vehicle in different initial positions.- A "trimming" process is necessary if it is desired to start the test run with the forces and moments balanced. A special trimming routine was implemented for this purpose. The desired aircraft configuration and position is input at the beginning of a series of runs. The calculations were made to trim the aircraft. These trim values were saved so each time the simulator was put in the reset mode they could be entered as initial conditions to the equations. A flow chart of the "trim" procedure is shown in Figure IE. 217 ENTER TRIM PARAMETERS TURN OPP EKJ6IK1ES AfJD MUD CALCULATE ALTITUDE DEPENDENT CALL. RUKJ -'-'•'' COMPUTE MEW T, CALL RUM COMPOTE. KJELO VMu/es o BASED OU ACCElffi/«TloMS . COMPUTE Mew VALUE s OP f is. IUITH T « T - G-B DTcO o( = « + ves RESTTORE BT VALUES Kese-r RESTDR&. AMD PtZlUT TRIM -.'•V J_ BKiD 218 | VOLUME II REFERENCES 1. Expansion of Flight Simulator Capability for Study and Solution of Aircraft Directional Control Problems on Runways, Phase I, MDC Report A3304. 2. Expansion of Flight Simulator Capability for Study and Solution of Aircraft Directional Control Problems on Runways, Phase II, NASA CR-145044. 3. Russell V. Parrish, James E. Dieudonne, and Dennis J. Martin, Jr.,'Motion Software for a Synergistic Six-Degree-Of-Freedom Motion Base,"NASA TND-7350, 1973. 4. Harry Passmore and C. R. Korba,"DC-9 Landing Gear Math Model for Directional Control on Runway Flight Simulation,"MDC Report A4816, 1977. 5. Sandy M. Stubbs and John A. Tanner ."Behavior of Aircraft Antiskid Braking Systems on Dry and Wet Runway Surf aces,"NASA TND-8332, 1976. 6. Douglas Report No. LB-31624, "Estimated Aerodynamics Data For Stability and Control Calculations, Model DC-9 Jet Transport, Series 10," dated December 31, 1964 with latest revision February 23, 1967. 7. N. M. Barr, D. Gangass and D. R. Schaeffer, "Wind Models for Flight Simulation and Certification of Landing and Approach Guidance and Control Systems," Report No. FAA-RD-74-206 by Boeing Commercial Airplane Co., for U.S. Dept. of Transportation, December, 1974. 8. R. E. McFarland: NASA-Ames Program Specification, titled 'Wind," Part No. NAPS-80, Computer Sciences Corporation NASA-Ames Site Operation. 9. R. V. Parrish, J. D. Rollins and Dennis J. Martin, Jr.: "Visual/Motion Simulation of CTOL Flare and Touchdown Comparing Data Obtained from Two Model Board Display Systems," AIM Paper No. 76-010, April 26-28, 1976. 10. Redifon Report No. SD/846/S. Issue 3, "Requirements for the Compatibility of a McDonnell Douglas Corporation Flight Simulator to the Redifon Rigid Model Visual Flight Attachment," January 12, 1971. 219 VOLUME II - REFERENCES (Cont'd) 11. E. A. Mechtly, "The International System of Units, Physical Constants and Conversion Factors," second revision, NASA Report No. SP-7012, 1973. 220 !•» WFT WFT FI nnnpn «;n-R3nn FI nnnpn FLOODED FLOODED ? .u WET WET npv 5300-5350 WFT WFT WFT Q. ,1 PPY DRY WET 5350-5400 FLOODED FLOODED FLOODED ' ft If WET - WET FLOODED 5400-5450 WET WET WET- -. 6 11 DRY DRY WFT 5450-5500 DRY DRY DRY "\. O v> WET WET FLOODED 5500-5600 ' WET WET WET • ' 0 'if FLOODFD WET WET Q 5600-5700 FLOODED FLOODED FLOODED e ^ WET WET FLOODED ^ WET WET FLOODED 8500-9000 WET WET - WET - •*) 1; FI nOOFO WFT WET 9QOfl--Qt5nn- - WFT WFT WFT 0 * W/T WFT pi nnnFn 9.500--10000J WET WET - WET—- ? « FLOODED WET - WET Cb (V" ^ Q ^TN c ^ ^jjd\I/ ^ e 1 ^B — i ^- 1 o ^C r> N to fy Mi Ov Cu 5 -\ fPi V3 •v t.b