src/FDM/LaRCsim/c172_gear.c

   1 /***************************************************************************
   2
   3         TITLE:  gear
   4
   5 ----------------------------------------------------------------------------
   6
   7         FUNCTION:       Landing gear model for example simulation
   8
   9 ----------------------------------------------------------------------------
  10
  11         MODULE STATUS:  developmental
  12
  13 ----------------------------------------------------------------------------
  14
  15         GENEALOGY:      Created 931012 by E. B. Jackson
  16
  17 ----------------------------------------------------------------------------
  18
  19         DESIGNED BY:    E. B. Jackson
  20
  21         CODED BY:       E. B. Jackson
  22
  23         MAINTAINED BY:  E. B. Jackson
  24
  25 ----------------------------------------------------------------------------
  26
  27         MODIFICATION HISTORY:
  28
  29         DATE    PURPOSE                                         BY
  30
  31         931218  Added navion.h header to allow connection with
  32                 aileron displacement for nosewheel steering.    EBJ
  33         940511  Connected nosewheel to rudder pedal; adjusted gain.
  34
  35         CURRENT RCS HEADER:
  36
  37 $Header$
  38 $Log$
  39 Revision 1.13  1999/12/13 20:43:41  curt
  40 Updates from Tony.
  41
  42
  43 ----------------------------------------------------------------------------
  44
  45         REFERENCES:
  46
  47 ----------------------------------------------------------------------------
  48
  49         CALLED BY:
  50
  51 ----------------------------------------------------------------------------
  52
  53         CALLS TO:
  54
  55 ----------------------------------------------------------------------------
  56
  57         INPUTS:
  58
  59 ----------------------------------------------------------------------------
  60
  61         OUTPUTS:
  62
  63 --------------------------------------------------------------------------*/
  64 #include <math.h>
  65 #include "ls_types.h"
  66 #include "ls_constants.h"
  67 #include "ls_generic.h"
  68 #include "ls_cockpit.h"
  69
  70 #define HEIGHT_AGL_WHEEL d_wheel_rwy_local_v[2]
  71
  72
  73 sub3( DATA v1[],  DATA v2[], DATA result[] )
  74 {
  75     result[0] = v1[0] - v2[0];
  76     result[1] = v1[1] - v2[1];
  77     result[2] = v1[2] - v2[2];
  78 }
  79
  80 add3( DATA v1[],  DATA v2[], DATA result[] )
  81 {
  82     result[0] = v1[0] + v2[0];
  83     result[1] = v1[1] + v2[1];
  84     result[2] = v1[2] + v2[2];
  85 }
  86
  87 cross3( DATA v1[],  DATA v2[], DATA result[] )
  88 {
  89     result[0] = v1[1]*v2[2] - v1[2]*v2[1];
  90     result[1] = v1[2]*v2[0] - v1[0]*v2[2];
  91     result[2] = v1[0]*v2[1] - v1[1]*v2[0];
  92 }
  93
  94 multtrans3x3by3( DATA m[][3], DATA v[], DATA result[] )
  95 {
  96     result[0] = m[0][0]*v[0] + m[1][0]*v[1] + m[2][0]*v[2];
  97     result[1] = m[0][1]*v[0] + m[1][1]*v[1] + m[2][1]*v[2];
  98     result[2] = m[0][2]*v[0] + m[1][2]*v[1] + m[2][2]*v[2];
  99 }
 100
 101 mult3x3by3( DATA m[][3], DATA v[], DATA result[] )
 102 {
 103     result[0] = m[0][0]*v[0] + m[0][1]*v[1] + m[0][2]*v[2];
 104     result[1] = m[1][0]*v[0] + m[1][1]*v[1] + m[1][2]*v[2];
 105     result[2] = m[2][0]*v[0] + m[2][1]*v[1] + m[2][2]*v[2];
 106 }
 107
 108 clear3( DATA v[] )
 109 {
 110     v[0] = 0.; v[1] = 0.; v[2] = 0.;
 111 }
 112
 113 gear()
 114 {
 115 char rcsid[] = "$Id$";
 116 #define NUM_WHEELS 4
 117 char gear_strings[NUM_WHEELS][12]={"nose","right main", "left main", "tail skid"};
 118   /*
 119    * Aircraft specific initializations and data goes here
 120    */
 121
 122
 123     static int num_wheels = NUM_WHEELS;             /* number of wheels  */
 124     static DATA d_wheel_rp_body_v[NUM_WHEELS][3] =  /* X, Y, Z locations,full extension */
 125     {
 126         {  3.91,  0.,   6.67 },            /*nose*/ /* in feet */
 127         { -1.47,  3.58, 6.71 },        /*right main*/
 128         { -1.47, -3.58, 6.71 },        /*left main*/
 129         { -15.67, 0, 2.42 }            /*tail skid */
 130     };
 131         static DATA gear_travel[NUM_WHEELS] = /*in Z-axis*/
 132         { -0.5, 2.5, 2.5, 0};
 133     static DATA spring_constant[NUM_WHEELS] =       /* springiness, lbs/ft */
 134         { 1200., 900., 900., 10000. };
 135     static DATA spring_damping[NUM_WHEELS] =        /* damping, lbs/ft/sec */
 136         { 200.,  300., 300., 400. };
 137     static DATA percent_brake[NUM_WHEELS] =         /* percent applied braking */
 138         { 0.,  0.,  0., 0. };                       /* 0 = none, 1 = full */
 139     static DATA caster_angle_rad[NUM_WHEELS] =      /* steerable tires - in */
 140         { 0., 0., 0., 0};                                   /* radians, +CW */
 141   /*
 142    * End of aircraft specific code
 143    */
 144
 145   /*
 146    * Constants & coefficients for tyres on tarmac - ref [1]
 147    */
 148
 149     /* skid function looks like:
 150      *
 151      *           mu  ^
 152      *               |
 153      *       max_mu  |       +
 154      *               |      /|
 155      *   sliding_mu  |     / +------
 156      *               |    /
 157      *               |   /
 158      *               +--+------------------------>
 159      *               |  |    |      sideward V
 160      *               0 bkout skid
 161      *                 V     V
 162      */
 163
 164
 165     static int it_rolls[NUM_WHEELS] = { 1,1,1,0};
 166         static DATA sliding_mu[NUM_WHEELS] = { 0.5, 0.5, 0.5, 0.3};
 167     static DATA rolling_mu[NUM_WHEELS] = { 0.01, 0.01, 0.01, 0.0};
 168     static DATA max_brake_mu[NUM_WHEELS] ={ 0.0, 0.6, 0.6, 0.0};
 169     static DATA max_mu       = 0.8;
 170     static DATA bkout_v      = 0.1;
 171     static DATA skid_v       = 1.0;
 172   /*
 173    * Local data variables
 174    */
 175
 176     DATA d_wheel_cg_body_v[3];          /* wheel offset from cg,  X-Y-Z */
 177     DATA d_wheel_cg_local_v[3];         /* wheel offset from cg,  N-E-D */
 178     DATA d_wheel_rwy_local_v[3];        /* wheel offset from rwy, N-E-U */
 179         DATA v_wheel_cg_local_v[3];    /*wheel velocity rel to cg N-E-D*/
 180     DATA v_wheel_body_v[3];             /* wheel velocity,        X-Y-Z */
 181     DATA v_wheel_local_v[3];            /* wheel velocity,        N-E-D */
 182     DATA f_wheel_local_v[3];            /* wheel reaction force,  N-E-D */
 183         DATA altitude_local_v[3];       /*altitude vector in local (N-E-D) i.e. (0,0,h)*/
 184         DATA altitude_body_v[3];        /*altitude vector in body (X,Y,Z)*/
 185     DATA temp3a[3], temp3b[3], tempF[3], tempM[3];
 186     DATA reaction_normal_force;         /* wheel normal (to rwy) force  */
 187     DATA cos_wheel_hdg_angle, sin_wheel_hdg_angle;      /* temp storage */
 188     DATA v_wheel_forward, v_wheel_sideward,  abs_v_wheel_sideward;
 189     DATA forward_mu, sideward_mu;       /* friction coefficients        */
 190     DATA beta_mu;                       /* breakout friction slope      */
 191     DATA forward_wheel_force, sideward_wheel_force;
 192
 193     int i;                              /* per wheel loop counter */
 194
 195   /*
 196    * Execution starts here
 197    */
 198
 199     beta_mu = max_mu/(skid_v-bkout_v);
 200     clear3( F_gear_v );         /* Initialize sum of forces...  */
 201     clear3( M_gear_v );         /* ...and moments               */
 202
 203   /*
 204    * Put aircraft specific executable code here
 205    */
 206
 207     percent_brake[1] = Brake_pct; /* replace with cockpit brake handle connection code */
 208     percent_brake[2] = percent_brake[1];
 209
 210     caster_angle_rad[0] = 0.52*Rudder_pedal;
 211
 212
 213         for (i=0;i<num_wheels;i++)          /* Loop for each wheel */
 214     {
 215                 /* printf("%s:\n",gear_strings[i]); */
 216
 217
 218
 219                 /*========================================*/
 220                 /* Calculate wheel position w.r.t. runway */
 221                 /*========================================*/
 222
 223
 224                 /* printf("\thgcg: %g, theta: %g,phi: %g\n",D_cg_above_rwy,Theta*RAD_TO_DEG,Phi*RAD_TO_DEG); */
 225
 226
 227                         /* First calculate wheel location w.r.t. cg in body (X-Y-Z) axes... */
 228
 229                 sub3( d_wheel_rp_body_v[i], D_cg_rp_body_v, d_wheel_cg_body_v );
 230
 231                 /* then converting to local (North-East-Down) axes... */
 232
 233                 multtrans3x3by3( T_local_to_body_m,  d_wheel_cg_body_v, d_wheel_cg_local_v );
 234
 235
 236                 /* Runway axes correction - third element is Altitude, not (-)Z... */
 237
 238                 d_wheel_cg_local_v[2] = -d_wheel_cg_local_v[2]; /* since altitude = -Z */
 239
 240                 /* Add wheel offset to cg location in local axes */
 241
 242                 add3( d_wheel_cg_local_v, D_cg_rwy_local_v, d_wheel_rwy_local_v );
 243
 244                 /* remove Runway axes correction so right hand rule applies */
 245
 246                 d_wheel_cg_local_v[2] = -d_wheel_cg_local_v[2]; /* now Z positive down */
 247
 248                 /*============================*/
 249                 /* Calculate wheel velocities */
 250                 /*============================*/
 251
 252                 /* contribution due to angular rates */
 253
 254                 cross3( Omega_body_v, d_wheel_cg_body_v, temp3a );
 255
 256                 /* transform into local axes */
 257
 258                 multtrans3x3by3( T_local_to_body_m, temp3a,v_wheel_cg_local_v );
 259
 260                 /* plus contribution due to cg velocities */
 261
 262                 add3( v_wheel_cg_local_v, V_local_rel_ground_v, v_wheel_local_v );
 263
 264                 clear3(f_wheel_local_v);
 265                 reaction_normal_force=0;
 266                 if( HEIGHT_AGL_WHEEL < 0. )
 267                         /*the wheel is underground -- which implies ground contact
 268                           so calculate reaction forces */
 269                         {
 270                         /*===========================================*/
 271                         /* Calculate forces & moments for this wheel */
 272                         /*===========================================*/
 273
 274                         /* Add any anticipation, or frame lead/prediction, here... */
 275
 276                                 /* no lead used at present */
 277
 278                         /* Calculate sideward and forward velocities of the wheel
 279                                 in the runway plane                                     */
 280
 281                         cos_wheel_hdg_angle = cos(caster_angle_rad[i] + Psi);
 282                         sin_wheel_hdg_angle = sin(caster_angle_rad[i] + Psi);
 283
 284                         v_wheel_forward  = v_wheel_local_v[0]*cos_wheel_hdg_angle
 285                                          + v_wheel_local_v[1]*sin_wheel_hdg_angle;
 286                         v_wheel_sideward = v_wheel_local_v[1]*cos_wheel_hdg_angle
 287                                          - v_wheel_local_v[0]*sin_wheel_hdg_angle;
 288
 289
 290                 /* Calculate normal load force (simple spring constant) */
 291
 292                 reaction_normal_force = 0.;
 293
 294                 reaction_normal_force = spring_constant[i]*d_wheel_rwy_local_v[2]
 295                                           - v_wheel_local_v[2]*spring_damping[i];
 296                         /* printf("\treaction_normal_force: %g\n",reaction_normal_force); */
 297
 298                 if (reaction_normal_force > 0.) reaction_normal_force = 0.;
 299                         /* to prevent damping component from swamping spring component */
 300
 301
 302                 /* Calculate friction coefficients */
 303
 304                         if(it_rolls[i])
 305                         {
 306                            forward_mu = (max_brake_mu[i] - rolling_mu[i])*percent_brake[i] + rolling_mu[i];
 307                            abs_v_wheel_sideward = sqrt(v_wheel_sideward*v_wheel_sideward);
 308                            sideward_mu = sliding_mu[i];
 309                            if (abs_v_wheel_sideward < skid_v)
 310                            sideward_mu = (abs_v_wheel_sideward - bkout_v)*beta_mu;
 311                            if (abs_v_wheel_sideward < bkout_v) sideward_mu = 0.;
 312                         }
 313                         else
 314                         {
 315                                 forward_mu=sliding_mu[i];
 316                                 sideward_mu=sliding_mu[i];
 317                         }
 318
 319                         /* Calculate foreward and sideward reaction forces */
 320
 321                         forward_wheel_force  =   forward_mu*reaction_normal_force;
 322                         sideward_wheel_force =  sideward_mu*reaction_normal_force;
 323                         if(v_wheel_forward < 0.) forward_wheel_force = -forward_wheel_force;
 324                         if(v_wheel_sideward < 0.) sideward_wheel_force = -sideward_wheel_force;
 325 /*                      printf("\tFfwdgear: %g Fsidegear: %g\n",forward_wheel_force,sideward_wheel_force);
 326  */
 327                         /* Rotate into local (N-E-D) axes */
 328
 329                         f_wheel_local_v[0] = forward_wheel_force*cos_wheel_hdg_angle
 330                                           - sideward_wheel_force*sin_wheel_hdg_angle;
 331                         f_wheel_local_v[1] = forward_wheel_force*sin_wheel_hdg_angle
 332                                           + sideward_wheel_force*cos_wheel_hdg_angle;
 333                         f_wheel_local_v[2] = reaction_normal_force;
 334
 335                          /* Convert reaction force from local (N-E-D) axes to body (X-Y-Z) */
 336                         mult3x3by3( T_local_to_body_m, f_wheel_local_v, tempF );
 337
 338                         /* Calculate moments from force and offsets in body axes */
 339
 340                         cross3( d_wheel_cg_body_v, tempF, tempM );
 341
 342                         /* Sum forces and moments across all wheels */
 343
 344                         add3( tempF, F_gear_v, F_gear_v );
 345                         add3( tempM, M_gear_v, M_gear_v );
 346
 347
 348                 }
 349
 350
 351
 352                 /* printf("\tN: %g,dZrwy: %g dZdotrwy: %g\n",reaction_normal_force,HEIGHT_AGL_WHEEL,v_wheel_cg_local_v[2]); */
 353
 354                 /*printf("\tFxgear: %g Fygear: %g, Fzgear: %g\n",F_X_gear,F_Y_gear,F_Z_gear);
 355                 printf("\tMgear: %g, Lgear: %g, Ngear: %g\n\n",M_m_gear,M_l_gear,M_n_gear); */
 356
 357
 358     }
 359 }