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 1.2  1999/08/19 21:24:03  curt
  40 Updated Tony's c172 model code.
  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
  71 sub3( DATA v1[],  DATA v2[], DATA result[] )
  72 {
  73     result[0] = v1[0] - v2[0];
  74     result[1] = v1[1] - v2[1];
  75     result[2] = v1[2] - v2[2];
  76 }
  77
  78 add3( DATA v1[],  DATA v2[], DATA result[] )
  79 {
  80     result[0] = v1[0] + v2[0];
  81     result[1] = v1[1] + v2[1];
  82     result[2] = v1[2] + v2[2];
  83 }
  84
  85 cross3( DATA v1[],  DATA v2[], DATA result[] )
  86 {
  87     result[0] = v1[1]*v2[2] - v1[2]*v2[1];
  88     result[1] = v1[2]*v2[0] - v1[0]*v2[2];
  89     result[2] = v1[0]*v2[1] - v1[1]*v2[0];
  90 }
  91
  92 multtrans3x3by3( DATA m[][3], DATA v[], DATA result[] )
  93 {
  94     result[0] = m[0][0]*v[0] + m[1][0]*v[1] + m[2][0]*v[2];
  95     result[1] = m[0][1]*v[0] + m[1][1]*v[1] + m[2][1]*v[2];
  96     result[2] = m[0][2]*v[0] + m[1][2]*v[1] + m[2][2]*v[2];
  97 }
  98
  99 mult3x3by3( DATA m[][3], DATA v[], DATA result[] )
 100 {
 101     result[0] = m[0][0]*v[0] + m[0][1]*v[1] + m[0][2]*v[2];
 102     result[1] = m[1][0]*v[0] + m[1][1]*v[1] + m[1][2]*v[2];
 103     result[2] = m[2][0]*v[0] + m[2][1]*v[1] + m[2][2]*v[2];
 104 }
 105
 106 clear3( DATA v[] )
 107 {
 108     v[0] = 0.; v[1] = 0.; v[2] = 0.;
 109 }
 110
 111 gear()
 112 {
 113 char rcsid[] = "$Id$";
 114
 115   /*
 116    * Aircraft specific initializations and data goes here
 117    */
 118
 119 #define NUM_WHEELS 3
 120
 121     static int num_wheels = NUM_WHEELS;             /* number of wheels  */
 122     static DATA d_wheel_rp_body_v[NUM_WHEELS][3] =  /* X, Y, Z locations */
 123     {
 124         { 10.,  0., 4. },                               /* in feet */
 125         { -1.,  3., 4. },
 126         { -1., -3., 4. }
 127     };
 128     static DATA spring_constant[NUM_WHEELS] =       /* springiness, lbs/ft */
 129         { 1500., 5000., 5000. };
 130     static DATA spring_damping[NUM_WHEELS] =        /* damping, lbs/ft/sec */
 131         { 100.,  150.,  150. };
 132     static DATA percent_brake[NUM_WHEELS] =         /* percent applied braking */
 133         { 0.,  0.,  0. };                           /* 0 = none, 1 = full */
 134     static DATA caster_angle_rad[NUM_WHEELS] =      /* steerable tires - in */
 135         { 0., 0., 0.};                              /* radians, +CW */
 136   /*
 137    * End of aircraft specific code
 138    */
 139
 140   /*
 141    * Constants & coefficients for tyres on tarmac - ref [1]
 142    */
 143
 144     /* skid function looks like:
 145      *
 146      *           mu  ^
 147      *               |
 148      *       max_mu  |       +
 149      *               |      /|
 150      *   sliding_mu  |     / +------
 151      *               |    /
 152      *               |   /
 153      *               +--+------------------------>
 154      *               |  |    |      sideward V
 155      *               0 bkout skid
 156      *                 V     V
 157      */
 158
 159
 160     static DATA sliding_mu   = 0.5;
 161     static DATA rolling_mu   = 0.01;
 162     static DATA max_brake_mu = 0.6;
 163     static DATA max_mu       = 0.8;
 164     static DATA bkout_v      = 0.1;
 165     static DATA skid_v       = 1.0;
 166   /*
 167    * Local data variables
 168    */
 169
 170     DATA d_wheel_cg_body_v[3];          /* wheel offset from cg,  X-Y-Z */
 171     DATA d_wheel_cg_local_v[3];         /* wheel offset from cg,  N-E-D */
 172     DATA d_wheel_rwy_local_v[3];        /* wheel offset from rwy, N-E-U */
 173     DATA v_wheel_body_v[3];             /* wheel velocity,        X-Y-Z */
 174     DATA v_wheel_local_v[3];            /* wheel velocity,        N-E-D */
 175     DATA f_wheel_local_v[3];            /* wheel reaction force,  N-E-D */
 176     DATA temp3a[3], temp3b[3], tempF[3], tempM[3];
 177     DATA reaction_normal_force;         /* wheel normal (to rwy) force  */
 178     DATA cos_wheel_hdg_angle, sin_wheel_hdg_angle;      /* temp storage */
 179     DATA v_wheel_forward, v_wheel_sideward,  abs_v_wheel_sideward;
 180     DATA forward_mu, sideward_mu;       /* friction coefficients        */
 181     DATA beta_mu;                       /* breakout friction slope      */
 182     DATA forward_wheel_force, sideward_wheel_force;
 183
 184     int i;                              /* per wheel loop counter */
 185
 186   /*
 187    * Execution starts here
 188    */
 189
 190     beta_mu = max_mu/(skid_v-bkout_v);
 191     clear3( F_gear_v );         /* Initialize sum of forces...  */
 192     clear3( M_gear_v );         /* ...and moments               */
 193
 194   /*
 195    * Put aircraft specific executable code here
 196    */
 197
 198     percent_brake[1] = 0.; /* replace with cockpit brake handle connection code */
 199     percent_brake[2] = percent_brake[1];
 200
 201     caster_angle_rad[0] = 0.03*Rudder_pedal;
 202
 203     for (i=0;i<num_wheels;i++)      /* Loop for each wheel */
 204     {
 205         /*========================================*/
 206         /* Calculate wheel position w.r.t. runway */
 207         /*========================================*/
 208
 209             /* First calculate wheel location w.r.t. cg in body (X-Y-Z) axes... */
 210
 211         sub3( d_wheel_rp_body_v[i], D_cg_rp_body_v, d_wheel_cg_body_v );
 212
 213             /* then converting to local (North-East-Down) axes... */
 214
 215         multtrans3x3by3( T_local_to_body_m,  d_wheel_cg_body_v, d_wheel_cg_local_v );
 216
 217             /* Runway axes correction - third element is Altitude, not (-)Z... */
 218
 219         d_wheel_cg_local_v[2] = -d_wheel_cg_local_v[2]; /* since altitude = -Z */
 220
 221             /* Add wheel offset to cg location in local axes */
 222
 223         add3( d_wheel_cg_local_v, D_cg_rwy_local_v, d_wheel_rwy_local_v );
 224
 225             /* remove Runway axes correction so right hand rule applies */
 226
 227         d_wheel_cg_local_v[2] = -d_wheel_cg_local_v[2]; /* now Z positive down */
 228
 229         /*============================*/
 230         /* Calculate wheel velocities */
 231         /*============================*/
 232
 233             /* contribution due to angular rates */
 234
 235         cross3( Omega_body_v, d_wheel_cg_body_v, temp3a );
 236
 237             /* transform into local axes */
 238
 239         multtrans3x3by3( T_local_to_body_m, temp3a, temp3b );
 240
 241             /* plus contribution due to cg velocities */
 242
 243         add3( temp3b, V_local_rel_ground_v, v_wheel_local_v );
 244
 245
 246         /*===========================================*/
 247         /* Calculate forces & moments for this wheel */
 248         /*===========================================*/
 249
 250             /* Add any anticipation, or frame lead/prediction, here... */
 251
 252                     /* no lead used at present */
 253
 254             /* Calculate sideward and forward velocities of the wheel
 255                     in the runway plane                                 */
 256
 257         cos_wheel_hdg_angle = cos(caster_angle_rad[i] + Psi);
 258         sin_wheel_hdg_angle = sin(caster_angle_rad[i] + Psi);
 259
 260         v_wheel_forward  = v_wheel_local_v[0]*cos_wheel_hdg_angle
 261                          + v_wheel_local_v[1]*sin_wheel_hdg_angle;
 262         v_wheel_sideward = v_wheel_local_v[1]*cos_wheel_hdg_angle
 263                          - v_wheel_local_v[0]*sin_wheel_hdg_angle;
 264
 265             /* Calculate normal load force (simple spring constant) */
 266
 267         reaction_normal_force = 0.;
 268         if( d_wheel_rwy_local_v[2] < 0. )
 269         {
 270             reaction_normal_force = spring_constant[i]*d_wheel_rwy_local_v[2]
 271                                   - v_wheel_local_v[2]*spring_damping[i];
 272             if (reaction_normal_force > 0.) reaction_normal_force = 0.;
 273                 /* to prevent damping component from swamping spring component */
 274         }
 275
 276             /* Calculate friction coefficients */
 277
 278         forward_mu = (max_brake_mu - rolling_mu)*percent_brake[i] + rolling_mu;
 279         abs_v_wheel_sideward = sqrt(v_wheel_sideward*v_wheel_sideward);
 280         sideward_mu = sliding_mu;
 281         if (abs_v_wheel_sideward < skid_v)
 282             sideward_mu = (abs_v_wheel_sideward - bkout_v)*beta_mu;
 283         if (abs_v_wheel_sideward < bkout_v) sideward_mu = 0.;
 284
 285             /* Calculate foreward and sideward reaction forces */
 286
 287         forward_wheel_force  =   forward_mu*reaction_normal_force;
 288         sideward_wheel_force =  sideward_mu*reaction_normal_force;
 289         if(v_wheel_forward < 0.) forward_wheel_force = -forward_wheel_force;
 290         if(v_wheel_sideward < 0.) sideward_wheel_force = -sideward_wheel_force;
 291
 292             /* Rotate into local (N-E-D) axes */
 293
 294         f_wheel_local_v[0] = forward_wheel_force*cos_wheel_hdg_angle
 295                           - sideward_wheel_force*sin_wheel_hdg_angle;
 296         f_wheel_local_v[1] = forward_wheel_force*sin_wheel_hdg_angle
 297                           + sideward_wheel_force*cos_wheel_hdg_angle;
 298         f_wheel_local_v[2] = reaction_normal_force;
 299
 300             /* Convert reaction force from local (N-E-D) axes to body (X-Y-Z) */
 301
 302         mult3x3by3( T_local_to_body_m, f_wheel_local_v, tempF );
 303
 304             /* Calculate moments from force and offsets in body axes */
 305
 306         cross3( d_wheel_cg_body_v, tempF, tempM );
 307
 308         /* Sum forces and moments across all wheels */
 309
 310         add3( tempF, F_gear_v, F_gear_v );
 311         add3( tempM, M_gear_v, M_gear_v );
 312
 313     }
 314 }