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 1.10  1999/11/03 16:46:24  curt
  40 Patches from Tony to enable brakes.
  41
  42 Revision 1.9  1999/11/01 18:17:16  curt
  43 c172 updates from Tony.  Fix extra yaw when using ailerons.  Flaps and elevator
  44 tweaks.
  45
  46
  47 ----------------------------------------------------------------------------
  48
  49         REFERENCES:
  50
  51 ----------------------------------------------------------------------------
  52
  53         CALLED BY:
  54
  55 ----------------------------------------------------------------------------
  56
  57         CALLS TO:
  58
  59 ----------------------------------------------------------------------------
  60
  61         INPUTS:
  62
  63 ----------------------------------------------------------------------------
  64
  65         OUTPUTS:
  66
  67 --------------------------------------------------------------------------*/
  68 #include <math.h>
  69 #include "ls_types.h"
  70 #include "ls_constants.h"
  71 #include "ls_generic.h"
  72 #include "ls_cockpit.h"
  73
  74
  75 sub3( DATA v1[],  DATA v2[], DATA result[] )
  76 {
  77     result[0] = v1[0] - v2[0];
  78     result[1] = v1[1] - v2[1];
  79     result[2] = v1[2] - v2[2];
  80 }
  81
  82 add3( DATA v1[],  DATA v2[], DATA result[] )
  83 {
  84     result[0] = v1[0] + v2[0];
  85     result[1] = v1[1] + v2[1];
  86     result[2] = v1[2] + v2[2];
  87 }
  88
  89 cross3( DATA v1[],  DATA v2[], DATA result[] )
  90 {
  91     result[0] = v1[1]*v2[2] - v1[2]*v2[1];
  92     result[1] = v1[2]*v2[0] - v1[0]*v2[2];
  93     result[2] = v1[0]*v2[1] - v1[1]*v2[0];
  94 }
  95
  96 multtrans3x3by3( DATA m[][3], DATA v[], DATA result[] )
  97 {
  98     result[0] = m[0][0]*v[0] + m[1][0]*v[1] + m[2][0]*v[2];
  99     result[1] = m[0][1]*v[0] + m[1][1]*v[1] + m[2][1]*v[2];
 100     result[2] = m[0][2]*v[0] + m[1][2]*v[1] + m[2][2]*v[2];
 101 }
 102
 103 mult3x3by3( DATA m[][3], DATA v[], DATA result[] )
 104 {
 105     result[0] = m[0][0]*v[0] + m[0][1]*v[1] + m[0][2]*v[2];
 106     result[1] = m[1][0]*v[0] + m[1][1]*v[1] + m[1][2]*v[2];
 107     result[2] = m[2][0]*v[0] + m[2][1]*v[1] + m[2][2]*v[2];
 108 }
 109
 110 clear3( DATA v[] )
 111 {
 112     v[0] = 0.; v[1] = 0.; v[2] = 0.;
 113 }
 114
 115 gear()
 116 {
 117 char rcsid[] = "$Id$";
 118
 119   /*
 120    * Aircraft specific initializations and data goes here
 121    */
 122
 123 #define NUM_WHEELS 3
 124
 125     static int num_wheels = NUM_WHEELS;             /* number of wheels  */
 126     static DATA d_wheel_rp_body_v[NUM_WHEELS][3] =  /* X, Y, Z locations */
 127     {
 128         { 10.,  0., 4. },                               /* in feet */
 129         { -1.,  3., 4. },
 130         { -1., -3., 4. }
 131     };
 132     static DATA spring_constant[NUM_WHEELS] =       /* springiness, lbs/ft */
 133         { 1500., 5000., 5000. };
 134     static DATA spring_damping[NUM_WHEELS] =        /* damping, lbs/ft/sec */
 135         { 100.,  150.,  150. };
 136     static DATA percent_brake[NUM_WHEELS] =         /* percent applied braking */
 137         { 0.,  0.,  0. };                           /* 0 = none, 1 = full */
 138     static DATA caster_angle_rad[NUM_WHEELS] =      /* steerable tires - in */
 139         { 0., 0., 0.};                              /* radians, +CW */
 140   /*
 141    * End of aircraft specific code
 142    */
 143
 144   /*
 145    * Constants & coefficients for tyres on tarmac - ref [1]
 146    */
 147
 148     /* skid function looks like:
 149      *
 150      *           mu  ^
 151      *               |
 152      *       max_mu  |       +
 153      *               |      /|
 154      *   sliding_mu  |     / +------
 155      *               |    /
 156      *               |   /
 157      *               +--+------------------------>
 158      *               |  |    |      sideward V
 159      *               0 bkout skid
 160      *                 V     V
 161      */
 162
 163
 164     static DATA sliding_mu   = 0.5;
 165     static DATA rolling_mu   = 0.01;
 166     static DATA max_brake_mu = 0.6;
 167     static DATA max_mu       = 0.8;
 168     static DATA bkout_v      = 0.1;
 169     static DATA skid_v       = 1.0;
 170   /*
 171    * Local data variables
 172    */
 173
 174     DATA d_wheel_cg_body_v[3];          /* wheel offset from cg,  X-Y-Z */
 175     DATA d_wheel_cg_local_v[3];         /* wheel offset from cg,  N-E-D */
 176     DATA d_wheel_rwy_local_v[3];        /* wheel offset from rwy, N-E-U */
 177     DATA v_wheel_body_v[3];             /* wheel velocity,        X-Y-Z */
 178     DATA v_wheel_local_v[3];            /* wheel velocity,        N-E-D */
 179     DATA f_wheel_local_v[3];            /* wheel reaction force,  N-E-D */
 180     DATA temp3a[3], temp3b[3], tempF[3], tempM[3];
 181     DATA reaction_normal_force;         /* wheel normal (to rwy) force  */
 182     DATA cos_wheel_hdg_angle, sin_wheel_hdg_angle;      /* temp storage */
 183     DATA v_wheel_forward, v_wheel_sideward,  abs_v_wheel_sideward;
 184     DATA forward_mu, sideward_mu;       /* friction coefficients        */
 185     DATA beta_mu;                       /* breakout friction slope      */
 186     DATA forward_wheel_force, sideward_wheel_force;
 187
 188     int i;                              /* per wheel loop counter */
 189
 190   /*
 191    * Execution starts here
 192    */
 193
 194     beta_mu = max_mu/(skid_v-bkout_v);
 195     clear3( F_gear_v );         /* Initialize sum of forces...  */
 196     clear3( M_gear_v );         /* ...and moments               */
 197
 198   /*
 199    * Put aircraft specific executable code here
 200    */
 201
 202     percent_brake[1] = Brake_pct; /* replace with cockpit brake handle connection code */
 203     percent_brake[2] = percent_brake[1];
 204
 205     caster_angle_rad[0] = 0.03*Rudder_pedal;
 206
 207     for (i=0;i<num_wheels;i++)      /* Loop for each wheel */
 208     {
 209         /*========================================*/
 210         /* Calculate wheel position w.r.t. runway */
 211         /*========================================*/
 212
 213             /* First calculate wheel location w.r.t. cg in body (X-Y-Z) axes... */
 214
 215         sub3( d_wheel_rp_body_v[i], D_cg_rp_body_v, d_wheel_cg_body_v );
 216
 217             /* then converting to local (North-East-Down) axes... */
 218
 219         multtrans3x3by3( T_local_to_body_m,  d_wheel_cg_body_v, d_wheel_cg_local_v );
 220
 221             /* Runway axes correction - third element is Altitude, not (-)Z... */
 222
 223         d_wheel_cg_local_v[2] = -d_wheel_cg_local_v[2]; /* since altitude = -Z */
 224
 225             /* Add wheel offset to cg location in local axes */
 226
 227         add3( d_wheel_cg_local_v, D_cg_rwy_local_v, d_wheel_rwy_local_v );
 228
 229             /* remove Runway axes correction so right hand rule applies */
 230
 231         d_wheel_cg_local_v[2] = -d_wheel_cg_local_v[2]; /* now Z positive down */
 232
 233         /*============================*/
 234         /* Calculate wheel velocities */
 235         /*============================*/
 236
 237             /* contribution due to angular rates */
 238
 239         cross3( Omega_body_v, d_wheel_cg_body_v, temp3a );
 240
 241             /* transform into local axes */
 242
 243         multtrans3x3by3( T_local_to_body_m, temp3a, temp3b );
 244
 245             /* plus contribution due to cg velocities */
 246
 247         add3( temp3b, V_local_rel_ground_v, v_wheel_local_v );
 248
 249
 250         /*===========================================*/
 251         /* Calculate forces & moments for this wheel */
 252         /*===========================================*/
 253
 254             /* Add any anticipation, or frame lead/prediction, here... */
 255
 256                     /* no lead used at present */
 257
 258             /* Calculate sideward and forward velocities of the wheel
 259                     in the runway plane                                 */
 260
 261         cos_wheel_hdg_angle = cos(caster_angle_rad[i] + Psi);
 262         sin_wheel_hdg_angle = sin(caster_angle_rad[i] + Psi);
 263
 264         v_wheel_forward  = v_wheel_local_v[0]*cos_wheel_hdg_angle
 265                          + v_wheel_local_v[1]*sin_wheel_hdg_angle;
 266         v_wheel_sideward = v_wheel_local_v[1]*cos_wheel_hdg_angle
 267                          - v_wheel_local_v[0]*sin_wheel_hdg_angle;
 268
 269             /* Calculate normal load force (simple spring constant) */
 270
 271         reaction_normal_force = 0.;
 272         if( d_wheel_rwy_local_v[2] < 0. )
 273         {
 274             reaction_normal_force = spring_constant[i]*d_wheel_rwy_local_v[2]
 275                                   - v_wheel_local_v[2]*spring_damping[i];
 276             if (reaction_normal_force > 0.) reaction_normal_force = 0.;
 277                 /* to prevent damping component from swamping spring component */
 278         }
 279
 280             /* Calculate friction coefficients */
 281
 282         forward_mu = (max_brake_mu - rolling_mu)*percent_brake[i] + rolling_mu;
 283         abs_v_wheel_sideward = sqrt(v_wheel_sideward*v_wheel_sideward);
 284         sideward_mu = sliding_mu;
 285         if (abs_v_wheel_sideward < skid_v)
 286             sideward_mu = (abs_v_wheel_sideward - bkout_v)*beta_mu;
 287         if (abs_v_wheel_sideward < bkout_v) sideward_mu = 0.;
 288
 289             /* Calculate foreward and sideward reaction forces */
 290
 291         forward_wheel_force  =   forward_mu*reaction_normal_force;
 292         sideward_wheel_force =  sideward_mu*reaction_normal_force;
 293         if(v_wheel_forward < 0.) forward_wheel_force = -forward_wheel_force;
 294         if(v_wheel_sideward < 0.) sideward_wheel_force = -sideward_wheel_force;
 295
 296             /* Rotate into local (N-E-D) axes */
 297
 298         f_wheel_local_v[0] = forward_wheel_force*cos_wheel_hdg_angle
 299                           - sideward_wheel_force*sin_wheel_hdg_angle;
 300         f_wheel_local_v[1] = forward_wheel_force*sin_wheel_hdg_angle
 301                           + sideward_wheel_force*cos_wheel_hdg_angle;
 302         f_wheel_local_v[2] = reaction_normal_force;
 303
 304             /* Convert reaction force from local (N-E-D) axes to body (X-Y-Z) */
 305
 306         mult3x3by3( T_local_to_body_m, f_wheel_local_v, tempF );
 307
 308             /* Calculate moments from force and offsets in body axes */
 309
 310         cross3( d_wheel_cg_body_v, tempF, tempM );
 311
 312         /* Sum forces and moments across all wheels */
 313
 314         add3( tempF, F_gear_v, F_gear_v );
 315         add3( tempM, M_gear_v, M_gear_v );
 316
 317     }
 318 }