LaRCsim/navion_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  1998/01/19 18:40:29  curt
  40 Tons of little changes to clean up the code and to remove fatal errors
  41 when building with the c++ compiler.
  42
  43 Revision 1.1  1997/05/29 00:10:02  curt
  44 Initial Flight Gear revision.
  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 void gear( SCALAR dt, int Initialize ) {
 116 char rcsid[] = "$Id$";
 117
 118   /*
 119    * Aircraft specific initializations and data goes here
 120    */
 121
 122 #define NUM_WHEELS 3
 123
 124     static int num_wheels = NUM_WHEELS;             /* number of wheels  */
 125     static DATA d_wheel_rp_body_v[NUM_WHEELS][3] =  /* X, Y, Z locations */
 126     {
 127         { 10.,  0., 4. },                               /* in feet */
 128         { -1.,  3., 4. },
 129         { -1., -3., 4. }
 130     };
 131     static DATA spring_constant[NUM_WHEELS] =       /* springiness, lbs/ft */
 132         { 1500., 5000., 5000. };
 133     static DATA spring_damping[NUM_WHEELS] =        /* damping, lbs/ft/sec */
 134         { 100.,  150.,  150. };
 135     static DATA percent_brake[NUM_WHEELS] =         /* percent applied braking */
 136         { 0.,  0.,  0. };                           /* 0 = none, 1 = full */
 137     static DATA caster_angle_rad[NUM_WHEELS] =      /* steerable tires - in */
 138         { 0., 0., 0.};                              /* radians, +CW */
 139   /*
 140    * End of aircraft specific code
 141    */
 142
 143   /*
 144    * Constants & coefficients for tyres on tarmac - ref [1]
 145    */
 146
 147     /* skid function looks like:
 148      *
 149      *           mu  ^
 150      *               |
 151      *       max_mu  |       +
 152      *               |      /|
 153      *   sliding_mu  |     / +------
 154      *               |    /
 155      *               |   /
 156      *               +--+------------------------>
 157      *               |  |    |      sideward V
 158      *               0 bkout skid
 159      *                 V     V
 160      */
 161
 162
 163     static DATA sliding_mu   = 0.5;
 164     static DATA rolling_mu   = 0.01;
 165     static DATA max_brake_mu = 0.6;
 166     static DATA max_mu       = 0.8;
 167     static DATA bkout_v      = 0.1;
 168     static DATA skid_v       = 1.0;
 169   /*
 170    * Local data variables
 171    */
 172
 173     DATA d_wheel_cg_body_v[3];          /* wheel offset from cg,  X-Y-Z */
 174     DATA d_wheel_cg_local_v[3];         /* wheel offset from cg,  N-E-D */
 175     DATA d_wheel_rwy_local_v[3];        /* wheel offset from rwy, N-E-U */
 176     DATA v_wheel_body_v[3];             /* wheel velocity,        X-Y-Z */
 177     DATA v_wheel_local_v[3];            /* wheel velocity,        N-E-D */
 178     DATA f_wheel_local_v[3];            /* wheel reaction force,  N-E-D */
 179     DATA temp3a[3], temp3b[3], tempF[3], tempM[3];
 180     DATA reaction_normal_force;         /* wheel normal (to rwy) force  */
 181     DATA cos_wheel_hdg_angle, sin_wheel_hdg_angle;      /* temp storage */
 182     DATA v_wheel_forward, v_wheel_sideward,  abs_v_wheel_sideward;
 183     DATA forward_mu, sideward_mu;       /* friction coefficients        */
 184     DATA beta_mu;                       /* breakout friction slope      */
 185     DATA forward_wheel_force, sideward_wheel_force;
 186
 187     int i;                              /* per wheel loop counter */
 188
 189   /*
 190    * Execution starts here
 191    */
 192
 193     beta_mu = max_mu/(skid_v-bkout_v);
 194     clear3( F_gear_v );         /* Initialize sum of forces...  */
 195     clear3( M_gear_v );         /* ...and moments               */
 196
 197   /*
 198    * Put aircraft specific executable code here
 199    */
 200
 201     percent_brake[1] = 0.; /* replace with cockpit brake handle connection code */
 202     percent_brake[2] = percent_brake[1];
 203
 204     caster_angle_rad[0] = 0.03*Rudder_pedal;
 205
 206     for (i=0;i<num_wheels;i++)      /* Loop for each wheel */
 207     {
 208         /*========================================*/
 209         /* Calculate wheel position w.r.t. runway */
 210         /*========================================*/
 211
 212             /* First calculate wheel location w.r.t. cg in body (X-Y-Z) axes... */
 213
 214         sub3( d_wheel_rp_body_v[i], D_cg_rp_body_v, d_wheel_cg_body_v );
 215
 216             /* then converting to local (North-East-Down) axes... */
 217
 218         multtrans3x3by3( T_local_to_body_m,  d_wheel_cg_body_v, d_wheel_cg_local_v );
 219
 220             /* Runway axes correction - third element is Altitude, not (-)Z... */
 221
 222         d_wheel_cg_local_v[2] = -d_wheel_cg_local_v[2]; /* since altitude = -Z */
 223
 224             /* Add wheel offset to cg location in local axes */
 225
 226         add3( d_wheel_cg_local_v, D_cg_rwy_local_v, d_wheel_rwy_local_v );
 227
 228             /* remove Runway axes correction so right hand rule applies */
 229
 230         d_wheel_cg_local_v[2] = -d_wheel_cg_local_v[2]; /* now Z positive down */
 231
 232         /*============================*/
 233         /* Calculate wheel velocities */
 234         /*============================*/
 235
 236             /* contribution due to angular rates */
 237
 238         cross3( Omega_body_v, d_wheel_cg_body_v, temp3a );
 239
 240             /* transform into local axes */
 241
 242         multtrans3x3by3( T_local_to_body_m, temp3a, temp3b );
 243
 244             /* plus contribution due to cg velocities */
 245
 246         add3( temp3b, V_local_rel_ground_v, v_wheel_local_v );
 247
 248
 249         /*===========================================*/
 250         /* Calculate forces & moments for this wheel */
 251         /*===========================================*/
 252
 253             /* Add any anticipation, or frame lead/prediction, here... */
 254
 255                     /* no lead used at present */
 256
 257             /* Calculate sideward and forward velocities of the wheel
 258                     in the runway plane                                 */
 259
 260         cos_wheel_hdg_angle = cos(caster_angle_rad[i] + Psi);
 261         sin_wheel_hdg_angle = sin(caster_angle_rad[i] + Psi);
 262
 263         v_wheel_forward  = v_wheel_local_v[0]*cos_wheel_hdg_angle
 264                          + v_wheel_local_v[1]*sin_wheel_hdg_angle;
 265         v_wheel_sideward = v_wheel_local_v[1]*cos_wheel_hdg_angle
 266                          - v_wheel_local_v[0]*sin_wheel_hdg_angle;
 267
 268             /* Calculate normal load force (simple spring constant) */
 269
 270         reaction_normal_force = 0.;
 271         if( d_wheel_rwy_local_v[2] < 0. )
 272         {
 273             reaction_normal_force = spring_constant[i]*d_wheel_rwy_local_v[2]
 274                                   - v_wheel_local_v[2]*spring_damping[i];
 275             if (reaction_normal_force > 0.) reaction_normal_force = 0.;
 276                 /* to prevent damping component from swamping spring component */
 277         }
 278
 279             /* Calculate friction coefficients */
 280
 281         forward_mu = (max_brake_mu - rolling_mu)*percent_brake[i] + rolling_mu;
 282         abs_v_wheel_sideward = sqrt(v_wheel_sideward*v_wheel_sideward);
 283         sideward_mu = sliding_mu;
 284         if (abs_v_wheel_sideward < skid_v)
 285             sideward_mu = (abs_v_wheel_sideward - bkout_v)*beta_mu;
 286         if (abs_v_wheel_sideward < bkout_v) sideward_mu = 0.;
 287
 288             /* Calculate foreward and sideward reaction forces */
 289
 290         forward_wheel_force  =   forward_mu*reaction_normal_force;
 291         sideward_wheel_force =  sideward_mu*reaction_normal_force;
 292         if(v_wheel_forward < 0.) forward_wheel_force = -forward_wheel_force;
 293         if(v_wheel_sideward < 0.) sideward_wheel_force = -sideward_wheel_force;
 294
 295             /* Rotate into local (N-E-D) axes */
 296
 297         f_wheel_local_v[0] = forward_wheel_force*cos_wheel_hdg_angle
 298                           - sideward_wheel_force*sin_wheel_hdg_angle;
 299         f_wheel_local_v[1] = forward_wheel_force*sin_wheel_hdg_angle
 300                           + sideward_wheel_force*cos_wheel_hdg_angle;
 301         f_wheel_local_v[2] = reaction_normal_force;
 302
 303             /* Convert reaction force from local (N-E-D) axes to body (X-Y-Z) */
 304
 305         mult3x3by3( T_local_to_body_m, f_wheel_local_v, tempF );
 306
 307             /* Calculate moments from force and offsets in body axes */
 308
 309         cross3( d_wheel_cg_body_v, tempF, tempM );
 310
 311         /* Sum forces and moments across all wheels */
 312
 313         add3( tempF, F_gear_v, F_gear_v );
 314         add3( tempM, M_gear_v, M_gear_v );
 315
 316     }
 317 }