1 /***************************************************************************
5 ----------------------------------------------------------------------------
7 FUNCTION: Landing gear model for example simulation
9 ----------------------------------------------------------------------------
11 MODULE STATUS: developmental
13 ----------------------------------------------------------------------------
15 GENEALOGY: Created 931012 by E. B. Jackson
17 ----------------------------------------------------------------------------
19 DESIGNED BY: E. B. Jackson
21 CODED BY: E. B. Jackson
23 MAINTAINED BY: E. B. Jackson
25 ----------------------------------------------------------------------------
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.
39 Revision 1.1 1999/06/17 18:07:34 curt
42 Revision 1.1.1.1 1999/04/05 21:32:45 curt
43 Start of 0.6.x branch.
45 Revision 1.6 1998/10/17 01:34:16 curt
48 Revision 1.5 1998/09/29 02:03:00 curt
49 Added a brake + autopilot mods.
51 Revision 1.4 1998/08/06 12:46:40 curt
54 Revision 1.3 1998/02/03 23:20:18 curt
55 Lots of little tweaks to fix various consistency problems discovered by
56 Solaris' CC. Fixed a bug in fg_debug.c with how the fgPrintf() wrapper
57 passed arguments along to the real printf(). Also incorporated HUD changes
60 Revision 1.2 1998/01/19 18:40:29 curt
61 Tons of little changes to clean up the code and to remove fatal errors
62 when building with the c++ compiler.
64 Revision 1.1 1997/05/29 00:10:02 curt
65 Initial Flight Gear revision.
68 ----------------------------------------------------------------------------
72 ----------------------------------------------------------------------------
76 ----------------------------------------------------------------------------
80 ----------------------------------------------------------------------------
84 ----------------------------------------------------------------------------
88 --------------------------------------------------------------------------*/
91 #include "ls_constants.h"
92 #include "ls_generic.h"
93 #include "ls_cockpit.h"
96 void sub3( DATA v1[], DATA v2[], DATA result[] )
98 result[0] = v1[0] - v2[0];
99 result[1] = v1[1] - v2[1];
100 result[2] = v1[2] - v2[2];
103 void add3( DATA v1[], DATA v2[], DATA result[] )
105 result[0] = v1[0] + v2[0];
106 result[1] = v1[1] + v2[1];
107 result[2] = v1[2] + v2[2];
110 void cross3( DATA v1[], DATA v2[], DATA result[] )
112 result[0] = v1[1]*v2[2] - v1[2]*v2[1];
113 result[1] = v1[2]*v2[0] - v1[0]*v2[2];
114 result[2] = v1[0]*v2[1] - v1[1]*v2[0];
117 void multtrans3x3by3( DATA m[][3], DATA v[], DATA result[] )
119 result[0] = m[0][0]*v[0] + m[1][0]*v[1] + m[2][0]*v[2];
120 result[1] = m[0][1]*v[0] + m[1][1]*v[1] + m[2][1]*v[2];
121 result[2] = m[0][2]*v[0] + m[1][2]*v[1] + m[2][2]*v[2];
124 void mult3x3by3( DATA m[][3], DATA v[], DATA result[] )
126 result[0] = m[0][0]*v[0] + m[0][1]*v[1] + m[0][2]*v[2];
127 result[1] = m[1][0]*v[0] + m[1][1]*v[1] + m[1][2]*v[2];
128 result[2] = m[2][0]*v[0] + m[2][1]*v[1] + m[2][2]*v[2];
131 void clear3( DATA v[] )
133 v[0] = 0.; v[1] = 0.; v[2] = 0.;
136 void gear( SCALAR dt, int Initialize ) {
137 char rcsid[] = "$Id$";
140 * Aircraft specific initializations and data goes here
145 static int num_wheels = NUM_WHEELS; /* number of wheels */
146 static DATA d_wheel_rp_body_v[NUM_WHEELS][3] = /* X, Y, Z locations */
148 { 10., 0., 4. }, /* in feet */
152 static DATA spring_constant[NUM_WHEELS] = /* springiness, lbs/ft */
153 { 1500., 5000., 5000. };
154 static DATA spring_damping[NUM_WHEELS] = /* damping, lbs/ft/sec */
155 { 100., 150., 150. };
156 static DATA percent_brake[NUM_WHEELS] = /* percent applied braking */
157 { 0., 0., 0. }; /* 0 = none, 1 = full */
158 static DATA caster_angle_rad[NUM_WHEELS] = /* steerable tires - in */
159 { 0., 0., 0.}; /* radians, +CW */
161 * End of aircraft specific code
165 * Constants & coefficients for tyres on tarmac - ref [1]
168 /* skid function looks like:
174 * sliding_mu | / +------
177 * +--+------------------------>
184 static DATA sliding_mu = 0.5;
185 static DATA rolling_mu = 0.01;
186 static DATA max_brake_mu = 0.6;
187 static DATA max_mu = 0.8;
188 static DATA bkout_v = 0.1;
189 static DATA skid_v = 1.0;
191 * Local data variables
194 DATA d_wheel_cg_body_v[3]; /* wheel offset from cg, X-Y-Z */
195 DATA d_wheel_cg_local_v[3]; /* wheel offset from cg, N-E-D */
196 DATA d_wheel_rwy_local_v[3]; /* wheel offset from rwy, N-E-U */
197 DATA v_wheel_body_v[3]; /* wheel velocity, X-Y-Z */
198 DATA v_wheel_local_v[3]; /* wheel velocity, N-E-D */
199 DATA f_wheel_local_v[3]; /* wheel reaction force, N-E-D */
200 DATA temp3a[3], temp3b[3], tempF[3], tempM[3];
201 DATA reaction_normal_force; /* wheel normal (to rwy) force */
202 DATA cos_wheel_hdg_angle, sin_wheel_hdg_angle; /* temp storage */
203 DATA v_wheel_forward, v_wheel_sideward, abs_v_wheel_sideward;
204 DATA forward_mu, sideward_mu; /* friction coefficients */
205 DATA beta_mu; /* breakout friction slope */
206 DATA forward_wheel_force, sideward_wheel_force;
208 int i; /* per wheel loop counter */
211 * Execution starts here
214 beta_mu = max_mu/(skid_v-bkout_v);
215 clear3( F_gear_v ); /* Initialize sum of forces... */
216 clear3( M_gear_v ); /* ...and moments */
219 * Put aircraft specific executable code here
222 /* replace with cockpit brake handle connection code */
223 percent_brake[1] = Brake_pct;
224 percent_brake[2] = percent_brake[1];
226 caster_angle_rad[0] = 0.03*Rudder_pedal;
228 for (i=0;i<num_wheels;i++) /* Loop for each wheel */
230 /*========================================*/
231 /* Calculate wheel position w.r.t. runway */
232 /*========================================*/
234 /* First calculate wheel location w.r.t. cg in body (X-Y-Z) axes... */
236 sub3( d_wheel_rp_body_v[i], D_cg_rp_body_v, d_wheel_cg_body_v );
238 /* then converting to local (North-East-Down) axes... */
240 multtrans3x3by3( T_local_to_body_m, d_wheel_cg_body_v, d_wheel_cg_local_v );
242 /* Runway axes correction - third element is Altitude, not (-)Z... */
244 d_wheel_cg_local_v[2] = -d_wheel_cg_local_v[2]; /* since altitude = -Z */
246 /* Add wheel offset to cg location in local axes */
248 add3( d_wheel_cg_local_v, D_cg_rwy_local_v, d_wheel_rwy_local_v );
250 /* remove Runway axes correction so right hand rule applies */
252 d_wheel_cg_local_v[2] = -d_wheel_cg_local_v[2]; /* now Z positive down */
254 /*============================*/
255 /* Calculate wheel velocities */
256 /*============================*/
258 /* contribution due to angular rates */
260 cross3( Omega_body_v, d_wheel_cg_body_v, temp3a );
262 /* transform into local axes */
264 multtrans3x3by3( T_local_to_body_m, temp3a, temp3b );
266 /* plus contribution due to cg velocities */
268 add3( temp3b, V_local_rel_ground_v, v_wheel_local_v );
271 /*===========================================*/
272 /* Calculate forces & moments for this wheel */
273 /*===========================================*/
275 /* Add any anticipation, or frame lead/prediction, here... */
277 /* no lead used at present */
279 /* Calculate sideward and forward velocities of the wheel
280 in the runway plane */
282 cos_wheel_hdg_angle = cos(caster_angle_rad[i] + Psi);
283 sin_wheel_hdg_angle = sin(caster_angle_rad[i] + Psi);
285 v_wheel_forward = v_wheel_local_v[0]*cos_wheel_hdg_angle
286 + v_wheel_local_v[1]*sin_wheel_hdg_angle;
287 v_wheel_sideward = v_wheel_local_v[1]*cos_wheel_hdg_angle
288 - v_wheel_local_v[0]*sin_wheel_hdg_angle;
290 /* Calculate normal load force (simple spring constant) */
292 reaction_normal_force = 0.;
293 if( d_wheel_rwy_local_v[2] < 0. )
295 reaction_normal_force = spring_constant[i]*d_wheel_rwy_local_v[2]
296 - v_wheel_local_v[2]*spring_damping[i];
297 if (reaction_normal_force > 0.) reaction_normal_force = 0.;
298 /* to prevent damping component from swamping spring component */
301 /* Calculate friction coefficients */
303 forward_mu = (max_brake_mu - rolling_mu)*percent_brake[i] + rolling_mu;
304 abs_v_wheel_sideward = sqrt(v_wheel_sideward*v_wheel_sideward);
305 sideward_mu = sliding_mu;
306 if (abs_v_wheel_sideward < skid_v)
307 sideward_mu = (abs_v_wheel_sideward - bkout_v)*beta_mu;
308 if (abs_v_wheel_sideward < bkout_v) sideward_mu = 0.;
310 /* Calculate foreward and sideward reaction forces */
312 forward_wheel_force = forward_mu*reaction_normal_force;
313 sideward_wheel_force = sideward_mu*reaction_normal_force;
314 if(v_wheel_forward < 0.) forward_wheel_force = -forward_wheel_force;
315 if(v_wheel_sideward < 0.) sideward_wheel_force = -sideward_wheel_force;
317 /* Rotate into local (N-E-D) axes */
319 f_wheel_local_v[0] = forward_wheel_force*cos_wheel_hdg_angle
320 - sideward_wheel_force*sin_wheel_hdg_angle;
321 f_wheel_local_v[1] = forward_wheel_force*sin_wheel_hdg_angle
322 + sideward_wheel_force*cos_wheel_hdg_angle;
323 f_wheel_local_v[2] = reaction_normal_force;
325 /* Convert reaction force from local (N-E-D) axes to body (X-Y-Z) */
327 mult3x3by3( T_local_to_body_m, f_wheel_local_v, tempF );
329 /* Calculate moments from force and offsets in body axes */
331 cross3( d_wheel_cg_body_v, tempF, tempM );
333 /* Sum forces and moments across all wheels */
335 add3( tempF, F_gear_v, F_gear_v );
336 add3( tempM, M_gear_v, M_gear_v );