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 1.3 1998/02/03 23:20:18 curt
40 Lots of little tweaks to fix various consistency problems discovered by
41 Solaris' CC. Fixed a bug in fg_debug.c with how the fgPrintf() wrapper
42 passed arguments along to the real printf(). Also incorporated HUD changes
45 Revision 1.2 1998/01/19 18:40:29 curt
46 Tons of little changes to clean up the code and to remove fatal errors
47 when building with the c++ compiler.
49 Revision 1.1 1997/05/29 00:10:02 curt
50 Initial Flight Gear revision.
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57 ----------------------------------------------------------------------------
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65 ----------------------------------------------------------------------------
69 ----------------------------------------------------------------------------
73 --------------------------------------------------------------------------*/
76 #include "ls_constants.h"
77 #include "ls_generic.h"
78 #include "ls_cockpit.h"
81 void sub3( DATA v1[], DATA v2[], DATA result[] )
83 result[0] = v1[0] - v2[0];
84 result[1] = v1[1] - v2[1];
85 result[2] = v1[2] - v2[2];
88 void add3( DATA v1[], DATA v2[], DATA result[] )
90 result[0] = v1[0] + v2[0];
91 result[1] = v1[1] + v2[1];
92 result[2] = v1[2] + v2[2];
95 void cross3( DATA v1[], DATA v2[], DATA result[] )
97 result[0] = v1[1]*v2[2] - v1[2]*v2[1];
98 result[1] = v1[2]*v2[0] - v1[0]*v2[2];
99 result[2] = v1[0]*v2[1] - v1[1]*v2[0];
102 void multtrans3x3by3( DATA m[][3], DATA v[], DATA result[] )
104 result[0] = m[0][0]*v[0] + m[1][0]*v[1] + m[2][0]*v[2];
105 result[1] = m[0][1]*v[0] + m[1][1]*v[1] + m[2][1]*v[2];
106 result[2] = m[0][2]*v[0] + m[1][2]*v[1] + m[2][2]*v[2];
109 void mult3x3by3( DATA m[][3], DATA v[], DATA result[] )
111 result[0] = m[0][0]*v[0] + m[0][1]*v[1] + m[0][2]*v[2];
112 result[1] = m[1][0]*v[0] + m[1][1]*v[1] + m[1][2]*v[2];
113 result[2] = m[2][0]*v[0] + m[2][1]*v[1] + m[2][2]*v[2];
116 void clear3( DATA v[] )
118 v[0] = 0.; v[1] = 0.; v[2] = 0.;
121 void gear( SCALAR dt, int Initialize ) {
122 char rcsid[] = "$Id$";
125 * Aircraft specific initializations and data goes here
130 static int num_wheels = NUM_WHEELS; /* number of wheels */
131 static DATA d_wheel_rp_body_v[NUM_WHEELS][3] = /* X, Y, Z locations */
133 { 10., 0., 4. }, /* in feet */
137 static DATA spring_constant[NUM_WHEELS] = /* springiness, lbs/ft */
138 { 1500., 5000., 5000. };
139 static DATA spring_damping[NUM_WHEELS] = /* damping, lbs/ft/sec */
140 { 100., 150., 150. };
141 static DATA percent_brake[NUM_WHEELS] = /* percent applied braking */
142 { 0., 0., 0. }; /* 0 = none, 1 = full */
143 static DATA caster_angle_rad[NUM_WHEELS] = /* steerable tires - in */
144 { 0., 0., 0.}; /* radians, +CW */
146 * End of aircraft specific code
150 * Constants & coefficients for tyres on tarmac - ref [1]
153 /* skid function looks like:
159 * sliding_mu | / +------
162 * +--+------------------------>
169 static DATA sliding_mu = 0.5;
170 static DATA rolling_mu = 0.01;
171 static DATA max_brake_mu = 0.6;
172 static DATA max_mu = 0.8;
173 static DATA bkout_v = 0.1;
174 static DATA skid_v = 1.0;
176 * Local data variables
179 DATA d_wheel_cg_body_v[3]; /* wheel offset from cg, X-Y-Z */
180 DATA d_wheel_cg_local_v[3]; /* wheel offset from cg, N-E-D */
181 DATA d_wheel_rwy_local_v[3]; /* wheel offset from rwy, N-E-U */
182 DATA v_wheel_body_v[3]; /* wheel velocity, X-Y-Z */
183 DATA v_wheel_local_v[3]; /* wheel velocity, N-E-D */
184 DATA f_wheel_local_v[3]; /* wheel reaction force, N-E-D */
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;
193 int i; /* per wheel loop counter */
196 * Execution starts here
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 */
204 * Put aircraft specific executable code here
207 percent_brake[1] = 0.; /* replace with cockpit brake handle connection code */
208 percent_brake[2] = percent_brake[1];
210 caster_angle_rad[0] = 0.03*Rudder_pedal;
212 for (i=0;i<num_wheels;i++) /* Loop for each wheel */
214 /*========================================*/
215 /* Calculate wheel position w.r.t. runway */
216 /*========================================*/
218 /* First calculate wheel location w.r.t. cg in body (X-Y-Z) axes... */
220 sub3( d_wheel_rp_body_v[i], D_cg_rp_body_v, d_wheel_cg_body_v );
222 /* then converting to local (North-East-Down) axes... */
224 multtrans3x3by3( T_local_to_body_m, d_wheel_cg_body_v, d_wheel_cg_local_v );
226 /* Runway axes correction - third element is Altitude, not (-)Z... */
228 d_wheel_cg_local_v[2] = -d_wheel_cg_local_v[2]; /* since altitude = -Z */
230 /* Add wheel offset to cg location in local axes */
232 add3( d_wheel_cg_local_v, D_cg_rwy_local_v, d_wheel_rwy_local_v );
234 /* remove Runway axes correction so right hand rule applies */
236 d_wheel_cg_local_v[2] = -d_wheel_cg_local_v[2]; /* now Z positive down */
238 /*============================*/
239 /* Calculate wheel velocities */
240 /*============================*/
242 /* contribution due to angular rates */
244 cross3( Omega_body_v, d_wheel_cg_body_v, temp3a );
246 /* transform into local axes */
248 multtrans3x3by3( T_local_to_body_m, temp3a, temp3b );
250 /* plus contribution due to cg velocities */
252 add3( temp3b, V_local_rel_ground_v, v_wheel_local_v );
255 /*===========================================*/
256 /* Calculate forces & moments for this wheel */
257 /*===========================================*/
259 /* Add any anticipation, or frame lead/prediction, here... */
261 /* no lead used at present */
263 /* Calculate sideward and forward velocities of the wheel
264 in the runway plane */
266 cos_wheel_hdg_angle = cos(caster_angle_rad[i] + Psi);
267 sin_wheel_hdg_angle = sin(caster_angle_rad[i] + Psi);
269 v_wheel_forward = v_wheel_local_v[0]*cos_wheel_hdg_angle
270 + v_wheel_local_v[1]*sin_wheel_hdg_angle;
271 v_wheel_sideward = v_wheel_local_v[1]*cos_wheel_hdg_angle
272 - v_wheel_local_v[0]*sin_wheel_hdg_angle;
274 /* Calculate normal load force (simple spring constant) */
276 reaction_normal_force = 0.;
277 if( d_wheel_rwy_local_v[2] < 0. )
279 reaction_normal_force = spring_constant[i]*d_wheel_rwy_local_v[2]
280 - v_wheel_local_v[2]*spring_damping[i];
281 if (reaction_normal_force > 0.) reaction_normal_force = 0.;
282 /* to prevent damping component from swamping spring component */
285 /* Calculate friction coefficients */
287 forward_mu = (max_brake_mu - rolling_mu)*percent_brake[i] + rolling_mu;
288 abs_v_wheel_sideward = sqrt(v_wheel_sideward*v_wheel_sideward);
289 sideward_mu = sliding_mu;
290 if (abs_v_wheel_sideward < skid_v)
291 sideward_mu = (abs_v_wheel_sideward - bkout_v)*beta_mu;
292 if (abs_v_wheel_sideward < bkout_v) sideward_mu = 0.;
294 /* Calculate foreward and sideward reaction forces */
296 forward_wheel_force = forward_mu*reaction_normal_force;
297 sideward_wheel_force = sideward_mu*reaction_normal_force;
298 if(v_wheel_forward < 0.) forward_wheel_force = -forward_wheel_force;
299 if(v_wheel_sideward < 0.) sideward_wheel_force = -sideward_wheel_force;
301 /* Rotate into local (N-E-D) axes */
303 f_wheel_local_v[0] = forward_wheel_force*cos_wheel_hdg_angle
304 - sideward_wheel_force*sin_wheel_hdg_angle;
305 f_wheel_local_v[1] = forward_wheel_force*sin_wheel_hdg_angle
306 + sideward_wheel_force*cos_wheel_hdg_angle;
307 f_wheel_local_v[2] = reaction_normal_force;
309 /* Convert reaction force from local (N-E-D) axes to body (X-Y-Z) */
311 mult3x3by3( T_local_to_body_m, f_wheel_local_v, tempF );
313 /* Calculate moments from force and offsets in body axes */
315 cross3( d_wheel_cg_body_v, tempF, tempM );
317 /* Sum forces and moments across all wheels */
319 add3( tempF, F_gear_v, F_gear_v );
320 add3( tempM, M_gear_v, M_gear_v );