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 1.2 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.
43 Revision 1.1 1997/05/29 00:10:02 curt
44 Initial Flight Gear revision.
47 ----------------------------------------------------------------------------
51 ----------------------------------------------------------------------------
55 ----------------------------------------------------------------------------
59 ----------------------------------------------------------------------------
63 ----------------------------------------------------------------------------
67 --------------------------------------------------------------------------*/
70 #include "ls_constants.h"
71 #include "ls_generic.h"
72 #include "ls_cockpit.h"
75 sub3( DATA v1[], DATA v2[], DATA result[] )
77 result[0] = v1[0] - v2[0];
78 result[1] = v1[1] - v2[1];
79 result[2] = v1[2] - v2[2];
82 add3( DATA v1[], DATA v2[], DATA result[] )
84 result[0] = v1[0] + v2[0];
85 result[1] = v1[1] + v2[1];
86 result[2] = v1[2] + v2[2];
89 cross3( DATA v1[], DATA v2[], DATA result[] )
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];
96 multtrans3x3by3( DATA m[][3], DATA v[], DATA result[] )
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];
103 mult3x3by3( DATA m[][3], DATA v[], DATA result[] )
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];
112 v[0] = 0.; v[1] = 0.; v[2] = 0.;
115 void gear( SCALAR dt, int Initialize ) {
116 char rcsid[] = "$Id$";
119 * Aircraft specific initializations and data goes here
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 */
127 { 10., 0., 4. }, /* in feet */
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 */
140 * End of aircraft specific code
144 * Constants & coefficients for tyres on tarmac - ref [1]
147 /* skid function looks like:
153 * sliding_mu | / +------
156 * +--+------------------------>
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;
170 * Local data variables
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;
187 int i; /* per wheel loop counter */
190 * Execution starts here
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 */
198 * Put aircraft specific executable code here
201 percent_brake[1] = 0.; /* replace with cockpit brake handle connection code */
202 percent_brake[2] = percent_brake[1];
204 caster_angle_rad[0] = 0.03*Rudder_pedal;
206 for (i=0;i<num_wheels;i++) /* Loop for each wheel */
208 /*========================================*/
209 /* Calculate wheel position w.r.t. runway */
210 /*========================================*/
212 /* First calculate wheel location w.r.t. cg in body (X-Y-Z) axes... */
214 sub3( d_wheel_rp_body_v[i], D_cg_rp_body_v, d_wheel_cg_body_v );
216 /* then converting to local (North-East-Down) axes... */
218 multtrans3x3by3( T_local_to_body_m, d_wheel_cg_body_v, d_wheel_cg_local_v );
220 /* Runway axes correction - third element is Altitude, not (-)Z... */
222 d_wheel_cg_local_v[2] = -d_wheel_cg_local_v[2]; /* since altitude = -Z */
224 /* Add wheel offset to cg location in local axes */
226 add3( d_wheel_cg_local_v, D_cg_rwy_local_v, d_wheel_rwy_local_v );
228 /* remove Runway axes correction so right hand rule applies */
230 d_wheel_cg_local_v[2] = -d_wheel_cg_local_v[2]; /* now Z positive down */
232 /*============================*/
233 /* Calculate wheel velocities */
234 /*============================*/
236 /* contribution due to angular rates */
238 cross3( Omega_body_v, d_wheel_cg_body_v, temp3a );
240 /* transform into local axes */
242 multtrans3x3by3( T_local_to_body_m, temp3a, temp3b );
244 /* plus contribution due to cg velocities */
246 add3( temp3b, V_local_rel_ground_v, v_wheel_local_v );
249 /*===========================================*/
250 /* Calculate forces & moments for this wheel */
251 /*===========================================*/
253 /* Add any anticipation, or frame lead/prediction, here... */
255 /* no lead used at present */
257 /* Calculate sideward and forward velocities of the wheel
258 in the runway plane */
260 cos_wheel_hdg_angle = cos(caster_angle_rad[i] + Psi);
261 sin_wheel_hdg_angle = sin(caster_angle_rad[i] + Psi);
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;
268 /* Calculate normal load force (simple spring constant) */
270 reaction_normal_force = 0.;
271 if( d_wheel_rwy_local_v[2] < 0. )
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 */
279 /* Calculate friction coefficients */
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.;
288 /* Calculate foreward and sideward reaction forces */
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;
295 /* Rotate into local (N-E-D) axes */
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;
303 /* Convert reaction force from local (N-E-D) axes to body (X-Y-Z) */
305 mult3x3by3( T_local_to_body_m, f_wheel_local_v, tempF );
307 /* Calculate moments from force and offsets in body axes */
309 cross3( d_wheel_cg_body_v, tempF, tempM );
311 /* Sum forces and moments across all wheels */
313 add3( tempF, F_gear_v, F_gear_v );
314 add3( tempM, M_gear_v, M_gear_v );