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 1.7 1999/08/17 19:18:16 curt
43 ----------------------------------------------------------------------------
47 ----------------------------------------------------------------------------
51 ----------------------------------------------------------------------------
55 ----------------------------------------------------------------------------
59 ----------------------------------------------------------------------------
63 --------------------------------------------------------------------------*/
66 #include "ls_constants.h"
67 #include "ls_generic.h"
68 #include "ls_cockpit.h"
71 sub3( DATA v1[], DATA v2[], DATA result[] )
73 result[0] = v1[0] - v2[0];
74 result[1] = v1[1] - v2[1];
75 result[2] = v1[2] - v2[2];
78 add3( DATA v1[], DATA v2[], DATA result[] )
80 result[0] = v1[0] + v2[0];
81 result[1] = v1[1] + v2[1];
82 result[2] = v1[2] + v2[2];
85 cross3( DATA v1[], DATA v2[], DATA result[] )
87 result[0] = v1[1]*v2[2] - v1[2]*v2[1];
88 result[1] = v1[2]*v2[0] - v1[0]*v2[2];
89 result[2] = v1[0]*v2[1] - v1[1]*v2[0];
92 multtrans3x3by3( DATA m[][3], DATA v[], DATA result[] )
94 result[0] = m[0][0]*v[0] + m[1][0]*v[1] + m[2][0]*v[2];
95 result[1] = m[0][1]*v[0] + m[1][1]*v[1] + m[2][1]*v[2];
96 result[2] = m[0][2]*v[0] + m[1][2]*v[1] + m[2][2]*v[2];
99 mult3x3by3( DATA m[][3], DATA v[], DATA result[] )
101 result[0] = m[0][0]*v[0] + m[0][1]*v[1] + m[0][2]*v[2];
102 result[1] = m[1][0]*v[0] + m[1][1]*v[1] + m[1][2]*v[2];
103 result[2] = m[2][0]*v[0] + m[2][1]*v[1] + m[2][2]*v[2];
108 v[0] = 0.; v[1] = 0.; v[2] = 0.;
113 char rcsid[] = "$Id$";
116 * Aircraft specific initializations and data goes here
121 static int num_wheels = NUM_WHEELS; /* number of wheels */
122 static DATA d_wheel_rp_body_v[NUM_WHEELS][3] = /* X, Y, Z locations */
124 { 10., 0., 4. }, /* in feet */
128 static DATA spring_constant[NUM_WHEELS] = /* springiness, lbs/ft */
129 { 1500., 5000., 5000. };
130 static DATA spring_damping[NUM_WHEELS] = /* damping, lbs/ft/sec */
131 { 100., 150., 150. };
132 static DATA percent_brake[NUM_WHEELS] = /* percent applied braking */
133 { 0., 0., 0. }; /* 0 = none, 1 = full */
134 static DATA caster_angle_rad[NUM_WHEELS] = /* steerable tires - in */
135 { 0., 0., 0.}; /* radians, +CW */
137 * End of aircraft specific code
141 * Constants & coefficients for tyres on tarmac - ref [1]
144 /* skid function looks like:
150 * sliding_mu | / +------
153 * +--+------------------------>
160 static DATA sliding_mu = 0.5;
161 static DATA rolling_mu = 0.01;
162 static DATA max_brake_mu = 0.6;
163 static DATA max_mu = 0.8;
164 static DATA bkout_v = 0.1;
165 static DATA skid_v = 1.0;
167 * Local data variables
170 DATA d_wheel_cg_body_v[3]; /* wheel offset from cg, X-Y-Z */
171 DATA d_wheel_cg_local_v[3]; /* wheel offset from cg, N-E-D */
172 DATA d_wheel_rwy_local_v[3]; /* wheel offset from rwy, N-E-U */
173 DATA v_wheel_body_v[3]; /* wheel velocity, X-Y-Z */
174 DATA v_wheel_local_v[3]; /* wheel velocity, N-E-D */
175 DATA f_wheel_local_v[3]; /* wheel reaction force, N-E-D */
176 DATA temp3a[3], temp3b[3], tempF[3], tempM[3];
177 DATA reaction_normal_force; /* wheel normal (to rwy) force */
178 DATA cos_wheel_hdg_angle, sin_wheel_hdg_angle; /* temp storage */
179 DATA v_wheel_forward, v_wheel_sideward, abs_v_wheel_sideward;
180 DATA forward_mu, sideward_mu; /* friction coefficients */
181 DATA beta_mu; /* breakout friction slope */
182 DATA forward_wheel_force, sideward_wheel_force;
184 int i; /* per wheel loop counter */
187 * Execution starts here
190 beta_mu = max_mu/(skid_v-bkout_v);
191 clear3( F_gear_v ); /* Initialize sum of forces... */
192 clear3( M_gear_v ); /* ...and moments */
195 * Put aircraft specific executable code here
198 percent_brake[1] = 0.; /* replace with cockpit brake handle connection code */
199 percent_brake[2] = percent_brake[1];
201 caster_angle_rad[0] = 0.03*Rudder_pedal;
203 for (i=0;i<num_wheels;i++) /* Loop for each wheel */
205 /*========================================*/
206 /* Calculate wheel position w.r.t. runway */
207 /*========================================*/
209 /* First calculate wheel location w.r.t. cg in body (X-Y-Z) axes... */
211 sub3( d_wheel_rp_body_v[i], D_cg_rp_body_v, d_wheel_cg_body_v );
213 /* then converting to local (North-East-Down) axes... */
215 multtrans3x3by3( T_local_to_body_m, d_wheel_cg_body_v, d_wheel_cg_local_v );
217 /* Runway axes correction - third element is Altitude, not (-)Z... */
219 d_wheel_cg_local_v[2] = -d_wheel_cg_local_v[2]; /* since altitude = -Z */
221 /* Add wheel offset to cg location in local axes */
223 add3( d_wheel_cg_local_v, D_cg_rwy_local_v, d_wheel_rwy_local_v );
225 /* remove Runway axes correction so right hand rule applies */
227 d_wheel_cg_local_v[2] = -d_wheel_cg_local_v[2]; /* now Z positive down */
229 /*============================*/
230 /* Calculate wheel velocities */
231 /*============================*/
233 /* contribution due to angular rates */
235 cross3( Omega_body_v, d_wheel_cg_body_v, temp3a );
237 /* transform into local axes */
239 multtrans3x3by3( T_local_to_body_m, temp3a, temp3b );
241 /* plus contribution due to cg velocities */
243 add3( temp3b, V_local_rel_ground_v, v_wheel_local_v );
246 /*===========================================*/
247 /* Calculate forces & moments for this wheel */
248 /*===========================================*/
250 /* Add any anticipation, or frame lead/prediction, here... */
252 /* no lead used at present */
254 /* Calculate sideward and forward velocities of the wheel
255 in the runway plane */
257 cos_wheel_hdg_angle = cos(caster_angle_rad[i] + Psi);
258 sin_wheel_hdg_angle = sin(caster_angle_rad[i] + Psi);
260 v_wheel_forward = v_wheel_local_v[0]*cos_wheel_hdg_angle
261 + v_wheel_local_v[1]*sin_wheel_hdg_angle;
262 v_wheel_sideward = v_wheel_local_v[1]*cos_wheel_hdg_angle
263 - v_wheel_local_v[0]*sin_wheel_hdg_angle;
265 /* Calculate normal load force (simple spring constant) */
267 reaction_normal_force = 0.;
268 if( d_wheel_rwy_local_v[2] < 0. )
270 reaction_normal_force = spring_constant[i]*d_wheel_rwy_local_v[2]
271 - v_wheel_local_v[2]*spring_damping[i];
272 if (reaction_normal_force > 0.) reaction_normal_force = 0.;
273 /* to prevent damping component from swamping spring component */
276 /* Calculate friction coefficients */
278 forward_mu = (max_brake_mu - rolling_mu)*percent_brake[i] + rolling_mu;
279 abs_v_wheel_sideward = sqrt(v_wheel_sideward*v_wheel_sideward);
280 sideward_mu = sliding_mu;
281 if (abs_v_wheel_sideward < skid_v)
282 sideward_mu = (abs_v_wheel_sideward - bkout_v)*beta_mu;
283 if (abs_v_wheel_sideward < bkout_v) sideward_mu = 0.;
285 /* Calculate foreward and sideward reaction forces */
287 forward_wheel_force = forward_mu*reaction_normal_force;
288 sideward_wheel_force = sideward_mu*reaction_normal_force;
289 if(v_wheel_forward < 0.) forward_wheel_force = -forward_wheel_force;
290 if(v_wheel_sideward < 0.) sideward_wheel_force = -sideward_wheel_force;
292 /* Rotate into local (N-E-D) axes */
294 f_wheel_local_v[0] = forward_wheel_force*cos_wheel_hdg_angle
295 - sideward_wheel_force*sin_wheel_hdg_angle;
296 f_wheel_local_v[1] = forward_wheel_force*sin_wheel_hdg_angle
297 + sideward_wheel_force*cos_wheel_hdg_angle;
298 f_wheel_local_v[2] = reaction_normal_force;
300 /* Convert reaction force from local (N-E-D) axes to body (X-Y-Z) */
302 mult3x3by3( T_local_to_body_m, f_wheel_local_v, tempF );
304 /* Calculate moments from force and offsets in body axes */
306 cross3( d_wheel_cg_body_v, tempF, tempM );
308 /* Sum forces and moments across all wheels */
310 add3( tempF, F_gear_v, F_gear_v );
311 add3( tempM, M_gear_v, M_gear_v );