diff --git a/trick_models/parachute/include/Parachutist.hh b/trick_models/parachute/include/Parachutist.hh index b20f8786..8363d6f2 100644 --- a/trick_models/parachute/include/Parachutist.hh +++ b/trick_models/parachute/include/Parachutist.hh @@ -14,24 +14,14 @@ LIBRARY DEPENDENCIES: class Parachutist { public: - double position ; /* m xyz-position */ + double altitude ; /* m xyz-position */ double velocity ; /* m/s xyz-velocity */ double acceleration ; /* m/s2 xyz-acceleration */ - double crossSectionalArea; /* m2 */ - double crossSectionalAreaRate; /* m2/s */ - double cooefficientOfDrag; /* -- */ - double cooefficientOfDragRate; /* -- */ + double area; /* m2 */ + double Cd; /* -- */ double mass; /* kg */ - double parachuteDeploymentStartTime; /* s */ - double parachuteDeploymentDuration; /* s */ - - static const double crossSectionalArea_freefall; /* m2 */ - static const double crossSectionalArea_parachute; /* m2 */ - static const double cooefficientOfDrag_freefall; /* -- */ - static const double cooefficientOfDrag_parachute; /* -- */ - bool touchDown; /* -- */ REGULA_FALSI rf ; @@ -40,10 +30,7 @@ class Parachutist { int state_init(); int state_deriv(); int state_integ(); - int parachute_control(); - double touch_down(); - private: - double parachuteDeploymentEndTime; /* s */ + double touch_down(double groundAltitude); }; #endif diff --git a/trick_models/parachute/src/Parachutist.cpp b/trick_models/parachute/src/Parachutist.cpp index caacb53d..d6b69962 100644 --- a/trick_models/parachute/src/Parachutist.cpp +++ b/trick_models/parachute/src/Parachutist.cpp @@ -13,7 +13,6 @@ PROGRAMMERS: // http://www.engineeringtoolbox.com/standard-atmosphere-d_604.html // U.S Standard Atmosphere Air Properties in SI Units #define NUM_ELEMENTS 21 - // Units = meters (above sea level). const double altitude_array[NUM_ELEMENTS] = { -1000.0, 0.0, 1000.0, 2000.0, 3000.0, 4000.0, 5000.0, 6000.0, @@ -33,78 +32,43 @@ const double gravity_array[NUM_ELEMENTS] = { 9.684, 9.654, 9.624, 9.594, 9.564 }; -const double Parachutist::crossSectionalArea_freefall = 0.75 ; -const double Parachutist::crossSectionalArea_parachute = 30.00; -const double Parachutist::cooefficientOfDrag_freefall = 0.75; -const double Parachutist::cooefficientOfDrag_parachute = 1.30; - int Parachutist::default_data() { - position = 38969.3; //38969.3 meters = 127852 feet + altitude = 38969.3; //38969.3 meters = 127852 feet velocity = 0.0; - acceleration = 0.0; - parachuteDeploymentStartTime = 259; /* 4 minutes, 19 seconds*/ - parachuteDeploymentDuration = 3; - crossSectionalArea = crossSectionalArea_freefall; - cooefficientOfDrag = cooefficientOfDrag_freefall; + area = 0.75; + Cd = 0.75; touchDown = false; mass = 82.0; - return (0); } int Parachutist::state_init() { - parachuteDeploymentEndTime = parachuteDeploymentStartTime + parachuteDeploymentDuration; - return (0); -} - -#include "sim_services/Executive/include/exec_proto.h" -int Parachutist::parachute_control() { - - double currentTime = exec_get_sim_time(); - - if ((currentTime > parachuteDeploymentStartTime) && - (currentTime <= parachuteDeploymentEndTime)) { - cooefficientOfDragRate = (cooefficientOfDrag_parachute - cooefficientOfDrag_freefall) - / parachuteDeploymentDuration; - crossSectionalAreaRate = (crossSectionalArea_parachute - crossSectionalArea_freefall) - / parachuteDeploymentDuration; - } else { - cooefficientOfDragRate = 0.0; - crossSectionalAreaRate = 0.0; - } return (0); } int Parachutist::state_deriv() { - // Calculate the force of gravity. -#if 1 - double g = 9.81; -#else - double g = interpolate( position, altitude_array, gravity_array, NUM_ELEMENTS ); -#endif +// Calculate the forces and acceleration. + // Calculate Force of gravity. + double g = interpolate( altitude, altitude_array, gravity_array, NUM_ELEMENTS ); double Force_gravity = mass * -g; - // Calculate the force of drag. - double air_density = interpolate( position, altitude_array, air_density_array, NUM_ELEMENTS ); - double Force_drag = cooefficientOfDrag * 0.5 * air_density * velocity * velocity * crossSectionalArea; + // Calculate Force of drag. + double air_density = interpolate( altitude, altitude_array, air_density_array, NUM_ELEMENTS ); + double Force_drag = Cd * 0.5 * air_density * velocity * velocity * area; - // Sum the forces and calculate acceleration. + // Calculate Total Force. double Force_total; - - // If skydiver has touched down then set state derivatives to zero. - if ( touchDown ) { + if ( !touchDown ) { + Force_total = Force_gravity + Force_drag ; + acceleration = Force_total / mass; + } else { Force_total = 0.0; velocity = 0.0; acceleration = 0.0; - } else { - Force_total = Force_gravity + Force_drag ; - acceleration = Force_total / mass; } - - /* RETURN: -- Always return zero. */ return(0); } @@ -112,39 +76,20 @@ int Parachutist::state_deriv() { int Parachutist::state_integ() { int integration_step; - - load_state( &position, - &velocity, - &cooefficientOfDrag, - &crossSectionalArea, - (double*)0 - ); - - load_deriv ( &velocity, - &acceleration, - &cooefficientOfDragRate, - &crossSectionalAreaRate, - (double*)0 - ); - + load_state( &altitude, &velocity, (double*)0); + load_deriv ( &velocity, &acceleration, (double*)0); integration_step = integrate(); - - unload_state( &position, - &velocity, - &cooefficientOfDrag, - &crossSectionalArea, - (double*)0 - ); + unload_state( &altitude, &velocity, (double*)0); return(integration_step); } -double Parachutist::touch_down() { +double Parachutist::touch_down(double groundAltitude) { double tgo ; double now ; /* error function: how far the skydiver is above ground */ - rf.error = position ; + rf.error = altitude - groundAltitude ; now = get_integ_time() ; tgo = regula_falsi( now, &rf ) ; diff --git a/trick_sims/SIM_parachute/DP_Product/DP_parachutist.xml b/trick_sims/SIM_parachute/DP_Product/DP_parachutist.xml index 5a4984d2..f9e25bb7 100644 --- a/trick_sims/SIM_parachute/DP_Product/DP_parachutist.xml +++ b/trick_sims/SIM_parachute/DP_Product/DP_parachutist.xml @@ -10,7 +10,7 @@ Plot sys.exec.out.time - dyn.parachutist.position + dyn.parachutist.altitude diff --git a/trick_sims/SIM_parachute/Modified_data/parachutist.dr b/trick_sims/SIM_parachute/Modified_data/parachutist.dr index e077b4ad..a7ab7d3a 100644 --- a/trick_sims/SIM_parachute/Modified_data/parachutist.dr +++ b/trick_sims/SIM_parachute/Modified_data/parachutist.dr @@ -11,10 +11,10 @@ drg.append(trick.DRBinary("parachutist")) drg[DR_GROUP_ID].set_freq(trick.DR_Always) drg[DR_GROUP_ID].set_cycle(0.1) drg[DR_GROUP_ID].set_single_prec_only(False) -drg[DR_GROUP_ID].add_variable("dyn.parachutist.position") +drg[DR_GROUP_ID].add_variable("dyn.parachutist.altitude") drg[DR_GROUP_ID].add_variable("dyn.parachutist.velocity") drg[DR_GROUP_ID].add_variable("dyn.parachutist.acceleration") -drg[DR_GROUP_ID].add_variable("dyn.parachutist.crossSectionalArea") -drg[DR_GROUP_ID].add_variable("dyn.parachutist.cooefficientOfDrag") +drg[DR_GROUP_ID].add_variable("dyn.parachutist.area") +drg[DR_GROUP_ID].add_variable("dyn.parachutist.Cd") trick.add_data_record_group(drg[DR_GROUP_ID], trick.DR_Buffer) drg[DR_GROUP_ID].enable() diff --git a/trick_sims/SIM_parachute/README.md b/trick_sims/SIM_parachute/README.md new file mode 100644 index 00000000..4717e568 --- /dev/null +++ b/trick_sims/SIM_parachute/README.md @@ -0,0 +1,106 @@ +### Background +On October 14, 2012, 43-year-old Austrian daredevel Felix Baumgartner broke the +world record for the highest-ever skydive after jumping from a balloon at an +altitude of 127,852 feet. He reached a top speed of 843.6 mph, spent approximately +4 minutes 19 seconds in free-fall, and landed safely approximately 11 minutes +after jumping. + +### Simulation +The simulation only considers the forces of gravity and drag, and only motion in +the vertical. The acceleration of the skydiver is determined by summing the +forces of gravity and drag acting on him and then dividing by his mass. His +velocity is determined by integrating his acceleration over time, and his +altitude by integrating his velocity over time. + +Desired outputs are: +* Plot of altitude vs. time. +* Plot of velocity vs. time. +* Time of touchdown. + +##### Gravity + + + + F + g + + = + m + ⁢ + g + + + +Where: + +* m = mass of the skydiver. +* g = acceleration of gravity. + +##### Drag + + + + F + d + + = + + 1 + 2 + + ⁢ + ρ + ⁢ + + v + 2 + + ⁢ + + C + d + + ⁢ + A + + + +Where: + +* Cd = Coefficient of drag +* ρ = air density +* v = instantaneous velocity +* A = cross-sectional area of the jumper + +#### Air Density and Gravity Data +The table at: + +provides both gravity (g) and air density (ρ) at various altitudes. +From these data we interpolate, to approximate the air density and gravity at +specific altitudes. + +#### Parachute Deployment +Parachute deployment is modeled, using a Trick event (in input.py) that simply increasing skydiver's + +1) cross-sectional area and +2) coefficient of drag. + +at the specified time. + +### Jump Scenario +dyn.groundAltitude = 1000 +dyn.parachutist.altitude = 38969.6 meters +dyn.parachutist.velocity = 0.0 +dyn.parachutist.area = 0.75 +dyn.parachutist.Cd = 0.75 +dyn.parachutist.mass = 82.0 + +# At 4 minutes and 19 seconds, pop the chute. +dyn.parachutist.Cd = 1.3 +dyn.parachutist.area = 30.0 + +#### Results + +![Plot of Altitude vs Time](images/plot_altitude_vs_time.png "Altitude vs. Time") +![Plot of Velocity vs Time](images/plot_velocity_vs_time.png "Velocity vs. Time") + diff --git a/trick_sims/SIM_parachute/RUN_Baumgartner_jump/input.py b/trick_sims/SIM_parachute/RUN_Baumgartner_jump/input.py index 41719761..c1d2e1ba 100644 --- a/trick_sims/SIM_parachute/RUN_Baumgartner_jump/input.py +++ b/trick_sims/SIM_parachute/RUN_Baumgartner_jump/input.py @@ -1,7 +1,27 @@ -#execfile("Modified_data/realtime.py") + execfile("Modified_data/parachutist.dr") - trick.TMM_reduced_checkpoint(0) -dyn_integloop.getIntegrator(trick.Runge_Kutta_4, 4) +dyn_integloop.getIntegrator(trick.Runge_Kutta_4, 2) +# The ground is a 1000 meters above sea level. +dyn.groundAltitude = 1000 + +# State of the skydiver when he jumps +dyn.parachutist.altitude = 38969.6 # 127852 feet +dyn.parachutist.velocity = 0.0 +dyn.parachutist.area = 0.75 +dyn.parachutist.Cd = 0.75 +dyn.parachutist.mass = 82.0 + +# At 4 minutes and 19 seconds, pop the chute. +deployChute = trick.new_event("deployChute") +deployChute.condition(0, "trick.exec_get_sim_time() >= 259.0") +deployChute.action(0, "dyn.parachutist.Cd = 1.3"); +deployChute.action(1, "dyn.parachutist.area = 30.0"); +deployChute.action(2, "print \"Parachute Deployed.\""); +deployChute.set_cycle(1.0) +deployChute.activate() +trick.add_event(deployChute) + +# Run for 800 seconds. trick.stop(800) diff --git a/trick_sims/SIM_parachute/S_define b/trick_sims/SIM_parachute/S_define index 0ae83bd1..406be669 100644 --- a/trick_sims/SIM_parachute/S_define +++ b/trick_sims/SIM_parachute/S_define @@ -13,6 +13,7 @@ class ParachutistSimObject : public Trick::SimObject { public: Parachutist parachutist; + double groundAltitude; ParachutistSimObject() { @@ -20,8 +21,7 @@ class ParachutistSimObject : public Trick::SimObject { ("initialization") parachutist.state_init() ; ("derivative") parachutist.state_deriv() ; ("integration") trick_ret = parachutist.state_integ() ; - ("dynamic_event") parachutist.touch_down() ; - (0.02, "scheduled") parachutist.parachute_control(); + ("dynamic_event") parachutist.touch_down(groundAltitude) ; } } ; diff --git a/trick_sims/SIM_parachute/images/force_of_drag.png b/trick_sims/SIM_parachute/images/force_of_drag.png new file mode 100644 index 00000000..8c1c0f7b Binary files /dev/null and b/trick_sims/SIM_parachute/images/force_of_drag.png differ diff --git a/trick_sims/SIM_parachute/images/force_of_gravity.png b/trick_sims/SIM_parachute/images/force_of_gravity.png new file mode 100644 index 00000000..de2f5859 Binary files /dev/null and b/trick_sims/SIM_parachute/images/force_of_gravity.png differ diff --git a/trick_sims/SIM_parachute/images/plot_altitude_vs_time.png b/trick_sims/SIM_parachute/images/plot_altitude_vs_time.png new file mode 100644 index 00000000..67e17ed2 Binary files /dev/null and b/trick_sims/SIM_parachute/images/plot_altitude_vs_time.png differ diff --git a/trick_sims/SIM_parachute/images/plot_velocity_vs_time.png b/trick_sims/SIM_parachute/images/plot_velocity_vs_time.png new file mode 100644 index 00000000..0f16baee Binary files /dev/null and b/trick_sims/SIM_parachute/images/plot_velocity_vs_time.png differ