# car_ride.mbd #----------------------------------------------------------------------------- # [Data Block] begin: data; problem: initial value; end: data; #----------------------------------------------------------------------------- # [Block] begin: initial value; initial time: 0.; final time: 12.; time step: 1.e-3; max iterations: 100; tolerance: 1.e-6; derivatives tolerance: 1.e-4; derivatives max iterations: 100; end: initial value; #----------------------------------------------------------------------------- # Design Variables set: real L_WheelBase = 2.8; #[m] Wheel base set: real L_Front = 1.2; #[m] Londitudinal distance from front axle to sprung mass cg set: real H_CG = 0.8; #[m] Vertical distance from front axle to sprung mass cg set: real L_Tread_Fr = 1.5; #[m] Front tread set: real L_Tread_Rr = 1.5; #[m] Rear tread set: real m_Sprung = 1400.; #[kg] Sprung mass set: real I_Sprung_roll = 430.; #[kg m^2] Sprung mass moment of inertia set: real I_Sprung_pitch = 1100.; #[kg m^2] Sprung mass moment of inertia set: real I_Sprung_yaw = 1150.; #[kg m^2] Sprung mass moment of inertia set: real m_Unsprung_Fr = 40.; #[kg] Front unsprung mass (at wheel center) set: real m_Unsprung_Rr = 40.; #[kg] Rear unsprung mass (at wheel center) set: real L_SwingArm_Fr = 1.5; #[m] Front swing arm length set: real L_SwingArm_Rr = 1.5; #[m] Rear swing arm length set: real K_Spring_Fr = 3.e4; #[N/m] Front spring stiffness set: real K_Spring_Rr = 5.e4; #[N/m] Rear spring stiffness set: real C_Damper_Fr = 3.e3; #[Ns/m] Front damper viscosity coefficient set: real C_Damper_Rr = 3.e3; #[Ns/m] Rear damper viscosity coefficient set: real K_Tire_Fr = 5.e5; #[N/m] Front tire stiffness set: real K_Tire_Rr = 5.e5; #[N/m] Rear tire stiffness set: real C_Tire_Fr = 1.e2; #[Ns/m] Front tire viscosity coefficient set: real C_Tire_Rr = 1.e2; #[Ns/m] Rear tire viscosity coefficient set: real V = 60; #[km/h] Speed of the car set: real g = 9.81; #[m/s^2] Gravity acceleration #----------------------------------------------------------------------------- # [Control Data Block] begin: control data; use: rigid bodies, gravity, in assembly; output meter: meter, 0., forever, steps, 10; structural nodes: 1 # Sprung mass +4 # Unsprung mass +4 # Road input rig ; rigid bodies: 1 # Sprung mass +4 # Unsprung mass ; joints: 4 # Revh - Arm +4 # Dfmd - Spring & Damper +4 # Dfmd - Tire +4 # Totp - Road input rig ; gravity; end: control data; #----------------------------------------------------------------------------- # Reference Labels set: integer Ref_WheelCenter_FrLh = 1; set: integer Ref_WheelCenter_FrRh = 2; set: integer Ref_WheelCenter_RrLh = 3; set: integer Ref_WheelCenter_RrRh = 4; set: integer Ref_JoRevh_SwingArm_FrLh = 11; set: integer Ref_JoRevh_SwingArm_FrRh = 12; set: integer Ref_JoRevh_SwingArm_RrLh = 13; set: integer Ref_JoRevh_SwingArm_RrRh = 14; # Node Labels set: integer NoDyn_Sprung = 1; set: integer NoDyn_Unsprung_FrLh = 11; set: integer NoDyn_Unsprung_FrRh = 12; set: integer NoDyn_Unsprung_RrLh = 13; set: integer NoDyn_Unsprung_RrRh = 14; set: integer NoDyn_Road_FrLh = 21; set: integer NoDyn_Road_FrRh = 22; set: integer NoDyn_Road_RrLh = 23; set: integer NoDyn_Road_RrRh = 24; # Body Labels set: integer Body_Sprung = 1; set: integer Body_Unsprung_FrLh = 11; set: integer Body_Unsprung_FrRh = 12; set: integer Body_Unsprung_RrLh = 13; set: integer Body_Unsprung_RrRh = 14; # Joint Labels set: integer JoRevh_SwingArm_FrLh = 1; set: integer JoRevh_SwingArm_FrRh = 2; set: integer JoRevh_SwingArm_RrLh = 3; set: integer JoRevh_SwingArm_RrRh = 4; set: integer JoDfmd_SpringDamper_FrLh = 11; set: integer JoDfmd_SpringDamper_FrRh = 12; set: integer JoDfmd_SpringDamper_RrLh = 13; set: integer JoDfmd_SpringDamper_RrRh = 14; set: integer JoDfmd_Tire_FrLh = 21; set: integer JoDfmd_Tire_FrRh = 22; set: integer JoDfmd_Tire_RrLh = 23; set: integer JoDfmd_Tire_RrRh = 24; set: integer JoTotp_RoadInput_FrLh = 31; set: integer JoTotp_RoadInput_FrRh = 32; set: integer JoTotp_RoadInput_RrLh = 33; set: integer JoTotp_RoadInput_RrRh = 34; #----------------------------------------------------------------------------- # Scalar Functions include: "sf_Road_LH.sub"; include: "sf_Road_RH.sub"; #----------------------------------------------------------------------------- # Intermediate Variables set: real L_Rear = L_WheelBase - L_Front; set: real Preload_Spring_Fr = L_Rear/L_WheelBase * m_Sprung * g /2.; set: real Preload_Spring_Rr = L_Front/L_WheelBase * m_Sprung * g /2.; set: real Preload_Tire_Fr = Preload_Spring_Fr + m_Unsprung_Fr * g; set: real Preload_Tire_Rr = Preload_Spring_Rr + m_Unsprung_Rr * g; #----------------------------------------------------------------------------- # References reference: Ref_WheelCenter_FrLh, 0., L_Tread_Fr/2., 0., # absolute position eye, # absolute orientation null, # absolute velocity null; # absolute angular velocity reference: Ref_WheelCenter_FrRh, 0., -L_Tread_Fr/2., 0., # absolute position eye, # absolute orientation null, # absolute velocity null; # absolute angular velocity reference: Ref_WheelCenter_RrLh, -L_WheelBase, L_Tread_Rr/2., 0., # absolute position eye, # absolute orientation null, # absolute velocity null; # absolute angular velocity reference: Ref_WheelCenter_RrRh, -L_WheelBase, -L_Tread_Rr/2., 0., # absolute position eye, # absolute orientation null, # absolute velocity null; # absolute angular velocity reference: Ref_JoRevh_SwingArm_FrLh, reference, Ref_WheelCenter_FrLh, 0., -L_SwingArm_Fr, 0., # absolute position reference, Ref_WheelCenter_FrLh, euler, 0., pi/2., 0., # absolute orientation reference, Ref_WheelCenter_FrLh, null, # absolute velocity reference, Ref_WheelCenter_FrLh, null; # absolute angular velocity reference: Ref_JoRevh_SwingArm_FrRh, reference, Ref_WheelCenter_FrRh, 0., L_SwingArm_Fr, 0., # absolute position reference, Ref_WheelCenter_FrRh, euler, 0., -pi/2., 0., # absolute orientation reference, Ref_WheelCenter_FrRh, null, # absolute velocity reference, Ref_WheelCenter_FrRh, null; # absolute angular velocity reference: Ref_JoRevh_SwingArm_RrLh, reference, Ref_WheelCenter_RrLh, 0., -L_SwingArm_Rr, 0., # absolute position reference, Ref_WheelCenter_RrLh, euler, 0., pi/2., 0., # absolute orientation reference, Ref_WheelCenter_RrLh, null, # absolute velocity reference, Ref_WheelCenter_RrLh, null; # absolute angular velocity reference: Ref_JoRevh_SwingArm_RrRh, reference, Ref_WheelCenter_RrRh, 0., L_SwingArm_Rr, 0., # absolute position reference, Ref_WheelCenter_RrRh, euler, 0., -pi/2., 0., # absolute orientation reference, Ref_WheelCenter_RrRh, null, # absolute velocity reference, Ref_WheelCenter_RrRh, null; # absolute angular velocity #----------------------------------------------------------------------------- # [Nodes Block] begin: nodes; #----------------------------------------------------------------------------- # Structural Nodes structural: NoDyn_Sprung, dynamic, -L_Front, 0., H_CG, # absolute position eye, # absolute orientation null, # absolute velocity null; # absolute angular velocity structural: NoDyn_Unsprung_FrLh, dynamic, reference, Ref_WheelCenter_FrLh, null, # absolute position reference, Ref_WheelCenter_FrLh, eye, # absolute orientation reference, Ref_WheelCenter_FrLh, null, # absolute velocity reference, Ref_WheelCenter_FrLh, null; # absolute angular velocity structural: NoDyn_Unsprung_FrRh, dynamic, reference, Ref_WheelCenter_FrRh, null, # absolute position reference, Ref_WheelCenter_FrRh, eye, # absolute orientation reference, Ref_WheelCenter_FrRh, null, # absolute velocity reference, Ref_WheelCenter_FrRh, null; # absolute angular velocity structural: NoDyn_Unsprung_RrLh, dynamic, reference, Ref_WheelCenter_RrLh, null, # absolute position reference, Ref_WheelCenter_RrLh, eye, # absolute orientation reference, Ref_WheelCenter_RrLh, null, # absolute velocity reference, Ref_WheelCenter_RrLh, null; # absolute angular velocity structural: NoDyn_Unsprung_RrRh, dynamic, reference, Ref_WheelCenter_RrRh, null, # absolute position reference, Ref_WheelCenter_RrRh, eye, # absolute orientation reference, Ref_WheelCenter_RrRh, null, # absolute velocity reference, Ref_WheelCenter_RrRh, null; # absolute angular velocity structural: NoDyn_Road_FrLh, dynamic, reference, Ref_WheelCenter_FrLh, null, # absolute position reference, Ref_WheelCenter_FrLh, eye, # absolute orientation reference, Ref_WheelCenter_FrLh, null, # absolute velocity reference, Ref_WheelCenter_FrLh, null; # absolute angular velocity structural: NoDyn_Road_FrRh, dynamic, reference, Ref_WheelCenter_FrRh, null, # absolute position reference, Ref_WheelCenter_FrRh, eye, # absolute orientation reference, Ref_WheelCenter_FrRh, null, # absolute velocity reference, Ref_WheelCenter_FrRh, null; # absolute angular velocity structural: NoDyn_Road_RrLh, dynamic, reference, Ref_WheelCenter_RrLh, null, # absolute position reference, Ref_WheelCenter_RrLh, eye, # absolute orientation reference, Ref_WheelCenter_RrLh, null, # absolute velocity reference, Ref_WheelCenter_RrLh, null; # absolute angular velocity structural: NoDyn_Road_RrRh, dynamic, reference, Ref_WheelCenter_RrRh, null, # absolute position reference, Ref_WheelCenter_RrRh, eye, # absolute orientation reference, Ref_WheelCenter_RrRh, null, # absolute velocity reference, Ref_WheelCenter_RrRh, null; # absolute angular velocity end: nodes; #----------------------------------------------------------------------------- # [Elements Block] begin: elements; #----------------------------------------------------------------------------- # Bodies body: Body_Sprung, NoDyn_Sprung, m_Sprung, # mass null, # relative center of mass diag, I_Sprung_roll, I_Sprung_pitch, I_Sprung_yaw; # inertia matrix body: Body_Unsprung_FrLh, NoDyn_Unsprung_FrLh, m_Unsprung_Fr, # mass null, # relative center of mass diag, 1.e-3, 1.e-3, 1.e-3; # inertia matrix body: Body_Unsprung_FrRh, NoDyn_Unsprung_FrRh, m_Unsprung_Fr, # mass null, # relative center of mass diag, 1.e-3, 1.e-3, 1.e-3; # inertia matrix body: Body_Unsprung_RrLh, NoDyn_Unsprung_RrLh, m_Unsprung_Rr, # mass null, # relative center of mass diag, 1.e-3, 1.e-3, 1.e-3; # inertia matrix body: Body_Unsprung_RrRh, NoDyn_Unsprung_RrRh, m_Unsprung_Rr, # mass null, # relative center of mass diag, 1.e-3, 1.e-3, 1.e-3; # inertia matrix #----------------------------------------------------------------------------- # Joints joint: JoRevh_SwingArm_FrLh, revolute hinge, NoDyn_Sprung, reference, Ref_JoRevh_SwingArm_FrLh, null, # relative offset hinge, reference, Ref_JoRevh_SwingArm_FrLh, eye, # relative axis orientation NoDyn_Unsprung_FrLh, reference, Ref_JoRevh_SwingArm_FrLh, null, # relative offset hinge, reference, Ref_JoRevh_SwingArm_FrLh, eye; # relative axis orientation joint: JoRevh_SwingArm_FrRh, revolute hinge, NoDyn_Sprung, reference, Ref_JoRevh_SwingArm_FrRh, null, # relative offset hinge, reference, Ref_JoRevh_SwingArm_FrRh, eye, # relative axis orientation NoDyn_Unsprung_FrRh, reference, Ref_JoRevh_SwingArm_FrRh, null, # relative offset hinge, reference, Ref_JoRevh_SwingArm_FrRh, eye; # relative axis orientation joint: JoRevh_SwingArm_RrLh, revolute hinge, NoDyn_Sprung, reference, Ref_JoRevh_SwingArm_RrLh, null, # relative offset hinge, reference, Ref_JoRevh_SwingArm_RrLh, eye, # relative axis orientation NoDyn_Unsprung_RrLh, reference, Ref_JoRevh_SwingArm_RrLh, null, # relative offset hinge, reference, Ref_JoRevh_SwingArm_RrLh, eye; # relative axis orientation joint: JoRevh_SwingArm_RrRh, revolute hinge, NoDyn_Sprung, reference, Ref_JoRevh_SwingArm_RrRh, null, # relative offset hinge, reference, Ref_JoRevh_SwingArm_RrRh, eye, # relative axis orientation NoDyn_Unsprung_RrRh, reference, Ref_JoRevh_SwingArm_RrRh, null, # relative offset hinge, reference, Ref_JoRevh_SwingArm_RrRh, eye; # relative axis orientation joint: JoDfmd_SpringDamper_FrLh, deformable displacement joint, NoDyn_Sprung, reference, Ref_WheelCenter_FrLh, null, # relative offset NoDyn_Unsprung_FrLh, reference, Ref_WheelCenter_FrLh, null, # relative offset linear viscoelastic generic, diag, 0., 0., K_Spring_Fr, # stiffness diag, 0., 0., C_Damper_Fr, # viscosity coefficient prestress, 0., 0., Preload_Spring_Fr; joint: JoDfmd_SpringDamper_FrRh, deformable displacement joint, NoDyn_Sprung, reference, Ref_WheelCenter_FrRh, null, # relative offset NoDyn_Unsprung_FrRh, reference, Ref_WheelCenter_FrRh, null, # relative offset linear viscoelastic generic, diag, 0., 0., K_Spring_Fr, # stiffness diag, 0., 0., C_Damper_Fr, # viscosity coefficient prestress, 0., 0., Preload_Spring_Fr; joint: JoDfmd_SpringDamper_RrLh, deformable displacement joint, NoDyn_Sprung, reference, Ref_WheelCenter_RrLh, null, # relative offset NoDyn_Unsprung_RrLh, reference, Ref_WheelCenter_RrLh, null, # relative offset linear viscoelastic generic, diag, 0., 0., K_Spring_Rr, # stiffness diag, 0., 0., C_Damper_Rr, # viscosity coefficient prestress, 0., 0., Preload_Spring_Rr; joint: JoDfmd_SpringDamper_RrRh, deformable displacement joint, NoDyn_Sprung, reference, Ref_WheelCenter_RrRh, null, # relative offset NoDyn_Unsprung_RrRh, reference, Ref_WheelCenter_RrRh, null, # relative offset linear viscoelastic generic, diag, 0., 0., K_Spring_Rr, # stiffness diag, 0., 0., C_Damper_Rr, # viscosity coefficient prestress, 0., 0., Preload_Spring_Rr; joint: JoDfmd_Tire_FrLh, deformable displacement joint, NoDyn_Unsprung_FrLh, reference, Ref_WheelCenter_FrLh, null, # relative offset NoDyn_Road_FrLh, reference, Ref_WheelCenter_FrLh, null, # relative offset linear viscoelastic generic, diag, K_Tire_Fr, K_Tire_Fr, K_Tire_Fr, # stiffness diag, C_Tire_Fr, C_Tire_Fr, C_Tire_Fr, # viscosity coefficient prestress, 0., 0., Preload_Tire_Fr; joint: JoDfmd_Tire_FrRh, deformable displacement joint, NoDyn_Unsprung_FrRh, reference, Ref_WheelCenter_FrRh, null, # relative offset NoDyn_Road_FrRh, reference, Ref_WheelCenter_FrRh, null, # relative offset linear viscoelastic generic, diag, K_Tire_Fr, K_Tire_Fr, K_Tire_Fr, # stiffness diag, C_Tire_Fr, C_Tire_Fr, C_Tire_Fr, # viscosity coefficient prestress, 0., 0., Preload_Tire_Fr; joint: JoDfmd_Tire_RrLh, deformable displacement joint, NoDyn_Unsprung_RrLh, reference, Ref_WheelCenter_RrLh, null, # relative offset NoDyn_Road_RrLh, reference, Ref_WheelCenter_RrLh, null, # relative offset linear viscoelastic generic, diag, K_Tire_Rr, K_Tire_Rr, K_Tire_Rr, # stiffness diag, C_Tire_Rr, C_Tire_Rr, C_Tire_Rr, # viscosity coefficient prestress, 0., 0., Preload_Tire_Rr; joint: JoDfmd_Tire_RrRh, deformable displacement joint, NoDyn_Unsprung_RrRh, reference, Ref_WheelCenter_RrRh, null, # relative offset NoDyn_Road_RrRh, reference, Ref_WheelCenter_RrRh, null, # relative offset linear viscoelastic generic, diag, K_Tire_Rr, K_Tire_Rr, K_Tire_Rr, # stiffness diag, C_Tire_Rr, C_Tire_Rr, C_Tire_Rr, # viscosity coefficient prestress, 0., 0., Preload_Tire_Rr; joint: JoTotp_RoadInput_FrLh, total pin joint, NoDyn_Road_FrLh, position, reference, Ref_WheelCenter_FrLh, null, # relative offset position, reference, Ref_WheelCenter_FrLh, null, # absolute position position constraint, active, active, active, single, 0., 0., 1., string, "model::sf::SF_Road_LH(V/3.6*Time) * 1.e-2", orientation constraint, active, active, active, null; joint: JoTotp_RoadInput_FrRh, total pin joint, NoDyn_Road_FrRh, position, reference, Ref_WheelCenter_FrRh, null, # relative offset position, reference, Ref_WheelCenter_FrRh, null, # absolute position position constraint, active, active, active, single, 0., 0., 1., string, "model::sf::SF_Road_RH(V/3.6*Time) * 1.e-2", orientation constraint, active, active, active, null; joint: JoTotp_RoadInput_RrLh, total pin joint, NoDyn_Road_RrLh, position, reference, Ref_WheelCenter_RrLh, null, # relative offset position, reference, Ref_WheelCenter_RrLh, null, # absolute position position constraint, active, active, active, single, 0., 0., 1., string, "model::sf::SF_Road_LH(V/3.6*Time-L_WheelBase) * 1.e-2", orientation constraint, active, active, active, null; joint: JoTotp_RoadInput_RrRh, total pin joint, NoDyn_Road_RrRh, position, reference, Ref_WheelCenter_RrRh, null, # relative offset position, reference, Ref_WheelCenter_RrRh, null, # absolute position position constraint, active, active, active, single, 0., 0., 1., string, "model::sf::SF_Road_RH(V/3.6*Time-L_WheelBase) * 1.e-2", orientation constraint, active, active, active, null; #----------------------------------------------------------------------------- # Gravity gravity: 0., 0., -1., const, g; end: elements;
# sf_Road_LH.sub scalar function: "SF_Road_LH", cubic spline, do not extrapolate, /* Distance (m), Road Height (cm) */ 0.,0., 0.803213,-0.561798, 2.81124,0.561798, 4.61847,1.68539, 6.62651,2.80899, 8.43373,1.68539, 9.83936,-1.68539, 11.4458,-6.17978, 13.0522,-8.42697, 15.0602,-8.98876, 16.8675,-6.17978, 18.4739,-3.37079, 20.4819,-2.24719, 22.2892,-3.93258, 24.0964,-6.17978, 26.1044,-7.30337, 27.9116,-5.61798, 29.5181,-2.24719, 30.7229,2.24719, 31.9277,6.74157, 33.5341,10.1124, 35.3414,11.236, 37.1486,8.98876, 38.5542,4.49438, 39.5582,0, 40.7631,-4.49438, 42.3695,-8.42697, 44.1767,-10.1124, 45.9839,-9.55056, 47.7912,-7.30337, 49.5984,-5.05618, 51.6064,-3.93258, 53.4137,-2.80899, 55.0201,0.561798, 56.8273,3.93258, 58.6345,5.61798, 60.4418,3.37079, 61.6466,-1.1236, 63.0522,-5.05618, 64.4578,-8.98876, 65.8635,-12.3596, 67.6707,-15.1685, 69.6787,-16.8539, 71.6867,-16.8539, 73.494,-16.2921, 75.502,-15.1685, 77.3092,-12.9213, 79.1165,-10.6742, 80.9237,-7.30337, 82.3293,-3.93258, 83.7349,0, 85.1406,3.93258, 86.9478,6.74157, 88.9558,8.42697, 90.7631,8.42697, 92.7711,6.74157, 94.5783,3.93258, 95.9839,0.561798, 97.3896,-3.93258, 98.5944,-7.86517, 100.201,-11.7978, 102.008,-14.0449, 103.815,-14.6067, 105.622,-12.3596, 107.229,-8.98876, 108.835,-5.61798, 110.643,-2.80899, 112.45,-0.561798, 114.458,-0.561798, 116.064,-3.37079, 117.871,-5.61798, 119.88,-6.17978, 121.687,-4.49438, 123.494,-2.24719, 125.502,-1.68539, 127.51,-2.80899, 129.317,-5.05618, 131.124,-7.86517, 132.731,-10.6742, 134.538,-12.9213, 136.546,-14.6067, 138.554,-14.6067, 140.562,-13.4831, 142.369,-11.236, 143.976,-8.42697, 145.582,-4.49438, 146.988,-0.561798, 148.394,2.80899, 150.201,5.61798, 152.008,7.30337, 153.815,6.74157, 155.622,6.74157, 157.631,7.30337, 159.639,7.86517, 161.647,7.86517, 163.655,6.74157, 165.261,4.49438, 166.867,0.561798, 168.072,-3.93258, 169.277,-7.86517, 170.683,-12.3596, 172.088,-16.2921, 173.494,-20.2247, 175.1,-23.5955, 176.908,-26.4045, 178.715,-27.5281, 180.723,-26.9663, 182.731,-26.4045, 184.739,-25.8427, 186.546,-24.7191, 188.353,-22.4719, 189.96,-19.1011, 191.165,-14.6067, 192.369,-10.1124, 193.775,-6.17978, 195.181,-1.68539, 196.787,0.561798, 198.795,2.80899;
# sf_Road_RH.sub scalar function: "SF_Road_RH", cubic spline, do not extrapolate, /* Distance (m), Road Height (cm) */ 0.,0., 0.803213,0, 2.61044,1.70455, 4.41767,3.97727, 6.4257,5.68182, 7.83133,2.84091, 9.23695,-1.13636, 11.0442,-3.40909, 12.8514,-5.11364, 14.8594,-5.68182, 16.6667,-3.40909, 18.2731,0, 20.2811,-0.568182, 21.8876,-3.40909, 23.6948,-6.25, 25.502,-8.52273, 27.51,-8.52273, 28.9157,-5.11364, 30.3213,-0.568182, 31.5261,3.97727, 32.9317,7.95455, 34.739,9.65909, 36.747,8.52273, 38.3534,5.11364, 39.759,1.13636, 41.1647,-2.84091, 42.7711,-5.68182, 44.5783,-7.38636, 46.5863,-6.25, 48.3936,-3.97727, 50.2008,-1.70455, 52.2088,-1.13636, 54.0161,0.568182, 55.8233,2.84091, 57.8313,4.54545, 59.6386,3.40909, 61.245,0, 62.6506,-3.97727, 64.0562,-7.95455, 65.8635,-10.7955, 67.6707,-11.9318, 69.6787,-13.0682, 71.6867,-13.0682, 73.6948,-13.0682, 75.7028,-11.9318, 77.51,-10.2273, 79.3173,-7.38636, 80.9237,-3.97727, 82.3293,0, 83.7349,3.97727, 85.3414,7.38636, 86.9478,10.2273, 88.9558,11.3636, 90.7631,10.2273, 92.5703,7.38636, 94.1767,4.54545, 95.5823,0.568182, 96.988,-3.40909, 98.1928,-7.95455, 99.7992,-11.3636, 101.606,-13.0682, 103.614,-11.9318, 105.422,-9.09091, 107.028,-6.25, 108.835,-3.40909, 110.643,-1.70455, 112.651,-1.13636, 114.458,-3.40909, 116.265,-6.25, 118.072,-7.95455, 120.08,-7.38636, 121.888,-5.11364, 123.695,-3.40909, 125.703,-2.84091, 127.51,-4.54545, 129.317,-6.81818, 131.124,-9.65909, 132.932,-12.5, 134.739,-14.7727, 136.546,-15.9091, 138.554,-15.9091, 140.562,-14.2045, 142.369,-11.9318, 143.976,-9.09091, 145.582,-5.68182, 146.787,-1.13636, 147.791,3.97727, 149.197,7.95455, 151.004,9.09091, 153.012,9.09091, 155.02,8.52273, 157.028,7.95455, 159.036,7.38636, 161.044,7.38636, 162.851,6.81818, 164.659,4.54545, 166.064,0.568182, 167.269,-3.97727, 168.474,-8.52273, 169.88,-13.0682, 171.285,-16.4773, 173.092,-19.3182, 174.9,-21.5909, 176.908,-23.2955, 178.916,-23.2955, 180.723,-22.7273, 182.731,-22.7273, 184.739,-22.1591, 186.747,-21.5909, 188.554,-19.8864, 189.96,-16.4773, 191.365,-11.9318, 192.57,-7.38636, 193.976,-3.40909, 195.582,0, 197.39,2.27273, 199.197,3.97727;