Apps

## Space Shuttle

## Space Shuttle Launch Simulation

The shuttle rises to 380 km and has a velocity of 7.68 km/sec at the final state.

! APMonitor Modeling Language ! http://www.apmonitor.com ! Endeavor shuttle launch simulation ! The shuttle rises to 380 km and has a ! velocity of 7.68 km/sec at the final state Model endeavor Parameters ! cross-sectional area of shuttle ! solid rocket booster (srb) ! cross-sectional area 10.8 m^2 ! diameter 3.71 m ! 1st stage ! cross-sectional area 55.4 m^2 ! diameter 8.4 m ! orbiter ! cross-sectional area ~ 20 m^2 d0 = 100.0 ! 1st drag constant (N/(m/s)^2) e0 = 1.0 ! 2nd drag constant (dimensionless) g0 = 9.8 ! gravity at launch (m/s^2) m0 = 2029203 ! mass of shuttle at launch h0 = 1000 ! initial height from earth's center (m) c = 1.5e7 ! impulse of rocket fuel (N/(kg/sec)) t_srb = 12.5e6 ! 2 solid rocket boosters (HMX) ! each have 12.5e6 N of thrust at lift-off ! they burn for 124 sec to height of 45.7 km ! they are released at 126 sec t_1st = 5.25e6 ! 1st stage fuel tank (liq H2/O2) has ! 5.25e6 N of thrust at lift-off ! it fires for 480 sec when it is released t_orb = 53.0e3 ! orbiter (MMH/N2O4) has 53e3 N of ! thrust at lift-off ! it fires for 1250 sec n_srb = 2 ! number of solid rocket boosters n_1st = 1 ! number of 1st stage thrusters n_orb = 1 ! number of orbiter thrusters End Parameters Variables t ! thrust force (N) ! 0 < t < t_max m = m0 ! mass of shuttle and fuel (kg) ! m_shuttle < m < m_full g = g0 ! gravitational force h = h0 ! altitude from earth's center (m) ! h > h0 d = 1 ! drag force (N) v = 0 ! velocity (m/s) a = 0 ! acceleration (m/s^2) End Variables Equations ! thrust t = n_srb * t_srb + n_1st * t_1st + n_orb * t_orb ! gravitational variation with height g = g0 * (h0/h)^2 ! velocity $h = v ! acceleration $v = a ! force balance ! inertial + gravitational + drag = thrust m*a + m*g + d = t ! aerodynamic drag force d = d0 * v^2 * exp(-e0*(h-h0)/h0) ! mass loss due to burn-off of fuel c * $m = -t + 0*m End Equations End Model