## 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
! https://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