scripts/EP1 04.02 Starting a Rocket_a.LACE

   1 # A rocket is started from the surface of the earth. Calculating the height as function of its mass and fuel consumption.
   2 # Approximation of gravity of earth by g
   3 # Equation of motion
   4 # r'' = alpha / (m0 - alpha*t) * v0 - g
   5 #   alpha: fuel consumption, e.g. 2000t in 2,5 min = 13,333*10^3 kg/s
   6 #   m0: initial mass of rocket, e.g. Saturn V: 2900 t = 2,9*10^6 kg
   7 #   v0: the velocity of the exhaust of the rocket: 3,180*10^3 m/s
   8 #   g: acceleration of earth = 9,81 m/s^2
   9
  10 include CompoundFunctions.LACE # include idivide
  11
  12 coefficient.1     -> alpha1
  13 coefficient.2(+1) -> alpha2 # == alpha1
  14 coefficient.3(-1) -> -m0
  15 coefficient.4     -> v0
  16 coefficient.5(+1) -> g
  17
  18 # generate t-ramp
  19 iintegrate (-1) -> t
  20
  21 cmultiply (alpha1, t) -> alpha*t
  22 isum (-m0, alpha*t) -> m0-alpha*t
  23 idivide (alpha2, m0-alpha*t) -> -alpha/(m0-alpha*t)
  24 cmultiply (-alpha/(m0-alpha*t), v0) -> -alpha/(m0-alpha*t)*v0
  25 isum(-alpha/(m0-alpha*t)*v0, g) -> alpha/(m0-alpha*t)*v0-g
  26
  27 iintegrate (alpha/(m0-alpha*t)*v0-g) -> -v
  28 invert (-v) -> v
  29 iintegrate (-v) -> z
  30
  31 output (t) -> out.x
  32 output (v) -> out.y
  33 output (z) -> out.z