scripts/EP1 04.02 Starting a Rocket_b.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 acceleration with Taylor series
   3 # Equation of motion
   4 # r'' = (alpha / m0)*v0 + (alpha/m0)²*v0*t - gamma * ME / r²
   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 #   gamma: gravitational constant: 6,6743E-11 m³/(kg*s²)
   9 #   ME: mass of earth: 5,97E+24 kg
  10
  11 # include idivide
  12 include CompoundFunctions.LACE
  13
  14 coefficient.1(+1) -> alpha/m0*v0
  15 coefficient.2(+1) -> (alpha/m0)^2*v0
  16 coefficient.3     -> scale
  17 coefficient.4(-1) -> -RE
  18 coefficient.5(+1) -> 10*gamma*ME
  19
  20 # generate t-ramp
  21 iintegrate (-1) -> t
  22
  23 # calculating altitude
  24 iintegrate (alpha/m0*v0, (alpha/m0)^2*v0*t, -gamma*ME/r^2) -> -v # input is a ### 3. Term fehlen noch ###
  25 cmultiply (scale, -v) -> -v.scaled
  26 iintegrate (-v) -> r
  27   IC: -RE
  28
  29 # calculating acceleration
  30 multiply (r,r) -> r^2
  31 idivide (10*gamma*ME, r^2) -> -10*gamma*ME/r^2
  32
  33 cmultiply ((alpha/m0)^2*v0, t) -> (alpha/m0)^2*v0*t
  34
  35 # inverting velocity for display
  36 invert (-v.scaled) -> v.scaled
  37
  38 # subtracting the radius of earth in order to get altitude above ground for display
  39 isum (-RE, r) -> -z
  40 invert (-z) -> z
  41
  42 output (t) -> out.x
  43 output (v) -> out.y
  44 output (z) -> out.z