permondes.de Git - Analog_Engine.git/blob - scripts/EP1 04.02 Starting a Rocket

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

11 # include idivide

12 include CompoundFunctions.LACE

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

20 # generate t-ramp

21 iintegrate (-1) -> t

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

29 # calculating acceleration

30 multiply (r,r) -> r^2

31 idivide (10*gamma*ME, r^2) -> -10*gamma*ME/r^2

33 cmultiply ((alpha/m0)^2*v0, t) -> (alpha/m0)^2*v0*t

35 # inverting velocity for display

36 invert (-v.scaled) -> v.scaled

38 # subtracting the radius of earth in order to get altitude above ground for display

39 isum (-RE, r) -> -z

40 invert (-z) -> z

42 output (t) -> out.x

43 output (v) -> out.y

44 output (z) -> out.z