X-Git-Url: https://permondes.de/gitweb/Analog_Engine.git/blobdiff_plain/6d26a6bd8b30ad893da0315655d2f68aee787515..68fb174e84f38b2d72c7a0325cbfc6dc4fe486cc:/scripts/EP1%2004.02%20Starting%20a%20Rocket_b.LACE?ds=inline

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+# A rocket is started from the surface of the earth. Calculating the height as function of its mass and fuel consumption. 
+# Approximation of acceleration with Taylor series
+# Equation of motion
+# r'' = (alpha / m0)*v0 + (alpha/m0)²*v0*t - gamma * ME / r²
+#   alpha: fuel consumption, e.g. 2000t in 2,5 min = 13,333*10^3 kg/s
+#   m0: initial mass of rocket, e.g. Saturn V: 2900 t = 2,9*10^6 kg
+#   v0: the velocity of the exhaust of the rocket: 3,180*10^3 m/s
+#   gamma: gravitational constant: 6,6743E-11 m³/(kg*s²)
+#   ME: mass of earth: 5,97E+24 kg
+
+# include idivide
+include CompoundFunctions.LACE 
+
+coefficient.1(+1) -> alpha/m0*v0
+coefficient.2(+1) -> (alpha/m0)^2*v0
+coefficient.3     -> scale 
+coefficient.4(-1) -> -RE
+coefficient.5(+1) -> 10*gamma*ME
+
+# generate t-ramp
+iintegrate (-1) -> t
+
+# calculating altitude
+iintegrate (alpha/m0*v0, (alpha/m0)^2*v0*t, -gamma*ME/r^2) -> -v # input is a ### 3. Term fehlen noch ###
+cmultiply (scale, -v) -> -v.scaled
+iintegrate (-v) -> r
+  IC: -RE
+
+# calculating acceleration
+multiply (r,r) -> r^2
+idivide (10*gamma*ME, r^2) -> -10*gamma*ME/r^2
+
+cmultiply ((alpha/m0)^2*v0, t) -> (alpha/m0)^2*v0*t
+
+# inverting velocity for display
+invert (-v.scaled) -> v.scaled
+
+# subtracting the radius of earth in order to get altitude above ground for display
+isum (-RE, r) -> -z
+invert (-z) -> z
+
+output (t) -> out.x
+output (v) -> out.y
+output (z) -> out.z