Throwing a stone on earth, starting a rocket from earth

Some rearrangements of the application examples
Application: Throwing a stone on earth
Application: Starting a rocket from earth

diff --git a/Analog Engine Example Applications.odt b/Analog Engine Example Applications.odt
index c59148e8d3b551f3d4f84c4cd6c2b212085e7968..4f83903a1b1c2cc8593373015a693c3e0b55dda1 100644 (file)
Binary files a/Analog Engine Example Applications.odt and b/Analog Engine Example Applications.odt differ

diff --git a/scripts/EP1 04.02 Starting a Rocket_a.LACE b/scripts/EP1 04.02 Starting a Rocket_a.LACE
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+++ b/scripts/EP1 04.02 Starting a Rocket_a.LACE
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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 gravity of earth by g
+# Equation of motion
+# r'' = alpha / (m0 - alpha*t) * v0 - g
+#   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
+#   g: acceleration of earth = 9,81 m/s^2
+
+include CompoundFunctions.LACE # include idivide
+
+coefficient.1     -> alpha1
+coefficient.2(+1) -> alpha2 # == alpha1
+coefficient.3(-1) -> -m0
+coefficient.4     -> v0
+coefficient.5(+1) -> g
+
+# generate t-ramp
+iintegrate (-1) -> t
+
+cmultiply (alpha1, t) -> alpha*t
+isum (-m0, alpha*t) -> m0-alpha*t
+idivide (alpha2, m0-alpha*t) -> -alpha/(m0-alpha*t)
+cmultiply (-alpha/(m0-alpha*t), v0) -> -alpha/(m0-alpha*t)*v0
+isum(-alpha/(m0-alpha*t)*v0, g) -> alpha/(m0-alpha*t)*v0-g
+
+iintegrate (alpha/(m0-alpha*t)*v0-g) -> -v
+invert (-v) -> v
+iintegrate (-v) -> z
+
+output (t) -> out.x
+output (v) -> out.y
+output (z) -> out.z

diff --git a/scripts/EP1 04.02 Starting a Rocket_b.LACE b/scripts/EP1 04.02 Starting a Rocket_b.LACE
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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

diff --git a/scripts/EP1 871102 Throwing a stone.LACE b/scripts/EP1 871102 Throwing a stone.LACE
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+# Throwing a stone on earth
+#
+# z'' = -g, with g=0,981 da*m/s^2
+# Initial speeds: v.z0 (vertical) and v.x0 (horizontal)
+
+coefficient.1(-1) -> -g    # set to 0,981
+coefficient.2(+1) -> v.z0  # initial vertical speed
+coefficient.3(+1) -> v.x0  # initial horizontal speed
+coefficient.4(-1) -> -z0   # initial altitude
+
+iintegrate (-g) -> -v
+  IC: v.z0
+iintegrate (-v) -> z
+  IC: -z0
+
+iintegrate (v.x0) -> x
+
+invert (-v) -> v
+
+output (x) -> out.x
+output (z) -> out.y
+output (v) -> out.z