| | 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 |
projects / Analog_Engine.git / blame_incremental