# 3D animation of rocket taking off from a flat Earth
# Version 3.0  9-25-09
# Plots the trajectory of the rocket and then its distance and speed vs. time
# Includes wind resistance in Version 2.0
# Includes variable mass in Version 3.0
# Includes a fairly accurate model of time dependent thrust in Version 4.0, as well as fall-off in density of air

# Lots of useful info from this hobbyist rocketeer site:  http://www.braeunig.us/space/propuls.htm
from visual import *
from visual.graph import *  # import graphing features

# initialization section

# Set up the values I will need
# space shuttle website with specs at:  http://www.braeunig.us/space/specs/shuttle.htm


dt = 1                  # timestep in seconds
m = 2.0e6               # mass in kilograms

Ntimesteps = 124        # total number of timesteps for the simulation

air_density = 1.0       # air density  kg/m^3 < --- correct for air pressure falling off with altitude!

drag_coefficient = 0.5  # values of 0.5 to 0.75 quoted in misc. rocketry sources as the appropriate drag for this geometry (0.5 for shuttle)
area = 400              # in m^2

F_thrust_solid = 29.36e6    # solid rocket booster thrust at maximum

F_thrust_SMME = 1.8e6*3.*0.65# each of 3 SMME's used can generate 1.8 MN of thrust, at 65% after 35 s


# data plotted on Wikipedia show a relatively constant thrust profile vs. time;  this depends on the fuel geometry and the surface
# area burning at each time.  Some solid fuel designs result in relatively constant thrust, others increasing, decreasing.  See main reference.

#Launch thrust: 34,677 kN sea level (three SSMEs firing at 104%/1,754 kN each, two SRBs at 14,680 kN each; SSMEs throttle down to 65% by 35 s and up to 104% by 65 s) 
#SSME = space shuttle main engines;  SRB = solid rocket booster
#SRB Thrust: combined thrust 29.36 MN SL (maximum thrust at launch reducing by 1/3 after 50 s)
#Pressure: 62.1 atm max, 45.0 atm average

oxa=70000               # For plotting, the wireframe dimensions along Cartesian axes
oya=70000
oza=70000

g = 9.8                 # acceleration of gravity--constant at first for a flat Earth
                        
v_yo = 0.               # initial speed along y axis--zero at launch
v_xo = 0.               # later maybe we will make it 2D!
v_zo = 0.               # or even 3D!

x_o = 0                 # initial value of x, y and z--starts at the origin
y_o = 0
z_o = 0

# create wireframe with dimensions of the pixel sizes along x,y,z for now 
square1 = curve(pos=[(oxa,oya,oza),(-oxa,oya,oza),(-oxa,-oya,oza),(oxa,-oya,oza),(oxa,oya,oza)])
square2 = curve(pos=[(oxa,oya,-oza),(-oxa,oya,-oza),(-oxa,-oya,-oza),(oxa,-oya,-oza),(oxa,oya,-oza)])
square3 = curve(pos=[(oxa,oya,oza),(oxa,oya,-oza),(oxa,-oya,-oza),(oxa,-oya,oza),(oxa,oya,oza)])
square4 = curve(pos=[(-oxa,oya,oza),(-oxa,oya,-oza),(-oxa,-oya,-oza),(-oxa,-oya,oza),(-oxa,oya,oza)])
# end of wireframe

rocket = cone (pos=(x_o,y_o,z_o), radius=1000, axis=(0,5000,0), color=color.white)     # initialize rocket's position at (xo,yo,zo), pointing along +y
rocket.velocity = vector(v_xo,v_yo,v_zo)                                # initialize rocket's velocity too                        

rocket_position=[]
rocket_speed=[]

c = curve(pos=(x_o,y_o,z_o),color=color.red)            # plots the rocket's trajectory

n=0

while n <= Ntimesteps:
    rate (20)                                           # screen refresh rate           

    F_drag = -0.5*air_density*drag_coefficient*area*mag(rocket.velocity)*mag(rocket.velocity)
    
    F_thrust = F_thrust_solid + F_thrust_SMME           # now we get thrust from ejected fuel at constant v_exhaust,constant thrust
    
    F_net_y = F_thrust - m*g + F_drag
   
    rocket_force = vector(0.,F_net_y,0.)        
    

    rocket.velocity = rocket.velocity + (rocket_force/m)*dt # these update rules conform to Euler-Cromer method; they
                                                        #   conserve energy over a periodic orbits:  important point:
    rocket.pos = rocket.pos + rocket.velocity*dt        #   first update velocity, then update position second!
                                                        #   If switched in order, it looses energy and orbits don't close!

    rocket_position.append(mag(rocket.pos))
    rocket_speed.append(mag(rocket.velocity))
    c.append(pos=rocket.pos)
    n=n+1

print "final speed at solid booster separation = ",mag(rocket.velocity)," m/s (measured 1390 m/s)"
# SRB's take the shuttle to 45km and 1390 m/s before separation
# a canned functional plotting program from the vpython manual--use to plot distance and speed vs. time

scene2 = display(title='Graph of position and speed')

#scene2=display() # new screen with the plots

funct1 = gcurve(color=color.cyan) 
funct2 = gcurve(delta=0.05, color=color.yellow)

print "cyan (light blue-green) curve = rocket position, yellow curve = 40.*rocket speed vs. time (s)"
n=0

while n < Ntimesteps:
    funct1.plot(pos=(n*dt,rocket_position[n]))      #  rocket altitude vs. time
    funct2.plot(pos=(n*dt,40.*rocket_speed[n]))     #  rocket speed vs. time--scaled to be on same plot as position
    n=n+1