#!/usr/bin/env pltthon3
# -*- coding: utf-8 -*-
"""
ENGG1811 lecture 7

Example: Simulate the parachutist's speed by formula
"""
# Import 
#import para_formula_lib as para
import matplotlib.pyplot as plt 
import numpy as np 
import math

# Constants
g = 9.81

# Problem parameters
mass = 70          # Mass of the parachutist 
tc = 4   # Time at which the parachute is deployed 
air_drag_coeff = 12.5     # Drag coefficient for air
para_drag_coeff = 80      # Drag coefficient for parachute 

# Create a list of regularly spaced time instants
# [0,0.25,0.5,0.75,...,20] 

start = 0
end = 20
step = 0.25
time_array = np.arange(start, end + step/2, step )

speed_by_formula_array = np.zeros_like(time_array)

for i in range(0, len(time_array)) :
    
    t = time_array[i] 
    
    if t < tc :
        speed = (g*mass/air_drag_coeff) * ( 1 - math.exp( -1*air_drag_coeff*t/mass ))

    else:
        vp0 = (g*mass/air_drag_coeff) * (1 - math.exp( -1*air_drag_coeff*tc/mass ) )
        speed = vp0 * math.exp((-1*para_drag_coeff/mass)*(t - tc)) + \
                (g*mass/para_drag_coeff)* (1 - math.exp((-para_drag_coeff/mass)*(t-tc)) )


    speed_by_formula_array[i]  = speed 



# Plot the figure 
fig1 = plt.figure() 
plt.plot(time_array,speed_by_formula_array,label = 'Parachute by formula')
plt.legend()
plt.xlabel('time [seconds]')
plt.ylabel('speed [m/s]')
plt.show()
# plt.savefig('para1.png')