#!/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_formula
import para_ODE_lib as para_ODE
import matplotlib.pyplot as plt 
import numpy as np 

# Problem parameters
mass = 70          # Mass of the parachutist 
time_deploy = 6    # Time at which the parachute is deployed 
air_drag_coeff = 12.5     # Drag coefficient for air
para_drag_coeff = 80      # Drag coefficient for parachute 
speed0 = 0  # Initial speed 

# Simulation parameters
time_start = 0
time_end = 20
time_increment = 0.25

# Create a list of regularly spaced time instants
# [0,0.25,0.5,0.75,...,20] 
# 
time_array = np.arange(time_start,time_end+time_increment/2,
                       time_increment)

# Use ODE to calculate the parachustist's speed
# The function for calculating speed is in para_ODE_lib
speed_by_ODE_array = para_ODE.para_speed_ODE(time_array, mass, speed0, 
                            air_drag_coeff, time_deploy, para_drag_coeff)

# As a comparison, 
# use formula to calculate the parachustist's speed
speed_by_formula_array = np.zeros_like(time_array)
for k in range(0,len(time_array)):
    time = time_array[k]
    speed_para = para_formula.parachute(time,mass,air_drag_coeff,time_deploy,para_drag_coeff)
    speed_by_formula_array[k] = speed_para

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