import numpy as np
import matplotlib.pyplot as plt


def temperature(altitude):
    if altitude > 25000:
        return -131.21 + 0.00299*altitude
    elif altitude > 11000:
        return -56.46
    else:
        return 15.04 - 0.00649*altitude


def pressure(altitude):
    T = temperature(altitude)
    if altitude > 25000:
        kpa = 2.488 * ((T+273.1)/216.6)**(-11.388)
    elif altitude > 11000:
        kpa = 22.65 * np.exp(1.73 - 0.000157*alititude)
    else:
        kpa = 101.29 * ((T+273.1)/288.08)**5.256
    return 1000*kpa

def atmospheric_density(altitude):
    p = pressure(altitude)
    T = temperature(altitude)
    return p / (286.9*(T+273.1))


def Mach(altitude, speed):
    return speed/speed_of_sound(altitude)


def speed_of_sound(altitude):
    gamma = 1.4
    p = pressure(altitude)
    rho = atmospheric_density(altitude)
    return (gamma*p/rho)**0.5


def dynamic_pressure(altitude, speed):
    rho = atmospheric_density(altitude)
    return rho * speed**2 / 2