126 lines
2.3 KiB
Python
126 lines
2.3 KiB
Python
import numpy as np
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import matplotlib.pyplot as plt
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# VARIABLES:
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v0 = 0.00 # Initial Balloon Velocity in [m/s]
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s0 = 0.00 # Initial Balloon Altitude in [m]
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p0 = 101325 # (Initial) Air Pressure in [Pa]
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rho_a = 1.2250 # (Initial) Air Density in [kg/m^3]
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tmax = 10000
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T_a = 288.15 # (Initial) Air Temperature in [K]
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g = 9.80665 # local gravitation in [m/s^2]
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dt = 0.01 # time step in [s]
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cD = 0.47 # drag coefficient balloon (spherical) [-]
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R_a = 287.1 # Specific Gas Constant Dry Air in [J/(kg * K)]
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R_He = 2077.1 # Specific Gas Constant Helium in [J/(kg * K)]
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m_B = 50 # Balloon (Start) Mass in [kg]
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m_PL = 10 # Balloon Payload (Start) Mass in [kg]
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pi = np.pi
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def T(h):
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if h >= 0 and h <= 11000:
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res = 288.15 - 0.0065 * h
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return res
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elif h > 11000 and h <= 20000:
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res = 216.65
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return res
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elif h >= 20000:
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res = 216.65 + 0.0010 * (h - 20000)
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return res
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def p(h):
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if h >= 0 and h <= 11000:
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res = 101325 * ((288.15 - 0.0065 * h)/288.15) ** 5.25577
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return res
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elif h > 11000 and h <= 20000:
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res = 22632 * np.exp(-(h - 11000)/6341.62)
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return res
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elif h > 20000:
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res = 5474.87 * ((216.65 + 0.0010 * (z - 20000))/216.65) ** (-34.163)
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return res
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def rho(h):
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res = p(h)/(R_a * T(h))
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return res
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# p_a = p0 # air pressure = constant
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p_He = 101325 # initial gas pressure = air pressure
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T_g = 288.15 # gas temperature = air temperature = constant
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# GAS DENSITY
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rho_g = p_He / (R_He * T_g)
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V_B = m_B / rho_g
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D_B = (6 * V_B / pi) ** (1/3)
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v = []
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time = []
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alt = []
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v_z = v0
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z = s0
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t = 0
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D = 0
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rho_plot = []
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T_plot = []
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p_plot = []
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D_plot = []
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while t < tmax:
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v.append(v_z)
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alt.append(z)
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time.append(t)
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rho_plot.append(rho(z))
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T_plot.append(T(z))
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p_plot.append(p(z))
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D_plot.append(D)
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D = 0.5 * cD * 0.25 * pi * rho(z) * v_z ** 2 * D_B ** 2
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I = g * V_B * (rho(z) - rho_g)
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G = g * m_PL
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dv_z = (I - np.sign(v_z) * D - G) / m_B * dt
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# print(z, v_z)
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v_z += dv_z * dt
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z += v_z * dt + 0.5 * dv_z * dt
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t += dt
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#plt.plot(time, rho_plot)
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#plt.plot(time, T_plot)
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###plt.plot(time, v)
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###plt.show()
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#plt.plot(time, ind)
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#plt.plot(time, D_plot)
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plt.plot(time, alt)
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plt.show()
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