new script about ussa76

pyatmos/standardatmos/ussa76.py

@@ -0,0 +1,106 @@
+"""
+The U.S. Standard Atmosphere 1976(USSA76) is an idealized, steady-state model of
+mean annual conditions of Earth's atmosphere from the surface to 86 km at
+latitude 45N, as it is assumed to exist during a period with moderate solar
+activity.
+"""
+
+import numpy as np
+
+from ..utils import Const
+    
+def lapse_tp(t_lower, p_lower, lr, h_lower, h_upper):
+    '''
+    Calculate the temperature and pressure at a given geopotential altitude above base of a specific layer.
+    The temperature is computed by the linear interpolation with the slope defined by lapse rates. 
+    The pressure is computed from the hydrostatic equations and the perfect gas law. 
+    See the detailed documentation in http://www.pdas.com/hydro.pdf
+
+    Usage:
+    [t_upper, p_upper] = lapse_tp(t_lower, p_lower, lr, h_lower, h_upper)
+
+    Inputs:
+    t_lower -> [float] temperature[K] at the lower boundary of the subset in the specific layer
+    p_lower -> [float] pressure[Pa] at the lower boundary of the subset in the specific layer
+    lr -> [float] lapse rate[K/m] for the specific layer
+    h_lower -> [float] geopotential altitude[m] at the lower boundary of the subset in the specific layer
+    h_upper -> [float] geopotential altitude[m] at the upper boundary of the subset in the specific layer
+    
+    Outputs:
+    t1 -> [float] temperature[K] at the upper boundary of the subset in the specific layer
+    p1 -> [float] pressure[Pa] at the upper boundary of the subset in the specific layer
+    
+    Reference: Public Domain Aeronautical Software(http://www.pdas.com/atmos.html) 
+               https://gist.github.com/buzzerrookie/5b6438c603eabf13d07e
+    '''
+    R_air,g0 = Const.R_air,Const.g0
+
+    if lr == 0:
+        t_upper = t_lower
+        p_upper = p_lower * np.exp(-g0 / R_air / t_lower * (h_upper - h_lower)*1e3)
+    else:
+        t_upper = t_lower + lr * (h_upper - h_lower)
+        p_upper = p_lower * (t_upper / t_lower) ** (-g0 / (lr/1e3) / R_air)
+
+    return t_upper,p_upper
+
+def ussa76(h):
+    '''
+    Implements the U.S. Standard Atmosphere 1976(USSA76) up to 86km. 
+    The standard atmosphere is defined as a set of layers by specified geopotential altitudes and lapse rates.
+    The temperature is computed by linear interpolation with the slope defined by the lapse rate. 
+    The pressure is computed from the hydrostatic equations and the perfect gas law; the density follows from the perfect gas law. 
+
+    Usage:
+    [rho, T, P, C, eta, Kc] = ussa76(h)
+
+    Inputs:
+    h -> [float] geopotentail altitude, [km]
+
+    Outputs:
+    rho -> [float] density at a given altitude, [kg/m^3]
+    T -> [float] temperature ..., [K]
+    P -> [float] pressure ..., [Pa]
+    C -> [float] speed of sound ..., [m/s]
+    eta -> [float] dynamic viscosity ..., [kg/m/s]
+    Kc -> [float] thermal conductivity ..., [J/(m*s*K)]
+    
+    Note: the geopotential altitude should be in [-0.610,84.852] km, otherwise the output will be extrapolated for those input altitudes.
+
+    Reference: 
+        U.S. Standard Atmosphere, 1976, U.S. Government Printing Office, Washington, D.C. 
+        Public Domain Aeronautical Software(http://www.pdas.com/atmos.html) 
+        https://gist.github.com/buzzerrookie/5b6438c603eabf13d07e
+        https://ww2.mathworks.cn/help/aerotbx/ug/atmosisa.
+        http://www.braeunig.us/space/atmmodel.htm#USSA1976
+    '''
+    t0,p0,h0 = Const.t0,Const.p0,Const.h0
+    R_air,M0,gamma = Const.R_air,Const.M0,Const.gamma
+
+    # the lower atmosphere below 86km is separated into seven layers 
+    geopotential_alt = [-np.inf, 11, 20, 32, 47, 51, 71, np.inf] # Geopotential altitudes above MSL, [km]
+
+    lr = np.array([-6.5, 0, 1, 2.8, 0, -2.8, -2]) # Lapse rate, [K/km]   
+
+    for i in range(len(lr)):
+        if h <= geopotential_alt[i+1]:
+            T, P = lapse_tp(t0, p0, lr[i], h0, h)
+            break
+        else:
+            # if altitudes are greater than the first several layers, then it has to integeate these layers first.
+            t0, p0 = lapse_tp(t0, p0, lr[i], h0, geopotential_alt[i+1])
+            h0 = geopotential_alt[i+1]
+
+    # density
+    rho = P / (R_air * T)
+
+    # speed of sound
+    C = np.sqrt(gamma * R_air * T)
+
+    # dynamic viscosity by Sutherland's law
+    eta = 1.458e-6*T**1.5/(T+110.4) 
+
+    # thermal conductivity
+    Kc = 2.64638e-3 * T ** 1.5 / (T + 245.4 * (10 ** (-12.0 / T))) 
+
+    return rho,T,P,C,eta,Kc