def alt2temp(H, alt_units=default_alt_units, temp_units=default_temp_units):
"""Return the standard temperature for the specified altitude. Altitude
units may be feet ('ft'), metres ('m'), statute miles, ('sm') or
nautical miles ('nm'). Temperature units may be degrees C, F, K or R
('C', 'F', 'K' or 'R')
If the units are not specified, the units in default_units.py are used.
Examples:
Calculate the standard temperature (in default temperature units) at
5,000 (default altitude units):
>>> alt2temp(5000)
5.0939999999999941
Calculate the standard temperature in deg F at sea level:
>>> alt2temp(0, temp_units = 'F')
59.0
Calculate the standard temperature in deg K at 11,000 m:
>>> alt2temp(11000, alt_units = 'm', temp_units = 'K')
216.64999999999998
Calculate the standard temperature at 11 statute miles in deg R:
>>> alt2temp(11, alt_units = 'sm', temp_units = 'R')
389.96999999999997
The input value may be an expression:
>>> alt2temp(11 * 5280, temp_units = 'R')
389.96999999999997
"""
# Validated to 84000 m
# uses meters and degrees K for the internal calculations
# function tested in tests/test_std_atm.py
H = U.len_conv(H, from_units=alt_units, to_units='km')
if H <= 11:
temp = T0 + H * L0
elif H <= 20:
temp = T11
elif H <= 32:
temp = T20 + (H - 20) * L20
elif H <= 47:
temp = T32 + (H - 32) * L32
elif H <= 51:
temp = T47
elif H <= 71:
temp = T51 + (H - 51) * L51
elif H <= 84.852:
temp = T71 + (H - 71) * L71
else:
raise ValueError(
'This function is only implemented for altitudes of 84.852 km and below.'
)
return U.temp_conv(temp, to_units=temp_units, from_units='K')
def temp2speed_of_sound(temp,
temp_units=default_temp_units,
speed_units=default_speed_units):
"""
Return the speed of sound, given the air temperature.
The temperature units may be deg C, F, K or R ('C', 'F', 'K' or 'R').
The speed units may be 'kt', 'mph', 'km/h', 'm/s' and 'ft/s'.
If the units are not specified, the units in default_units.py are used.
Examples:
Determine speed of sound in knots at 15 deg (default temperature units):
>>> temp2speed_of_sound(15)
661.47882487301808
Determine speed of sound in mph at 120 deg F:
>>> temp2speed_of_sound(120, speed_units = 'mph', temp_units = 'F')
804.73500154991291
"""
# function tested in tests/test_std_atm.py
temp = U.temp_conv(temp, from_units=temp_units, to_units='K')
speed_of_sound = M.sqrt((1.4 * Rd) * temp)
speed_of_sound = U.speed_conv(speed_of_sound,
from_units='m/s',
to_units=speed_units)
return speed_of_sound
def density_alt2temp(
density_alt_seek,
press_alt,
alt_units=default_alt_units,
temp_units=default_temp_units,
):
"""
Return temperature to achieve a desired density altitude.
If the units are not specified, the units in default_units.py are used.
"""
low = -100 # initial lower guess
high = 100 # initial upper guess
# confirm initial low and high are OK:
da_low = density_alt(press_alt, low, alt_units=alt_units)
if da_low > density_alt_seek:
raise ValueError('Initial low guess too high.')
da_high = density_alt(press_alt, high, alt_units=alt_units)
if da_high < density_alt_seek:
raise ValueError('Initial high guess too low.')
guess = (low + high) / 2.
da_guess = density_alt(press_alt, guess, alt_units=alt_units)
# keep iterating until da is within 1 ft of desired value
while M.fabs(da_guess - density_alt_seek) > 1:
if da_guess > density_alt_seek:
high = guess
else:
low = guess
guess = (low + high) / 2.
da_guess = density_alt(press_alt, guess, alt_units=alt_units)
guess = U.temp_conv(guess, from_units='C', to_units=temp_units)
return guess
def sat_press(
T='FALSE',
DP='FALSE',
RH=0.0,
temp_units=default_temp_units,
press_units=default_press_units,
):
"""
Return the saturated vapour pressure of water. Either the dew point, or
the temperature and the relative humidity must be specified. If both the
dew point and relative humidity are specified, the relative humidity value
is ignored.
If the temperature and dew point are both specified, the dew point cannot
be greater than the temperature:
If the units are not specified, the units in default_units.py are used.
>>> sat_press(T=10, DP=11)
Traceback (most recent call last):
File '<stdin>', line 1, in <module>
File 'std_atm.py', line 795, in sat_press
raise ValueError, 'The dew point cannot be greater than the temperature.'
ValueError: The dew point cannot be greater than the temperature.
Dew point is 11 deg (default temperature units). Find the water vapour
pressure in default pressure units:
>>> sat_press(DP=11)
0.38741015927568667
Dew point is 65 deg F. Find the water vapour pressure in default pressure units:
>>> sat_press(DP=65, temp_units = 'F')
0.62207710701956165
Dew point is 212 deg F (the boiling point of water at sea level).
Find the water vapour pressure in lb per sq. inch:
>>> sat_press(DP=212, temp_units = 'F', press_units = 'psi')
14.696764873564959
Temperature is 30 deg C. Find the water vapour pressure in default pressure units:
for 50% relative humidity:
>>> sat_press(T=30, RH = 0.5)
0.62647666996057927
"""
if DP != 'FALSE':
# use dew point method
if T != 'FALSE':
if DP > T:
raise ValueError(
'The dew point cannot be greater than the temperature.')
DP = U.temp_conv(DP, from_units=temp_units, to_units='C')
# calculate vapour pressure
Pv = _sat_press(DP) * 100
else:
if RH == 'FALSE':
raise ValueError(
'Either DP (dew point) or RH (relative humidity) must be specified.'
)
# relative humidity is specified
# confirm relative humidity is in range
if RH < 0 or RH > 1:
raise ValueError(
'The relative humidity must be in the range of 0 to 1.')
if T == 'FALSE':
raise ValueError(
'If the relative humidity is specified, the temperature must also be specified.'
)
T = U.temp_conv(T, from_units=temp_units, to_units='C')
Pv = _sat_press(T) * 100
Pv *= RH
Pv = U.press_conv(Pv, from_units='pa', to_units=press_units)
return Pv
def density_alt(
H,
T,
alt_setting=P0,
DP='FALSE',
RH=0.0,
alt_units=default_alt_units,
temp_units=default_temp_units,
):
"""
Return density altitude, given the pressure altitude and the
temperature with altitudes in units of feet ('ft'), metres ('m'),
statute miles, ('sm') or nautical miles ('nm'), and temperature in units
of deg C, F, K or R ('C', 'F', 'K' or 'R').
Mandatory parametres:
H = altitude
T = temperature
Optional parametres:
alt_setting = altimeter setting (defaults to 29.9213 if not provided
DP = dew point
RH = relative humidity
alt_units = units for the altitude. 'ft', 'm', or 'km'.
temp_units = units for the temperature and dew point. 'C', 'F', 'K'
or 'R'.
The altimeter setting units are assumed to be inches of HG, unless the
value is greater than 35. In this case the units are assumed to be mb.
If the dew point or relative humidity are not specified, the air is
assumed to be completely dry. If both the dew point and relative humidity
are specified, the relative humidity value is ignored.
If the units are not specified, the units in default_units.py are used.
The method is from: http://wahiduddin.net/calc/density_altitude.htm
Examples:
Calculate the density altitude in default altitude units for a pressure
altitude of 7000 default altitude units and a temperature of 15 deg
(default temperature units). The altimeter setting is not specified, so it
defaults to standard pressure of 29.9213 in HG or 1013.25 mb:
>>> density_alt(7000, 15)
8595.3465863232504
Calculate the density altitude in default altitude units for a pressure
altitude of 7000 default altitude units and a temperature of 85 deg F.
The altimeter setting is not specified, so it defaults to standard pressure
of 29.9213 in HG or 1013.25 mb. The dew point and relative humidity are
not specified, so the air is assumed to be dry:
>>> density_alt(7000, 85, temp_units = 'F')
10159.10696106757
Calculate the density altitude in default altitude units for a pressure
altitude of 7000 default altitude units, an altimeter setting of 29.80 and
a temperature of 85 deg F and a dew point of 55 deg F:
>>> density_alt(7000, 85, 29.80, 55, temp_units = 'F')
10522.776013011618
Calculate the density altitude in metres for a pressure altitude of
2000 m, an altimeter setting of 1010 mb, a temperature of 15 deg (default
temperature units) and a relative humidity of 50%:
>>> density_alt(2000, 15, 1010, alt_units = 'm', RH = 0.5)
2529.8230634449737
The dew point may be specified in one of two ways: as the fourth
argument on the command line, or via the keyword argument DP.
>>> density_alt(2000, 15, 1010, alt_units = 'm', DP = 5)
2530.7528237990618
The relative humidity must be in the range of 0 to 1:
>>> density_alt(2000, 15, 1010, alt_units = 'm', RH = 1.1)
Traceback (most recent call last):
File '<stdin>', line 1, in ?
File 'std_atm.py', line 533, in density_alt
raise ValueError, 'The relative humidity must be in the range of 0 to 1.'
ValueError: The relative humidity must be in the range of 0 to 1.
"""
Rv = 461.495 # gas constant for water vapour
# saturated vapour pressure
if DP == 'FALSE' and RH == 0:
Pv = 0
else:
Pv = sat_press(T, DP, RH, temp_units, press_units='pa')
# dry air pressure
Pd = dry_press(H,
Pv,
alt_setting=alt_setting,
alt_units=alt_units,
press_units='pa')
T = U.temp_conv(T, from_units=temp_units, to_units='K')
D = Pd / (Rd * T) + Pv / (Rv * T)
DR = D / Rho0
return density_ratio2alt(DR, alt_units)
def density_alt_table(
density_alt_seek,
alt_range=2000,
alt_inc=100,
alt_units=default_alt_units,
temp_units=default_temp_units,
multi_units=False,
file='',
format='text',
):
"""
Return a text or html table of required temperature vs pressure altitude.
If the units are not specified, the units in default_units.py are used.
"""
line_buffer = []
if format == 'text':
line_buffer.append(
'Pressure altitudes and temperatures for a density ')
line_buffer.append('altitude of ' + str(density_alt_seek) + ' ' +
alt_units)
line_buffer.append('(assuming dry air)\n')
if multi_units:
line_buffer.append(' Pressure Temp Temp')
line_buffer.append(' Altitude')
line_buffer.append(' (' + alt_units + ') (deg C) (deg F)')
else:
line_buffer.append(' Pressure Temp')
line_buffer.append(' Altitude')
line_buffer.append(' (' + alt_units + ') (deg ' +
temp_units + ')')
elif format == 'html':
print('creating html')
else:
raise ValueError('Invalid format. Must be either "text" or "html"')
if multi_units:
for alt in range(max(density_alt_seek - alt_range / 2., 0),
density_alt_seek + alt_range / 2. + alt_inc, alt_inc):
temp_c = density_alt2temp(density_alt_seek,
alt,
alt_units=alt_units)
temp_f = U.temp_conv(temp_c, from_units='C', to_units='F')
alt_str = L.format('%.*f', (0, alt), grouping=True)
temp_c_str = '%.1f' % temp_c
temp_f_str = '%.1f' % temp_f
line_buffer.append(
alt_str.rjust(6) + temp_c_str.rjust(11) + temp_f_str.rjust(10))
else:
for alt in range(max(density_alt_seek - alt_range / 2., 0),
density_alt_seek + alt_range / 2. + alt_inc, alt_inc):
alt_str = L.format('%.*f', (0, alt), grouping=True)
temp_str = '%.1f' % density_alt2temp(density_alt_seek,
alt,
temp_units=temp_units,
alt_units=alt_units)
line_buffer.append(alt_str.rjust(6) + temp_str.rjust(11))
if file != '':
OUT = open(file, 'w')
for line in line_buffer:
OUT.write(line + '\n')
print('file selected')
else:
return '\n'.join(line_buffer)