def pwr(rpm, MP, altitude, temp='std', alt_units='ft', temp_units='C'):
"""
Returns horsepower for Lycoming IO-360-A series engines, given:
rpm - engine speed in revolutions per minute
MP - manifold pressure (" HG)
altitude - pressure altitude
temp - ambient temperature (optional - std temperature is used if no
temperature is input).
alt_units - (optional) - units for altitude, ft, m, or km
(default is ft)
temp_units - (optional) - units for temperature, C, F, K or R
(default is deg C)
The function replicates Lycoming curve 12700-A, and is valid at mixture
for maximum power.
Examples:
Determine power at 2620 rpm, 28 inches HG manifold pressure, 0 ft, and
-10 deg C:
>>> pwr(2620, 28, 0, -10)
197.71751932574702
Determine power at 2500 rpm, 25" MP, 5000 ft and 0 deg F:
>>> pwr(2500, 25, 5000, 0, temp_units = 'F')
171.87810350172663
Determine power at 2200 rpm, 20" MP, 2000 metres and -5 deg C
>>> pwr(2200, 20, 2000, -5, alt_units = 'm')
108.60284092217333
Determine power at 2200 rpm, 20" MP, 2000 metres and standard
temperature:
>>> pwr(2200, 20, 2000, alt_units = 'm')
107.2124765533882
"""
# convert units
altitude = unit_conversion.length_conv(altitude,
from_units=alt_units,
to_units='ft')
if temp == 'std':
temp = std_atm.alt2temp(altitude, temp_units=temp_units)
temp = unit_conversion.temp_conv(temp, from_units=temp_units, to_units='K')
# get standard temperature
temp_std = std_atm.alt2temp(altitude, temp_units='K')
# get power at standard temperature
pwr_std = _pwr_std_temp(rpm, MP, altitude)
# correct power for non-standard temperature
pwr = pwr_std * np.sqrt(temp_std / temp)
return pwr
def test_04(self):
# check deg F at 25,000 m
# change order of units specifications
T = round(SA.alt2temp(25000, temp_units='F', alt_units='m'), 2)
self.assertEqual(T, -60.7)
def __init__(self, h):
# Cantera Solution object
self.gas = ct.Solution('air.xml')
# Discretised altitude steps
self.h = h
# Average molecular diameter of gas
self.d = 4E-10
self.steps = len(h)
self.rho = np.zeros(self.steps)
self.p = np.zeros(self.steps)
self.T = np.zeros(self.steps)
self.a = np.zeros(self.steps)
self.k = np.zeros(self.steps)
self.mu = np.zeros(self.steps)
for index, alt in enumerate(self.h):
self.rho[index] = atm.alt2density(alt, alt_units='m', density_units='kg/m**3')
self.p[index] = atm.alt2press(alt, press_units='pa', alt_units='m')
self.T[index] = atm.alt2temp(alt, alt_units='m', temp_units='K')
self.a[index] = atm.temp2speed_of_sound(self.T[index], temp_units='K', speed_units='m/s')
for index, alt in enumerate(self.h):
self.gas.TP = self.T[index], self.p[index]
self.k[index] = self.gas.cp / self.gas.cv
self.mu[index] = self.gas.viscosity
print 'ATMOSPHERIC MODEL COMPUTED (US76)'
return None
def test_01(self):
# speed of sound at 5,000 ft
# Truth value from NASA RP 1046
Value = SA.temp2speed_of_sound(SA.alt2temp(5000))
Truth = 650.01
self.assertLessEqual(RE(Value, Truth), 1e-5)
def test_02(self):
# speed of sound in mph at 8,000 ft
# Truth value from NASA RP 1046
Value = SA.temp2speed_of_sound(SA.alt2temp(8000),
speed_units='mph')
Truth = 739.98
self.assertLessEqual(RE(Value, Truth), 1e-5)
def test_03(self):
# speed of sound in km/h at 2,000 m, with temp in deg R
# Truth value from NASA RP 1046
Value = SA.temp2speed_of_sound(SA.alt2temp(2000, alt_units='m',
temp_units='R'), speed_units='km/h', temp_units='R')
Truth = 1197.1
self.assertLessEqual(RE(Value, Truth), 1e-5)
def test_04(self):
# speed of sound at 10,000 m
# Truth value from NASA RP 1046
Value = SA.temp2speed_of_sound(SA.alt2temp(10000, alt_units='m'
))
Truth = 582.11
self.assertLessEqual(RE(Value, Truth), 1e-5)
def pp(rpm, MP, altitude, temp='std', alt_units='ft', temp_units='C'):
"""
Returns percent power for Lycoming IO-360-A series engines, given:
rpm - engine speed in revolutions per minute
MP - manifold pressure (" HG)
altitude - pressure altitude
temp - ambient temperature (optional - std temperature is used if no
temperature is input).
alt_units - (optional) - units for altitude, ft, m, or km
(default is ft)
temp_units - (optional) - units for temperature, C, F, K or R
(default is deg C)
The function replicates Lycoming curve 12700-A, and is valid at mixture
for maximum power.
Note: the output is rounded off to two decimal places.
Examples:
Determine power at 2620 rpm, 28 inches HG manifold pressure, 0 ft, and
-10 deg C:
>>> pp(2620, 28, 0, -10)
'98.86%'
Determine power at 2500 rpm, 25" MP, 5000 ft and 0 deg F:
>>> pp(2500, 25, 5000, 0, temp_units = 'F')
'85.94%'
Determine power at 2200 rpm, 20" MP, 2000 metres and -5 deg C
>>> pp(2200, 20, 2000, -5, alt_units = 'm')
'54.30%'
Determine power at 2200 rpm, 20" MP, 2000 metres and standard
temperature:
>>> pp(2200, 20, 2000, alt_units = 'm')
'53.61%'
"""
altitude = unit_conversion.length_conv(altitude,
from_units=alt_units,
to_units='ft')
if temp == 'std':
temp = std_atm.alt2temp(altitude, temp_units=temp_units)
temp = unit_conversion.temp_conv(temp, from_units=temp_units, to_units='C')
pp = pwr(rpm, MP, altitude, temp) / 2
# return pp
return '%.2f' % (pp) + '%'
def prop_eff(prop,
bhp,
rpm,
tas,
altitude,
temp='std',
power_units='hp',
alt_units='ft',
temp_units='C',
speed_units='kt',
dia_units='in'):
"""
Returns propeller efficiency based on engine power provided to the propeller.
"""
press_ratio = SA.alt2press_ratio(altitude, alt_units=alt_units)
if temp == 'std':
temp = SA.alt2temp(altitude,
temp_units=temp_units,
alt_units=alt_units)
temp_ratio = U.temp_conv(temp, from_units=temp_units,
to_units='K') / 288.15
density_ratio = press_ratio / temp_ratio
density = density_ratio * SA.Rho0
Cp = bhp2Cp(bhp,
rpm,
density,
prop.dia,
power_units=power_units,
density_units='kg/m**3',
dia_units=dia_units)
J = advance_ratio(tas,
rpm,
prop.dia,
speed_units=speed_units,
dia_units=dia_units)
blade_tip_mach = tip_mach(tas,
rpm,
temp,
prop.dia,
speed_units=speed_units,
temp_units=temp_units,
dia_units=dia_units)
prop_eff = cp2eff(prop, Cp, J, blade_tip_mach)
if N.isnan(prop_eff):
raise ValueError('Out of range inputs')
return prop_eff
def blade_angle2bhp(prop,
blade_angle,
rpm,
tas,
altitude,
temp='std',
power_units='hp',
alt_units='ft',
temp_units='C',
speed_units='kt',
dia_units='in'):
"""
Returns returns engine power, given blade angle, rpm and flight conditions.
"""
press_ratio = SA.alt2press_ratio(altitude, alt_units=alt_units)
if temp == 'std':
temp = SA.alt2temp(altitude,
temp_units=temp_units,
alt_units=alt_units)
temp_ratio = U.temp_conv(temp, from_units=temp_units,
to_units='K') / 288.15
density_ratio = press_ratio / temp_ratio
density = density_ratio * SA.Rho0
# Cp = bhp2Cp(bhp, rpm, density, prop.dia, power_units = power_units, density_units = 'kg/m**3', dia_units = dia_units)
J = advance_ratio(tas,
rpm,
prop.dia,
speed_units=speed_units,
dia_units=dia_units)
blade_tip_mach = tip_mach(tas,
rpm,
temp,
prop.dia,
speed_units=speed_units,
temp_units=temp_units,
dia_units=dia_units)
Cp = blade_angle2cp(prop, blade_angle, J, blade_tip_mach)
bhp = cp2bhp(Cp,
rpm,
density,
prop.dia,
power_units=power_units,
density_units='kg/m**3',
dia_units=dia_units)
return bhp
def pp2mp(percent_power,
rpm,
altitude,
temp='std',
alt_units='ft',
temp_units='C'):
"""
Returns manifold pressure in inches of mercury for a given percent
power, rpm, altitude and temperature (temperature input is optional
- standard temperature is used if no temperature is input).
Note: the output is rounded off to two decimal places.
Examples:
Determine manifold pressure required for 62.5% power at 2550 rpm
at 8000 ft and 10 deg C:
>>> pp2mp(62.5, 2550, 8000, 10)
'19.45'
Determine manifold pressure required for 75% power at 2500 rpm at
7500 ft at 10 deg F:
>>> pp2mp(75, 2500, 7500, 10, temp_units = 'F')
'22.25'
Determine manifold pressure required for 55% power at 2400 rpm at
9,500 ft at standard temperature:
>>> pp2mp(55, 2400, 9500)
'18.18'
"""
if percent_power <= 0:
raise ValueError('Power input must be positive.')
# convert units
altitude = unit_conversion.length_conv(altitude,
from_units=alt_units,
to_units='ft')
if temp == 'std':
temp = std_atm.alt2temp(altitude, temp_units=temp_units)
temp = unit_conversion.temp_conv(temp, from_units=temp_units, to_units='C')
pwr_seek = percent_power * 2
mp = pwr2mp(pwr_seek, rpm, altitude, temp)
return mp
def blade_angle(prop,
bhp,
rpm,
tas,
altitude,
temp='std',
power_units='hp',
alt_units='ft',
temp_units='C',
speed_units='kt',
dia_units='in'):
"""
Returns propeller blade angle.
"""
press_ratio = SA.alt2press_ratio(altitude, alt_units=alt_units)
if temp == 'std':
temp = SA.alt2temp(altitude,
temp_units=temp_units,
alt_units=alt_units)
temp_ratio = U.temp_conv(temp, from_units=temp_units,
to_units='K') / 288.15
density_ratio = press_ratio / temp_ratio
density = density_ratio * SA.Rho0
Cp = bhp2Cp(bhp,
rpm,
density,
prop.dia,
power_units=power_units,
density_units='kg/m**3',
dia_units=dia_units)
J = advance_ratio(tas,
rpm,
prop.dia,
speed_units=speed_units,
dia_units=dia_units)
blade_tip_mach = tip_mach(tas,
rpm,
temp,
prop.dia,
speed_units=speed_units,
temp_units=temp_units,
dia_units=dia_units)
blade_angle = cp2blade_angle(prop, Cp, J, blade_tip_mach)
return blade_angle
def pp2rpm(percent_power,
mp,
altitude,
temp='std',
alt_units='ft',
temp_units='C'):
"""
Returns rpm for a given percent power, manifold pressure in inches of
mercury, altitude and temperature (temperature input is optional -
standard temperature is used if no temperature is input).
Examples:
Determine rpm required for 125 hp at 20 inches HG manifold pressure at
8000 ft and 10 deg C:
>>> pp2rpm(62.5, 20, 8000, 10)
2477
Determine rpm required for 75% power at 22 inches HG manifold pressure
at 6500 ft and 10 deg F:
>>> pp2rpm(75, 22, 6500, 10, temp_units = 'F')
2547
Determine rpm required for 55% power at at 18 inches HG manifold
pressure at 9,500 ft at standard temperature:
>>> pp2rpm(55, 18, 9500)
2423
"""
if percent_power <= 0:
raise ValueError('Power input must be positive.')
# convert units
altitude = unit_conversion.length_conv(altitude,
from_units=alt_units,
to_units='ft')
if temp == 'std':
temp = std_atm.alt2temp(altitude, temp_units=temp_units)
temp = unit_conversion.temp_conv(temp, from_units=temp_units, to_units='C')
pwr_seek = percent_power * 2
rpm = pwr2rpm(pwr_seek, mp, altitude, temp)
return rpm
def __init__(self, h, T_thermosphere):
# Cantera Solution object
self.gas = ct.Solution('air.xml')
# Discretised altitude steps
self.h = h
# Average molecular diameter of gas
self.d = 4E-10
# Ratio of specific heats
self.steps = len(h)
self.rho = np.zeros(self.steps)
self.p = np.zeros(self.steps)
self.T = np.zeros(self.steps)
self.a = np.zeros(self.steps)
self.k = np.zeros(self.steps)
self.mu = np.zeros(self.steps)
# Call Jacchia77 model
data = j77.j77sri(np.max(h), T_thermosphere)
data_np = np.array(data)
h_int = spint.griddata
T_int = spint.griddata
mw_int = spint.griddata
n = spint.griddata
for index, alt in enumerate(self.h):
self.rho[index] = atm.alt2density(alt, alt_units='m', density_units='kg/m**3')
self.p[index] = atm.alt2press(alt, press_units='pa', alt_units='m')
self.T[index] = atm.alt2temp(alt, alt_units='m', temp_units='K')
self.a[index] = atm.temp2speed_of_sound(self.T[index], temp_units='K', speed_units='m/s')
for index, alt in enumerate(self.h):
self.gas.TP = self.T[index], self.p[index]
self.k[index] = self.gas.cp / self.gas.cv
self.mu[index] = self.gas.viscosity
return None
def test_03(self):
# check deg R at 19 km
T = round(SA.alt2temp(19, alt_units='km', temp_units='R'), 2)
self.assertEqual(T, 389.97)
def test_08(self):
# check at 80 km
T = round(SA.alt2temp(80, alt_units='km'), 2)
self.assertEqual(T, -76.5)
def test_07(self):
# check at 60 km
T = round(SA.alt2temp(60, alt_units='km'), 2)
self.assertEqual(T, -27.7)
def test_06(self):
# check at 50 km
T = round(SA.alt2temp(50, alt_units='km'), 2)
self.assertEqual(T, -2.5)
def test_05(self):
# check at 40 km
T = round(SA.alt2temp(40, alt_units='km'), 2)
self.assertEqual(T, -22.1)
def pwr2mp(pwr_seek,
rpm,
altitude,
temp='std',
alt_units='ft',
temp_units='C'):
"""
Returns manifold pressure in inches of mercury for a given power, rpm,
altitude and temperature (temperature input is optional - standard
temperature is used if no temperature is input).
Note: the output is rounded off to two decimal places.
Examples:
Determine manifold pressure required for 125 hp at 2550 rpm at 8000 ft
and 10 deg C:
>>> pwr2mp(125, 2550, 8000, 10)
'19.45'
Determine manifold pressure required for 75% power at 2500 rpm at
7500 ft at 10 deg F:
>>> pwr2mp(.75 * 200, 2500, 7500, 10, temp_units = 'F')
'22.25'
Determine manifold pressure required for 55% power at 2400 rpm at
9,500 ft at standard temperature:
>>> pwr2mp(.55 * 200, 2400, 9500)
'18.18'
"""
if pwr_seek <= 0:
raise ValueError('Power input must be positive.')
low = 0 # initial lower guess
high = 35 # initial upper guess
# convert units
altitude = unit_conversion.length_conv(altitude,
from_units=alt_units,
to_units='ft')
if temp == 'std':
temp = std_atm.alt2temp(altitude, temp_units=temp_units)
temp = unit_conversion.temp_conv(temp, from_units=temp_units, to_units='C')
# confirm initial low and high are OK:
pwr_low = pwr(rpm, low, altitude, temp)
if pwr_low > pwr_seek:
raise ValueError('Initial low guess too high.')
pwr_high = pwr(rpm, high, altitude, temp)
if pwr_high < pwr_seek:
raise ValueError('Initial high guess too low.')
guess = (low + high) / 2.
pwr_guess = pwr(rpm, guess, altitude, temp)
# keep iterating until power is within 0.1% of desired value
while np.fabs(pwr_guess - pwr_seek) / pwr_seek > 1e-3:
if pwr_guess > pwr_seek:
high = guess
else:
low = guess
guess = (low + high) / 2.
pwr_guess = pwr(rpm, guess, altitude, temp)
# result = int(guess) + round(guess % 1, 2))
# return guess
# return result
return '%.2f' % (guess)
def pwr2rpm(pwr_seek,
mp,
altitude,
temp='std',
alt_units='ft',
temp_units='C'):
"""
Returns rpm for a given power, manifold pressure in inches of mercury,
altitude and temperature (temperature input is optional - standard
temperature is used if no temperature is input).
Note: the output is rounded off to the nearest rpm.
Examples:
Determine rpm required for 125 hp at 20 inches HG manifold pressure at
8000 ft and 10 deg C:
>>> pwr2rpm(125, 20, 8000, 10)
2477
Determine rpm required for 75% power at 22 inches HG manifold pressure
at 6500 ft and 10 deg F:
>>> pwr2rpm(.75 * 200, 22, 6500, 10, temp_units = 'F')
2547
Determine rpm required for 55% power at at 18 inches HG manifold
pressure at 9,500 ft at standard temperature:
>>> pwr2rpm(.55 * 200, 18, 9500)
2423
"""
if pwr_seek <= 0:
raise ValueError('Power input must be positive.')
low = 1000 # initial lower guess
high = 3500 # initial upper guess
# convert units
altitude = unit_conversion.length_conv(altitude,
from_units=alt_units,
to_units='ft')
if temp == 'std':
temp = std_atm.alt2temp(altitude, temp_units=temp_units)
temp = unit_conversion.temp_conv(temp, from_units=temp_units, to_units='C')
# confirm initial low and high are OK:
pwr_low = pwr(low, mp, altitude, temp)
# print("pwr_low=", pwr_low)
if pwr_low > pwr_seek:
raise ValueError('Initial low guess too high.')
pwr_high = pwr(high, mp, altitude, temp)
# print("pwr_high=", pwr_high)
if pwr_high < pwr_seek:
# print("pwr_high=", pwr_high)
print("Function called was IO.pwr(%f, %f, %f, %f)" %
(high, mp, altitude, temp))
raise ValueError('Initial high guess too low.')
guess = (low + high) / 2.
pwr_guess = pwr(guess, mp, altitude, temp)
# keep iterating until power is within 0.1% of desired value
while np.fabs(pwr_guess - pwr_seek) / pwr_seek > 1e-4:
if pwr_guess > pwr_seek:
high = guess
else:
low = guess
guess = (low + high) / 2.
pwr_guess = pwr(guess, mp, altitude, temp)
return int(round(guess, 0))
def test_02(self):
# check deg K at 10 km
T = round(SA.alt2temp(10, alt_units='km', temp_units='K'), 2)
self.assertEqual(T, 223.15)
def test_01(self):
# check at -1000 ft
T = round(SA.alt2temp(-1000), 2)
self.assertEqual(T, 16.98)
def prop_data(prop,
bhp,
rpm,
tas,
altitude,
temp='std',
power_units='hp',
alt_units='ft',
temp_units='C',
speed_units='kt',
dia_units='in',
thrust_units='lb'):
"""
Returns advance ratio, power coefficient, thrust coefficient, blade tip
mach number, propeller efficiency and thrust.
Validated against Excel spreadsheet provided by Les Doud (Hartzell).
"""
press_ratio = SA.alt2press_ratio(altitude, alt_units=alt_units)
if temp == 'std':
temp = SA.alt2temp(altitude,
temp_units=temp_units,
alt_units=alt_units)
temp_ratio = U.temp_conv(temp, from_units=temp_units,
to_units='K') / 288.15
density_ratio = press_ratio / temp_ratio
density = density_ratio * SA.Rho0
Cp = bhp2Cp(bhp,
rpm,
density,
prop.dia,
power_units=power_units,
density_units='kg/m**3',
dia_units=dia_units)
J = advance_ratio(tas,
rpm,
prop.dia,
speed_units=speed_units,
dia_units=dia_units)
blade_tip_mach = tip_mach(tas,
rpm,
temp,
prop.dia,
speed_units=speed_units,
temp_units=temp_units,
dia_units=dia_units)
prop_eff = cp2eff(prop, Cp, J, blade_tip_mach)
try:
Ct = cp2ct(prop, Cp, J, blade_tip_mach)
except BaseException:
Ct = cp2ct_alt(prop,
Cp,
bhp,
rpm,
tas,
altitude,
temp=temp,
power_units=power_units,
alt_units=alt_units,
temp_units=temp_units,
speed_units=speed_units)
if prop_eff > 0.1:
thrust = eff2thrust(prop_eff,
bhp,
tas,
power_units=power_units,
speed_units=speed_units,
thrust_units=thrust_units)
else:
thrust = ct2thrust(Ct,
density,
rpm,
prop.dia,
thrust_units=thrust_units,
density_units='kg/m**3',
dia_units=dia_units)
# data_block = 'J = ' + str(J) + '\nCp = ' + str(Cp) + '\n Tip mach = ' + str(blade_tip_mach) + '\n Ct = ' + str(Ct) + '\n Thrust = ' + str(thrust) + ' ' + thrust_units + '\n Prop efficiency = ' + str(prop_eff)
print(' prop = ', prop.prop)
print(' J = %.3f' % J)
print(' Cp = %.5f' % Cp)
print(' Tip Mach = %.3f' % blade_tip_mach)
print(' Ct = %.3f' % Ct)
print(' Thrust = %.2f' % thrust, thrust_units)
print('Prop efficiency = %.4f' % prop_eff)
print(' Thrust HP = %.2f' % bhp * prop_eff)
return
piece.append('2100'.center(cols))
piece.append('2200'.center(cols))
piece.append('2300'.center(cols))
piece.append('2400'.center(cols))
piece.append('2200'.center(cols))
piece.append('2300'.center(cols))
piece.append('2400'.center(cols))
piece.append('2500'.center(cols))
full_line = '|'.join(piece)
print('|' + full_line + '|')
for alt in range(0, 16000, 1000):
piece = []
piece.append(str(alt).rjust(col1))
temp = SA.alt2temp(alt, temp_units='F')
temp = int(temp)
piece.append(str(temp).rjust(col2))
press = SA.alt2press(alt)
pwr = .55 * max_pwr
for rpm in range(2100, 2500, 100):
mp = float(io360a.pwr2mp(pwr, rpm, alt))
if press - mp < diff:
piece.append('FT'.center(col2))
else:
piece.append(str(round(mp, 1)).center(col2))
pwr = .65 * max_pwr
for rpm in range(2100, 2500, 100):
mp = float(io360a.pwr2mp(pwr, rpm, alt))
