def test_03(self):
# Truth values from NASA RP 1046
Value = SA.alt2press_ratio(20000, alt_units='m')
Truth = 5474.87 / 101325
self.assertTrue(RE(Value, Truth) <= 1e-5)
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 test_02(self):
# Truth values from NASA RP 1046
Value = SA.alt2press_ratio(-1000)
Truth = 2193.82 / 2116.22
self.assertTrue(RE(Value, Truth) <= 1e-5)
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 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 test_03(self):
# Truth values from NASA RP 1046
Value = SA.alt2press_ratio(20000, alt_units='m')
Truth = 5474.87 / 101325
self.failUnless(RE(Value, Truth) <= 1e-5)
def test_02(self):
# Truth values from NASA RP 1046
Value = SA.alt2press_ratio(-1000)
Truth = 2193.82 / 2116.22
self.failUnless(RE(Value, Truth) <= 1e-5)
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 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 test_01(self):
PR = SA.alt2press_ratio(0)
self.assertEqual(PR, 1)
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:
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
def tas2ssec2(tas,
ind_alt,
oat,
ias,
std_alt=0,
speed_units=default_speed_units,
alt_units=default_alt_units,
temp_units=default_temp_units,
press_units=default_press_units):
"""
Return static source position error as speed error, pressure error and
altitude error at sea level using speed course method.
Returns delta_Vpc, delta_Ps and delta_Hpc
tas = true airspeed determined by speed course method, or GPS
ind_alt = pressure altitude, corrected for instrument error
oat = outside air temperature, corrected for instrument error and ram temperature rise
ias = indicated airspeed, corrected for instrument error
std_alt = altitude to provide delta_Hpc for
delta_Vpc = error in airspeed = calibrated airspeed - indicated airspeed
corrected for instrument error
delta_Ps = error in the pressure sensed by the static system = pressure
sensed in the static system - ambient pressure
delta_Hpc = altitude error at std_alt = actual altitude - altitude
sensed by the static system
Uses analysis method from USAF Test Pilot School. Unlike some other
methods (e.g.. that in FAA AC 23-8B, or NTPS GPS_PEC.xls), this method
provides an exact conversion from TAS to CAS (some other methods assume
CAS = EAS), and it accounts for the effect of position error of altitude
on the conversion from TAS to CAS (some other methods assume pressure
altitude = indicated pressure altitude).
"""
tas = U.speed_conv(tas, speed_units, 'kt')
ind_alt = U.length_conv(ind_alt, alt_units, 'ft')
oat = U.temp_conv(oat, temp_units, 'C')
M = A.tas2mach(tas, oat, temp_units='C', speed_units='kt')
if M > 1:
raise ValueError('This method only works for Mach < 1')
delta_ic = SA.alt2press_ratio(ind_alt, alt_units='ft')
qcic_over_Psl = A.cas2dp(ias, speed_units='kt',
press_units=press_units) / U.press_conv(
constants.P0, 'pa', to_units=press_units)
qcic_over_Ps = qcic_over_Psl / delta_ic
Mic = A.dp_over_p2mach(qcic_over_Ps)
delta_mach_pc = M - Mic
if Mic > 1:
raise ValueError('This method only works for Mach < 1')
deltaPp_over_Ps = (1.4 * delta_mach_pc * (Mic + delta_mach_pc / 2)) / (
1 + 0.2 * (Mic + delta_mach_pc / 2)**2)
deltaPp_over_qcic = deltaPp_over_Ps / qcic_over_Ps
delta_Hpc = SA.alt2temp_ratio(
std_alt, alt_units='ft') * deltaPp_over_Ps / 3.61382e-5
# experimental - alternate way to calculate delta_Hpc that gives same answer
Ps = SA.alt2press(ind_alt, alt_units='ft', press_units=press_units)
delta_Ps = deltaPp_over_Ps * Ps
P_std = SA.alt2press(std_alt, alt_units='ft', press_units=press_units)
deltaPs_std = deltaPp_over_Ps * P_std
delta_Hpc2 = SA.press2alt(P_std - deltaPs_std,
press_units=press_units) - std_alt
delta_std_alt = SA.alt2press_ratio(std_alt, alt_units='ft')
asl = U.speed_conv(constants.A0, 'm/s', 'kt')
delta_Vpc_std_alt = deltaPp_over_Ps * delta_std_alt * asl**2 / (
1.4 * ias * (1 + 0.2 * (ias / asl)**2)**2.5)
actual_alt = SA.press2alt(Ps + delta_Ps,
press_units=press_units,
alt_units='ft')
cas = A.tas2cas(tas,
actual_alt,
oat,
speed_units='kt',
alt_units='ft',
temp_units='C')
return delta_Vpc, delta_Ps, delta_Hpc, cas
def test_01(self):
PR = SA.alt2press_ratio(0)
self.assertEqual(PR, 1)
def tas2ssec2(tas, ind_alt, oat, ias, std_alt = 0, speed_units=default_speed_units, alt_units=default_alt_units, temp_units=default_temp_units, press_units = default_press_units):
"""
Return static source position error as speed error, pressure error and
altitude error at sea level using speed course method.
Returns delta_Vpc, delta_Ps and delta_Hpc
tas = true airspeed determined by speed course method, or GPS
ind_alt = pressure altitude, corrected for instrument error
oat = outside air temperature, corrected for instrument error and ram temperature rise
ias = indicated airspeed, corrected for instrument error
std_alt = altitude to provide delta_Hpc for
delta_Vpc = error in airspeed = calibrated airspeed - indicated airspeed
corrected for instrument error
delta_Ps = error in the pressure sensed by the static system = pressure
sensed in the static system - ambient pressure
delta_Hpc = altitude error at std_alt = actual altitude - altitude
sensed by the static system
Uses analysis method from USAF Test Pilot School. Unlike some other
methods (e.g.. that in FAA AC 23-8B, or NTPS GPS_PEC.xls), this method
provides an exact conversion from TAS to CAS (some other methods assume
CAS = EAS), and it accounts for the effect of position error of altitude
on the conversion from TAS to CAS (some other methods assume pressure
altitude = indicated pressure altitude).
"""
tas = U.speed_conv(tas, speed_units, 'kt')
ind_alt = U.length_conv(ind_alt, alt_units, 'ft')
oat = U.temp_conv(oat, temp_units, 'C')
M = A.tas2mach(tas, oat, temp_units='C', speed_units='kt')
if M > 1:
raise ValueError, 'This method only works for Mach < 1'
delta_ic = SA.alt2press_ratio(ind_alt, alt_units='ft')
qcic_over_Psl = A.cas2dp(ias, speed_units='kt', press_units=press_units) / U.press_conv(constants.P0, 'pa', to_units=press_units)
qcic_over_Ps = qcic_over_Psl / delta_ic
Mic = A.dp_over_p2mach(qcic_over_Ps)
delta_mach_pc = M - Mic
if Mic > 1:
raise ValueError, 'This method only works for Mach < 1'
deltaPp_over_Ps = (1.4 * delta_mach_pc * (Mic + delta_mach_pc / 2)) / (1 + 0.2 * (Mic + delta_mach_pc / 2 )**2)
deltaPp_over_qcic = deltaPp_over_Ps / qcic_over_Ps
delta_Hpc = SA.alt2temp_ratio(std_alt, alt_units='ft') * deltaPp_over_Ps / 3.61382e-5
# experimental - alternate way to calculate delta_Hpc that gives same answer
Ps = SA.alt2press(ind_alt, alt_units='ft', press_units=press_units)
delta_Ps = deltaPp_over_Ps * Ps
P_std = SA.alt2press(std_alt, alt_units='ft', press_units=press_units)
deltaPs_std = deltaPp_over_Ps * P_std
delta_Hpc2 = SA.press2alt(P_std - deltaPs_std, press_units = press_units) - std_alt
delta_std_alt = SA.alt2press_ratio(std_alt, alt_units='ft')
asl = U.speed_conv(constants.A0, 'm/s', 'kt')
delta_Vpc_std_alt = deltaPp_over_Ps * delta_std_alt * asl**2 / (1.4 * ias * (1 + 0.2 * (ias / asl)**2)**2.5)
actual_alt = SA.press2alt(Ps + delta_Ps, press_units = press_units, alt_units = 'ft')
cas = A.tas2cas(tas, actual_alt, oat, speed_units='kt', alt_units='ft', temp_units='C')
return delta_Vpc, delta_Ps, delta_Hpc, cas
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:
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
