def run_tests(cd0 = 0.0221, e = 0.825):
"""
Run all test cases to compare drag polar model against CAFE results.
"""
sum_sq = 0
wt_value_tot = 0
wing_area = 110
prop = PM.Prop('7666-4RV')
for n, test in enumerate(level_test_cases):
tas = test[0]
dalt = test[1]
wt = test[2]
rpm = test[3]
mp = test[4]
wt_value = test[5]
eas = A.tas2eas(tas, dalt, speed_units = 'mph')
tas_fts = U.speed_conv(tas, from_units = 'mph', to_units = 'ft/s')
cl = FT.eas2cl(eas, wt, wing_area, speed_units = 'mph')
cd = FT.cl2cd_test(cl, cd0, e, flap = 0)
drag = FT.cd2drag(cd, eas, wing_area, speed_units = 'mph')
drag_power = drag * tas_fts / 550.
power = IO.pwr(rpm, mp, dalt)
prop_eff = PM.prop_eff(prop, power, rpm, tas, dalt, speed_units = 'mph')
thrust_power = power * prop_eff
excess_power = thrust_power - drag_power
print 'Case', n, 'Altitude =', dalt, 'TAS =', tas, 'EAS =', eas, 'Excess power =', excess_power
sum_sq += wt_value * excess_power ** 2
wt_value_tot += wt_value
print 'Average sum of squares of excess power =', \
(sum_sq / wt_value_tot) ** 0.5
def cafe_speed():
"""
Check the calculated speeds against the data from the CAFE tests for the RV-8A
"""
prop = PM.Prop('7666-4RV')
for n, test in enumerate(level_test_cases):
tas = test[0]
dalt = test[1]
wt = test[2]
rpm = test[3]
mp = test[4]
wt_value = test[5]
eas = A.tas2eas(tas, dalt, speed_units = 'mph')
calc_tas = speed(prop, dalt, wt, IO.pwr(rpm, mp, dalt), rpm, \
speed_units = 'mph')
print 'Actual TAS =', tas, 'Calc TAS =', calc_tas
def cafe_speed():
"""
Check the calculated speeds against the data from the CAFE tests for the RV-8A
"""
prop = PM.Prop('7666-4RV')
for n, test in enumerate(level_test_cases):
tas = test[0]
dalt = test[1]
wt = test[2]
rpm = test[3]
mp = test[4]
wt_value = test[5]
eas = A.tas2eas(tas, dalt, speed_units='mph')
calc_tas = speed(prop, dalt, wt, IO.pwr(rpm, mp, dalt), rpm, \
speed_units = 'mph')
print('Actual TAS =', tas, 'Calc TAS =', calc_tas)
def p(tas, dalt, wt, rpm, mp, prop):
"""
test function for RV-8A drag, to compare against CAFE foundation level
flt data.
prop is a prop_map.Prop instance.
"""
eas = A.tas2eas(tas, dalt, speed_units='mph')
# tas = A.cas2tas(cas, dalt, speed_units = 'mph')
tas_fts = U.speed_conv(tas, from_units='mph', to_units='ft/s')
drag = FT.eas2drag(eas, wt, 110, rv='8a', speed_units='mph')
drag_power = drag * tas_fts / 550.
power = IO.pwr(rpm, mp, dalt)
prop_eff = PM.prop_eff(prop, power, rpm, tas, dalt, speed_units='mph')
thrust_power = power * prop_eff
excess_power = thrust_power - drag_power
return excess_power
def p(tas, dalt, wt, rpm, mp, prop):
"""
test function for RV-8A drag, to compare against CAFE foundation level
flt data.
prop is a prop_map.Prop instance.
"""
eas = A.tas2eas(tas, dalt, speed_units = 'mph')
# tas = A.cas2tas(cas, dalt, speed_units = 'mph')
tas_fts = U.speed_conv(tas, from_units = 'mph', to_units = 'ft/s')
drag = FT.eas2drag(eas, wt, 110, rv = '8a', speed_units = 'mph')
drag_power = drag * tas_fts / 550.
power = IO.pwr(rpm, mp, dalt)
prop_eff = PM.prop_eff(prop, power, rpm, tas, dalt, speed_units = 'mph')
thrust_power = power * prop_eff
excess_power = thrust_power - drag_power
return excess_power
def tas2cl(
tas,
altitude,
weight,
wing_area,
temperature='std',
load_factor=1,
speed_units=default_speed_units,
alt_units=default_alt_units,
temp_units=default_temp_units,
weight_units=default_weight_units,
area_units=default_area_units,
):
"""
Returns the coefficient of lift, given true airspeed, altitude, weight,
and wing area.
Temperature and load factor are optional inputs. The temperature, if
not provided, defaults to the standard temperature for the altitude.
The load factor, if not provided, defaults to 1.
"""
eas = A.tas2eas(
tas,
altitude,
temperature,
speed_units,
alt_units,
temp_units,
)
Cl = eas2cl(
eas,
weight,
wing_area,
load_factor,
speed_units,
weight_units,
area_units,
)
return Cl
def tas2cl(
tas,
altitude,
weight,
wing_area,
temperature='std',
load_factor=1,
speed_units=default_speed_units,
alt_units=default_alt_units,
temp_units=default_temp_units,
weight_units=default_weight_units,
area_units=default_area_units,
):
"""
Returns the coefficient of lift, given true airspeed, altitude, weight,
and wing area.
Temperature and load factor are optional inputs. The temperature, if
not provided, defaults to the standard temperature for the altitude.
The load factor, if not provided, defaults to 1.
"""
eas = A.tas2eas(
tas,
altitude,
temperature,
speed_units,
alt_units,
temp_units,
)
Cl = eas2cl(
eas,
weight,
wing_area,
load_factor,
speed_units,
weight_units,
area_units,
)
return Cl
def alt2FP_speed(engine, prop, blade_angle, alt, weight = 1800, temp = 'std', \
temp_units = 'C', rv = '8', wing_area = 110, alt_units='ft', speed_units = 'kt' , \
MP_loss = 1.322, ram = 0.5, pwr_factor=1, mixture='pwr', MP='WOT', wheel_pants=1):
"""
Returns the predicted speed at full throttle for aircraft with fixed pitch prop.
The MP_loss is the MP lost in the induction tract at full throttle at 2700
rpm at MSL. The default value is from the Lycoming power charts.
The ram is the percentage of available ram recovery pressure that is
achieved in the MP.
"""
tas_low = 80
tas_high = 250
pwr_tolerance = .1
while 1:
tas_guess = (tas_low + tas_high) / 2.
tas_guess_fts = U.speed_conv(tas_guess, from_units = speed_units, to_units = 'ft/s')
rpm = tas2rpm(tas_guess, engine, prop, blade_angle, alt, temp=temp, alt_units=alt_units, temp_units=temp_units, speed_units=speed_units, MP=MP)
if MP == 'WOT':
MP = MP_pred(tas_guess, alt, rpm, rpm_base = 2700., MP_loss = MP_loss, ram = ram, temp=temp)
bhp = engine.pwr(rpm, MP, alt, temp=temp, alt_units=alt_units, temp_units=temp_units)
prop_eff = PM.prop_eff(prop, bhp, rpm, tas_guess, alt, temp = temp, temp_units = temp_units, speed_units = speed_units)
power_avail = bhp * prop_eff
eas_guess = A.tas2eas(tas_guess, alt, temp)
drag = FT.eas2drag(eas_guess, weight, wing_area, rv = rv, flap = 0, speed_units = speed_units, wheel_pants = wheel_pants)
power_req = tas_guess_fts * drag / 550.
if M.fabs(power_avail - power_req) < pwr_tolerance:
# print "MP = %.3f" % MP
# print "Pwr = %.2f"% bhp
# print "Prop Efficiency = %.3f, and power available = %.1f thp" % (prop_eff, power_avail)
return tas_guess, rpm, bhp
if power_req > power_avail:
tas_high = tas_guess
else:
tas_low = tas_guess
def run_tests(cd0=0.0221, e=0.825):
"""
Run all test cases to compare drag polar model against CAFE results.
"""
sum_sq = 0
wt_value_tot = 0
wing_area = 110
prop = PM.Prop('7666-4RV')
for n, test in enumerate(level_test_cases):
tas = test[0]
dalt = test[1]
wt = test[2]
rpm = test[3]
mp = test[4]
wt_value = test[5]
eas = A.tas2eas(tas, dalt, speed_units='mph')
tas_fts = U.speed_conv(tas, from_units='mph', to_units='ft/s')
cl = FT.eas2cl(eas, wt, wing_area, speed_units='mph')
cd = FT.cl2cd_test(cl, cd0, e, flap=0)
drag = FT.cd2drag(cd, eas, wing_area, speed_units='mph')
drag_power = drag * tas_fts / 550.
power = IO.pwr(rpm, mp, dalt)
prop_eff = PM.prop_eff(prop, power, rpm, tas, dalt, speed_units='mph')
thrust_power = power * prop_eff
excess_power = thrust_power - drag_power
print('Case', n, 'Altitude =', dalt, 'TAS =', tas, 'EAS =', eas,
'Excess power =', excess_power)
sum_sq += wt_value * excess_power**2
wt_value_tot += wt_value
print('Average sum of squares of excess power =', \
(sum_sq / wt_value_tot) ** 0.5)
def descent_data(prop, weight=1600., alt_max=20000., fuel_units='USG', \
alt_interval=500., isa_dev=0, temp_units='C', rv='8', wing_area=110., \
tas=180., ROD=-500., angle='', speed_units='kt', rpm=2100., sfc=0.45, output='raw'):
"""
Returns a table of descent performance vs altitude.
The items in each row of the table are altitude, time, fuel burned and distance.
Time is in units of minutes, rounded to the nearest half minute.
Fuel units are selectable, with a default of USG.
Distances are in nm.
The output may be specified as raw, latex (a LaTeX table for the POH), or array.
tas is the TAS in descent (overridden by the angle, if the angle is provided).
angle is the flight path angle in degrees.
"""
tas_fts = U.speed_conv(tas, speed_units, 'ft/s')
if angle:
ROD = tas_fts * 60 * M.sin(angle * M.pi / 180)
rod_fts = ROD / 60
tas = U.speed_conv(tas, speed_units, 'kt')
alt = alt_max + alt_interval
temp = SA.isa2temp(isa_dev, alt, temp_units=temp_units)
time = 0
fuel_used = 0
dist = 0
if output == 'raw':
print S.center('Altitude', 10),
print S.center('ROD', 10),
print S.center('Time', 10),
print S.center('Fuel Used', 10),
print S.center('Dist', 10),
print S.center('Speed', 10)
print S.center('(ft)', 10),
print S.center('(ft/mn)', 10),
print S.center('(mn)', 10),
f_units = '(' + fuel_units + ')'
print S.center(f_units, 10),
print S.center('(nm)', 10),
print S.center('(KCAS)', 10)
# # data for max altitude
# print S.rjust(locale.format('%.0f', alt_max, True), 7),
# print S.rjust(locale.format('%.0f', round(ROD / 10.) * 10, True), 10),
# print S.rjust('%.1f' % (0), 10),
# print S.rjust('%.1f' % (fuel_used), 10),
# print S.rjust('%.1f' % (dist), 10),
# print S.rjust('%3d' % (A.tas2cas(tas, alt_max, temp, temp_units=temp_units)), 10)
# elif output == 'latex':
# # temp = 15 + isa_dev
# MSL_line = []
# MSL_line.append(str(locale.format('%.0f', weight, True)))
# MSL_line.append('0')
# MSL_line.append(str(locale.format('%.0f', temp)))
# MSL_line.append(str(locale.format('%.0f', A.tas2cas(tas, alt, temp, temp_units=temp_units))))
# MSL_line.append(str(locale.format('%.0f', round(ROD / 10.) * 10, True)))
# MSL_line.append('0')
# MSL_line.append(str(fuel_used))
# MSL_line.append(str(dist))
#
# print '&'.join(MSL_line) + '\\\\'
# print '\\hline'
# elif output == 'array':
# # no header rows, but make blank array
# array = [[alt_max,0,0,0]]
alts = []
RODs = []
times_temp = []
CASs = []
dists_temp = []
fuel_useds_temp = []
temps = []
calc_alt = alt_max - alt_interval / 2.
while alt > 0:
temp = SA.isa2temp(isa_dev, alt, temp_units = temp_units)
eas = A.tas2eas(tas, alt)
drag = FT.eas2drag(eas, weight)
pwr_level_flt = tas_fts * drag / 550
thrust_power = pwr_level_flt + FT.Pexcess_vs_roc(weight, ROD)
prop_eff = PM.prop_eff(prop, thrust_power, rpm, tas, alt, temp, temp_units=temp_units)
calc_pwr = thrust_power / prop_eff
#fuel_flow = IO.pwr2ff(calc_pwr, rpm, ff_units = 'lb/hr')
fuel_flow = calc_pwr * sfc
# print "Level flt pwr = %.1f, thrust power = %.1f, prop eff = %.3f, fuel flow = %.3f" % (pwr_level_flt, thrust_power, prop_eff, fuel_flow)
slice_time = alt_interval / rod_fts * -1.
slice_dist = tas_fts * slice_time
slice_fuel = fuel_flow * slice_time / 3600
fuel_used += slice_fuel
fuel_out = (U.avgas_conv(fuel_used, from_units = 'lb', \
to_units = fuel_units))
weight -= slice_fuel
alt -= alt_interval
cas_out = A.tas2cas(tas, alt, temp, temp_units=temp_units)
temp_out = SA.isa2temp(isa_dev, alt)
time += slice_time / 60.
dist += slice_dist / 6076.115
alts.append(alt)
CASs.append(cas_out)
RODs.append(ROD)
times_temp.append(time)
fuel_useds_temp.append(fuel_out)
dists_temp.append(dist)
temps.append(temp_out)
calc_alt += alt_interval
alts.reverse()
CASs.reverse()
RODs.reverse()
temps.reverse()
times = []
fuel_useds = []
dists = []
for n, time in enumerate(times_temp):
times.append(times_temp[-1] - time)
fuel_useds.append(fuel_useds_temp[-1] - fuel_useds_temp[n])
dists.append(dists_temp[-1] - dists_temp[n])
times.reverse()
fuel_useds.reverse()
dists.reverse()
if output == 'raw':
for n, alt in enumerate(alts):
print S.rjust(locale.format('%.0f', alt, True), 7),
# calculate ROC at the displayed altitude
print S.rjust(locale.format('%.0f', RODs[n], True), 10),
print S.rjust('%.1f' % (times[n]), 10),
print S.rjust('%.1f' % (fuel_useds[n]), 10),
print S.rjust('%.1f' % (dists[n]), 10),
print S.rjust('%3d' % (int(CASs[n])), 10)
elif output == 'latex':
for n, alt in enumerate(alts):
line = []
line.append(str(locale.format('%.0f', alt, True)))
line.append(str(locale.format('%.0f', round(temps[n]))))
line.append(str(locale.format('%.0f', CASs[n])))
line.append(str(locale.format('%.0f', round(RODs[n] / 10.) * 10, True)))
line.append(str(locale.format('%.0f', times[n])))
line.append(str(locale.format('%.1f', fuel_useds[n])))
line.append(str(locale.format('%.0f', dists[n])))
print '&' + '&'.join(line) + '\\\\'
print '\\hline'
elif output == 'array':
array = []
for n, alt in enumerate(alts):
array.append([alt, times[n], fuel_useds[n], dists[n]])
return array
def descent_data(prop, weight=1600., alt_max=20000., fuel_units='USG', \
alt_interval=500., isa_dev=0, temp_units='C', rv='8', wing_area=110., \
tas=180., ROD=-500., angle='', speed_units='kt', rpm=2100., sfc=0.45, output='raw'):
"""
Returns a table of descent performance vs altitude.
The items in each row of the table are altitude, time, fuel burned and distance.
Time is in units of minutes, rounded to the nearest half minute.
Fuel units are selectable, with a default of USG.
Distances are in nm.
The output may be specified as raw, latex (a LaTeX table for the POH), or array.
tas is the TAS in descent (overridden by the angle, if the angle is provided).
angle is the flight path angle in degrees.
"""
tas_fts = U.speed_conv(tas, speed_units, 'ft/s')
if angle:
ROD = tas_fts * 60 * M.sin(angle * M.pi / 180)
rod_fts = ROD / 60
tas = U.speed_conv(tas, speed_units, 'kt')
alt = alt_max + alt_interval
temp = SA.isa2temp(isa_dev, alt, temp_units=temp_units)
time = 0
fuel_used = 0
dist = 0
if output == 'raw':
print(S.center('Altitude', 10), end=' ')
print(S.center('ROD', 10), end=' ')
print(S.center('Time', 10), end=' ')
print(S.center('Fuel Used', 10), end=' ')
print(S.center('Dist', 10), end=' ')
print(S.center('Speed', 10))
print(S.center('(ft)', 10), end=' ')
print(S.center('(ft/mn)', 10), end=' ')
print(S.center('(mn)', 10), end=' ')
f_units = '(' + fuel_units + ')'
print(S.center(f_units, 10), end=' ')
print(S.center('(nm)', 10), end=' ')
print(S.center('(KCAS)', 10))
# # data for max altitude
# print S.rjust(locale.format('%.0f', alt_max, True), 7),
# print S.rjust(locale.format('%.0f', round(ROD / 10.) * 10, True), 10),
# print S.rjust('%.1f' % (0), 10),
# print S.rjust('%.1f' % (fuel_used), 10),
# print S.rjust('%.1f' % (dist), 10),
# print S.rjust('%3d' % (A.tas2cas(tas, alt_max, temp, temp_units=temp_units)), 10)
# elif output == 'latex':
# # temp = 15 + isa_dev
# MSL_line = []
# MSL_line.append(str(locale.format('%.0f', weight, True)))
# MSL_line.append('0')
# MSL_line.append(str(locale.format('%.0f', temp)))
# MSL_line.append(str(locale.format('%.0f', A.tas2cas(tas, alt, temp, temp_units=temp_units))))
# MSL_line.append(str(locale.format('%.0f', round(ROD / 10.) * 10, True)))
# MSL_line.append('0')
# MSL_line.append(str(fuel_used))
# MSL_line.append(str(dist))
#
# print '&'.join(MSL_line) + '\\\\'
# print '\\hline'
# elif output == 'array':
# # no header rows, but make blank array
# array = [[alt_max,0,0,0]]
alts = []
RODs = []
times_temp = []
CASs = []
dists_temp = []
fuel_useds_temp = []
temps = []
calc_alt = alt_max - alt_interval / 2.
while alt > 0:
temp = SA.isa2temp(isa_dev, alt, temp_units=temp_units)
eas = A.tas2eas(tas, alt)
drag = FT.eas2drag(eas, weight)
pwr_level_flt = tas_fts * drag / 550
thrust_power = pwr_level_flt + FT.Pexcess_vs_roc(weight, ROD)
prop_eff = PM.prop_eff(prop,
thrust_power,
rpm,
tas,
alt,
temp,
temp_units=temp_units)
calc_pwr = thrust_power / prop_eff
#fuel_flow = IO.pwr2ff(calc_pwr, rpm, ff_units = 'lb/hr')
fuel_flow = calc_pwr * sfc
# print "Level flt pwr = %.1f, thrust power = %.1f, prop eff = %.3f, fuel flow = %.3f" % (pwr_level_flt, thrust_power, prop_eff, fuel_flow)
slice_time = alt_interval / rod_fts * -1.
slice_dist = tas_fts * slice_time
slice_fuel = fuel_flow * slice_time / 3600
fuel_used += slice_fuel
fuel_out = (U.avgas_conv(fuel_used, from_units = 'lb', \
to_units = fuel_units))
weight -= slice_fuel
alt -= alt_interval
cas_out = A.tas2cas(tas, alt, temp, temp_units=temp_units)
temp_out = SA.isa2temp(isa_dev, alt)
time += slice_time / 60.
dist += slice_dist / 6076.115
alts.append(alt)
CASs.append(cas_out)
RODs.append(ROD)
times_temp.append(time)
fuel_useds_temp.append(fuel_out)
dists_temp.append(dist)
temps.append(temp_out)
calc_alt += alt_interval
alts.reverse()
CASs.reverse()
RODs.reverse()
temps.reverse()
times = []
fuel_useds = []
dists = []
for n, time in enumerate(times_temp):
times.append(times_temp[-1] - time)
fuel_useds.append(fuel_useds_temp[-1] - fuel_useds_temp[n])
dists.append(dists_temp[-1] - dists_temp[n])
times.reverse()
fuel_useds.reverse()
dists.reverse()
if output == 'raw':
for n, alt in enumerate(alts):
print(S.rjust(locale.format('%.0f', alt, True), 7), end=' ')
# calculate ROC at the displayed altitude
print(S.rjust(locale.format('%.0f', RODs[n], True), 10), end=' ')
print(S.rjust('%.1f' % (times[n]), 10), end=' ')
print(S.rjust('%.1f' % (fuel_useds[n]), 10), end=' ')
print(S.rjust('%.1f' % (dists[n]), 10), end=' ')
print(S.rjust('%3d' % (int(CASs[n])), 10))
elif output == 'latex':
for n, alt in enumerate(alts):
line = []
line.append(str(locale.format('%.0f', alt, True)))
line.append(str(locale.format('%.0f', round(temps[n]))))
line.append(str(locale.format('%.0f', CASs[n])))
line.append(
str(locale.format('%.0f',
round(RODs[n] / 10.) * 10, True)))
line.append(str(locale.format('%.0f', times[n])))
line.append(str(locale.format('%.1f', fuel_useds[n])))
line.append(str(locale.format('%.0f', dists[n])))
print('&' + '&'.join(line) + '\\\\')
print('\\hline')
elif output == 'array':
array = []
for n, alt in enumerate(alts):
array.append([alt, times[n], fuel_useds[n], dists[n]])
return array
def alt2FP_speed(engine, prop, blade_angle, alt, weight = 1800, temp = 'std', \
temp_units = 'C', rv = '8', wing_area = 110, alt_units='ft', speed_units = 'kt' , \
MP_loss = 1.322, ram = 0.5, pwr_factor=1, mixture='pwr', MP='WOT', wheel_pants=1):
"""
Returns the predicted speed at full throttle for aircraft with fixed pitch prop.
The MP_loss is the MP lost in the induction tract at full throttle at 2700
rpm at MSL. The default value is from the Lycoming power charts.
The ram is the percentage of available ram recovery pressure that is
achieved in the MP.
"""
tas_low = 80
tas_high = 250
pwr_tolerance = .1
while 1:
tas_guess = (tas_low + tas_high) / 2.
tas_guess_fts = U.speed_conv(tas_guess,
from_units=speed_units,
to_units='ft/s')
rpm = tas2rpm(tas_guess,
engine,
prop,
blade_angle,
alt,
temp=temp,
alt_units=alt_units,
temp_units=temp_units,
speed_units=speed_units,
MP=MP)
if MP == 'WOT':
MP = MP_pred(tas_guess,
alt,
rpm,
rpm_base=2700.,
MP_loss=MP_loss,
ram=ram,
temp=temp)
bhp = engine.pwr(rpm,
MP,
alt,
temp=temp,
alt_units=alt_units,
temp_units=temp_units)
prop_eff = PM.prop_eff(prop,
bhp,
rpm,
tas_guess,
alt,
temp=temp,
temp_units=temp_units,
speed_units=speed_units)
power_avail = bhp * prop_eff
eas_guess = A.tas2eas(tas_guess, alt, temp)
drag = FT.eas2drag(eas_guess,
weight,
wing_area,
rv=rv,
flap=0,
speed_units=speed_units,
wheel_pants=wheel_pants)
power_req = tas_guess_fts * drag / 550.
if M.fabs(power_avail - power_req) < pwr_tolerance:
# print "MP = %.3f" % MP
# print "Pwr = %.2f"% bhp
# print "Prop Efficiency = %.3f, and power available = %.1f thp" % (prop_eff, power_avail)
return tas_guess, rpm, bhp
if power_req > power_avail:
tas_high = tas_guess
else:
tas_low = tas_guess