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Fuel Flow Calculation
Example calculation of aircraft fuel flow in descent
=== Bada4Aircraft | BADA DUMMY | Mass: 65000 kg ===
FL Alt(ft) Cfg M FF (kg/s)
---------------------------------------
0 0 LD 0.201 0.852485
10 1000 LD 0.212 0.822006
20 2000 AP 0.279 0.378778
30 3000 CR 0.351 0.172248
40 4000 CR 0.357 0.166989
50 5000 CR 0.364 0.162016
60 6000 CR 0.420 0.151997
70 7000 CR 0.428 0.148105
80 8000 CR 0.436 0.144442
90 9000 CR 0.444 0.140994
100 10000 CR 0.541 0.134151
110 11000 CR 0.551 0.131689
120 12000 CR 0.561 0.129358
130 13000 CR 0.571 0.127143
140 14000 CR 0.582 0.125033
150 15000 CR 0.593 0.123014
160 16000 CR 0.604 0.121075
170 17000 CR 0.615 0.119203
180 18000 CR 0.627 0.117385
190 19000 CR 0.639 0.115608
200 20000 CR 0.651 0.113860
210 21000 CR 0.664 0.112127
220 22000 CR 0.677 0.110397
230 23000 CR 0.690 0.108656
240 24000 CR 0.703 0.106892
250 25000 CR 0.717 0.105090
260 26000 CR 0.731 0.103238
270 27000 CR 0.745 0.101320
280 28000 CR 0.760 0.099325
290 29000 CR 0.775 0.097236
300 30000 CR 0.790 0.095065
310 31000 CR 0.790 0.093420
320 32000 CR 0.790 0.091818
330 33000 CR 0.790 0.090260
340 34000 CR 0.790 0.088744
350 35000 CR 0.790 0.087271
360 36000 CR 0.790 0.085839
370 37000 CR 0.790 0.084911
380 38000 CR 0.790 0.084067
390 39000 CR 0.790 0.083261
400 40000 CR 0.790 0.082493
=== Bada3Aircraft | BADA DUMMY | Mass: 58000 kg ===
FL Alt(ft) Cfg M FF (kg/s)
---------------------------------------
0 0 LD 0.222 0.609352
10 1000 LD 0.233 0.611392
20 2000 AP 0.300 0.332968
30 3000 CR 0.351 0.232042
40 4000 CR 0.357 0.227339
50 5000 CR 0.364 0.222637
60 6000 CR 0.420 0.217934
70 7000 CR 0.428 0.213232
80 8000 CR 0.436 0.208529
90 9000 CR 0.444 0.203826
100 10000 CR 0.523 0.199124
110 11000 CR 0.533 0.194421
120 12000 CR 0.543 0.189718
130 13000 CR 0.553 0.185016
140 14000 CR 0.563 0.180313
150 15000 CR 0.574 0.175610
160 16000 CR 0.585 0.170908
170 17000 CR 0.596 0.166205
180 18000 CR 0.607 0.161503
190 19000 CR 0.619 0.156800
200 20000 CR 0.631 0.152097
210 21000 CR 0.643 0.147395
220 22000 CR 0.655 0.142692
230 23000 CR 0.668 0.137989
240 24000 CR 0.681 0.133287
250 25000 CR 0.694 0.128584
260 26000 CR 0.708 0.123882
270 27000 CR 0.722 0.119179
280 28000 CR 0.737 0.114476
290 29000 CR 0.740 0.109774
300 30000 CR 0.740 0.105071
310 31000 CR 0.740 0.100368
320 32000 CR 0.740 0.095666
330 33000 CR 0.740 0.090963
340 34000 CR 0.740 0.086260
350 35000 CR 0.740 0.081558
360 36000 CR 0.740 0.076855
370 37000 CR 0.740 0.072153
380 38000 CR 0.752 0.067450
390 39000 CR 0.783 0.062747
400 40000 CR 0.816 0.058045
from math import sin
import matplotlib.pyplot as plt
import numpy as np
from pyBADA import atmosphere as atm
from pyBADA import constants as const
from pyBADA import conversions as conv
from pyBADA import utils
from pyBADA.bada3 import Bada3Aircraft
from pyBADA.bada4 import Bada4Aircraft
# create an aircraft
ACList = [
Bada4Aircraft(badaVersion="DUMMY", acName="Dummy-TWIN"),
Bada3Aircraft(badaVersion="DUMMY", acName="J2M"),
]
# deviation from ISA temperature
deltaTemp = 0
# definition of altitude range
fl_array = np.arange(0, 401, 10)
altitude_array = conv.ft2m(fl_array * 100)
# --- collect per-aircraft series here ---
series = [] # list of dicts: {"label": str, "alt_ft": list[float], "ff": list[float]}
for AC in ACList:
# define aircraft mass - here as reference mass
mass = AC.MREF
# get the original speed schedule for descent for this aircraft
[Vdes1, Vdes2, Mdes] = AC.flightEnvelope.getSpeedSchedule(phase="Descent")
# crossover altitude
crossAlt = atm.crossOver(cas=Vdes2, Mach=Mdes)
label = f"({AC.BADAFamilyName}) {AC.acName.strip('_')} (BADA {getattr(AC, 'BADAVersion')}) {mass} kg"
alt_ft_vals = []
ff_vals = []
print(
f"\n=== {AC.__class__.__name__} | BADA {AC.BADAVersion} | Mass: {mass:.0f} kg ==="
)
print(
f"{'FL':>4} {'Alt(ft)':>8} {'Cfg':>3} {'M':>6} {'FF (kg/s)':>10}"
)
print("-" * 39)
for alt in altitude_array:
# atmosphere properties
theta, delta, sigma = atm.atmosphereProperties(
h=alt, deltaTemp=deltaTemp
)
# determine the speed acording to BADA ARPM
[cas, speedUpdated] = AC.ARPM.descentSpeed(
h=alt, mass=mass, theta=theta, delta=delta, deltaTemp=deltaTemp
)
# general speed conversion
[M, CAS, TAS] = atm.convertSpeed(
v=conv.ms2kt(cas),
speedType="CAS",
theta=theta,
delta=delta,
sigma=sigma,
)
# determine the aerodynamic configuration if necesary
config = AC.flightEnvelope.getConfig(
h=alt, phase="Descent", v=CAS, mass=mass, deltaTemp=deltaTemp
)
# calculate Energy Share Factor depending if aircraft is flying constant M or CAS (based on crossover altitude)
if alt < crossAlt:
ESF = AC.esf(
h=alt, flightEvolution="constCAS", M=M, deltaTemp=deltaTemp
)
else:
ESF = AC.esf(
h=alt, flightEvolution="constM", M=M, deltaTemp=deltaTemp
)
# =====
# BADA4
# =====
if AC.BADAFamily.BADA4:
# =================================================================================
# for altitudes where aircraft descends on 3degree slope in AP and LD configuration
# =================================================================================
if config == "AP" or config == "LD":
gamma = -3.0
temp_const = (theta * const.temp_0) / (
theta * const.temp_0 - deltaTemp
)
ROCD_gamma = sin(conv.deg2rad(gamma)) * TAS * (1 / temp_const)
n = 1.0
[HLid, LG] = AC.flightEnvelope.getAeroConfig(config=config)
CL = AC.CL(M=M, delta=delta, mass=mass, nz=n)
CD = AC.CD(M=M, CL=CL, HLid=HLid, LG=LG)
Drag = AC.D(M=M, delta=delta, CD=CD)
Thrust = (ROCD_gamma * mass * const.g) * temp_const / (
ESF * TAS
) + Drag
CT = AC.CT(Thrust=Thrust, delta=delta)
ff = AC.ff(
CT=CT, delta=delta, theta=theta, M=M, deltaTemp=deltaTemp
)
# =============================================================
# for altitudes where aircraft descends in IDLE engine settings
# =============================================================
else:
ff = AC.ff(
rating="LIDL",
delta=delta,
theta=theta,
M=M,
deltaTemp=deltaTemp,
) # [kg/s]
# =====
# BADA3
# =====
elif AC.BADAFamily.BADA3:
adaptedThrust = False
if AC.engineType in ("PISTON", "ELECTRIC"):
# PISTON and ELECTRIC uses LIDL throughout the whole descent phase
config = "CR"
adaptedThrust = True
# =================================================================================
# for altitudes where aircraft descends on 3degree slope in AP and LD configuration
# =================================================================================
if config in ("AP", "LD"):
gamma = -3.0
temp_const = (theta * const.temp_0) / (
theta * const.temp_0 - deltaTemp
)
ROCD_gamma = sin(conv.deg2rad(gamma)) * TAS * (1 / temp_const)
n = 1.0
CL = AC.CL(sigma=sigma, mass=mass, tas=TAS, nz=n)
CD = AC.CD(CL=CL, config=config)
Drag = AC.D(sigma=sigma, tas=TAS, CD=CD)
Thrust = AC.Thrust(
rating="ADAPTED",
v=TAS,
config=config,
h=alt,
ROCD=ROCD_gamma,
mass=mass,
acc=0,
deltaTemp=deltaTemp,
Drag=Drag,
)
ff = AC.ff(
flightPhase="Descent",
v=TAS,
h=alt,
T=Thrust,
config=config,
adapted=adaptedThrust,
)
# =============================================================
# for altitudes where aircraft descends in IDLE engine settings
# =============================================================
else:
ff = AC.ff(
v=TAS,
h=alt,
T=Thrust,
flightPhase="Descent",
config=config,
)
fl = int(utils.proper_round(conv.m2ft(alt) / 100))
alt_ft = conv.m2ft(alt)
print(f"{fl:>4d} {alt_ft:>8.0f} {config:>3} {M:>6.3f} {ff:>10.6f}")
alt_ft_vals.append(alt_ft)
ff_vals.append(float(ff))
series.append(
{
"label": label,
"alt_ft": np.array(alt_ft_vals),
"ff": np.array(ff_vals),
}
)
# --- PLOT: Fuel flow vs Altitude for all aircraft ---
plt.figure(figsize=(8, 5))
for s in series:
plt.plot(s["alt_ft"], s["ff"], label=s["label"])
plt.xlabel("Altitude (ft)")
plt.ylabel("Fuel Flow (kg/s)")
plt.title("Descent Fuel Flow vs Altitude")
plt.grid(True, which="both", linestyle="--", linewidth=0.5)
plt.legend()
plt.tight_layout()
plt.show()
Total running time of the script: (0 minutes 0.283 seconds)