airplane sizing - itlims-zsis.meil.pw.edu.pl
TRANSCRIPT
2010-10-11
1
Airplane sizing
climb w=X1m/s
descend w=-X8km/h
hold t=X9h
cruise V=X4km/h
loiter t=X6h
cruise V=X7km/h
X3 km
H1=
X2
m
H2=
X5
m
H1=
X1
0m
X8 km
takeoff landing
Mission profile
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Commercial airplane
Agricultural airplane
Motorized glider
Dogfight
Mission profile
epfcTO WWWWW
expnexppWWW
WTO – takeoff weight
Wc – crew weight
Wf – fuel weight
Wp – payload weight
We – empty weight
Wexp – expendable payload weight
Wnexp – nonexpendable payload weight
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Airplanes expending their payloads in flight
1) Assume the takeoff weight
2) Calculate weight after takeoff
3) Calculate weight after climb (ATTENTION: weight before this
phase is equal to the weight after previous phase)
4) Calculate weight after cruise (ATTENTION: as above)
5) Calculate weight after task execution (ATTENTION1: as above,
ATTENTION2: airplane can release a parto of its payload)
6) Calculate weight after return cruise (ATTENTION: as above)
7) Calculate weight after holding (ATTENTION: as above)
8) Calculate weight after landing and taxi (ATTENTION: as above)
9) Calculate an empty weight (ATTENTION: subtract weights of
crew, remaining payload, fuel reserve weight and trapped fuel
weight from weight after landing)
10) Calculate realistic empty weight from We/WTO=f(WTO) plot
11) Calculate the difference between weights calculated in points
9) i 10)
12) Modify takeoff weight
Takeoff
Takeoff = engine ignition and warmup + taxi + takeoff run +
+ climbing to prescribed altitude
975,0)W/W(97,0 fTO1
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Climb and acceleration
P
Corke
Wf/W
i
1)
2)
Ad 1 jet airplane
Ad 2 propeller airplane
L – Lift
D – Drag
- propeller acceleration
C – specific fuel consumption in lbfuel/h/lbthrust for jets
lbfuel/h/SHP for propeller
driven airplanes
Cruise - Breguet’s equations
)W/Wln(D
L
C
VR
1nn
)W/Wln(D
L
CR
1nn
(Imperial)
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)W/Wln(C
C
gC
VR
1nn
x
z
Cruise - Breguet’s equations
)W/Wln(C
C
gCR
1nn
x
z
1)
2)
Ad 1 jet airplane
Ad 2 propeller airplane
Cz – Lift coefficient (CL in English)
Cx – Drag coefficient (CD in English)
- propeller acceleration
C – specific fuel consumption in kg/h/kN for jets
kg/h/kW for propeller
driven airplanes
(SI+Polish symbols)
or
E. Cichosz „Charakterystyka i zastosowanie napędów”
Raymer
8,0
Piston
Turboprop
Turbofan
Bypass turbojet
Turbojet
Ramjet
Turbojet with afterburner
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Raymer
maxD
L
D
L
C
C94,0
C
C
Raymer
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Raymer
B-47 Avro Vulcan
Sr reference area 1430 3446
Sw wetted area 11300 9600
Wing span 116 90
Sw/Sr 7,9 2,8
AR 9,4 3,0
AR*Sr/Sw 1,2 1,1
L/D max 17,2 17,0
B-47
Vulcan
Acceleration
P
M
1
1,0
P
1,0
M
1,0
M
P
1,0
1,0
1,0
P
M
P
M
n
1n
W
W
W
W
W
W
W
W
W
W
W
W
W
W
W
W
Corke
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Combat
tTCWWmaxmax1nn
n
maxmax
n
1n
W
tTC1
W
W
T- thrust
t - time
Loiter
e.g. reconnaissance aircraft
)W/Wln(C
C
gC
1t 1nn
D
L
)W/Wln(V
1
C
C
gCt 1nn
D
L
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Return cruise
)W/Wln(C
C
gC
VR 1nn
D
L
)W/Wln(C
C
gCR 1nn
D
L
W is lower so it is advantageous to fly higher. Airplane should
be re-trimmed what increases the drag.
Holding before landing
)W/Wln(C
C
gC
1t 1nn
D
L
)W/Wln(V
1
C
C
gCt 1nn
D
L
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Landing
975,0)W/W(97,0fn1n
Airplanes expending their payloads in flight
1) Assume the takeoff weight
2) Calculate weight after takeoff
3) Calculate weight after climb (ATTENTION: weight before this
phase is equal to the weight after previous phase)
4) Calculate weight after cruise (ATTENTION: as above)
5) Calculate weight after task execution (ATTENTION1: as above,
ATTENTION2: airplane can release a part of its payload)
6) Calculate weight after return cruise (ATTENTION: as above)
7) Calculate weight after holding (ATTENTION: as above)
8) Calculate weight after landing and taxi (ATTENTION: as above)
9) Calculate an empty weight (ATTENTION: subtract weights of
crew, remaining payload, fuel reserve weight and trapped fuel
weight from weight after landing)
10) Calculate realistic empty weight from We/WTO=f(WTO) plot
11) Calculate the difference between weights calculated in points
9) i 10)
12) Modify takeoff weight
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11
emptyfuelpayloadcrewTO WWWWW
TO
TO
eTO
TO
fpaycrTO W
W
WW
W
WWWW
TO
e
TO
f
paycr
TO
W
W
W
W1
WWW
Airplanes not expending their payloads in flight
m
L
1
2
TO
1
m
m
2
2
1
1
TO
LfTOL
W
W...
W
W
W
W
W
W...
W
W
W
W
W
W)W/W(
W1...m – airplane weights after each phase of the flight
)/1(06,1/ TOLTOF WWWW
TOF
L W06,1
WW
1W06,1
W
W
W
TO
F
TO
L
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Wing and power loading
estimation
Takeoff
1
T
W
C
1
S
WTOP
TOmaxLTO
SLTO/
)W/T)(TOP(87)TOP(9,20sTO
ang. - CL= CZ – pol.
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Landing
maxLC
1
S
WLP
400)LP(118sL
Climb
GW
DTsin
dH
dV
g
V1
W/PsinV
dt
dH s
)DT(VPs
for dV/dH=0
Ps – excess power
G - gradient
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Climb
0S
WG
W
T
Aeq
1
S
WqC
2
0D
Climb
Aeq
2
Ae
C4G
W
TG
W
T
S
W
0D
2
Ae
C2G
W
T 0D
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Range – propeller driven airplane
)W/Wln(C
C
gCR 1nn
D
L
Maximum range will be reached for CL
reflecting maximum gliding ratio:
0DCeAqS
W
Range – jet airplane
)W/Wln(C
C
gC
VR 1nn
D
L
Maximum range will be reached when VCL/CD
achieves the maximum
3
AeCq
S
W 0D
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Turn
r
L
sinLr
mV
cosLW
2
nW
L
cos
1
Turn
V
1ng2
1g
V
qC
S
W
2
maxL
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Sustained turn
DT
Sustained turn
CD0
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Sustained turn
Aeq
n2
Ae
Cn4
W
T
W
T
S
W2
0D
22
Ae
Cn2
W
T 0D
Sustained turn
S/W
qC
W
T
S/W
Aeqn 0D
max
max
V
1S/W
qC
W
T
S/W
Aeqg 0D
max
max
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Maximum altitude
1n
2
VCqC
S
W2
maxh
maxLmaxL
1
T
W
C
1
S
WTOP
TOmaxLTO
)W/T)(TOP(87)TOP(9,20sTO
maxLC
1
S
WLP
400)LP(118s
L
Aeq
2
Ae
C4G
W
TG
W
T
S
W0D
2
Ae
C2G
W
T0D
0DAeC
n
q
S
W
0DCeAq
S
W
3
AeCq
S
W0D
1g
V
qC
S
W2
maxL
Aeq
n2
Ae
Cn4
W
T
W
T
S
W2
0D
22
Ae
Cn2
W
T0D
2
VCqC
S
W2
maxhmaxLmaxL
Takeoff
Landing
Climb
Acceleration
Range
Turn
Sustained turn
Maximum altitude
or
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T/W
W/S
Takeoff
Landing
Climb
Cruise
Example
Assumptions:
Takeoff weight 33100kg
Fuel weight 9700kg
Cruise airspeed 780km/h na 10000m
Minimum airspeed 200km/h
Aspect ratio 8
L/D 15
Takeoff & landing distance 1100m
Climb 9m/s
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Takeoff
)W/T)(TOP(87)TOP(9,20sTO
1
T
W
C
1
S
WTOP
TOmaxLTO
maxL
TO
maxL
CS
W834,3S
C
1
S
W133,0
W
T
Imperial
SI
Takeoff
2C maxL
takeoff
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Landing
400)LP(118sL
maxLC
1
S
WLP
75,0
C122S
S
W maxLL
Imperial
SI
Landing
2/2920 mN
S
W
L
17,2C maxL
75,0
C122S
S
W maxLL
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Example
Assumptions:
Takeoff weight 33100kg
Fuel weight 9700kg
Cruise airspeed 780km/h na 10000m
Minimum airspeed 200km/h
Aspect ratio 8
L/D 15
Takeoff & landing distance 1100m
Climb 9m/s
Landing
2/2920 mN
S
W
L
17,2C maxL
75,0
C122S
S
W maxLL
kgmL 23400970033100
279
2920
81,923400mS
2/4130
79
81,933100mN
S
W
TO
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Takeoff and landing
Takeoff
Landing
Climb
G
S
W
Aeq
1
S
WqC
W
T
2
0D
0S
WG
W
T
Aeq
1
S
WqC
2
0D
V
wG z
0DmaxD
L
C
eA
2
1
C
C
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Takeoff, climb and landingVclimb = 350 km/h G=0,094, CD0 = 0,0222
T/W
W/S
Takeoff
Landing
Climb
Climb
Aeq
2
Ae
C4G
W
TG
W
T
S
W
0D
2
Ae
C2G
W
T 0D
0S
WG
W
T
Aeq
1
S
WqC
2
0D
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Takeoff, climb and landing
Ae
C2G
W
T 0D
T/W
W/S
Takeoff
Landing
Climb
Cruise
2m/N3757
S
W
3
AeCq
S
W 0D
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Cruise
2m/N3757
S
W
W/S
t
Cruise
2m/N3757
S
W
W/S
t
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Cruise
2m/N3757
S
W
W/S
t
Cruise
t
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Example
Assumptions:
Takeoff weight 33100kg
Fuel weight 9700kg
Cruise airspeed 780km/h na 10000m
Minimum airspeed 200km/h
Aspect ratio 8
L/D 15
Takeoff & landing distance 1100m
Climb 9m/s
Cruise
2m/N3757
S
W
274
3757
81,9*28250mS
kgm 28250485033100
3
AeCq
S
W 0D
2/4405
74
81,933100mN
S
W
TO
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Design point
If smallest engine is desired
T/W
W/S
Takeoff
Landing
Climb
Cruise
If maximum range is desired