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Asst. Prof. Yongki Go
MA6641 Flight Performance & Dynamics
Takeoff and Landing Performance
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Takeoff Segments
We will consider only conventional takeoff The total takeoff distance consists of three parts:
the ground-roll distance
the transition distance the climbout distance over an obstacle
The height of the obstacle is 50 ft for military aircraft and 35 ft for
commercial aircraft
Takeoff flare
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Critical Engine
Critical engine in a multi-engine aircraft: engine whosefailure results in the most adverse effect
Exists e.g. in propeller-driven aircraft with the propellers
turning in the same direction In the example below, the left-hand engine is the critical
engine of the aircraft
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Important Speeds during Ground Roll (1)
: minimum control speed on the ground Minimum speed at which the rudder has become effective to
counteract moment due to critical engine failure on theground
At this speed the aircraft must be able to continue a straightpath down the runway with a failed engine
: minimum control speed in the air
Minimum speed at which the rudder has become effective tocounteract moment due to critical engine failure in the air
At this speed the aircraft must be able to continue a straightflight with a failed engine
: decision speed
Minimum speed to continue the takeoff in the presence ofengine failure
Takeoff must be aborted if engine failure occurs below
mcgV
mcaV
1V
)( mcgmca VV >
1V
)( 1 mcgVV >
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Important Speeds during Ground Roll (2)
: rotation speed The speed to initiate rotation to increase angle of attack
: minimum unstick speed
The minimum speed at which the aircraft can becomeairborne
This speed is determined based on the assumption ofmaximum angle of attack before stall or allowable by tail
clearance : liftoff speed
The speed at which the aircraft can safely lift off ground and
continue take-off This speed is usually achieved at angle of attack lower than
the maximum before stall or maximum allowable by tailclearance
Usually stall1.1 VVLO
RV )( 1VVR >
muV )( Rmu VV >
LOV )( muLO VV >
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Important Speeds during Ground Roll (3)
: ground roll distance
Total distance covered along the ground from zero speed to
: takeoff safety speed
Minimum speed at 35 ft above the ground to continue safe
climb with one engine failure
Usually
stallV
mcgV
mcaV1V RV
muV
LOV
0
gs
gs
LOV
2V
2V
stall2 2.1 VV
Accelerating ground run Rotation
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Balanced Field Length
Balanced Field Length (BFL) is determined by thecondition that the distance to continue a takeoff following
failure of an engine at some critical speed ( ) be equal to
the distance required to abort it
1V
(35 ft above ground)
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EOM Ground Roll
Forces on the aircraft during takeoff:
T D
L
WN
R
Normal force:
Rolling friction:
Parallel to the ground:
LWN =
)( LWNR rr == )( LWDT
dt
dVm r =
For detailed analysis, this equation must be integratednumerically to obtain the takeoff ground distance
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Some Notes on Ground Effects
During takeoff ground roll, is not the same as in the air Two primary reasons:
Higher due to the extended landing gear
Lower induced drag ( ) due to ground effect Proximity to the ground inhibits the downwash effect
DC
0DC
2
2
)16(1
)16(
effect)ground-of-out(
effect)ground-in(
bh
bhG
C
C
i
i
D
D
+=Approximation:
h: altitude above ground
b: wing span
iDC
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Approximate Ground Roll Analysis (1)
Distance traveled during ground roll:
dtdV
dV
dtdV
dVVdtVds
===
2
2
)( LWDTdt
dVm r = Using
)(2
2
LWDT
dVmds
r =
Since
g
Wm=
= LOV
r
gLWDT
dV
g
Ws
0
2
)(2 Note:
net force in the horizontal direction
consists of ground accelerating distance ( ) and
rotation distance ( )
)( LWDT r
gs gas
grs
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Approximate Ground Roll Analysis (2)
Ground accelerating distance:
Setting and recalling :
LOVV 7.0=
does not vary
much
Usually assumed constant at its
value at
)( LWDT r
[ ]LOVr
LOga
LWDTgWVs
7.0
2
)(1
2 =
stall1.1 VVLO =max
12stall
LCSWV
=
[ ] LOVrLga WLWDWTCg
SWs
7.0)1(
)(21.1
max =
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Approximate Ground Roll Analysis (3)
If at , further simplification:
increases with an increase in
decreases with an increase in
decreases with an increase in Note:
Ground roll is very sensitive to weight of aircraft
Ground roll is dependent on ambient density
WT
[ ])( LWDT r >>
)(
)(21.1
maxWTCg
SWs
L
ga
gas
gas
gas
SW
maxLC
LOV7.0
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Approximate Ground Roll Analysis (4)
Rotation distance: Reasonable to assume speed is constant at during
rotation
Hence, rotation distance is just rotation time ( ) multiplied by 1 for small aircraft, 3 for large aircraft
Setting :
Total ground roll distance:
Note that in normal takeoff situation:gagr ss
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Rotation Angle Limitation
Rotation is usually done at small angle to avoid tailstrike
Maximum rotation angle depends on the geometrical
configuration of the aircraft, mainly determined by: Landing gear height
Distance between rear wheels and strike point
Rough approximation:
t
t
l
h1max sin
=th
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Approximate Takeoff Flare Analysis (1)
Takeoff flare can be approximated as pull-up maneuver is between and
Assume
For safety, is kept slightly less thanAssume
stall1.1 VVLO = stall2 2.1 VV =V
stall15.1 VV =
maxLCLCmax
9.0 LL CC =
From pull-up maneuver theory:
)1(
2
=
ng
VR
Expressing in terms of :stallV
max
12stall
LCS
WV
=
W
max
2stall2
1LSCVW =
tf
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tf
Approximate Takeoff Flare Analysis (2)
Takeoff flare distance:
Total takeoff distance:
19.1
)9.0()15.1(
max
max
2
stall21
2stall21
=
==
L
L
SCV
CSV
W
Ln
g
VR
2
stall96.6=
From the geometry:
)1(cos OB1
R
htf =
tftf Rs sin=
tfgTO sss +=
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Example: Takeoff Distance Calculation (1)
Estimate the total takeoff distance at sea level for theGulfstream airplane. Assume that during ground roll, the
thrust equation can be approximated by:
and the drag polar is given by . Also
assume that the runway is dry concrete with .
Use in the ground-roll calculation andfor the takeoff configuration. Note: W=73,000 lb, S=950 ft2
04.0=r
86.1max=
LC
lb)01117.028.21700,27(
2
+=
VVT 2055.0033.0 LD CC +=
1.0=
LC
ft/s4.18612
max
stall == LCS
WV
ft/s1.2051.1 stall == VVLO
Airspeed to use in ground-roll calculation: ft/s6.1437.0 == LOVVAt this airspeed:
lb875,2401117.028.21700,27 2 =+= VVT
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Example: Takeoff Distance Calculation (2)
lb61.791)034.0)(950()6.143)(002377.0( 221221 === DSCVD
lb3.328,2)1.0)(950()6.143)(002377.0( 2212
21 === LSCVL
During ground roll: 034.0055.0033.02
=+= LD CC1.0=LC
[ ]
[ ]ft4.232,2
)032.01(04.0011.0341.0)86.1)(002377.0(2.32
)48.76(21.1
)1(
)(21.1
7.0max
=
=
= LOVrLga WLWDWTCg
SW
s
Lift and drag at 0.7 VLO:
Ground accelerating distance:
032.0000,733.328,2011.0000,7361.791
341.0000,73875,24
====
==
WLWD
WT
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Example: Takeoff Distance Calculation (3)
ft2.724sin == tftf Rs
Takeoff flare:
ft510,796.6 2stall ==
g
VR
== 534.5)1(cos OB1R
htf
ft)35(OB=h
Total takeoff distance: ft9.571,3=+= tfgTO sss
Rotation distance (use ): ft3.615== LORgr Vts3=Rt
Ground roll distance: ft2.915,1)(
)(21.1
max
= WTCg
SWs
L
ga
Total takeoff distance: ft7.254,3=+= tfgTO sss
If we use the more approximate ground-accelerating distance formula:
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Landing Segments (1)
Again we will only consider conventional landing here The total landing distance consists of three parts:
the approach distance, started from clearance of 50 ft obstacle
Straight path with speed at the obstacle clearancefor commercial aircraft, for military aircraft
the landing flare distance: transition (round-out) from approach
until touchdown at
for commercial aircraft, for military aircraft
the ground roll distance: free roll + braking distance
TDV
aVstall3.1 VVa = stall2.1 V
stall15.1 VVTD = stall1.1 V
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Landing Segments (2)
aVV =
TDVV =
0=
V
f
a
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Approximate Approach Distance Analysis
Assume equilibrium flight condition during approach:
W
T
DLa =
1sin
aWL cos=
aWTD sin+=
W
T
W
Da =sin
For transport aircraft, : 3a
WL
Assuming circular flare: fa =
)cos1( af Rh =Flare height:
Approach distance:
a
fa
hs
tan
50 =
a
a
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Approximate Landing Flare Distance Analysis
Consider circular flare: varies from to
For commercial aircraft: from to
For military aircraft: from to Assume:
for commercial aircraft, for military aircraft
V aV TDV
stall3.1 V
stall2.1 V
stall15.1 V
stall1.1 V
stall23.1 VVf = stall15.1 V2.1=n
From pull-up maneuver theory:
g
VR f
2.0
2
=
Flare distance:
aff RRs sinsin ==a
f
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Landing Ground Roll Analysis
EOM similar to takeoff ground roll with or : reverse thrust, for aircraft equipped with thrust reversers
This equation can be integrated numerically to find landing
ground roll distance ( )
consists of free roll distance ( ) and braking ground rundistance ( )
Free roll depends on pilot technique and the time for free
roll ( ) is usually of the order 1 to 3 s
Reasonable to assume speed is constant at during free
roll
0=T revTT =revT
)( LWDT
dt
dVm rrev =
dsdbs
frs
ds
TDV
TDfrfr Vts =
fr
t
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Bank Angle Limitation
During roll and after touchdown, the aircraft must beprevented from having too much bank to avoid wing strike
On some aircraft, the limitation could be due to possible
engine strike
Rough approximation
for max beforewing strike:
where
t
w
bb
h
= 2
tan 1max
+= tan
2
bhh Gw
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Approximate Landing Ground Roll Analysis (1)
As in the takeoff accelerating ground run, the distancetraveled during braking ground run distance from the end of
the free roll until fully stop:
or
Typically: is reasonably constant
If is constant, can assume constant
Value taken is usually at
)( LWDT rrev ++
=
0 2
)(2TDV rrev
dbLWDT
dVg
Ws
++=
TDV
rrev
dbLWDT
dVg
Ws0
2
)(2
)( LWD r +
revT
TDVV 7.0=
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Approximate Landing Ground Roll Analysis (2)
By recalling , can be expressed as:
[ ]TDVrrev
TDdb
LWDTg
WVs
7.0
2
)(
1
2 ++=
stallVjVTD =
max
12
stallLCS
WV
=
[ ] TDVrrevLdb
WLWDWTCg
SWjs
7.0
2
)1(
)(
max
++
=
Also we can write:
1.1
15.1
=
=j for commercial aircraft
for military aircraft
lbs
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Approximate Landing Ground Roll Analysis (3)
Total landing ground roll distance: Effects of aircraft parameters:
increases with an increase in
decreases with an increase in decreases with an increase in
As in takeoff, landing ground roll is also sensitive to weight
of the aircraft and dependent on the ambient air density and have same effect to both takeoff and
landing ground rolls
Total landing distance:
dbfrd sss +=
[ ]TDVrrevL
dbWLWDWTCg
SWjs
7.0
2
)1(
)(
max++
=
ds
ds
SW
maxLCWTrev
ds
SWmaxL
C
dfaLD ssss ++=
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Example: Landing Distance Calculation (1)
Estimate the total landing distance at sea level for theGulfstream airplane. Assume that no reverse thrust is used.
Assume the drag polar during landing ground roll is given by
and the rolling friction coefficient ofrunway with brakes-on is . Use during
ground roll and for landing configuration. The
approach angle is 3
o
. Note: W=73,000 lb, S=950 ft
2
ft/s4.1327.0 == TDVV
39.2max
=LC
ft/s5.16412
max
stall == LCS
WV
Airspeed to use in ground-roll calculation:
2
055.0027.0 LD CC += 4.0=r 1.0=LC
ft/s3.20223.1 stall == VVf
ft/s2.18915.1 stallVVTD =
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Example: Landing Distance Calculation (2)
ft6.5672.1893 === TDfrfr Vts
Approach distance :
ft71.8)cos1( == af Rh
ft9.787tan
50=
=
a
fa
hs
ft9.354,62.0
2
==g
VR f
= 3a
Flare distance:
ft6.332sinsin === aff RRs
Ground roll distance:Free roll :s3=frt
Braking ground run: 15.1=j
028.0055.0027.0 2 =+= LD CC1.0=LC
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Example: Landing Distance Calculation (3)
[ ]
[ ]ft1392
)027.01(4.0008.0)39.2)(002377.0(2.32
)84.76()15.1(
)1()(
2
7.0
2
max
=+=
++=
TDVrrevL
dbWLWDWTCg
SWjs
Lift and drag at 0.7 VTD:lb2.979,1)1.0)(950()4.132)(002377.0( 2
212
21 === LSCVL
lb2.554)028.0)(950()4.132)(002377.0( 2212
21 === DSCVD
027.0000,732.979,1
008.0000,732.554
used)isthrustreverse(no0
====
=
WL
WD
WTrev
ft1.3080=++= dfaLD ssssTotal landing distance:
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