Takeoff Landing.pdf

8/14/2019 Takeoff Landing.pdf

1/31

Asst. Prof. Yongki Go

MA6641 Flight Performance & Dynamics

Takeoff and Landing Performance


2/31

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


3/31

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
http://en.wikipedia.org/wiki/Image:Criticalengine1.jpg


4/31

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 >


5/31


: 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 >


6/31


: 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


7/31

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)


8/31

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


9/31

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


10/31

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


11/31


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 =


12/31


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


13/31


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


14/31

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


15/31

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


16/31

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 +=


17/31

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


18/31


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


19/31


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:


20/31

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


21/31

Landing Segments (2)

aVV =

TDVV =

0=

V

f

a


22/31

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


23/31

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


24/31

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


25/31

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


26/31

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=


27/31


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


28/31


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 ++=


29/31

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 =


30/31


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


31/31


[ ]

[ ]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:

Takeoff Landing.pdf

Documents

Transcript of Takeoff Landing.pdf