flight and orbital mechanics - tu delft

1Challenge the future

Flight and Orbital Mechanics

Lecture slides

Semester 1 - 2012

Challenge the future

DelftUniversity ofTechnology

Flight and Orbital MechanicsLecture hour 10 – Landing

Mark Voskuijl

2AE2104 Flight and Orbital Mechanics |

Content

• Introduction

• Equations of motion

• Analytical solution landing distance

• Spoilers, thrust reversers, etc.

• Tire, runway and brake properties

• Airworthiness Regulations

• Example exam question

• Summary


Content

• Introduction







• Summary


Introduction

Typical numbersdA = 3°Va 1.3 Vmin

VT 1.15 Vmin

hs = 50 ft


Introduction

The landing is the maneuver by which the airplane is brought from a steady approach

speed VA over a 15 m obstacle at the runway threshold to standstill at the runway.


Content

• Introduction







• Summary


Equations of motion

Assumption: T = 0

dV

dt

dV

dt

// : sin

: cos

V

V

W dVF T D W

g dt

W dF V L W

g dt

Airborne phase


Equations of motion

N W

L

T

Dg

D

r

W dVT D W L

g dt

dV/dt

V V

Free body diagram Kinetic diagram

Ground phase


Content

• Introduction







• Summary


Analytical solution

// : sin

: cos

V

V

W dVF T D W

g dt

W dF V L W

g dt

sinW dV ds

T D Wg ds dt

(Equations of motion)

sinW

VdV T D ds W dsg

W

VdV T D ds Wdhg

0

2

02

T

A scr

V s

V h

WdV T D ds Wdh

g

2 2

2T A scr

WV V T D s Wh

g

(Introduce variable s)

(Rewrite)

(dh sinds)

(Integrate)

(Result)

Airborne phase


Analytical Solution

2 2

2T A scr

WV V T D s Wh

g

2

A TT D T D

T D

T DWhat is ???

TA, DA

VA VT

TD, DD

Approach

Assume steady flight

0 sin

sin

A

AA

T D W

T D W

Touch down

, W dV

T D L Wg dt

0T

D

T

L T

T

CD W

C

D

T

L T

CT D W

C

Airborne phase


Analytical solution

2 2

sin2 2

A T DA scr

L T

V V Csh

g C

2 2

2T A scr

WV V T D s Wh

g

sin

2 2 2

A T D

A

L T

T D T D CW WT D

C

Airborne phase

2 2

12

2 2

sin

A Tscr

DA

L T

V Vh

g gs

C

C


Analytical solution

dV dVa V

dt ds

0 2

2T

T

V

VVdVs

a a

g rev g

g ga T D D T D D

W W

Reverse thrust At VT / 2

r

W dVT D W L

g dt

N W

L

T

Dg

D

r

W dVT D W L

g dt

Ground run


Analytical solution

max

22 1.15 1

2g

L rev g

W Ws

g S C T D D

2

2

Tg

rev g

VWs

g T D D

Final result:

Ground run

min1.15TV V


Content

• Introduction







• Summary


Spoilers, thrust reversers, etc.

• W2 !!

• Flaps and small W/S

• Trev (but: asymmetry)

• D: Spoilers, chute

• Dg: ABS, Lift dumpers, clean runway

max

22 1.15 1

2

g

L rev g

W Ws

g S C T D D

Overview


Propeller

Jet Turbofan


Spoilers, thrust reversers, etc.Special devices

http://www.airliners.net/photo/USA---Air/Boeing-B-52H-Stratofortress/1400838/L/&sid=17a6be13f6ab36a465f9a50a8544c227

http://www.airliners.net/photo/USA---Air/Boeing-B-52H-Stratofortress/1400838/L/&sid=17a6be13f6ab36a465f9a50a8544c227


Spoilers, thrust reversers, etc.Speed brakes and spoilers

http://www.airliners.net/photo/USA---Air/McDonnell-Douglas-F-15C/1489557/L/&sid=cca57ba07e8c88bae7c907b8a22a9962

http://www.airliners.net/photo/USA---Air/McDonnell-Douglas-F-15C/1489557/L/&sid=cca57ba07e8c88bae7c907b8a22a9962

http://www.airliners.net/photo/Lufthansa/Airbus-A330-343X/1569505/L/&sid=eab367334e7be08075ed13936c7a53f8

http://www.airliners.net/photo/Lufthansa/Airbus-A330-343X/1569505/L/&sid=eab367334e7be08075ed13936c7a53f8


Spoilers, thrust reversers, etc.

• Speed brakes

• Used to increase aerodynamic drag (D)

• Lift Dumpers

• Reduce lift and thereby increase normal force on wheels, which

increases Dg

• Spoilers

• Used both to reduce lift and to increase aerodynamic drag.

Furthermore, used for (high-speed) roll control

Summary


Spoilers, thrust reversers, etc.Airspeed - Flaps


Content

• Introduction



• Spoilers, thrust reverser, etc.




• Summary


Tire, runway and brake properties

gD r Q

d

dt

Moments about centre of wheel:

Accelerations about centre of wheel:

Combined

g

dI D r Q

dt

Equation of motion



R

V

V Rslip

V

s = 1blocked

s = 0Free roll

Ng1

Ng2 > Ng1

N

Dg

Dg

Experiment


Images from: Jazar, R. “Vehicle Dynamics: Theory and Application”



g

g

D

N

max

slip

Tire deformation Partly slipping

V Rs

V

Dimensionless



Dg

Q V

V Rslip

V

unstablestable

Qbrake

gN r

Brake stability


Tire, runway and brake propertiesSummarized


http://www.youtube.com/watch?v=UPnaBN95Npw

http://www.youtube.com/watch?v=UPnaBN95Npw



• Take-off with blocked brakes on

icy runway

• glide = 0.025 (Compare to roll =

0.02)

• Normal ground run acceleration

• Tire blow out at V1

• Increasing wear: no acceleration

at V>V1

Lessons:

1. Function indication: not position

of controls

2. Take-off monitoring system

DC-8 Anchorage 1970


Content

• Introduction







• Summary


Airworthiness regulations

• Va 1.3 Vmin

• Required field length = 10/6 x demonstrated landing distance

• Wet: x 1.15

• Landing climb potential: All engines and flaps in landing

configuration

Summary


Content

• Introduction







• Summary


Example exam question


Content

• Introduction







• Summary


Summary

• Airborne distance required for

landing:

• Distance required on ground

during landing

max

22 1.15 1

2g

L rev g

W Ws

g S C T D D

Landing procedure

You should be able to derive these equations

2 2

12

2 2

sin

A Tscr

DA

L T

V Vh

g gs

C

C


Summary

• Landing performance is influenced by

• Aircraft weight

• Airspeed (CLmax, flaps)

• Drag devices (speed brakes, spoilers)

• Thrust reversers

• Lift dumpers

• Tire and brake properties

• If tires block due to brake instability, then the friction reduces;

need for ABS


Questions?

flight and orbital mechanics - tu delft

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