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
3AE2104 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
4AE2104 Flight and Orbital Mechanics |
Introduction
Typical numbersdA = 3°Va 1.3 Vmin
VT 1.15 Vmin
hs = 50 ft
5AE2104 Flight and Orbital Mechanics |
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.
6AE2104 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
7AE2104 Flight and Orbital Mechanics |
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
8AE2104 Flight and Orbital Mechanics |
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
9AE2104 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
10AE2104 Flight and Orbital Mechanics |
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
11AE2104 Flight and Orbital Mechanics |
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
12AE2104 Flight and Orbital Mechanics |
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
13AE2104 Flight and Orbital Mechanics |
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
14AE2104 Flight and Orbital Mechanics |
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
15AE2104 Flight and Orbital Mechanics |
16AE2104 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
17AE2104 Flight and Orbital Mechanics |
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
18AE2104 Flight and Orbital Mechanics |
Propeller
Jet Turbofan
19AE2104 Flight and Orbital Mechanics |
Spoilers, thrust reversers, etc.Special devices
20AE2104 Flight and Orbital Mechanics |
Spoilers, thrust reversers, etc.Speed brakes and spoilers
21AE2104 Flight and Orbital Mechanics |
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
22AE2104 Flight and Orbital Mechanics |
Spoilers, thrust reversers, etc.Airspeed - Flaps
23AE2104 Flight and Orbital Mechanics |
Content
• Introduction
• Equations of motion
• Analytical solution landing distance
• Spoilers, thrust reverser, etc.
• Tire, runway and brake properties
• Airworthiness Regulations
• Example exam question
• Summary
24AE2104 Flight and Orbital Mechanics |
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
25AE2104 Flight and Orbital Mechanics |
Tire, runway and brake properties
R
V
V Rslip
V
s = 1blocked
s = 0Free roll
Ng1
Ng2 > Ng1
N
Dg
Dg
Experiment
26AE2104 Flight and Orbital Mechanics |
Images from: Jazar, R. “Vehicle Dynamics: Theory and Application”
27AE2104 Flight and Orbital Mechanics |
Tire, runway and brake properties
g
g
D
N
max
slip
Tire deformation Partly slipping
V Rs
V
Dimensionless
28AE2104 Flight and Orbital Mechanics |
Tire, runway and brake properties
Dg
Q V
V Rslip
V
unstablestable
Qbrake
gN r
Brake stability
29AE2104 Flight and Orbital Mechanics |
Tire, runway and brake propertiesSummarized
30AE2104 Flight and Orbital Mechanics |
http://www.youtube.com/watch?v=UPnaBN95Npw
31AE2104 Flight and Orbital Mechanics |
Tire, runway and brake properties
• 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
32AE2104 Flight and Orbital Mechanics |
Content
• Introduction
• Equations of motion
• Analytical solution landing distance
• Spoilers, thrust reverser, etc.
• Tire, runway and brake properties
• Airworthiness Regulations
• Example exam question
• Summary
33AE2104 Flight and Orbital Mechanics |
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
34AE2104 Flight and Orbital Mechanics |
Content
• Introduction
• Equations of motion
• Analytical solution landing distance
• Spoilers, thrust reverser, etc.
• Tire, runway and brake properties
• Airworthiness Regulations
• Example exam question
• Summary
35AE2104 Flight and Orbital Mechanics |
Example exam question
36AE2104 Flight and Orbital Mechanics |
Example exam question
37AE2104 Flight and Orbital Mechanics |
Example exam question
38AE2104 Flight and Orbital Mechanics |
Example exam question
39AE2104 Flight and Orbital Mechanics |
40AE2104 Flight and Orbital Mechanics |
41AE2104 Flight and Orbital Mechanics |
42AE2104 Flight and Orbital Mechanics |
43AE2104 Flight and Orbital Mechanics |
Content
• Introduction
• Equations of motion
• Analytical solution landing distance
• Spoilers, thrust reverser, etc.
• Tire, runway and brake properties
• Airworthiness Regulations
• Example exam question
• Summary
44AE2104 Flight and Orbital Mechanics |
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
45AE2104 Flight and Orbital Mechanics |
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
46AE2104 Flight and Orbital Mechanics |
Questions?