Summary
Aircraft
Performance
Aviation
Academy
Faculty
of
Technology
Amsterdam
University
of
Applied
Sciences
,Block
5
Aircraft
Performance
2ENG
Index
LECTURE
1
..............................................................................................................................................
4
Transonic
aerodynamics
..................................................................................................................
4
Transonic
flow
.................................................................................................................................
4
Incompressible
subsonic
flow
..........................................................................................................
4
Compressible
transonic
flow
............................................................................................................
4
Mcrit
..................................................................................................................................................
4
The
BOB
chart
..................................................................................................................................
5
LECTURE
2:
PERFORMANCE
GRAPHS
............................................................................................................
6
The
drag
polar
CL
-‐
CD
Graph
............................................................................................................
6
Performance
Graph
(D-‐IAS)
.............................................................................................................
6
𝐶𝐿𝐶𝐷𝑚𝑎𝑥 = 𝐷𝑚𝑖n
.........................................................................................................................
7
LECTURE
3:
CRUISE
..................................................................................................................................
7
Laws
of
performance
.......................................................................................................................
7
Max
Endurance
................................................................................................................................
7
Max
Range
......................................................................................................................................
8
Weight
on
cruise
performance
of
jet
aircraft
..................................................................................
8
Altitude
on
cruise
performance
of
jet
aircraft
.................................................................................
8
LECTURE
4:
CRUISE
..................................................................................................................................
8
Long
Range
Cruise
System
...............................................................................................................
8
Economy
cruise
system
....................................................................................................................
9
Thrust
Specific
Fuel
Consumption
(TSFC)
.........................................................................................
9
Endurance
formula
of
Breguet
........................................................................................................
9
Range
formula
of
Breguet
...............................................................................................................
9
LECTURE
5:
DESCENT
..............................................................................................................................
10
Descent
speed
................................................................................................................................
10
Speed
polar
curve
..........................................................................................................................
10
Glide
ratio
of
the
aircraft
(gliding
angle)
.......................................................................................
11
LECTURE
6:
DESCENT
..............................................................................................................................
11
Influence
of
weight
on
descent
performance
................................................................................
11
Influence
of
altitude
on
descent
performance:
..............................................................................
11
Influence
of
selection
of
flaps/slats
on
descent
performance:
......................................................
12
Top
Off
Descent
(TOD)
...................................................................................................................
12
LECTURE
7:
CLIMB
.................................................................................................................................
13
As
economical
as
possible
from
A
to
B
..........................................................................................
13
Climb
speed
...................................................................................................................................
13
Maximum
climb
angle
𝛾
................................................................................................................
13
LECTURE
8:
CLIMB
.................................................................................................................................
14
Influence
of
weight
on
climb
performance
(climb
angle
𝛾 )
...........................................................
14
Influence
of
altitude
on
climb
performance
(max
climb
angle
𝛾 )
..................................................
14
Influence
of
aircraft
configuration
on
the
climb
angle
𝛾
...............................................................
14
LAW
(operations)
...........................................................................................................................
14
Climb
gradient
...............................................................................................................................
14
CS-‐23
.............................................................................................................................................
15
EU-‐OPS
subpart
H
performance
class
B
.........................................................................................
15
Take-‐off
obstacle
clearance
...........................................................................................................
15
CS-‐25/EU-‐OPS
1
performance
class
A
............................................................................................
16
2
,Block
5
Aircraft
Performance
2ENG
Landing
climb
................................................................................................................................
16
N-‐1
approach
climb
gradient
.........................................................................................................
16
Take
off
in
case
of
obstacles
..........................................................................................................
16
Engine
failure
during
cruise
obstacle
clearance
............................................................................
16
Cross
gradient
................................................................................................................................
17
Double
engine
failure
during
cruise
obstacle
clearance
................................................................
17
LECTURE
9:
TURNS
.................................................................................................................................
17
Forces
during
turns
........................................................................................................................
17
Load
factor
....................................................................................................................................
17
Stall
speed
depending
on
the
load
factor
......................................................................................
18
Radius
of
turn:
radius
of
curvature
................................................................................................
18
Minimum
radius
of
turn:
...............................................................................................................
18
LECTURE
10:
TAKE-‐OFF
..........................................................................................................................
19
Engine
failure
speed
vs.
Distance
..................................................................................................
19
CS-‐23
.............................................................................................................................................
19
CS-‐25
and
performance
class
A
.....................................................................................................
20
V1
is
take-‐off
decision
speed
.........................................................................................................
20
Influence
of
weight
on
V1
&
BTOD
................................................................................................
20
Influence
of
down
slope
on
V1
&
BTOD
.........................................................................................
20
Influence
of
headwind
on
V1&
BTOD
............................................................................................
20
Influence
of
less
thrust
on
V1
&
BTOD
...........................................................................................
21
Influence
of
runway
condition
on
V1
&
BTOD
...............................................................................
21
Clearway
........................................................................................................................................
21
Stop
way
........................................................................................................................................
22
Take-‐off
speeds
.............................................................................................................................
22
Thing
that
can
influence
the
allowable
take-‐off
weight
................................................................
23
LECTURE
11:
LANDING
...........................................................................................................................
23
EASA
CS-‐23
certified
landing
distance
...........................................................................................
23
EU-‐OPS
1
performance
class
B
......................................................................................................
23
EASA
CS-‐25
Certified
landing
distance
...........................................................................................
23
EU-‐OPS
1
performance
class
A
......................................................................................................
24
Operator
shall
take
into
account:
..................................................................................................
24
3
,Block
5
Aircraft
Performance
2ENG
Lecture
1
Transonic
aerodynamics
If
flow
is
delayed
in
a
supersonic
area,
a
shock
wave
may
occur.
Transonic
flow
What
changes
in
comparison
to
subsonic
flow:
§ Critical
Mach
number
§ Normal
shock
waves
§ Consequences
of
exceeding
the
critical
Mach
number
§ The
Buffet
Onset
Boundary
chart
§ The
area
rule
§ Increasing
the
critical
Mach
number
§ Super
critical
profiles
Incompressible
subsonic
flow
Bernoulli’s
equation
and
the
continuity
law.
P
and
V
are
variable.
Compressible
transonic
flow
𝑃, 𝑉, 𝜌
𝑎𝑛𝑑
𝑇
𝑎𝑟𝑒
𝑣𝑎𝑟𝑖𝑎𝑏𝑙𝑒
Bernoulli’s
law
doesn’t
apply
anymore,
only
the
continuity
law.
𝑇𝐴𝑆
𝑀𝑎𝑐ℎ
𝑀 =
𝛼
𝑆𝑝𝑒𝑒𝑑
𝑜𝑓
𝑠𝑜𝑢𝑛𝑑
𝛼 = 𝛾 ∙ 𝑅 ∙ 𝑇
𝑐𝑝 J
γ=
R = 287
∙ K
𝑐𝑣 kg
2
𝑇𝐴𝑆
Temperature
changes
in
transonic
flow:
𝑇𝐴𝑇 = 𝑆𝐴𝑇 +
2∙𝑐𝑝
Temperature
rise
has
nothing
to
do
with
friction.
Temperature
increases
in
transonic
flow.
Total
air
temperature:
𝑇𝐴𝑇 = 𝑆𝐴𝑇 + 0,2 ∙ 𝑀 P
∙
𝑆𝐴𝑇
SAT
=
Static
Air
Temperature.
Ram
rise
Ram
rise
is
the
temperature
rise
in
Kelvin
due
to
the
sudden
stop
of
air
molecules.
Mcrit
The
critical
Mach
number
is
the
flight
Mach
number
where
somewhere
on
the
airplane
construction,
the
speed
of
sound
is
reached.
Exceeding
the
critical
Mach
number-‐>
increasing
drag
&
decreasing
lift
&
vibration
of
aircraft
and
controls
4
, Block
5
Aircraft
Performance
2ENG
Mach
number
Type
of
Flow
<
0,3
Incompressible
subsonic
flow
0,3
–
0,8
Compressible
subsonic
flow;
the
speed
of
all
the
airflow
around
the
aircraft
is
still
below
Mach
1
0,8
–
1,2
Transonic
flow;
the
speed
of
the
airflow
around
the
aircraft
is
both
below
and
above
Mach
1
>
1,2
Supersonic
flow;
the
speed
of
all
the
airflow
around
the
aircraft
is
above
Mach
1
>
5
Hypersonic
flow;
this
is
of
course
also
a
supersonic
flow,
but
the
friction
of
air
causes
huge
temperature
problems
Low
speed
buffet
Item
Shock
buffet
Large
AOA
Small
Low
Mach
no.
High
Large
amplitude
Small
amplitude
Characteristic
low
frequency
High
frequency
Lower
AOA
and
increase
speed
Action
taken
by
pilot
Decrease
Mach
no.
The
BOB
chart
Stall
speed
increases
with
altitude
due
to
compressibility
effects.
Stall
with
a
load
factor
greater
than
one
is
an
acceleration
of
a
G-‐stall.
Shock
stall
starts
at
the
root
of
a
wing.
Coffin
Corner
is
the
region
of
flight
where
a
fast
fixed-‐wing
aircraft's
stall
speed
is
near
the
critical
Mach
number,
at
a
given
gross
weight
and
G-‐force
loading.
In
this
region
of
flight,
it
is
very
difficult
to
keep
the
airplane
in
stable
flight.
Coke
Bottle
is
when
the
transonic
drag
becomes
less
due
to
a
smaller
body
at
the
wing.
2∙n∙W
𝐸𝐴𝑆RSTUU =
𝐶W,XTY ∙ ρ ∙ S
Means
of
increasing
the
critical
Mach
number:
§ Thin
profiles
§ Swept
back
wings
§ Vortex
generators
§ Super
critical
profiles
5
Aircraft
Performance
Aviation
Academy
Faculty
of
Technology
Amsterdam
University
of
Applied
Sciences
,Block
5
Aircraft
Performance
2ENG
Index
LECTURE
1
..............................................................................................................................................
4
Transonic
aerodynamics
..................................................................................................................
4
Transonic
flow
.................................................................................................................................
4
Incompressible
subsonic
flow
..........................................................................................................
4
Compressible
transonic
flow
............................................................................................................
4
Mcrit
..................................................................................................................................................
4
The
BOB
chart
..................................................................................................................................
5
LECTURE
2:
PERFORMANCE
GRAPHS
............................................................................................................
6
The
drag
polar
CL
-‐
CD
Graph
............................................................................................................
6
Performance
Graph
(D-‐IAS)
.............................................................................................................
6
𝐶𝐿𝐶𝐷𝑚𝑎𝑥 = 𝐷𝑚𝑖n
.........................................................................................................................
7
LECTURE
3:
CRUISE
..................................................................................................................................
7
Laws
of
performance
.......................................................................................................................
7
Max
Endurance
................................................................................................................................
7
Max
Range
......................................................................................................................................
8
Weight
on
cruise
performance
of
jet
aircraft
..................................................................................
8
Altitude
on
cruise
performance
of
jet
aircraft
.................................................................................
8
LECTURE
4:
CRUISE
..................................................................................................................................
8
Long
Range
Cruise
System
...............................................................................................................
8
Economy
cruise
system
....................................................................................................................
9
Thrust
Specific
Fuel
Consumption
(TSFC)
.........................................................................................
9
Endurance
formula
of
Breguet
........................................................................................................
9
Range
formula
of
Breguet
...............................................................................................................
9
LECTURE
5:
DESCENT
..............................................................................................................................
10
Descent
speed
................................................................................................................................
10
Speed
polar
curve
..........................................................................................................................
10
Glide
ratio
of
the
aircraft
(gliding
angle)
.......................................................................................
11
LECTURE
6:
DESCENT
..............................................................................................................................
11
Influence
of
weight
on
descent
performance
................................................................................
11
Influence
of
altitude
on
descent
performance:
..............................................................................
11
Influence
of
selection
of
flaps/slats
on
descent
performance:
......................................................
12
Top
Off
Descent
(TOD)
...................................................................................................................
12
LECTURE
7:
CLIMB
.................................................................................................................................
13
As
economical
as
possible
from
A
to
B
..........................................................................................
13
Climb
speed
...................................................................................................................................
13
Maximum
climb
angle
𝛾
................................................................................................................
13
LECTURE
8:
CLIMB
.................................................................................................................................
14
Influence
of
weight
on
climb
performance
(climb
angle
𝛾 )
...........................................................
14
Influence
of
altitude
on
climb
performance
(max
climb
angle
𝛾 )
..................................................
14
Influence
of
aircraft
configuration
on
the
climb
angle
𝛾
...............................................................
14
LAW
(operations)
...........................................................................................................................
14
Climb
gradient
...............................................................................................................................
14
CS-‐23
.............................................................................................................................................
15
EU-‐OPS
subpart
H
performance
class
B
.........................................................................................
15
Take-‐off
obstacle
clearance
...........................................................................................................
15
CS-‐25/EU-‐OPS
1
performance
class
A
............................................................................................
16
2
,Block
5
Aircraft
Performance
2ENG
Landing
climb
................................................................................................................................
16
N-‐1
approach
climb
gradient
.........................................................................................................
16
Take
off
in
case
of
obstacles
..........................................................................................................
16
Engine
failure
during
cruise
obstacle
clearance
............................................................................
16
Cross
gradient
................................................................................................................................
17
Double
engine
failure
during
cruise
obstacle
clearance
................................................................
17
LECTURE
9:
TURNS
.................................................................................................................................
17
Forces
during
turns
........................................................................................................................
17
Load
factor
....................................................................................................................................
17
Stall
speed
depending
on
the
load
factor
......................................................................................
18
Radius
of
turn:
radius
of
curvature
................................................................................................
18
Minimum
radius
of
turn:
...............................................................................................................
18
LECTURE
10:
TAKE-‐OFF
..........................................................................................................................
19
Engine
failure
speed
vs.
Distance
..................................................................................................
19
CS-‐23
.............................................................................................................................................
19
CS-‐25
and
performance
class
A
.....................................................................................................
20
V1
is
take-‐off
decision
speed
.........................................................................................................
20
Influence
of
weight
on
V1
&
BTOD
................................................................................................
20
Influence
of
down
slope
on
V1
&
BTOD
.........................................................................................
20
Influence
of
headwind
on
V1&
BTOD
............................................................................................
20
Influence
of
less
thrust
on
V1
&
BTOD
...........................................................................................
21
Influence
of
runway
condition
on
V1
&
BTOD
...............................................................................
21
Clearway
........................................................................................................................................
21
Stop
way
........................................................................................................................................
22
Take-‐off
speeds
.............................................................................................................................
22
Thing
that
can
influence
the
allowable
take-‐off
weight
................................................................
23
LECTURE
11:
LANDING
...........................................................................................................................
23
EASA
CS-‐23
certified
landing
distance
...........................................................................................
23
EU-‐OPS
1
performance
class
B
......................................................................................................
23
EASA
CS-‐25
Certified
landing
distance
...........................................................................................
23
EU-‐OPS
1
performance
class
A
......................................................................................................
24
Operator
shall
take
into
account:
..................................................................................................
24
3
,Block
5
Aircraft
Performance
2ENG
Lecture
1
Transonic
aerodynamics
If
flow
is
delayed
in
a
supersonic
area,
a
shock
wave
may
occur.
Transonic
flow
What
changes
in
comparison
to
subsonic
flow:
§ Critical
Mach
number
§ Normal
shock
waves
§ Consequences
of
exceeding
the
critical
Mach
number
§ The
Buffet
Onset
Boundary
chart
§ The
area
rule
§ Increasing
the
critical
Mach
number
§ Super
critical
profiles
Incompressible
subsonic
flow
Bernoulli’s
equation
and
the
continuity
law.
P
and
V
are
variable.
Compressible
transonic
flow
𝑃, 𝑉, 𝜌
𝑎𝑛𝑑
𝑇
𝑎𝑟𝑒
𝑣𝑎𝑟𝑖𝑎𝑏𝑙𝑒
Bernoulli’s
law
doesn’t
apply
anymore,
only
the
continuity
law.
𝑇𝐴𝑆
𝑀𝑎𝑐ℎ
𝑀 =
𝛼
𝑆𝑝𝑒𝑒𝑑
𝑜𝑓
𝑠𝑜𝑢𝑛𝑑
𝛼 = 𝛾 ∙ 𝑅 ∙ 𝑇
𝑐𝑝 J
γ=
R = 287
∙ K
𝑐𝑣 kg
2
𝑇𝐴𝑆
Temperature
changes
in
transonic
flow:
𝑇𝐴𝑇 = 𝑆𝐴𝑇 +
2∙𝑐𝑝
Temperature
rise
has
nothing
to
do
with
friction.
Temperature
increases
in
transonic
flow.
Total
air
temperature:
𝑇𝐴𝑇 = 𝑆𝐴𝑇 + 0,2 ∙ 𝑀 P
∙
𝑆𝐴𝑇
SAT
=
Static
Air
Temperature.
Ram
rise
Ram
rise
is
the
temperature
rise
in
Kelvin
due
to
the
sudden
stop
of
air
molecules.
Mcrit
The
critical
Mach
number
is
the
flight
Mach
number
where
somewhere
on
the
airplane
construction,
the
speed
of
sound
is
reached.
Exceeding
the
critical
Mach
number-‐>
increasing
drag
&
decreasing
lift
&
vibration
of
aircraft
and
controls
4
, Block
5
Aircraft
Performance
2ENG
Mach
number
Type
of
Flow
<
0,3
Incompressible
subsonic
flow
0,3
–
0,8
Compressible
subsonic
flow;
the
speed
of
all
the
airflow
around
the
aircraft
is
still
below
Mach
1
0,8
–
1,2
Transonic
flow;
the
speed
of
the
airflow
around
the
aircraft
is
both
below
and
above
Mach
1
>
1,2
Supersonic
flow;
the
speed
of
all
the
airflow
around
the
aircraft
is
above
Mach
1
>
5
Hypersonic
flow;
this
is
of
course
also
a
supersonic
flow,
but
the
friction
of
air
causes
huge
temperature
problems
Low
speed
buffet
Item
Shock
buffet
Large
AOA
Small
Low
Mach
no.
High
Large
amplitude
Small
amplitude
Characteristic
low
frequency
High
frequency
Lower
AOA
and
increase
speed
Action
taken
by
pilot
Decrease
Mach
no.
The
BOB
chart
Stall
speed
increases
with
altitude
due
to
compressibility
effects.
Stall
with
a
load
factor
greater
than
one
is
an
acceleration
of
a
G-‐stall.
Shock
stall
starts
at
the
root
of
a
wing.
Coffin
Corner
is
the
region
of
flight
where
a
fast
fixed-‐wing
aircraft's
stall
speed
is
near
the
critical
Mach
number,
at
a
given
gross
weight
and
G-‐force
loading.
In
this
region
of
flight,
it
is
very
difficult
to
keep
the
airplane
in
stable
flight.
Coke
Bottle
is
when
the
transonic
drag
becomes
less
due
to
a
smaller
body
at
the
wing.
2∙n∙W
𝐸𝐴𝑆RSTUU =
𝐶W,XTY ∙ ρ ∙ S
Means
of
increasing
the
critical
Mach
number:
§ Thin
profiles
§ Swept
back
wings
§ Vortex
generators
§ Super
critical
profiles
5
