High-Order Numerical Methods for BiGlobal Flow Instability Analysis and Control 45
Fig. 10. Upper: Amplitude functions of the least-damped eigenmode of geometry "in
1
"at
Re
= 1000, α = 1 González, Rodríguez & Theofilis (2008).Lower: Amplitude functions of the
least-damped eigenmode of geometry "in
2
"atRe = 1000, α = 1 González, Rodríguez &
Theofilis (2008). Left to right column:
ˆ
u
1
,
ˆ
u
2
,
ˆ
u
3
.
229
High-Order Numerical Methods for BiGlobal Flow Instability Analysis and Control
46 Will-be-set-by-IN-TECH
Fig. 11. Upper-Left: Leading eigenmode in the wake of the T106-300 LPT flow at Re = 890.
Upper-Right: Leading (wake) eigenmode in flow over an aspect ratio 8 ellipse at Re
= 200
Kitsios et al. (2008). Lower: Leading LPT Floquet mode at Re
= 2000 Abdessemed et al. (2004).
230

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vibrations. (Kufeld & Bousman, 1995; Hansford & Vorwald, 1996; Datta & Chopra, 2002)
The primary cause of pilot control difficulties and high-workload situations is that even
modern helicopters often have poor Handling Qualities (HQs) (Padfield, 1998). Cooper and
Harper (Cooper & Harper, 1969), pioneers in this subject, defined these as: “those qualities or
characteristics of an aircraft that govern the ease and precision with which a pilot is able to perform a
mission”. Below, the current practice in rotorcraft handling qualities assessment will be
discussed, introducing the key problem addressed in this chapter.
1.1 State-of-the-art in rotorcraft handling qualities – The aeronautical design standard
ADS-33
Helicopter handling qualities used to be assessed with requirements defined for fixed-wing
aircraft, as stated in the FAR (civil) and MIL (military) standards. In the 1960’s, however, it
became clear that these standards were not sufficient (Key, 1982). Helicopters have strong
cross-coupling effects between longitudinal and directional controls, their behaviour is highly
non-linear and requires more degrees of freedom in modelling than the rigid-body models used
for aircraft. Therefore, the MIL-H-8501A standard (MIL-H-8501A, 1962) was developed. This
standard was used up until mid 1980’s. From a safety perspective, these requirements were
merely ‘good minimums’, and a new standard was developed in the 1970’s, that is used up
until today, the Aeronautical Design Standard ADS-33 (ADS-33, 2000)

Aeronautics and Astronautics

238
The crucial point, understood by ADS-33, is that helicopter HQ requirements need to be
related to the mission executed, as this will determine the needed pilot effort. E.g., a
shipboard landing at night and in high sea with strong ship motions demands more
precision of control from the pilot than when flying in daytime and good weather.2 ADS-
33 introduced handling qualities metrics (HQM), a combination of flight parameters such as
rate of climb, turn rate, etc., that reflect how much manoeuvre-capability the pilot has per
specific mission. These metrics are then mapped into handling qualities criteria (HQC) that
yield boundaries between ‘good’ (Level 1), ‘satisfactory’ (Level 2) and ‘poor’ (Level 3)

Tail
stress
RPM droop
Gravity fed
hydraulics
A
D
S
-
3
3
Defining OFE/SFE
Airspeed (kts)
Load
factor
1
2
3
0
50 100 150 2000
OFE
SFE
Control
loads
Blade
stall
Tail
stress
RPM droop
Gravity fed

SFE
Control
loads
Blade
stall
Tail
stress
RPM droop
Gravity fed
hydraulics
A
D
S
-
3
3
Example of mission in the
simulator of Univ. of Liverpool
Missions
Defining OFE/SFE
Airspeed (kts)
Load
factor
1
2
3
0
50 100 150 2000
OFE
SFE

Load
factor
1
2
3
0
50 100 150 2000
OFE
SFE
Control
loads
Blade
stall
Tail
stress
RPM droop
Gravity fed
hydraulics
A
D
S
-
3
3
Defining OFE/SFE
Airspeed (kts)
Load
factor
1
2

RPM droop
Gravity fed
hydraulics
Defining OFE/SFE
Airspeed (kts)
Load
factor
1
2
3
0
50 100 150 2000
OFE
SFE
Control
loads
Blade
stall
Tail
stress
RPM droop
Gravity fed
hydraulics
Airspeed (kts)
Load
factor
1
2
3
0

Blade
stall
Tail
stress
RPM droop
Gravity fed
hydraulics
Airspeed (kts)
Load
factor
1
2
3
0
50 100 150 2000
OFE
SFE
Control
loads
Blade
stall
Tail
stress
RPM droop
Gravity fed
hydraulics
A
D
S
-

ensure safety, see Fig. 1.
In this first experimental assessment of the helicopter’s handling qualities, the first problems
arise, as more often than not, large differences arise between the theoretical predictions and
the experimentally-determined pilot judgments. The gaps that occur are bridged by
applying optimisation techniques using the simulation models developed in preliminary
design, to improve the designs of helicopter, load alleviation system and flight control
system (Celi, 1991; Celi, 1999; Celi, 2000; Fusato & Celi, 2001, Fusato & Celi, 2002a,2002b;
Ganduli, 2004; Sahasrabudhe & Celi, 1997). Computational approaches have three important
disadvantages, however. First, many designs that “roll out” of the procedure are unfeasible,
the optimisation “pushing” the solution along the boundaries of the problem and not inside
of the feasible region. Second, optimising for ADS-33 requires calculations of the helicopter
time-domain responses, and the numerical methods become computationally very intensive
(Sahasrabudhe & Celi, 1997; Tischler et. al., 1997) Third, and most important, the lack of
quantitative, validated helicopter pilot models, capable of accurately predicting the effects of
helicopter vibrations on pilot control behaviour, prevents the proper inclusion of pilot-
centred considerations in mathematical optimization techniques (Mitchell et. al., 2004;
Tischler et. al., 1996)
Whereas the first and second disadvantages are common in multi-dimensional design
problems, the lack of knowledge on how helicopter vibrations affect pilot performance is a
typical and fundamental problem of modern helicopter design (Mitchell et. al., 2004,
Padfield, 1998). Although ADS-33 proposes criteria and missions regarding helicopter
limits, these only characterize a helicopter’s performance, and do not require an adequate
knowledge of helicopter vibratory loads (Kolwey, 1996; Tischler et. al., 1996). This
shortcoming stems from the fact that, when the ADS-33 criteria were defined, helicopter
missions were not so demanding, and the vibratory loads associated with them were low. In
the last twenty years, however, ever-increasing performance requirements and extended
flight envelopes were defined, for reasons of heavy competition, demanding manoeuvres
that impose heavy vibrations on both structure and pilot. These vibrations, combined with
cross-coupling effects, rapidly lead to pilot overload and degradation in performance
(Padfield, 2007).

alternative metrics proposed in the 90’s for better capturing the transient characteristics of
the agility; Then, based on the rational developments of the metrics from the previous two
sections, fourth section will propose the new approach that can better quantify the agility
from the designer point of view. Finally, general conclusions and potential extension of this
work will be discussed.
2. Traditionally design of aircraft for pitch agility
One of the most important flying quality concepts defining the upper limits of performance
is the so-called “agility”. Generally, it is well known that the level of performance achieved
by the pilot depends on the task complexity. Fig. 2 presents generically this situation,
showing that there is a line of saturation up to which the pilot is able to perform optimally
the specified mission; increasing the task difficulty above this line leads quickly to stress,
panic and even incapacity to cope anymore with the task complexity and blocking,
sometimes with fatal consequences.
It is difficult to point precisely to the origins of the concept of agility but probably these
go back to the moment when it was realized that, in a combat, a “medium performance”
fighter could win over its superior opponent if the first aircraft possesses the potential for
faster transient motions, i.e. superior agility. In its most general sense, the concept of
agility is defined with respect to the overall combat effectiveness in the so-called
“Operational agility”. Operational agility according to measures the ‘ability to adapt and
respond rapidly and precisely, with safety and poise, to maximize mission effectiveness’(McKay,
1994). In the mid 80’s a strong wave of interest arose in seeking metrics and criteria that
could quantify the aircraft agility (Mazza, 1990; McKay, 1994). However, there have been
developed almost as many criteria of agility as there were investigators in the field. The
problem was partially due to the lack of coordination in the research studies performed
but also due to a disagreement on the most fundamental level: there simply was very little
agreement on what agility was.

Rotorcraft Design for Maximized Performance at Minimized Vibratory Loads

241

m
a
n
c
e
Optimum
Stress
Panic
Block
Level
performance
High
Low
High
Low
Level task difficulty
Relation between
TASK DIFFICULTY AND PERFORMANCE

Fig. 2. Correlation between task difficulty and performance
Within the framework of operational agility one can see agility as a function of the airframe,
avionics, weapons and pilot. Airframe agility is probably the most crucial component in the
operational agility as it is designed in from the onset and cannot be added later. The present
chapter focuses on airframe agility and within this, the chapter will relate to the airframe
agility in the pitch axis.
A large number of agility metrics have been proposed during the years to determine the
aircraft realm of agility. The AGARD Working Group 19 on Operational Agility (McKay,
1994) put together all the different metrics and criteria existing on agility and fit them into a
generalizable framework for further agility evaluations. The present section presents the
traditional approach on pitch agility using as example a tiltrotor aircraft. This specific

The first class of metrics developed to quantify the agility corresponds to the so-called
“transient metrics”. The transient class contains metrics which can be calculated at any
moment for any manoeuvre. For pitch agility these metrics are pitch rate (entitled attitude
manoeuvrability metric) and accelerations along the axes a
x
, a
y
, a
z
(entitled manoeuvrability
of the flight path). These metrics are next studied for the pull up manoeuvres flown with the
FXV-15 in a 1 second pulse given from the initial trim at 120kts in helicopter mode and 300
kts in airplane mode. The presentation of the transient metric information is best achieved
through a time history plot. Fig. 4 presents the transient metrics parameters of pitch rate q
and vertical acceleration n
z
(in the form of normal load factor). Looking at Fig. 4 one may see
local maxima in the metric parameters q and n
z
illustrating peak events in the agility
characteristics. This clearly demonstrates that in a “real” manoeuvre sequence, the agility
characteristics occur at key moments, depending on the manoeuvre.
2.2 Experimental metrics
The above conclusion gave the idea to develop a new class of agility metrics, the so-called
“experimental metrics” formulated as discrete parameters during a real manoeuvre
sequence. These metrics are actually the basic building blocks for understanding the agility
and can be related to flying qualities and aircraft design. The metrics describing pitch agility
during aggressive manoeuvring in vertical plane were defined by (Murphy et. al., 1991) and
are described in the next section. They referred to the ability of an aircraft to pint the nose in
at an opponent and commented that what was not clear in such manoeuvres was the

z
Forward flight V=120 kts 1 sec pulse
Helicopter mode
Pitch rate q
(deg/sec)
Load Factor
n
z
0 1 2 3 4 5 6
-10
0
10
0 1 2 3 4 5 6
1
1.5
2
2.5
time (sec)
Forward flight V=300 kts 1 sec pulse
Airplane mode
time (sec)
0 1 2 3 4 5 6
0
0.5
1
0 1 2 3 4 5 6
-5
0
5
0 1 2 3 4 5 6

0 1 2 3 4 5 6
-10
0
10
0 1 2 3 4 5 6
1
1.5
2
2.5
time (sec)
0 1 2 3 4 5 6
-10
0
10
0 1 2 3 4 5 6
1
1.5
2
2.5
time (sec)
Forward flight V=300 kts 1 sec pulse
Airplane mode
time (sec)

Fig. 4. Transient agility metrics for pull-up manoeuvres with the tiltrotor
2.2.1 Peak and time to peak pitch rates
The peak and time to peak pitch rates metrics were proposed by (Murphy et. al., 1991) for
fixed wing aircraft. These metrics measure the time to reach peak pitch rate and the
corresponding pitch rate. Fig. 5 presents charts of peak pitch rate and time to reach this peak
as a function of the velocity for the tiltrotor flying pull-up manoeuvres of increasing pulse

t

1

s
e
c
1
i
n

i
n
p
u
t

5

s
e
c
v
H90
o
H90
o
C60
o
A0

A0
o
q
pk
(deg/sec)
Velocity (kts)
H90
o
= 90
o
nacelle, helicopter mode
C60
o
= 60
o
nacelle, conversion mode
A0
o
= 0
o
nacelle, airplane mode
I
n
c
r
e
a
s
i
n


i
n
p
u
t

1

s
e
c
1
i
n

i
n
p
u
t

5

s
e
c
v
H90
o

o
C60
o
A0
o
A0
o
q
pk
(deg/sec)
Velocity (kts)
H90
o
= 90
o
nacelle, helicopter mode
C60
o
= 60
o
nacelle, conversion mode
A0
o
= 0
o
nacelle, airplane mode
I
n
c
r

i
n
i
np
ut

1

s
e
c
1
i
n

i
n
p
u
t

2

s
e
c
1
i
n


o
H90
o
H90
o
H90
o
H90
o
C60
o
C60
o
C60
o
C60
o
A0
o
A0
o
Time to Peak pitch rate
in pull-up manoeuvres
(sec)
pk
q
t |
Velocity (kts)
fast
slow

2

s
e
c
1
i
n

i
n
p
u
t

3

s
e
c
1
i
n

i
n
p
u
t
4

Time to Peak pitch rate
in pull-up manoeuvres
(sec)
pk
q
t |
Velocity (kts)
fast
slow

Fig. 5. Peak and time to peak pitch rates in pull-up manoeuvres
2.2.2 Peak and time to peak pitch accelerations
(Murphy et. al., 1991) considered the so-called peak and timer to peak pitch accelerations as
the primary metrics for pitch motion agility. The time to peak acceleration provides insight
into the jerk characteristics of pitch motion: if it is too slow, then the pilot may complain that
the aircraft is too sluggish for tracking-type tasks; if it is too fast, then the pilot may
complain of jerkiness or over-sensitivity. Fig. 6 presents charts of peak and time to leak pitch
acceleration as a function of velocity when flying pull-ups manoeuvres. One can see that as
the velocity increases the pilot is able to obtain higher pitch accelerations but as is passing
from the helicopter to aircraft mode this capability diminishes. For fixed wing aircraft,
(Murphy et. al., 1991) commented on the differences in the data for the peak accelerations in
the body and wind axes. This effect has implications on the pilot selection of flight path or
nose pointing control during manoeuvring.

Rotorcraft Design for Maximized Performance at Minimized Vibratory Loads

245 0 20 40 60 80 100 120 140 160 180 200

o
nacelle, helicopter mode
C60
o
= 60
o
nacelle, conversion mode
A0
o
= 0
o
nacelle, airplane mode
H90
o
H90
o
H90
o
C60
o
C60
o
A0
o
1i
n

i
n
p

i
n

i
n
p
u
t

3

s
e
c
1
i
n

i
n
p
u
t

5

s
e
c
0 20 40 60 80 100 120 140 160 180 200

o
nacelle, helicopter mode
C60
o
= 60
o
nacelle, conversion mode
A0
o
= 0
o
nacelle, airplane mode
H90
o
H90
o
H90
o
C60
o
C60
o
A0
o
1i
n

i
n
p

i
n

i
n
p
u
t

3

s
e
c
1
i
n

i
n
p
u
t

5

s
e
c


H90
o
H90
o
C60
o
A0
o
1
i
n

i
n
p
u
t

1

s
e
c
1
i
n

i
n
p

s
i
n
g

p
u
l
s
e

d
u
r
a
t
i
o
n
fast
(sec)
0 20 40 60 80 100 120 140 160 180 200
0
0.005
0.01
0.015
0.02
0.025
0.03
0.035

n

i
n
p
u
t

1

s
e
c
1
i
n

i
n
p
u
t

3

s
e
c
1
i


d
u
r
a
t
i
o
n
fast
(sec)

Fig. 6. Peak and time to peak pitch angle acceleration in pull-ups with the tiltrotor
2.2.3 Peak and time to peak load factor
Peak and time to peak load factor metrics describe the peak and the transition time to the
peak normal load factor during a manoeuvre in pitch axis. They can be used at best to
determine the flight path bending capability of an aircraft. Fig. 7 presents these two
metrics as a function of the velocity for the tiltrotor example. One may see that as the
velocity increases the pilot is able to pull more g’s as going from the airplane to helicopter
mode.

Aeronautics and Astronautics

246
0 20 40 60 80 100 120 140 160 180 200
1
1.1
1.2
1.3
1.4


3

s
e
c
1
i
n

i
n
p
u
t

5

s
e
c
H90
o
H90
o
H90
o
H90
o
C60

o
nacelle, airplane mode
0 20 40 60 80 100 120 140 160 180 200
1
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
1.9
2
1
i
n

i
n
p
u
t

1

s
e
c
1

o
H90
o
H90
o
H90
o
C60
o
C60
o
C60
o
A0
o
A0
o
A0
o
Peak normal factor
in pull-up manoeuvres
n
z pk
(g’s)
Velocity (kts)
H90
o
= 90
o
nacelle, helicopter mode

A0
o
A0
o
A0
o
A0
o
C60
o
A0
o
A0
o
C60
o
H90
o
H90
o
H90
o
Velocity (kts)
pkz
n
t |
(sec)
Time to Peak normal load factor
in pull-up manoeuvres
0 50 100 150 200 250 300

o
C60
o
H90
o
H90
o
H90
o
Velocity (kts)
pkz
n
t |
(sec)

Fig. 7. Peak and time to peak normal load factor
2.2.4 Pitch attitude quickness parameter
One of the most important pitch agility metrics introduced by ADS-33 helicopter standard
(ADS-33, 2000) is the so-called “pitch attitude quickness” parameter and is defined as the
ratio of the peak pitch rate to the pitch angle change:


1
sec
def
pk
q
Q



1.5
2
2.5
1 sec
2 sec
3 sec
4 sec
5 sec
1 sec
1 sec
1 sec
2 sec
3 sec
4 sec
5 sec
5 sec
5 sec
3 sec
M
I
L

S
T
D

1
7
9
7

v
e
l

1
/
2

b
o
u
n
d
a
r
y
60kts,1in helicopter mode
120kts, 1in helicopter mode
120kts, 1in airplane mode
300kts, 1in airplane mode
Level 1 MIL
Level 2 MIL
Level 1 ADS
Level 2 ADS

sec/1


pk
q

S
T
D

1
7
9
7
A

L
e
v
e
l

1
/
2

b
o
u
n
d
a
r
y
A
D

Level 1 ADS
Level 2 ADS
0 5 10 15 20 25 30
0
0.5
1
1.5
2
2.5
1 sec
2 sec
3 sec
4 sec
5 sec
1 sec
1 sec
1 sec
2 sec
3 sec
4 sec
5 sec
5 sec
5 sec
3 sec
M
I
L

S
T

3
3
E

L
e
v
e
l

1
/
2

b
o
u
n
d
a
r
y
60kts,1in helicopter mode
120kts, 1in helicopter mode
120kts, 1in airplane mode
300kts, 1in airplane mode
Level 1 MIL
Level 2 MIL
Level 1 ADS
Level 2 ADS

.

Aeronautics and Astronautics

248

ln(0.1)
def
im
f
am
Tt
A
Tt





(2)
where
i
Tt
is the control pulse duration (1 to 5 sec), Ta is the time to reduce the pitch angle
to 10% of the peak value achieved and m is the fundamental first-order break frequency or
pitch damping which for this simple case represents the maximum achievable value of
quickness. Fig. 9 illustrates the variation of Af with 
m
t -thus the quickness. The values
considered for 

o
nacelle helicopter mode
120 kts, 60
o
nacelle conversion mode
Low moderate
agility set
by ADS-33
High agility

m
t
A
f
0 2 4 6 8 10 12 14 16 18
0.4
0.45
0.5
0.55
0.6
0.65
0.7
0.75
0.8
0.85
0.9
Hover, 90
o
nacelle, helicopter mode
60 kts, 90

q
s
z
q
CAP
n


(3)

Rotorcraft Design for Maximized Performance at Minimized Vibratory Loads

249
MIL standard defines CAP boundaries for fixed-wing aircraft. Fig. 10 presents the agility
of the FXV-15 CAP as a function of speed (60 kts, 120 kts and 200 kts) in the MIL
boundaries. Looking at this figure one can see the tiltrotor meets Level 1 MIL performance
and some degradation to Level 2 is seen when flying at high speeds in airplane mode.

10
-1
10
0
10
-1
10
0
10
1
SP


)/sec/(
2
gradCAP
Level 1
Category A
flight phases
Level 2
Level 3
V=60kts H90
o
V=120 kts C60
o
V=200 kts A0
o
V=300 kts A0
o

Fig. 10. CAP boundaries for the tiltrotor
3.3 Rate pitch quickness
For helicopters a similar metric to CAP was introduced by (Padfield & Hodkinson, 1993).
This metric was called ‘rate pitch quickness’ and was defined as the ratio of pitch
acceleration to the pitch angle change:


2
sec
def
pk
q
Q

0.04 0.05 0.06 0.07 0.08 0.09 0.1 0.11 0.12
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
Rate quickness

m
t
pk


Q
m

1
60 kts, 90
o
nacelle, helicopter mode
120 kts, 60
o
nacelle helicopter mode
200 kts, 0

0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
Rate quickness

m
t
pk


Q
m

1
60 kts, 90
o
nacelle, helicopter mode
120 kts, 60
o
nacelle helicopter mode
200 kts, 0
o
nacelle airplane mode


z
n
QCAP





(5)
Equation (5) gives the idea that rate quickness and CAP can be related to each other through
a new metric which will be presented in the next paragraph.
4.1 Agility quickness metric as a measurement of performance
As a potential successful metric for agility, (Pavel & Padfield, 2002) proposed a new metric for
characterizing agility, the so-called ‘agility quickness’ defined as the ratio of peak quasi-steady
normal acceleration
q
s
z
p
k
n
in g units corresponding to a step change in flight path angle :

'
deg
qs
def
zpk
n

physical interpretation, in the limiting case for small-amplitude maneuvers giving the heave
damping, for large amplitudes giving the attitude quickness (Pavel & Padfield, 2002).

0 5 10 15 20 25 30 35 40
0
0.05
0.1
0.15
0.2
0.25
1sec
2sec
3sec
4sec,5sec
1sec
1sec
2sec
3sec
L
e
v
e
l

1
/
2

Ag
i






n
qs
pkz
Q
(g’s/deg)
(
de
g)


Test data
0 5 10 15 20 25 30 35 40
0
0.05
0.1
0.15
0.2
0.25
1sec
2sec
3sec
4sec,5sec
1sec
1sec
2sec

o
120kts, 1in airplane mode A0
o
300kts, 1in airplane mode A0
o
60kts,1in helicopter mode H90
o
120kts, 1in helicopter mode H90
o
120kts, 1in airplane mode A0
o
300kts, 1in airplane mode A0
o
Level 1
Level 2











n
qs
pkz
Q

M
F
lbf ft
QQ
W

  


  

  
(7)
where
vib
p
k
F
,
vib
p
k
M
represent the peak amplitudes in the critical vibratory components for
respectively hub shears and hub moments corresponding to a change  in flight path
angle. The peak load amplitude can be calculated by using the FFT and time representations
of the hub shears (
Fx hub
, F
y hub

(deg)


1 sec
5 10 15 20 25 30 35
0
1
2
3
4
5
6
x 10
-3
2 sec
3 sec
4 sec
5 sec
1 sec
2 sec
3 sec
4 sec
5 sec
60 kts
120 kts
0 2 4 6
8
-200
0
200

e
v
e
l

1
/
2

v
i
b
r
a
t
o
r
y

b
o
u
n
d
a
r
y

Helicopter Mode
(a)

3 sec
4 sec
5 sec
60 kts
120 kts
0 2 4 6
8
-200
0
200
400
0 2 4 6
8
-200
0
200
400
0 2 4 6 8
0
200
400
600
0 2 4 6 8
0
200
400
600
hubFz
(lbf)
hubFz


1
/
2

v
i
b
r
a
t
o
r
y

b
o
u
n
d
a
r
y

Helicopter Mode
(a)



/

120 kts, 2/rev
300 kts, 2/rev
300 kts, 3/rev
120 kts, 3/rev
120 kts, 2/rev
300 kts, 3/rev
300 kts, 2/rev
1 sec
2 sec
3 sec
4 sec
5 sec
1 sec
2 sec
3 sec 4 sec
5 sec
0 2 4 6
800
900
1000
0 2 4 6
800
900
1000
t (sec)
hubFz
(lbf)
f
vib
pkhubz

-4
120 kts, 3/rev
120 kts, 2/rev
300 kts, 2/rev
300 kts, 3/rev
120 kts, 3/rev
120 kts, 2/rev
300 kts, 3/rev
300 kts, 2/rev
120 kts, 3/rev
120 kts, 2/rev
300 kts, 3/rev
300 kts, 2/rev
300 kts, 3/rev
300 kts, 2/rev
1 sec
2 sec
3 sec
4 sec
5 sec
1 sec
2 sec
3 sec 4 sec
5 sec
0 2 4 6
800
900
1000
0 2 4 6
800

pkhubz
f
vib
pkhubz
hubFz
(lbf)
300 kts, 1 sec pulse
120 kts, 1 sec pulse
t (sec)
(b)
Airplane mode

Fig. 13. Vibratory quickness envelopes for the critical components of the hub vertical shear
during a pull-up maneuver

Rotorcraft Design for Maximized Performance at Minimized Vibratory Loads

253
For helicopter mode it was plotted a presumable vibratory quickness boundary as derived in
(Pavel & Padfield, 2003) when flying piloted yo-yo’s in the simulator with the UH-60A
helicopter. It was there showed that actually, increasing the flight path change enables the
pilot to pull more g’s of course but also increases the vibratory activity in the rotor. The
presumable vibratory boundary would mean then that the structural designer would aim for a

5 101520253035
0
50
100
150
200









m
vib
pkblz
l
Q
(lbf ft/deg)
(deg)


0 2 4 6 8
0
2000
4000
6000
0 2 4 6 8
0
2000
4000
6000
Blade m
z
(lbf ft)

5 sec
3 sec
3 sec3 sec
4 sec
5 sec
4 sec
5 sec
4 sec
5 sec
60 kts, 2/rev
120 kts
2/rev
60 kts, 1/rev
60 kts, 2/rev
120 kts, 1/rev
120 kts, 2/rev
60 kts, 1/rev
60 kts, 2/rev
120 kts, 1/rev
120 kts, 2/rev
120 kts, 1/rev
120 kts, 2/rev









pkblz
Blade m
z
(lbf ft)
0 2 4 6 8
0
2000
4000
6000
0 2 4 6 8
0
2000
4000
6000
0 2 4 6 8
0
2000
4000
6000
Blade m
z
(lbf ft)
t (sec)
t (sec)
60 kts, 1 sec pulse
120 kts, 1 sec pulse
m
vib
pkblz
m

1 sec
1 sec
2 sec
3 sec
4 sec
5 sec
2 sec
3 sec
4 sec
5 sec
1 sec
2 sec
3 sec
4 sec
5 sec
1 sec
2 sec
3 sec
4 sec
5 sec
0 2 4 6
3000
4000
5000
6000
7000
0 2 4 6
6000
8000
10000

300 kts, 1/rev
300 kts, 2/rev
120 kts, 1/rev
120 kts, 2/rev
300 kts, 1/rev
300 kts, 2/rev
300 kts, 1/rev
300 kts, 2/rev
(lbf ft/deg)
(deg)


0 10 20 30 40 50 60
0
10
20
30
40
50
60
120 kts
1/rev
300 kts
1/rev
120 kts, 2/rev
300 kts
2/rev
1 sec
1 sec
2 sec

m
vib
pkblz
Blade m
z
(lbf ft)
120 kts, 1 sec pulse
300 kts, 1 sec pulse
0 2 4 6
3000
4000
5000
6000
7000
0 2 4 6
6000
8000
10000
0 2 4 6
6000
8000
10000
Blade m
z
(lbf ft)
m
vib
pkblz
m
vib