F-15
FLIGHT FLUTTER TEST PROG
Henry Katz, Francis
6,
Foppe,
and Daniel
T.
Grossrnan
McDonnell Aircraft Company
ABSTRACT
The
F-15
flight flutter
test
program
is
described.
Special emphasis
is
given to
test
philosophy, data reduction techniques, and
test
results. The
approach utilized for this program not only provided the data necessary to
establish
a
measure of stability for
all”
important flutter mechanisms
at
each
test
point, but also allowed extrapolation of the
data to actually define
all
critical flutter boundaries. Such quantitative information
was
not only use-
ful to definitively establish the flutter status of the aircraft
as
it
was
flown, but also provided
a
solid foundation for assessing the impact of any
future design changes.
INTRODUCTION
With very few exceptions, flight flutter
conducted on
a
rather qualitative basis; that
the damping available
at
the
test
point being
testing has historically been
is,
the only data obtained
were
flown,
with
a
possible extrapo-
There generally
was
no lation of damping
trends
of the lower damped-modes.
quantitative indication
as
to the amount of stability remaining
at
any given
point.
The goal
set
for the
F-15
flight flutter
test
program
was
to provide
a
system which would
-
accurately,
quickly, and with
a
high degree of visi-
bility
-
allow extrapolation of the data to actually define
critical
flutter
boundaries, in addition to providing
a
measure of stability for
-
all
the
important mechanisms
at
each
test
point. This
was
accomplished by designing
the aircraft excitation and instrumentation systems to provide high-quality
response data which could be speedily and accurately converted to complete
(i.e.$
concerning
all
modes of interest) damping and frequency information
which
-
in turn
-
could be utilized for reliable flutter margin predictions
by the methods
of
Reference
1.
The accuracy and reliability of these flight
flutter
test
system data not only permitted the pursuit of
a
minimum flutter
margin design concept (and with
it
optimum weight
-
see
Reference
2)
through
inflight verification
of
actual flutter margins of safety, but also provided
a
quantitative basis
on which to quickly
assess
the impact of future design
changes.
This paper concerns
itself primarily with
test
philosophy, data reduction
techniques and systems, and
test
results.
tions
are
covered in Reference
3.
Aircraft systems and
test
opera-
413
ABBREVIATIONS
AND
SYMBOLS
CRT
H
PC
Im
KEAS
M
NBFM
PCM
Q
Re
T~~
T-plot
vE
vT
lJ
w
w
n
cathode ray tube
structural damping coefficient
pressure altitude, calibrated
imaginary part of transfer function
at
frequency
w
knots eqdvalent airspeed
left-hand side
Mach number
narrow band frequency modulation
pulse code modulation
dynamic pressure
real
part of transfer function
at
frequency
w
right-hand side
temperature
at
altitude
transmissibility plot
equivalent airspeed
true airspeed
ratio of structural
mass
to aerodynamic
mass
density
at
altitude
frequency
natural frequency
APPROACH
The quantitative definition of F-15 flutter boundaries from flight
test
data
was
accomplished by means of the Flutter Margin technique of Reference
1.
This technique permits reliable prediction of flutter speeds on the basis of
subcritical
test
data.
Its
application requires knowledge
-
at
every
test
414
point
-
of damping
flutter mechanisms.
tained from
a
unique data reduction facility operating on the aircraft data
provided by the
exciter
and instrumentation systems described in detail
in
Reference
3.
frequency of every mode involved in potentially critical
This complete damping and frequency information
was
ob-
The method of Reference
1
assumes that data
is
obtained
at
different
vel-
ocities while maintaining the
same
aerodynamic center and lift curve slopes.
Strictly speaking,
it
is
therefore valid only when Mach number
is
kept con-
stant.
The
emphasis in this program
was,
therefore, to obtain constant Mach
number cross sections which could be utilized for extrapolation
of
the data to
projected flutter boundaries.
number cross sections to obtain
a
high subsonic extrapolation point for refer-
ence and for correlation with subsonic analyses and wind tunnel
tests.
primary cross section
was
taken
at
M
=
1.2,
the F-15
sea-level
design Mach
number. Additional Mach numbers
at
which cross sections
were
taken
were
selected
on the basis of analyses, wind tunnel
tests,
and
the early portion of
the
test
program, which
was
dedicated to determining
critical
Mach numbers by
obtaining
test
data from
0.73
to 1.5 Mach numbers while maintaining
a
constant
dynamic pressure
(442
KEAS).
The data obtained
at
this constant dynamic pres-
sure
were
then reduced in
terms
of the Flutter Margin parameter to aid in
sel-
ecting
critical
Mach numbers for the various
critical
flutter mechanisms.
M
=
0.80
was
selected
as
one of the primary Mach
AnotBer
Figure
1
shows Flutter Margin
as
a
function of Mach number for one of the
Basically,
a
subsonic and
a
supersonic level can be observed
-
with
critical
flutter mechanisms:
rotation.
some secondary altitude (or
11)
effects. The highest Mach number
at
which the
lower subsonic
level
occurs
is
just slightly above
M
=
0.9.
data, and
similar
results for other modes,
M
=
.93
and
M
=
1.1
were
selected
as
additional primary Mach numbers and
'a
cross .section with three or more
flight
test
points
was
taken
at
these points.. Secondary Mach numbers of
0.98,
1.04,
and 1.15 (with only two flight
test
points)
were
selected to provide
intermediate checks
at
a
minimum cost in
terms
of flights required.
antisymmetric boom torsion versus stabilator
Based on such
A
typical flutter prediction
at
a
critical
Mach number
is
shown in Figure
2.
It
should be noted that the extrapolation
is
made on the basis
of
a
para-
bola through the flight
test
points and the zero airspeed point. Wind tunnel
test
data have shown that the actual flutter speed
will
be offset slightly from
the parabolic extrapolation toward
a
point obtained by
a
straight-line
extra-
polation through ,the inflight
test
points alone.
convex (curving toward the abcissa), the results
will
be slightly conservative,
and the parabola
will
be
used to establish the flutter boundary. In the
case
of
a
concave parabola, the straight-line extrapolation
will
be more conserva-
tive and should therefore
receive
more consideration.
Thus, when the parabola
is
Although, in
its
strictest
sense, the prediction method
is
invalid for
constant altitude data, secondary extrapolations
were
made
at
constant
alti-
tudes of 1525 and
10
400
m
(5000 and
34
000
ft) by taking advantage of the fact
that, once supersonic flow
is
established,
the
aerodynamic center and lift
curve slope
are
again quite
well
behaved.
extrapolation
is
shown in Figure
3.
An example of
a
constant altitude
415
Figure
4
shows the points
at
which flight flutter data
were
taken and also
indicates the direction of the extrapolations,
EXCITER
SYSTEM
The aircraft exciter system, described ;In detail in Reference
3,
furnishes
the known forcing function to which aircraft response can be measured.
It
has
the capability to oscillate either the stabilators or the ailerons. Either
set
of control surfaces can be excited symmetrically (in-phase) or antisymmetrically
(out-of-phase). Excitation can be provided
either
in the form of sweeps
(slowly
varying frequency through
a
given range) or dwells/decays
(excitation
at
a
given
frequency for
a
certain short
time,
followed by an abrupt exciter shut-off).
INSTRUMENTATION
SYSTEM
As
described in Reference
3,
the aircraft instrumentation system consists
primarily of strain gages, which provide not only the desired response charac-
teristics but also permit relatively independent measurement of the modes of
interest. This
is
important, since
it
is
desired to separate the response in
the various modes, especially when these modes
are
close to each other in
fre-
quency.
Figure
5
shows the sensor locations on the aircraft and also denotes
the primary degree of freedom to be measured by each.
DATA
SYSTEM
The heart of the F-15 flight flutter
test
system
is
the data handling
system,
It
reduces the information provided by aircraft instrumentation in
response
to
the forcing function furnished by the aircraft exciter system to
several
forms useful to the flutter engineer.
The
F-15
data system can be divided into two parts:
a.
The on-line system, which aids in the assessment of stability
at
the
test
point being flown
at
the
time;
and
b.
The post-flight system, which provides
a
complete evaluation of
all
the data available to aid in arriving
at
damping and Flutter Margin
trends
so
as
to establish the flutter safety of the next point(s) to
be flown and also to extrapolate to predicted flutter boundaries.
On-Line
Data
System
This portion of the data system provides
real-time
information
as
to
the
stability of the aircraft
at
the point(s) being flown.
represented in Figure
6.
As
can be seen,
it
involves
a
mixture of conventional
It
is
schematically
416
displays (strip recorders and Lissajous figures) and
less
conventional informa-
tion
in
the form of digitally computed transmissibility plots,
Strip chart recorders
Thirty-two channels of narrow band frequency modulated
(NBFM)
data
are
displayed
on
four strip chart recorders.
strain gages to describe aircraft response and forcing functions.
The
channels
are
arranged
so
that components of critical flutter mechanisms (for example,
boom
lateral
bending and fin bending)
are
side-by-side to enable close monitor-
ing for the development of any correlktion between these degrees of freedom.
These channels present the output of
The data displayed on the recorders perform the following functions:
a.
Allow observation of any correlation between any two degrees of free-
dom during acceleration into an unexplored flight regime.
lation could indicate the approach to an instability.
Such corre-
b.
Permit
real-time
determination of
critical
modal frequencies during
turbulence excitation.
c.
Obtain the damping of modes of interest whenever dwell/decay excita-
tion
is
utilized.
d,
Indicate the frequencies of maximum response during
a
frequency sweep.
e.
Monitor the quality
of
the forcing function during sweeps.
f. Allow observation of the
level
of turbulence, to determine if acqui-
sition of excitation response data
is
feasible.
Lissajous displays
Four Lissajous figures each
are
displayed on four oscilloscopes.
The
pairs
are
chosen to provide
maximum
information on the stability of potential
flutter mechanisms.
gages, e.g. from boom
lateral
bending and fin bending, against each other. The
signal from any of the thirty-two NBFM channels can be selected for either
axis
of any of the
sixteen
Lissajous figures. These figures
are
used to observe the
phase and frequency relationship between important modal pairs during
accelera-
tion into an unexplored flight regime,
and
are
also used to observe the fre-
quency dependence of amplitude and phase during sweeps.
This
is
accomplished by "beating" the signals from two
Transmissibility plots
Transmissibility plots
are
obtained by normalizing response parameters to
a
parameter which
is
a
measure of the forcing function,
e.g. stabilator hinge
moment when the stabilators
are
oscillated.
digitized aircraft response data and present amplitude and phase information
as
a
function of frequency.
These plots
are
computed from
Figure
7
shows
a
typical transmissibility plot.
417
One
real-time
transmissibility p
t
(T-plot) for
a
se
ata
channel
is
displayed on
a
cathode ray tube (C
)
during
a
sweep.
obtain response information for the
critical
mode of
interest.
is
more accurate than can be obtained from the strip recorders in
a
real-time
environment.
A
side benefit of the
real-time
T-plot
is
the immediate acquisi-
tion of corrected flight parameters (equivalent airspeed, Mach number, altitude,
etc.)
t
is
used to
The information
which
are
also displayed on the
CRT.
Hard-copy transmissibility plots for
six
selected data channels
are
pro-
duced on
a
Gould plotter within
90
seconds after
a
sweep.
these plots, in conjunction
with
that already obtained from
the
real-time
T-plot, affords the opportunity to obtain
a
check on frequency and damping
values for most of the modes of interest.
frequencies almost immediately permits the selection of accurate dwell fre-
quencies during the flight, thus providing good-quality decay data.
The information from
The ability to determine resonant
Post Flight
Data
System
This system involves
a
complete evaluation of
all
the data available to
arrive
at
damping and Flutter Margin trends
so
as
to establish the flutter
safety of the next
test
point(s), and also to extrapolate to predicted flutter
boundaries.
formation by the methods of Reference
4
and to provide the data storage and
computational capabilities required for the Flutter Margin calculations and
predictions,
As
can be seen,
there
is
considerable madmachine interaction.
A
digital computer
is
used to
extract
frequency and damping in-
Figure
8
shows the data flow in this system.
Extraction of frequency and damping data
After
the completion of each
test
flight, transmissibility plots
are
gen-
erated from the onboard tape for
all
parameters of interest, nominally
12
per
sweep,
6
for each side of the aircraft. Frequency and damping
are
obtained
manually from these transmissibility plots by observing resonant peaks and
calculating damping on the basis of bandwidth and/or the slope of the phase
shift
e
This information
is
combined with frequency and damping data ob rained
from the dwell/decays and the output generated by the automatic modal
extrac-
tion technique.
computer capacity there.
)
(The
latter
is
performed in St, Louis because of the larger
In the automatic technique, based on Reference
4,
the resonant frequencies
are
considered to occur when the derivatives of the Argand arc-length reaches
a
maximum with respect to frequency. These
maxima
are
extracted using
a
least-
squares straight-line-slope testing technique. Plots of the derivative
are
provided to the flutter engineer by the computer (see Figure
9).
that
a
Hanning smoothing technique, applied to both the transfer function and
to the derivative data,
substantially reduces the error induced by experimental
scatter
(turbulence,
etc.).
It
was
found
To automatically obtain the damping values from the transfer function,
the
The bandwidth of these segments depends on the frequency
multi-degree of freedom function
is
initially separated into single degree of
freedom segments.
418
separation of the modes and
is
not
the
same
for
all
modes, Damping values
ar
extracted for each of the segments by first fitting
a
le
-squares
circle
to
the transfer function data in the complex plane.
culated for each data point used to define the
circle,
utilizing the equation
Damping values
are
then
cal-
22
0
--w
ww
Im
n
g=--
Re
.
The damping values obtained on the basis of the points
n
farthest from the natural frequency
are
considered to be the most accurate,
since they
are
least
sensitive
to any error in the frequency
term.
emphasis
is
placed
on
the four poirits which
are
farthest from the resonant peak
(two on each side).
average, in
a
table included with the derivative plot, Figure 9.
Therefore,
The four damping values
are
presented, along with the
Generally, the automatically extracted modes
will
fall into three
cate-
gories:
good
modes, other physical modes, and fictitious modes. In
a
"good"
mode the four damping values
will
be very close to each other and the
same
resonant frequency
will
be shown in the tabulation, the derivative plot and the
original transmissibility plot. For example, on Figure 9 the 18.6
Hz
boom
lateral
bending mode and the 33.8
Hz
fin tip
roll
mode
are
the only good modes
to be extracted from this particular gage.
The second category of modes has the following characteristics:
a.
Similarity in damping of the two "lower" points and the two "upper"
points
,
but
a
difference between the ''upper" and "lower" points.
b.
Good phase-shift
at
the resonant frequency.
c.
Different resonant frequencies indicated by the tabulation, the deri-
vative plot
,
and the transmissibility plot.
Such modes
are
generally physical,
i.e.
real,
modes of the airplane, but
this particular gage
is
not the best
to discern them; they
are
better picked
off from
some
other sensor. The 9.9, 13.4, 23.5 and 26.7
Hz
modes tabulated
in Figure 9 fall into this category.
The
35.4, 37.3 and 39.8
Hz
modes
are
fictitious and can be recognized
as
such by
:
a.
Unequal damping values within the "low" and "high" points,
b.
Low or even negative damping indications not substantiated by deriva-
tive
and transmissibility plots.
Utilization of frequency and damping data
Frequency and damping data obtained
from
the various sources
are
cross-
plotted versus altitude and Mach number for each mode of interest to make sure
that they
are
properly tracked.
damping versus Mach number
at
a
constant altitude
of
1525
m
(5000 ft).
Figure
10
shows
a
sample plot of frequency and
Two
419
modes, fin bending and boo
1
bending,
are
shown for one side of th
craft, to demonstrate the
r
be
As
is
generally quite consistent,
the higher damped modes
(see
the fin-bending mode in Figure
lo),
there may be
some disagreement between the different bits of information. In such
cases,
the input data
are
reviewed regarding their
relative
merit,
e.g. the quality of
the decay data,
the consistency of the automatically extracted data, and the
adequacy of the manually obtained data,
Based on
a
ju
quality of the different pieces of information,
a
dete tion
is
made on the
"final" frequency and damping values to be used for this mode
and
its
"reason-
ableness"
is
evaluated by reviewing cross-plots versus altitude and Mach number.
This "final" information for each side of the aircraft
is
then entered into
computer storage by means of
a
remote "Execuport" terminal located
at
the
test
site.
These data can be retrieved either in tabular form
or
as
Gould plots of
frequency, damping, and Flutter Margin versus altitude and Mach number.
be seeng the frequency and information
o
fro ous
However,
in some
casesp
especially for some of
At
this point, the following data
are
therefore available to the flutter
engineer:
a.
Plots of frequency and damping versus altitude for each mode of
interest
at
each cross-section Mach number
-
Figure
11
is
an example
of such
a
plot.
b.
Plots of frequency and damping versus Mach number for each mode of
interest
at
each constant altitude cross section
-
see
Figure 10 for
sample data of this kind.
c.
Plots of Flutter Margin versus equivalent airspeed for each modal
combination of
interest
at
each cross-section Mach number
(this
also
includes
a
prediction of the flutter speed based on
a
parabolic ex-
trapolation)
-
see
Figure
12.
d.
Plots of Flutter Margin versus Mach number for each modal pair of
interest
at
each cross-section altitude
-
see
Figure
13.
Constant altitude flutter velocity predictions
are
then obtained by manu-
ally selecting the Mach number from the constant altitude flutter margin plots
at
which supersonic flow characteristics appear to be established (e.g.
M
=
1.18
on the plot in Figure
13),
and utilizing only
test
data above that Mach
number for the supersonic extrapolatiou
at
this altitude.
A
cross-plot
of
all
the
Flutter Margin predictions
is
then made for each
modal pair of interest
(see
Figure
14
for an example) and evaluated in
terms
of
minimum flutter margin.
It
should be noted that, although modes
as
determined
from left-hand and right-hand data
were
tracked independent-ly, on the F-15 they
were
close enough to each other that one flutter boundary could be used to
represent them both,
420
RESULTS
The
modes to be observed during the
F-4.
selected on the basis of the
res
and ground vibration
tests,
The
tracked on this basis
were:
fin first bend
stabilator bending, stabilator pitch, boom
lateral
bending, boom torsion, boom
vertical bending, wing first bending, wing second bending, wing first torsion,
outer wing torsion, and aileron rotation.
Data
obtained for these various modes
were
then evaluated
in
terms
of damp-
ing versus airspeed
at
1525
m
(5000
ft), damping versus altitude
at
the cross-
section Mach numbers (to extrapolate to the damping value to be expected
at
sea
level), and flutter boundaries on the basis of Flutter Margin of various
modal pairs representing potential flutter mechanisms.
Tables
I
and
I1
summarize
the results of these evaluations in
terms
of
minimum predicted flutter margin for the various mechanisms.
that there
are
six flutter mechanisms (three symmetric and three antisymmetric)
with predicted flutter margins between
15
and 20 percent, substantiating the
success of the minimum
weight
design concept pursued on the F-15.
It
can be noted
Based on our experience to date,
we
feel that predictions can reliably be
carried only to
a
velocity which
is
no farther from the
last
test
point than
about
1.5
times
the difference between the first and
last
inflight
test
points.
On
this basis, since our
tests
were
between altitudes
of
6100
and 1525
m
(20
000
and
5000
ft), flutter velocity predictions showing greater than 25%
flutter margin
of
safety have no specific quantitative values attached to them.
Shapes of flutter boundaries
Shapes of predicted flutter boundaries
were
generally either in the form
of
the boundary given in Figure
14,
with Mach numbers between
0.9
and
1.1
being
critical, or
as
shown in Figure
15,
with
the
maximum sea-level Mach number being
critical.
Application to design changes
The quantitative knowledge of actual flutter margins provides
a
firm basis
on which to assess
the impact of prospective design changes. For example,
we
may want to incorporate an aircraft modification which, according to analysis
(which has been substantially verified by correlation with quantitative flight
test
data) and possibly also wind tunnel tests, lowers the flutter speed of
a
certain mechanism by 5%. If
we
have flight
test
data in hand that show that
we
now have
25%
margin
in
this mechanism,
we
not only have considerable confidence
that
we
can go ahead, but
we
also have no need to go into another involved
flight flutter
test
program,
We
have already had several such opportunities to apply the quantitative
F-15 flight flutter
test
data to the evaluation of design changes.
421
ight flutter
test
procedure used on the F-15 provides not only
a
demonstration
of
adequate damping throughout the aircraft flight envelope, but
also permits quantitative demonstration of margin of safety,
information
is
not
only
useful to definitively establish the flutter status of
the
aircraft
as
it
was
flown, but also provides
a
solid foundation on which to
assess
the impact of any future design changes.
Such quantitative
REFERENCES
1.
Zimmerman,
N.H.,
and Weissenburger,
J.T.:
Prediction of Flutter
Onset
Speed Based on Flight Flutter Testing
at
Subcritical Speeds.
of Aircraft,
Vol.
1,
No.
4,
1964.
Journal
2.
Shelton,
J.D.,
and Tucker,
P.B.:
Minimum Weight Design of the F-15
Empennage for Flutter.
AIAA/ASME 16th Structures Meeting, May 1975.
3.
Nash,
D.E.,
Katz,
H.,
and Moody,
W.C.:
F-15 Flight Flutter Testing:
Aircraft Systems and
Test
Operations.
AIAA
1975 Aircraft Systems and
Technology Meeting, August 1975.
4. Kennedy,
C.C.
and Pancu,
C.D.P.:
Use
of Vectors in Vibration Measurement
and
Analysis. Journal of Aeronautical Sciences,
Vol.
14, 1947.
422
MECHANISM
FIN BENDING
vs
BOOM LATERAL BENDING
STABILATOR BENDING
vs
STABILATOR ROTATION
WING FIRST BENDING
vs
OUTER WING TORSION
BOOM VERTICAL BENDING
vs
STABILATOR ROTATION
BOOM LATERAL BENDING
vs
BOOM TORSION
STABILATOR BENDING
vs
BOOM TORSION
STABILATOR ROTATION
vs
BOOM TORSION
FIN BENDING
vs
FIN TORSION
STABILATOR BENDING
vs
BOOM VERTICAL BENDING
BOOM TORSION
vs
BOOM VERTICAL BENDING
FIN TORSION
vs
FIN TIP ROLL
WING FIRST BENDING
vs
WING FIRST TORSION
WING SECOND BENDING
vs
WING FIRST TORSION
WING SECOND BENDING
vs
OUTER WING TORSION
MARGIN OF
SAFETY
15%
19%
20%
25%
>
25%
>
25%
>
25%
>
25%
>
25%
>
25%
>
25%
>
25%
>
25%
>
25%
GP15.07102
TABLE
I1:
MlNlMUM FLUTTER VELOCITY MARGINS FOR ANTI SYMMETRIC MECHANISMS
MECHANISM
FIN BENDING
vs
BOOM LATERAL BENDING
STABILATOR ROTATION
vs
BOOM TORSION
BOOM LATERAL BENDING
vs
BOOM TORSION
WING FIRST BENDING
vs
OUTER WING TORSION
STABILATOR BENDING
vs
BOOM TORSION
BOOM VERTICAL BENDING
vs
STAB1 LATOR ROTATION
WING SECOND BENDING
vs
OUTER WING TORSION
STABILATOR BENDING
vs
STABILATOR ROTATION
FIN BENDING
vs
FIN TORSION
STABILATOR BENDING
vs
BOOM VERTICAL BENDING
BOOM TORSION
vs
BOOM VERTICAL BENDING
FIN TORSION
vs
FIN
TIP
ROLL
WING FIRST BENDING
vs
WING FIRST TORSION
WING SECOND BENDING
vs
WING FIRST TORSION
MARGIN OF
SAFETY
16%
17%
20%
25%
>
25%
>
25%
>
25%
>
25%
>
25%
>
25%
>
25%
>
25%
>
25%
>
25%
423
NORMALIZED
FLUTTER
MARGIN
MACH NUMBER
GP75
07104
Figure
1.-
Flutter margin at constant dynamic pressure.
Antisymmetric
boom
torsion versus stabilator rotation
at
442
KEAS.
PROJECTED FLUTTER
VELOCITY (STRAIGHT
INE EXTRAPOLATION;
FLIGHT TEST
POINTS ONLY)
6000
rn
(20
000
FT)
NORMALIZED
FLUTTER
MARGIN
3000
rn
(IO
000
FT) TEST POlN
1500
rn
(5000
FT) TEST POlN
PROJECTED FLUTTER
VELOCITY (PARABOLIC
EXTRAPOLATION INCL.
ZERO-AIRSPEED POINT)
OWbOllOll
VELOCITY
Figure
2.-
Flutter prediction at constant Mach number.
424
0.2
NORMALIZED
FLUTTER
MARGIN
0
PROJECTED
SUPERSONIC
\
\\
FLUlTER
CRITICAL TRANSONIC
MACH NUMBER
FOR THIS MECHANISM
PROJECTED
0.6
NORMALIZED
FLUTTER
MARGIN
0.4
CRITICAL TRANSONIC
MACH NUMBER
FOR THIS MECHANISM
0.2
0
\
PROJECTED SUBSONIC
FLUTTER VELOCITY\
MACH NUMBER
OP7*0110
7
Figure
3.-
Flutter prediction at constant altitude.
3000
t
I
I
I
I I
AIRSPEED
KEAS
MACH NUMBER
Figure
4.-
F-15
flight flutter test points.
425
TYPE
-_
FIN TORSION RUDDER ROTATION
OF GAGE
0
BENDING
A
TORSION STRAIN GAGES STABlLATOR
0
HINGEMOMEN
0
ACCELEROMETER
(BOTH SIDES GAGED)
OUTER WING BENDING
BENDING (WITH STORES) NDAMENTAL WING
FUNDAMENTAL WING BENDING (CLEAN)
TORSION (CLEAN)
OP,B071010
Figure
5.-
Location
of
instrumentation.
32
CHANNELS
NARROW BAND FM;
1
"REAL-TIME"
TRANSFER FUNCTION TR
DISPLAYED DURING FU
SWEEP ON CATHODE
90
RAY TUBE AFTER SWEEP
COMPLETION
32
NARROW BAND
16
LISSAJOUS
FM PARAMETERS FIGURES
DISPLAYED DISPLAYED
CONTINUOUSLY ON CONTINUOUSLY ON
4
STRIP RECORDERS
4
OSCILLOSCOPES
OP75071012
Figure
6.-
On-line data reduction
of
telemetered signals.
426
PHASE
.....................
1
.oo
DATE
.......................
01/24n4
RUN NUMBER
.................... 02
Hpc 1512
m
(4959 FT)
M
.............................
1.105
CONDITION OF SWEEP EMPEN. SYMMETRIC
VE 663.4
KTS
VT
...........................
718.7 KTS
(1
...................
72.35
kPa
(1511 PSF)
TAF 4% (392'F)
..................
0.75
............................
0.50
........................
0.25
PA
.......
1.06
kg/J
(0.002057 SLUGS/FT3)
R/H
Boom Lateral Bending
Normalized
to
R/H
Stabilator Rotation
180
90
0
-90
-180
Figure
7.-
St.
Louis
transmissibility plot.
DATA STORAGE
AND MANAGEMENT
MANUAL EXTRACTION
AND DAMPING VALUES
EXCITATION
Figure
8.-
Post-flight data system schematic.
427
FIRST
DERIVATIVE
R/H
Boom Lateral Bending
Normalized
to
R/H
Stabilator Rotation
F'-15
FLIGHT FLUTTER ANALYSIS SYSTEM
AIRCRAFTNO.
................
1280
FLIGHT
RO.
..................
.341
DATE
...................
01/24/74
RUN NUMBER
..................
.02
Hpc
...............
1512m (4959 FT)
M
........................
1.105
CONDITION OF SWEEP EMPEN.SYMMETRIC
VE
....................
663.4KT-S
VT
....................
718.7KTS
Q
..............
72.35kPa (1511 PSF)
TAF
.................
.4OC
(392'F)
PA
.....
.1.06
kg/m3
(0.002057 SLUGS/FT3)
NUM
1
2
3
4
5
6
7
9
10
11
12
a
-
HERTZ
FREQUENCY AND DAMPING DATA
AVG
FREQ DAMP DAMP DAMP DAMP DAMP
9.90 0.123 0.114 0.169 0.164 0.142
13.40 0.038 0.031 0.024 0.024 0.029
18.60 0.019 0.018 0.020 0.021 0.019
23.50 0.118 0.100 0.272 0.240 0.183
26.69
0.005
0.001 0.034 8.033 0.018
33.80 0.025 0.026 0.023 0.028 0.026
35.48 -0.002
4.002
0.001 0.001 0.001
37.31
0.033
0.027 0.007 0.008 0.019
39.80
0.005
-0.008 -0.009 -0.014
0.005
Figure
9.-
St.
Louis Argand derivative plot and automatic
frequency
and
damping extraction results.
STRUCTURAL
DAMPING
g
(XI
FREQUENCY
HZ
y
Manual Techniques
y
Automatic Techniques
0.7
0.8
0.9
1
.o
1
.l
1.2
MACH NUMBER
GP7i07lC14
Figure
10.-
Frequency and damping versus Mach number for
symmetric fin bending and boom lateral bending modes.
L/H
data at 1525
m
(5000
ft)
altitude.
428
0
STRUCTURAL
DAMPING
g
(%)
-7
0
-20
20
FREQUENCY
'9
HZ
18
17
0-
AIRSPEED
SEA
LEVEL ALTITUDE
-
krn
(iP75-0710
14
Figure
11.-
Frequency and damping versus altitude for
symmetric
boom
lateral
bending
at
constant Mach number of
1.10.
1.50
1
.oo
NORMALIZED
FLUTTER
MARGIN
0.50
I
I
1
150
300
450
600
750
900
EQUIVALENT
AIRSPEED
-
KTS
GPX
0,105
Figure
12.-
Flutter margin versus equivalent airspeed.
Symmetric boom
lateral
bending versus fin bending for
constant Mach number
of
1.10.
429
MACH NUMBER
OP76.071DIS
Figure
13.-
Flutter margin versus Mach number.
Synrmetric
boom
lateral
bending versus fin bending
at
constant
altitude of
1525
m
(5000
ft).
AIRSPEED
KEAS
DP75-07,016
MACH NUMBER
Figure
14.-
Flutter boundary for fin bending versus
boom
lateral
bending mechanism
-
symmetric.
430
MACH
NUMBER
GPIS
07,017
Figure
15.-
Flutter boundary for wing first bending versus
outer panel. torsion mechanism
-
symmetric.
431
