,L'  I' rF
k/ )II
THE UNIVERSITY OF MICHIGAN
COLLEGE OF ENGINEERING
DEPARTMENT OF ELECTRICAL ENGINEERING
Radiation Laboratory
INFLIGHT AIRCRAFT VIBRATION MODES
AND THEIR EFFECT ON AIRCRAFT RADAR
CROSSSECTION
Final Technical Report
August 1977August 1978
Prepared By:
2 William J. Anderson
^ Dipak L. Sengupta
Sanjay Correa
April, 1979
Prepared for:
Rome Air Development Center
Griffiss Air Force Base, New York
13441
157871F = RL2283
Ann Arbor, Michigan
CU i F ' .' r
EOR OFCC; NiN AGE
~ L*'~ K TIJN PAGE:
READ INSTRU'CTIONS
 3I'FORE tCOMPLET:NC, FORN
t
REP,:C " A JE.,J Et: 'i2. GOVT ACCESSION NO. 3. RECIPiENT'S CATALOG NUMBER
LA'.C TR7972 i___!_____ ___________________
TiTFLE (and Subtitle) 5. TYPE OF REPORT & PERIOD COVERED:NFLIGHT AIRCRAFT VIBRATION MODES AND THEIR Final Technical Report:FFECT ON AIRCRAFT RADAR CROSSSECTION August 1977  August 1978
6. PERFORMING ORG. REPORT NUMBER
N/A
AUTHO R(s) 8. CONTRACT OR GRANT NUMBER(s)
William J. Anderson
)ipak Sengupta F1962877C0232
anjay Correa
PERFORMING ORGANIZATION NAME AND ADDRESS 10. PROGRAM ELEMENT, PROJECT, TASK
AREA & WORK UNIT NUMBERS;he University of Michigan Radiation Lab
+072 East Engineering Building 61102F
inn Arbor MI 48109 2305J424
CONTROLLING OFFICE NAME AND ADDRESS 12. REPORT DATE
)eputy for Electronic Technology (RADC/EEC) April 1979
ianscom AFB MA 01731 13. NUMBER OF PAGES
MONITORING AGENCY NAME & ADDRESS(if different from Controlling Office) 15. SECURITY CLASS. (of this report)
*ame UNCLASSIFIED
15a. DECLASSIFICATION/DOWNGRADING
/ SCHEDULE
_________________________________________ N/A
DISTHIBUTION STATEMENT (of this Report)
)istribution limited to U.S. Government agencies only; test and evaluation;
kpril 1979. Other requests for this document must be referred to RADC/EEC,
ianscom AFB MA 01731.. DISTRIBUTION STATEMENT (of the abstract entered in Block 20, if different from Report)
Same
SUPPLEMENTARY NOTES
RADC Project Engineer: John F. Lennon/EEC
KEY WORDS (Continue on reverse side if necessary and identify by block number)
Vibration Aeroelasticity Surveillance
Turbulence Crosssection Radar Signature
Aircraft Mode Identification
Radar Dynamic RCS
Structural Dynamics Gust
ABSTRACT (Continue on reverse side if necessary and identify by block number)
A theoretical study is done for the identification of aircraft by type
through elastic inflight modes and their radar signature. Three contemporary
U.S. fighter and fighterbomber aircraft are studied for inflight vibration
amplitudes due to sharpedged gusts and random turbulence. The resulting
elastic and rigid body motions are found to be relatively small and at
relatively low frequencies for radar detection. The rigid body response to
turbulence at frequencies above 2 hz for these aircraft is found to be less
than 0.01 inch rms over 95 percent of the flight path.
j
FORM 1473
) 1 JAN 73 1473
UNCLASSIFIED
SECURITY CLASSIFICATION OF THIS PAGE (When Data Entered)
', urKI Trv CL AbSIF1CATION 0P Tjji1 rP..,rWtf Data zntereoq.

_ 4IIII  .. . I ....... —,       
Response to sharpedged gusts can be more pronounced. Elastic wing tip
deflections range from 3/4" to 1/8" over 2 ft/sec. gusts; gusts of this severity
are routinely observed over only 5 percent of the typical flight path.
In addition to small deflections, another problem lies in the unique characterization of aircraft by their modes. For two of the three aircraft, the
modal frequencies and shapes vary greatly with fuel and armament load. The
third aircraft (the fighterbomber), however, has a fundamental elastic frequenc3
which is relatively invariant with change in airspeed, fuel load and wing sweep.
This mode is predominantly fuselagebending and was used as a candidate for
radar crosssection studies.
Radar crosssection studies were done for varying view angles lying in the
vertical plane of symmetry for the aircraft. An RCS model was based on a
collection of independent scatterers identified with various components of the
aircraft. Elastic deflections due to a 2 ft/sec. sharpedged gust were
observable with 3 cm radar wavelength. A number of figures are given for static
and dynamic radar scattering crosssection. The frequency content of the radar
return has quite strong third harmonic components at 3 cm.
I
Iur 2~ux.aY ICl 1   .1 L I — * —u  ~r I I  r#
UNCLASSIFIED
SECURITY CLASSIFICATION OF THIS PAGE(When Data Entered)
EVALUATION
1. For noncooperative tactical aircraft identification, it is
essential to get as much supportive evidence as possible to make
valid decisions. Studies at RADC/EE raised the question of whether
substructural motions of a target could generate identification
information. The present study by the University of Michigan was
initiated as part of a program in target modulated signatures. Its
specific goal was to determine whether aeroelastic airframe motions
induced by atmospheric forces could be used to obtain a radar signature.
The approach involved studying the mechanical phenomena involved in such
interactions to obtain data about the frequencies, mode shapes, and
displacements for three classes of tactical aircraft. The variations
that occur for ranges of velocity, fuel loading, external stores, and
wing position were examined. The scope of the study was restricted; the
implications of the calculated substructural motions in relation to
corresponding changes of electromagnetic scattering centers were addressed
only peripherally. The complexity of the vibrational patterns and the
limited deflections that result would tend to make it difficult to observe
characteristic modulations of a radar signal.
F. LENNON,Wontract Monitor
iii
"I
TABLE OF CONTENTS
I. INTRODUCTION.......................
II. TURBULENCE..................... 3
III. INFLIGHT STRUCTURAL MODES...................6
3. 1 Inflight Frequencies 6
3.2 Frequencies for Type A Aircraft 7
3.3 Frequencies for Type B Aircraft 7
3.4 Frequencies for Type C Aircraft 8
3.5 Composite Frequency Study 8
3. 6 Inflight Mode Shapes 9
3.7 "Optimal" Mode Tracking 12
IV. INVARIANCE OF INFLIGHT MODES.....................13
V. AMPLITUDE RESPONSE TO GUSTS AND TURBULENCE..... 15
5. 1 Rigid Body Response to SharpEdged Gusts 15
5.2 Elastic Response to SharpEdged Gusts 17
5.3 Dynamic Response to Continuous Atmospheric Turbulence:
Rigid Body Plunging 26
5.4 Interpretation of the Aircraft Motion for RCS Work to Follow 30
VI. RADAR CROSSSECTION (RCS) STUDIES. 31
6. 1 General Considerations 31
6.2 Scattering Model 31
6.3 Dynamic RCS 34
6.4 Scattering Model of the Aircraft 36
6. 5 Numerical Results 38
VII. CONCLUSIONS AND RECOMMENDATIONS........... 41
7. 1 Conclusions 41
7.2 Recommendations 43
7. 3 Unresolved Points 43
7.4 Acknowledgement 44
VIII. REFERENCES...................... 45
IX. TABLE........................ 47
X. FIGURES........... 48
APPENDIX. BIBLIOGRAPHY.................. 89
v
vi
I. INTRODUC TION
This report covers theoretical studies of structural motion, aeroelastic
vibration and radar scattering characteristics of aircraft subject to gusts and
turbulence. Three aircraft have been chosen as test cases, a variable configuration fighter/bomber (hereafter called Type A and typified by the Flll),
a sweptwing fighter (Type B, typified by the F4) and a small fighter with
relatively straight wings (Type C, typified by the F5). The weights of these
aircraft are given in Table I. The weight range studied varies from 77, 302
lb. (Type A, with wet wing and fuselage) to 15, 265 (Type C). The modes of
vibration for these aircraft have been studied as functions of fuel load, armament load and airspeed. Both frequencies and mode shapes in flight have been
determined.
A major tool for this study has been the computer program "FACES,
developed by the Flight Dynamics Laboratory at WrightPatterson Air Force
Base [1, 2, 3]. This program considers the elastic forces in the fuselage and
wings, the inertial characteristics of the entire plane, and the aerodynamic
forces on the wings (strip theory). With substantial effort and computational
cost, the aerodynamic forces can be extended to the fuselage through the use
of the doubletlattice method. Strip theory has been used here, however.
This report (1) studies 12 combinations of aircraft type and weight,
(2) considers mode shape as well as frequency, (3) discusses the invariance
of modes and frequencies, (4) establishes expected amplitudes of motion,
and (5) constructs and studies a radar scattering model of the aircraft.
1
In several regards, the work done here differs from conventional
structural studies of aircraft in flight. Most structural studies concentrate
on stresses at the wing root, accelerations, or possibly interaction of
structure and the fluid flow (as in flutter). The emphasis here, however,
is on the motion of the aircraft as perceived by a distant radar site. In
this regard, the internal stress, strain and accelerations of the aircraft
are of no importance, whereas the displacement field is very important.
2
II. TURBULENCE
A literature survey has been carried out for references on (1) atmospheric turbulence, (2) methodology for calculating elastic aircraft response
to turbulence, (3) structural data and vibration characteristics of specific
aircraft, (4) effects of aging on structural response. Approximately 250 references have been cited in this survey, which have been entered into a computer file for convenient modification. Twentyfive of the more relevant papers
have been read, and a brief critical summary given following the references.
The most often cited journals are the AIAA Journal, Journal of Aircraft and
Journal of Atmospheric Sciences as well as Air Force and NASA reports. The
bibliography is included as an Appendix to this report.
The literature in the field of atmospheric turbulence appears to be
well developed. There are also many papers available in the area of elastic
aircraft response to turbulence. Papers on specific aircraft (such as the F4)
are less prevalent in the open literature and the few papers on aging seem to
concentrate on composites and glue strength. The literature appears to be adequate for the purpose of obtaining general information on aerodynamic motion
required by the project.
There are several causes of atmospheric turbulence with the primary
ones being the sun's energy and the whirling motion of the earth [4]. The
mechanics of turbulence involve wind shear and convection along with some manmade effects, such as wake turbulence behind aircraft.
For the radar return problem, turbulence caused by convection will be
of the most interest since it is the only source of excitation over most flight
paths. This convective turbulence occurs in patches hovering over the earth's
surface. An aircraft spends perhaps five percent of a typical flight in one or
more of these patches. The patches consist of repeated patterns of convection
3
cells of which two varieties have been observed. Hardy and Ottersten [5]
state: "One pattern consists of small thermallike cells which are 13 km in
diameter and several hundred meters in height.... The other pattern is made
up of clear air Bernardlike convection cells... which are 510 km in diameter and 12 km in height...t".
An airplane passing through such a turbulence patch experiences a random
force field due to velocity fluctuations u, v and w in the relative velocity
between aircraft and air mass. The most significant perturbation is the upward perturbation component (indeed, it is the only one considered in the related problem of sharpedged gusts). The velocity fler'ations are approximately isotropic and a stationary random theory is usually employed. There is
general agreement that von Karman has presented the best expression for power
spectral density of velocity fluctuations in isotropic turbulence. The turbulence is often considered "cylindrical," i.e., constant in magnitude along
the wing span. Along with the assumption of stationarity, this twodimensional assumption makes the problem of finding aircraft response tractable.
One could imagine the nonstationary random problem to be important,
i.e., the shorttime behavior of an airplane suddenly exposed to turbulence might be more severe than the stationary case. This has been studied
by several researchers using an envelopemodulated stationary random input.
Fujimora [6,7] found that sudden onset of a stationary random forcing function
can cause 28% more acceleration at the aircraft center of gravity than stationary random forcing. This fact is much more of a concern in stress analysis
than in the radar return problem, however, and should be ignored here.
Finally, the cylindrical nature of the turbulence is examinred by Coupry
[8]. He claims that spanwise variations in the turbulence cause enough carLcellation of lift to smooth out the predicted ride. For the purposes or
4
radar modulation by elastic modes, this is important because it means that simpler theories ("cylindrical" waves) will overpredict the aircraft response.
There is a scale factor involved, i.e., the ratio of length of coherence over
wingspan. For aircraft as large as the Concorde, the spanwise effect reduces
the peak response by a factor of two. For fighter aircraft, the cylindrical
assumption will probably overpredict response by about ten percent.
Several solutions using classical methods have been carried out for
aircraft response to continuous random turbulence and to sharpedged gusts.
(See Section V.) These provide some feeling for the amplitudes of motion.
In one calculation, a type B aircraft flying at 600 mph at sea level has an
rms vertical velocity in rigidbody plunging of 3 in/sec while passing through
continuous, moderate turbulence with rms vertical velocity component of 6 in/
sec. In other calculations, the elastic response to a 2 ft/sec sharpedged
vertical gust is found to be less than 3/4inch over the entire aircraft and
as little as 1/8inch in many cases. Observation of motion this small may require Xband or shorter wavelength radar.
5
III. INFLIGHT STRUCTURAL MODES AND FREQUENCIES
3.1 Inflight Frequencies
The program FACES provides the natural frequencies and modes of the aircraft structure on the ground and in flight. These results stem from a solution of the coupled eigenvalue problem including effects of elastic fuselage,
elastic wing, elastic stores and aerodynamic flow. The inflight frequencies
are given directly in numerical tables whereas the inflight modes are given
indirectly in tables of modal participation factors. A coordinate transformation must therefore be done to recover the inflight modes. No information is
given in FACES about the response problem (specific motion due to external
forces); however, the eigenvalue work from it serves as the background for
all such response work done here.
Volume I of the FACES manual [1] illustrates many of the natural frequencies and natural mode shapes for the type B aircraft. Volume II of the
FACES manual [2] gives extensive inflight modal frequency data for the type B
aircraft. Inflight mode shapes are not given in these manuals, however.
In the current study, the type A, B and C aircraft have been modelled
using data provided by the FACES manual (type B) and by WrightPatterson Air
Force Base (types A and C). In each case the properties of the elastic wing,
elastic fuselage and elastic stores are separately found and entered into the
program. These data can be calculated with some accuracy and have been tabotlated in company reports on basic data for each aircraft. Perhaps the weakest a:ect of the structural model of the airplane is the choice of elastic root restraint. The stiffness of the wing carrythrough structure in the fuselage is
not well documented; indeed, the "attachment point" called for in the FACES program is an artifice. The root restraint, which accounts for the fuselagew`ing
*
The exception is in the swingswing aircraft where the pivot point is lite'.
an attachment point. Even here, however, the properties are not tabulated in
the form needed by FACES.
6
interaction, is given values that are "strictly the user's own choice"
(Ferman [1], p. 93). In practice, stiffnesses about ten times the wing stiffness at the root give reasonable answers.
3.2 Frequencies for Type A Aircraft (Swingwing Fighter Bomber)
Inflight modal frequencies are given in Figures 15 (full forward sweep),
and Figures 610 (full rearward sweep). A sequence of cases is studied for dry,
partially fueled and fullyfueled cases. Several of the modal frequencies remain constant with airspeed; these same frequencies have mode shapes with little phase lag in time, and tend to remain relatively "pure," i.e., do not couple with adjacent modes. Figures 4 and 9 are crossplots of Figures 13 and
68 respectively, taking data at 500 knots and considering the effect of fuel
load on flight frequencies. The fuel is carried internally in the fuselage
and wings and has a moderate effect on the modal frequencies. The numbering
system given on the curves has to do with mode shapes and will be discussed
in Section 3.6.
Ground vibration frequencies for forward and swept wings are shown in
Figures 5 and 10 respectively. These are helpful for mode identification
studies done later.
3.3 Frequencies for Type B Aircraft (Sweptwing Fighter)
Inflight modal frequencies are given in Figures 1113. Each figure has
a different number of pylons and armament. Figure 11 is a partially fueled
aircraft with no armament and. Figures 12 and 13 consider 4 and 8 pylons respectively. The corresponding armament is listed in Table 1. Some of the
modal frequencies remain constant with airspeed, but as seen in the crossplot
in Figure 14, there is a substantial drop in modal frequencies with increasing armament load on pylons. The figures include all effects of the coupled
7
elastic fuselage and elastic wing. In this particular study, the pylons were assummed rigid so as to eliminate the additional elastic degrees of freedom,
which are interspersed with the dominant wing and fuselage motion and which
make problems in identifying modes. The neglect of elastic pylon effects means
that candidate modes for identification will have to be studied further for this
complication. The fully elastic pylon cases have been run for the Type B airplane and are very difficult to interpret.
Ground vibration frequencies are given in Figure 15.
3.4 Frequencies for Type C Aircraft (Straightwing, lightweight fighter)
The inflight modal frequencies are given in Figures 1619. These frequencies are higher than for the larger aircraft. The crossplot of frequency
variation with weight in Figure 19 shows a dramatic decrease of frequencies
as armament load increases. This aircraft was the most sensitive of the three
in this regard.
The ground frequencies are shown in Figure 20.
This aircraft, more than the others, poses a real threat to mode identification as armament weight changes. Both the inflight and ground frequencies
become very scrambled as weight changes, which is why no connecting lines are
given between data points in Figures 19 and 20. A numerical mode tracking
ame_thod to be discussed in Section 3.6 attempts to provide the continuity as.h^own in Figures 21 and 22, but is not very helpful.
3.5 Composite Frequency Study (Types A, B and C)
Because there seems to be a relation between the weight of the aircraft
and the modal frequencies, a composite plot of modal frequencies at 500 knots
is given in Figure 23. There is no general trend in the data; however, one
might speculate whether the modes of the empty aircraft of each fighter type
might be somewhat more predi.ctable than Ihavlyloaded aircraft
~:c vz~:. ode arc':ft
3. 6 Infight Mode Shapes
The previous work has dealt primarily with modal frequencies. Let us
now Lurni outr;ttent ion to the modal shapes.
The inflight mode shapes are the eigenfunctions for the airplane in the
presence of an airstream. These modes are aerodynamically damped at speeds
below the flutter speed. Above the flutter speed, one or more of the modes
are unstable and grow in amplitude with time.
The previous sections considered inflight and ground frequencies (eigenvalues), and the variation of inflight frequencies with airspeed and loading
(Figures 123). It is necessary,however,to consider the mode shapes for two
reasons. The first is that the radar return depends on the relative amplitudes
of different reflection points, lines and surfaces. The second is that mode
tracking (following each mode as airspeed and weight change) is difficult without knowledge of mode shapes to distinguish them when frequencies are closely
packed.
The modes and frequencies are calculated through the idealized models
shown in Sketches 13. The structural stiffness is developed using finite
sections of beams which can be serially kinked. The inertia of fuselage and
wing sections is located appropriately within each section at the center of
gravity of the section. Each section has rotary as well as translational
moment of inertia. The degrees of freedom are identified at section boundaries
and consist of wing z deflection and torsional angle about the elastic axis,
as well as fuselage vertical deflection, forward displacement and rotation
about the pitch axis. The aerodynamic forces used in the model are based on
strip theory, and act on the wing only (Sketch 3).
Of the five available degrees of freedom at each section boundary, three
are considered relevant to the radar problem for symmetric motion. These are
9
Sketch 1. Elastic model used in FACES. Beam theory. Fuselage and wing
can be kinked.
lumped moss
Sketch 2.
Finite sections used in FACES. Can be serially kinked. Three
degrees of freedom at fuselage stations and two degrees of freedom at wing stations for symmetric motion.
U
Sketch 3. Aerodynamic model used in FACES. No aerodynaric forces on
fuselage or tail.
C)
the wing bending deflection, wing torsional rotation and fuselage bending
deflection, as plotted in Figures 24a to 27c. These twelve figures show the
fundamental mode for each of the four major geometries studied, with all at
medium weight. The z deflections are in feet and the torsion is in radians.
The motion in each case consists of an inphase and leading component. The
motion is not synchronous, i.e., different points along wing and fuselage are
not in phase with each other. The deflection for the wing w(y,t) could be
written
iw.t i(w.t + 7/2)
w(y,t) = f1(y)e + f2(y)e 1
for instance, where f1(y) and f2(y) are plotted as solid and dotted lines.
Discussing mode shapes for a complex structure is more difficult than
discussing frequencies, which are scalars. An attempt is made here to quantify
the mode shapes so that modes can be "tracked" and their invariance (or lack
of it) determined. The method used is to consider the maximum amplitudes in
wing bending, wing torsion and fuselage bending. To compare on the basis of length
scales, the wing torsional angle is multiplied by the mean half chord of the
wing. This corresponds approximately to the distance the leading edge and
trailing edge move vertically and is a reasonable way to judge the effect of
torsion on the radar return. (Leading edges may be good reflectors.) A code
for each mode shape has been worked out for a normalized vector of length 100,
where the mode illustrated in Figures 2426 would be represented by
(17 02 98)
t A, t
'4'
component of wing / — fuselage
bending wing bending
torsion bendg
Sketch 4. Modeshape code.
11
This mode is easily seen from the code to be dominantly fuselage bending,
whereas deducing this from the figures takes some effort. Furthermore, comparisons between mode shapes can be made, and differences quantified. Using
the code discussed above, the frequencies displayed in Figures 123 have been
"tagged" with their corresponding mode shapes.
3.7 "Optimal" Mode Tracking
Both modal shapes and modal frequencies change with the three parameters
considered: airplane load, airspeed and wing sweep. Modetracking thus involves following a particular mode as any parameter is varied. The modal frequency is not a good indicator of the modal pcnibr, because a modal crossover
upsets a notation that is frequencyordered. This leaves the mode shape as
the possible "tag" on a mode; the shape has been described with a numerical
string quantifying the contributions from wing bending, wing torsion and fuselage bending. This sixdigit code is used as the "tracer" in the modetracking
process.
The modetracking is optimized on the basis of shape. The eight "variable" modes in Sketch 5 can be permuted in 8! or 40,320 ways; each permutation
represents a unique mapping of the "reference" modes onto the "variable" modes,
frequency "reference"
* modes
"variable"
c modes
~ o
Parametezr of
 interest
Sketch 5. Permutation of modal frequencies.
12
For each of these mappings, the sum, over all eight modes, of the squares of
the differences between the twodigit code numbers, for a reference mode and
the variable mode, is computed. The minimum of the 40,320 sums thus obtained
corresponds to the "optimal" modetracking; a rootmeansquare error can be
obtained from this minimum sum. This procedure:
(1) searches for a global minimum and so often discards intuitively
"comfortable" mappings between lower modes.
(2) disregards the possibility of picking up variable modes from
or losing reference modes to higher frequencies.
Typical results of this modetracking procedure are illustrated for aircraft
Types B and C in Figures 21 and 22. One can appreciate from these figures
the difficult in tracking modes for aircraft Types B and C.
If one can track the modes with enough confidence in a given case,
the next question is whether the frequencies and mode shapes along the properly tracked mode are invariant or not. This is a more detailed question
than tracking and is discussed in the next section.
IV. INVARIANCE OF INFLIGHT MODES
The information contained in Figures 123 is the factual basis for
determining invariance for the three aircraft. The question of how to define
invariance of modes is somewhat subjective, but is basically whether modal
frequencies and shapes vary excessively with change in aircraft loading,
speed and configuration. What is excessive from the radar return pattern is
critical and cannot be completely determined at this point.
Although the first 8 modes have been studied, identification doesn't
require invariance of all 8 modes. The aircraft motion can be shown to be dominated by the fundamental mode with some contribution from the second and:hird modes.
13
Some generalizations to be drawn from the results include:
(1) Variation of mode shape and frequency with airspeed is generally
modest and could be accounted for if it were the sole effect.
(2) Variation of rro de shape and frequency with fuel and armament
load is great. Modes are scrambled so much that it is difficult to
track them, even analytically for a given aircraft where no noise
is present (at discrete, calculated points).
(3) Variation of mode shape and frequency with wing sweep for the
type A aircraft is not severe and could be accounted for if it were
the only effect.
Only the Type A aircraft appears to be a candidate for identification by
invariance of an elastic mode. Its fundamental mode (fuselage bending) varies
only from 5.8 to 6.8 hz with wide changes in airspeed, loading and wing
sweep. Unfortunately, other fighter aircraft in the air with their profusion
of frequencies can, for certain stores combinations as seen in Figure 23,
mnimic the Type A aircraft elastic frequency. Therefore, one would have to
search for a unique radar return due to the mode shape of the Type A aircraft.
Another necessary condition for identification is that the modes in question itust be excited enough by gusts and turbulence to be observed. The
amtirplitude of this response is studied in the next section.
14
V. AMPLITUDE RESPONSE TO GUSTS AND TURBULENCE
Three separate gust and turbulence problems will now be considered. The
purpose will be to develop insight into the amplitude of response of the aircraft.
The cases studied differ in whether the airplane is considered rigid or elastic,
and whether the turbulence is modelled by a sharpedged gust or as a stationaryrandom process. Of the four possible combinations of these effects, the most
complicated one (elastic response to stationary random turbulence) is not considered because of its difficulty and limited scope of this study. One can determine the major effects from the first three cases, however.
5.1 Rigid Body Response to SharpEdged Gusts
A simple calculation of the rigid body response to a sharpedged gust
will be made. Only the plunging motion, and not pitching, will be considered.
The type B aircraft will be assumed to have the following flight characteristics:
mass = m = 1696 slugs
weight  W = 54,600 lb. z(t)
2
wing area S = 530 ft
Sketch 6. Coordinate System.
speed  U = 880 ft/sec (600 mph)
W(t)
air density at 10,000 ft =
=.000582 slugs/ft3 0
air density at sea level =
= 0.002378 slugs/ft Sketch 7. Sharpedged Gust.
The liftcurve slope, C, could be calculated by procedures outlined by
Roskam [9]. The procedure is somewhat involved, however; therefore, CL will
be estimated at an intermediate value of C = 3.0.
L
The sharpedged gust will be assumed to have intensity w = 2.0 ft/sec,
15
which corresponds to the extreme value measured at least once per ten seconds
in "turbulent patches." These turbulent patches cover only five percent of the
flight path, hence, this magnitude of sharpedged gust is an upper limit to
gusts that could be observed routinely.
The response in plunging of a rigid aircraft to a sharpedged gust is
given by Fung [10]. For a gust velocity
w(t) = w H(t) (positive upward)
one obtains a response
1 Xt
z(t)  wO(le )  wt
where the characteristic time required to appre::n a steady motion is where
p US LdC
2m da
1
For our problems, at sea level, X = 0.981 sec and at 40,000 ft,
1
A = 0.240 sec. Hence
e981t)
ZS(t) = 2.039 (le *1)  2t (ft, where t is in seconds)
SL
.240t
z40,000( = 8333 (le )  2t (ft, where t is in seconds)
The solution for this plunging response is shown in Figure 28. The figure confirms the characteristic time of 1 second at sea level and 4 seconds at altitude during which the aircraft accelerates upward to a terminal velocity equal
to the gust speed.
The maximum acceleration of the aircraft is at t = 0 and is  w XA To
o
compare this acceleration with that due to gravity, one divides to get the
load factor An:
An  I maxi
An 
g
W X
o
  e
16
At sea level
An = 0.061 g.
At 40,000 feet
An = 0.015 g.
Both values are relatively small and indicate that the gust is mild.
5.2 Eto SharEdged Gusts
Background
The vibration signatures of structures are characterized by mode shapes,
frequencies and amplitudes of response to various inputs. The response is
divided between the various modes, with modal content typically decreasing for
the higher modes. For aircraft structures, the ambient turbulent field provides aerodynamic inputs which excite these modes. The sharpedged gust, a
simplification of the actual (random) field, provides useful information on
the aircraft vibrationsignature.
Beyond this simplification of the input, the aircraft structure itself
will be idealized as a rigid fuselage with an unswept, straight, slender wing.
Arbitrary spanwise distributions of mass, stiffness and chord are allowed.
The entire airplane is free in vertical translation, or 'plunging,' and the
wing is elastic in bending; all torsional modes are assumed to be restrained.
The modal analysis detailed here follows Bisplinghoff, et al. [11]
It is to be expected that these theoretical results will overestimate
the elastic response. The actual wings on the aircraft studied are swept,
causing less lift per unit span and initiating lift at different times along
the span. In contrast, the theory applies to a larger lift instantaneously
along the entire wing, which is a more severe loading condition.
The theory is intended to provide approximate values for elastic wing
motion. This will serve as an indication of the wavelength of radar required
17
to observe the motion. Each of the modes will respond with its own amplitude;
hence the results should distinguish between observable and nonobservable
modes.
Symbols
bR
a(y)
b
S
m
M
U
w (a)
WG
p
1
w( y,t)
k;). (y)
)(t)
1T
Clt),*..^(t)
iY
 1.
M.
( )
reference semichord
spanwise chord distribution
semichord at station y
wing area
running wingmass
wing semispan
total airplane mass
airplane forward velocity
gust velocity profile
density of ambient air
total number of modes considered
bending frequencies of wing, L = 0
nondimens ional time
vertical displacement at station y
rigidbody mode shape, 1 (y) = 1.0
shapes of vibratory modes of wing
response of 'plunging' mode
normal coordinates representing responses of vibratory modes
Wagner function
Kussner function
generalized forces due to gust
generalized forces due to motion
prime denotes derivative with respect to the argument
18
Equations of Motion
The response of the aircraft is separated into a timedependent component (t) and a spatial component P(y), with the total response then given by
n
w (y,t) = Z j. (t)j ((y).
j=l J
The mode shapes are normalized so that
Q 2
M = 2 fi m.i dy i=l,...,n.
Positive coordinate directions are indicated in Sketch 8.
z
Sketch 8. Coordinate System.
The response is given by the solution of the differential equations
2 n n
A~i(s) + XQ2.i(s) + Z A ijj(s) + 2 E B..s j (o) (sa)da
1j1 j. i j 70
w (a)
= 2 b Bi  Y' (sa)do
R li 0 U
i=l,...,n;
eI = 0
19
where:
b = a(y)bR
s = Ut/bR
X = M/(T p S bR),= wi b/U
i i R
+ 2
A = (bR/S) f a(y) i j dy
Bi = (bR/S) f a(y) i j dy (5.1)
[Eq. 10149, Ref. [ii].]
With a stepfunction gust velocity input, the gust velocity profile
WG (o) is
wG(a) = wG(O+) = WG,
which allows modification of the nonhomogeneous terms in the system of equations. From Eq. 5382 [11], the unsteady lift due to the gust is
sd wG(a)
L = 27r p U b {wG(O)Y(s) + f da (sG)dc}
G 0
which, for w (a) = WG, reduces to
G G r
L = 27 p U b wG(O)Y(s),
s in ce
d w (a)
d a Y(sa)da = 0.
0 d
Hence, the spanwise lift due to the gust is
LG(y,s) = 2Tr p U a(y)bR wG Y(s).
The definition of generalized force due to the gust is (Eq. 10143, Ref. [.1!)5
20
D.
+Q
= 7

i LG dy
or
D +Q
27 p U bR wG (s)f i. a(y
R G 1
From Eq. 10142 [11], the equations of motion are
2 2 M D.
i dt2 Si + Mi i i = i 1 i
M. = 3 +3
Transforming to nondimensional time,
U2 I + M2 +
Mi 2 i ' b 2 i i
bR bR
)dy
(5.2)
D.
 1
and so
M. D.
+, 2 R bR
i i p S U Ir p S U2
The last term becomes, on substitution from (5.2),
D.
bR 2 b
_ R
p U2 WG (s) Bi
Hence, for a stepfunction gust velocity input and for symmetrical motion, equations (5.1) become
2 n n s
() + (s) + Z Ai i(s) + 2 B.. / "(o) ( so)du
j=l 1J J j=l 1j 0l
2 bR wG
U Bli Y(s) i=l,...,n; 10 (5.
3)
with b, s, A, S defined as before and
21
A..
13
B..
lj
= (2 b /S) f
R 0
= (2 bR/S) f
R 0
a (y) ~(ij dy
a(y) 4ij. dy
Rewriting (5.3) in matrix notation
{E"(s)} + [, Q2 _{t(s)} + [_i {U"(s)} +
2[B]s
2[B] { "(o)} (so)do
0
2bR WG
AU
{B} I (s)
where
t Q2 a
{B}
[A]
[B]
2
R R 2 
U2
T
= [A I
[Aij]
= [Bi ]
13
+ x )
{g"(s)} + E Q2 _ {g(s)}
2b R wG
x u
(s)  [B
s
f { "(o)} (so) da
0
(5.4)
Numerical Solutions
Numerical solution of equations (5.4) requires some modification to the
system, which is implicit in g. Define I such that
S
{I} = / {"(o) (s)dao (5.5)
0
22
Hamming [12] has shown that this convolution integral has poor convergence
properties unless handled carefully. The following procedure is related to
Hamming's suggestion for separating out a portion of the integrand.
With a sufficiently small time interval As, the displacements can be
assumed constant within each interval, and a trapezoidal integration rule can
be used; thus
(k+l) As
{I} = ( s)
(k+ ) As
2
P(sa)dO + Z {I"(iAs)}
i=l J (
(i ) As
2
(kAsa) do
(5.6)
Equation (5.6) assumes that
s = (k+l)As
(current time)
and
{i"(0) } = 0
The latter is an approximation to an initial steadyflight condition. Adopting
a polynomial approximation to the Wagner function
~ s+2
~(s) = s+4 '
cs/ s+4
it can be shown that
1
" (i+ )As
J(i 2) As
(ki 1)As + 4
(k Asa)da = 21n 1( (k + As
(ki+ )As + 4
(5.7)
(k+l) As
(k+ ) As
2
> (so)dc =
2 in 4 7 + As
As+4 2
(5.8)
Combining equations (5.6), (5.7) and (5.8),
23
k (ki )As+41
{I}.= {"((k+l)As)} 2 n As + + "(iAs)}(2
+ 4 i=l (ki+ )As+4
2 /
(5.9)
Finally, combining equations (5.4), (5.5), (5.6) and (5.9),
2bRWG k (ki ~)As+4 )
 {B} }((k+l)As)  2[B] Z {"(iAs)}(2 In + As)
Equations (5.11) are in a form suitable for direct integration by the
Newmark method. The following algorithm may be used (Ref. [13]):
A. Initial Calculations
1. Initialize
{} = {0} at s = 0
{'} = {0} at s = 0
{"} = {0} at s = 0
2. Select 'time' step size As and parameters a and 6;
calculate integration constants.
6 > 0.050; a > 0.25 (0.5 + 6)2
1 6 1
a0 2; al 2 ' 1s; a2 = aAs
a = 4  1; a = 
a3 = a ( 1; a4 = as 1; a 2
a6 = As (16); a7 = 6As.
24
3. Form mass [M] and stiffness [K] as defined by equations (5.10)
and (5.11). Form effective stiffness [K]:
[K] = [K] + a0[M]
4. Triangularize [K]:
T
[K] = [L][D][L]
B. Iterative Loop
1. Calculate effective loads at s + As:
s+As = {R}s+s + [M](a0{} + a2 {'} =a3{})
2. Solve for displacements at s + As:
[L][D][L] } = {R}
s+As s+As
3. Calculate accelerations and velocities at s + As:
{ s }+As ao( { }s+As )s s 3 s
{i} As { + 6"s +a7 s+As
Results
Each of three aircraft types was studied at the medium weight to provide
typical response values. In each case, the aircraft penetrated a two fps
sharpedged gust applied instantaneously along the entire wing. The results
yield elastic displacements which are rather small, ranging from 3/4inch
wing tip displacement on the type B aircraft, to response as low as 1/8inch
wing tip displacement for the type A aircraft (swingwing fighterbomber).
Figures 2931 show the elastic response at the wing tip. The rigid body plunging mode is not included. The bulk of the motion in all cases was due to the
first aircraft mode. The second mode participates in a minor way and the third
and higher modes are scarcely excited. In addition to the graphical results
in these figures, a wealth of tabular output is available for each aircraft.
25
5.3 Dynamic Response to Continuous Atmospheric Turbulence: Rigid Body Plunging
An airplane penetrating an atmospheric turbulence field experiences continuous rather than discrete gusts; hence a statistical approach is needed to
model the continuous properties of atmospheric turbulence. The general method
consists of applying a random input (the power spectrum of atmospheric turbulence) to a linear system (the mechanics of the rigid body plunging mode) and
studying the response of this system. Only statistical properties of the response, e.g., rootmeansquare displacements, may be determined by this method;
explicit timehistories will not be known.
The aircraft is modeled by a rigid wing of constant chord 2b flying at a
forward velocity U. The wing thickness and the magnitude of the vertical
translations are assumed small compared to the chord. The fluctuating turbulence velocities u,v,w are assumed small compared to U. The components u,v
may be neglected as the wing is free in vertical translation only. Thus, the
wing is subjected to a fluctuating angle of attack
w
a = U.
U
It is further assumed that the gust field is twodimensional (no spanwise
variations) and the turbulence pattern does not change during the time required
for one particle of air to traverse the wing, i.e., during time 2b/U.
Inpirt
The turbulence w is assumed to be a stationary random function given by
the von Karman power spectrum, ~((Q):
8 2 1/
 2 1 + (1.339 L Q)I
[1 + (1.339 L Q)2
26
where:
Q = space frequency (rad/ft)
I. = scale of turbulence (ft)
= RMS gust velocity (ft/sec)
W
The function ~(w) satisfies the relation:
00
0
0 2 == f (w)dw.
RigidBody Admittance
To calculate the mechanical admittance of the system, the wing is subjected to a sinusoidal gust described by the real part of:
 ik(sx*)
w = e
G G
where k is the nondimensional frequency:
wb
k  Ub= b.
The response of the wing is given by the solution of the equation of motion:
U2
M "(s) = span L dy + fp dy
b2 span G span M
where:
M = airplane mass
= normal coordinate
Ut
s = nondimensional time, s =
b
L = lift due to gust
L = lift due to the motion
Substituting as a solution:
iks
a = w e
and writing the expressions for LG and iL, we have:
27
b 2K(k)
wG U k[2i C(k)  (2X+l)k]
where:
X = M/TT p Sb
3
p = density of the air (slugs/ft )
S = wing area (ft )
C(k) = Theodorsen Function
K(k) = C(k)[Jo(k)  i Jl(k)] + i J1(k)
The expression for  is the admittance function with resp:ct to vertical
wG
displacement.
Output
Let P(w) be the power spectrum of the airplane response. Then
~2 oo
= fS j(w)dw
where j is the rootmeansquare displacement.
The following relation then holds:
I 2
4(w) = X ~(w)
Using polynomial approximations to the complex terms in the admittance expression, the power spectrum of the response becomes:
b2 4K(k)l2
2(w) (W2
U k 22i C(k)  (2X+l)k (
b 4 1 1
2 l+27rk 2 2 2 4(w)
U +27k k 4+k2 (2X+1)2
or
28
2L 2 8 Lk
b2 1+ (1.339 — )
b 4 1 x_ w 3 b
Uk) 2 1+2rk 2 4+k2(2+1)2 [1 + (1.339 L)211/6
b
The meansquare displacement becomes:
L 2 8 Lk 2
1w 1+ (1.339 —)
2 = b 4 1 TW 3 b dk
0 U2 l+27k k2 4+k2(2X+l)2 [1 + (1.339 Lk)2116/
b
4Lbo 2 oo 8 Lk 2
4Lb 1 1 + 8(1.339 — )
4 3 b dk
u2 0 +27k k2 4+k2(2X+1)2 [1 + (1.339 Lk)2111/6
b
Frequency Limits
The integrand in the above expression is singular at k=O; hence, a
lower frequency limit (c) on the power spectrum of the response is needed.
This corresponds to an artificial highpass filter. Since radar returns are
garbled at very low frequencies (less than 5 Hz), this filtering is acceptable.
The meansquare displacement then becomes
8 Lk)2
C 1+ (1.339 
2 4Lb w 2 4 1 1 3 b 1
Tr U 0 1+27rk k2 4+k2(2X+l)2 [1 + (1.339 Lk)2]1116
b
In practice, integration to a finite upper frequency limit suffices as
the response becomes vanishingly small at the higher frequencies.
Results
The rigid body plunging responses of the three aircraft types (A,B,C:
medium weight) were computed with the low frequency cutoff point as the parameter. The upper frequency cutoff was set at 100 Hz. Results are shown in Figure 32 for a rootmeansquare gust velocity of 2 ft/sec. The meansquare displacement of the airplane as a whole is not large, unless one is willing to
29
attempt to detect frequencies below 1 hertz, say.
5.4 Interpretation of the Aircraft Motion for RCS Work to Follow
The elastic motion of an aircraft in flight has been studied in a deterministic as well as a random approach. There is a question as to which way provides more information for identification.. The random approach of section 5.3
is not encouraging because of the small rigid body displacements which were
found  approximately 0.01 inch r.m.s. when signals above 2 hz only are processed. The deterministic approach for the sharpedged gust does not give
much more hope. Peak elastic response at the wingtip Wa only 0.12" for a
type A aircraft, 0.75" for a type B, and 0.33" for a type C, all at medium
weight. The dominant elastic motion in response to the sharpedged gust is in
the fundamental mode (corresponding to the lowest frequency).
A deterministic approach will be used in the following RCS work. The
response of aircraft type A with wings fully forward will be the test case.
The vertical motion of the aircraft will be assumed harmonic and consisting
solely of the first elastic mode. The halfamplitude of motion of the wing tip
will be taken as 0.3 cm (0.12"). This number is as large as can be reasonably
inferred from Figure 29 and achieving it would require successive upward and
downward gusts. The RCS calculations therefore study a motion which is an
upper bound to what one could observe in typical turbulence cells occupying
5% of the earth's surface. Finally, it is noted that the type A aircraft has
a relatively large fuselage displacement in the first mode as can be seen by
comparing Figures 24ac.
Even if this value of 0.01 inch rms were doubled or tripled at the vwingtip
due to inclusion of elastic effects, it would still be small.
30
VI. RADAR CROSSSECTION (RCS) STUDIES
Structural motion and aeroelastic vibration of aircraft subject to gusts
and turbulence have been discussed in earlier chapters. The present chapter
theoretically studies the effects, if any, of these aerodynamically induced
motion of the aircraft on its RCS.
6. 1 General Considerations
Theoretical determination of the RCS of a complex body (with regard to
its electromagnetic scattering) such as an aircraft is an extremely difficult
boundaryvalue problem in electromagnetics. A plot of the RCS versus time
for an aircraft in flight often appears as a noiselike fluctuation even when
the nominal aspect of the aircraft is constant. Because of the uncertainties
about the aspect (due to roll, pitch, etc.), the RCS is often best described
statistically in terms of various distribution functions [15,16]. In general,
however, these distributions point out that there is no simple solution. to the
RCS problem for all aircraft [17]. To avoid unnecessary complications we will
avoid the statistical approach. Instead, we confine our attention to a deterministic study of the effects on the ambient RCS of an aircraft produced by
some of its identifiable motion induced by airturbulence, etc. The next section describes the simplified electromagnetic model of an aircraft, and how the
static and dynamic cross sections are obtained.
6.2 Scattering Model
The fundamental assumption of the theoretical method for obtaining the RCS
of an aircraft is that electromagnetic scattering by the aircraft may be assumed to be that due to a collection of independent scatterers which may be
identified with the various components of the aircraft (e.g., fuselage, wing,
etc.) [18]. Usually, this is possible at sufficiently high radar frequencies
31
where the appropriate dimensions of the aircraft are large compared to the
radar wavelength. To this end, the aircraft is considered to be an ensemble
of components, each of which can be geometrically approximated by a simple
shape in such a way that the RCS of the simple shape approximates the RCS of
the component it models. Once the component scatterers are identified, their
cross sections are obtained from known results. Each of the components is then
replaced by a point scatterer located at its scattering (or phase) center, and
having a scattering area equivalent to that of the component. Finally, the component cross sections are combined appropriately to estimate the RCS of the
entire aircraft. This method has been found usofFul in the theoretical estimation of RCS of aircraft, missiles and the results have been found to be in fair
agreement with measured values [19,20,21].
Let us assume that for a given combination of aircraft aspect angle, wavelength and polarization of the radar, N scattering components have been identified
for which the radar cross sections are a&, 2,...,.N One of the methods of
combination of these cross sections involves the relative phase angles between
the scattered fields from the N scatterers. This leads to the following expression, denoted by a (cross section by relative phase), for the RCS of tlhe
entire aircraft:
N 1/2 (.12
a  Z (a.) exp(ir.), (6.1)
p j=l
wlhere G. is the crosssection of the jth component and 3. is the relative phase
J J
angle associated with the radar return from the jth component. The magnitudes
of B.'s are determined by selecting a reference point (or origin) on the airJ
craft and obtaining the phase angle of the return from each component from its
distance from the origin. For this purpose consider a rectangular coordinate
system (x,y,z) with origin at 0 which also serves as the origin of a spherical
32
polar coordinate system (r,9, ) with its polar axis oriented along the zdirection. Let the aircraft be oriented horizontally (in the yz plane) with
its nose aligned along the zaxis and its center of the fuselage located at
the origin 0, as shown in Figure 33. Let the coordinates of the jth scattering center be (xj,y.,zj). Under these assumptions it can be shown that in
the radar direction (6,0 ) the phase angle.j appropriate for the jth scatterer is given by:
(3. = 2k[x. sin 6 cos (o + y. sin 6 sin $ + z. cos e ] (6.2)
27T
where k = 2, X being the wavelength of the radar waves. Observe that for
0 = 0, i.e., in the xz plane of Figure 35, Equation (6.2) reduces to
3. = 2k[x. sin e + z. cos 6 ] (6.3)
c o j o
which indicates that 3. is independent of the ycoordinate of the scattering
center. Also, note that in the ideal case when all the returns combine in
phase one obtains the maximum RCS of the aircraft as:
N 1/2i 2(6.4)
a = I (a.)2!4)
Pmax j=l J
It is evident that in the above approach one must know the distances of
the scattering centers from the chosen origin. These can be estimated either
from the aircraft drawings or from their scale models. However, Equation (6.2)
or (6.3) indicates that the phase angle 6. depends directly upon the ratios
xj/X, etc. Therefore, for a large aircraft at small wavelengths it may be
impossible to obtain these distances from the drawings or models with suffi2ient accuracy [18, 19] *
As an alternative to the relative phase method, there exists another
iethod often referred to as the random phase method [19]. This method is
33
based upon the assumption that many different j.'s are randomly distributed,
then upon averaging over B. we obtain the average RCS, denoted by a', as
N
a' = ~ o. (6.5)
j=l 3
The deviations of the observed RCS from the average crosssection a' are
characterized by employing the concept of RMS spread, denoted by S. This
measure of the probable variations in cross section due to the relative phase
effects leads to the bounds (a' + S) for the observed total RCS where
2 N 2 N
S = ( Z a.)  o.. (6.6)
j=l J j=1 3
It is evident from the above discussion that the random phase method
gives estimates of the amount by which the cross section might deviate from the
average value because of the phase effects. On the other hand, the relative
phase method of combination not only estimates the amount by which the crosssection deviates from the average value but also the locations (in aspect or
wavelength) of the relative peaks and nulls in the RCS.
So far, it has been assumed that the aircraft is static and hence, the
RCS values obtained from the above expressions will be independent of time an!,
thus, will be referred to as the static RCS. In the next section we describe
h..e method of obtaining the RCS of an aircraft undergoing vibratory motion
nduced by air turbulence.
6. 3 Dynamic RCS
In earlier chapters we have obtained the frequencies and modes of vibration of the aircraft caused by air turbulence. It was found that the vertical
displacement of the aircraft was significant; the mode shape and frequencies of these displacements were obtained numerically. We shall assume tha t;
34
tne scattering centers of the aircraft experience similar kinds of vertical
motion in time. Thus, for any mode of vibration, the xcoordinate of the
scattering center will vary in time according to that mode shape and at a
frequency corresponding to that modal frequency. It should be noted that the
modal shapes obtained from free vibration considerations (see Chapter III)
must be scaled properly to obtain the scattering center displacements.
In accordance with our earlier notation, let the xcoordinate of the
jth scattering center (associated with the wing) undergoing the ith mode
of vibration will be denoted by
x. = nj cos(W.t + j.), (6.7)
where,
j = [fl(Yj)2 + f2(Y 1/2 (6.8)
f2(y,)
tan C. = f (  (6.9)
The quantities fl(Y.), f2(y.) and oa identify the shape of the induced motion
of the scattering center caused by the ith mode of radian frequency w.. Vertical motions of the scattering centers associated with the fuselage and other
components are included in a similar manner.
N
(, t) = (a)1/2 exp(ij)2 (6.10)
P 0 j1
with
Sj = 2k[nj sin e cos o~ cos(Oit + c.j) + yj sin 0 sin Cp
+ z. cos 0 ], (6.11)
J o
where the dependence of time and radar direction are shown explicitly in a
If the radar is located in the vertical xz plane, ~0 = 0, the RCS expression
35
reduces to: N
o(0O t) E (a.)1/2 exp i 2k[nj sin 0 cos(w.t + a.) + z. cos e ]12
(6.12)
Note that with this model, the noseon (6 =0) RCS of the aircraft is unaffected by the vibration.
6.4 Scattering Model of the Aircraft
Aerodynamic studies, discussed in earlier chapters, indicated that the
vibration mode of type A aircraft is reasonably invariant to airspeed, fuel
load and wing sweep. For this reason we have chosen to study tLie RCS of the
aircraft model Flll which belongs to type A., ie component scatters and the
location of the corresponding scattering centers are obtained by studying a
1/72scale model of the aircraft. The orientation of the aircraft is as shown
in Figure 33 and it will be assumed that the radar is located in the xz
plane. Dominant scattering components are identified from a study of the
scale model. The approximate geometrical shapes and the corresponding theoretical expressions for their cross sections are as follows [1821]:
(i) The nose of the aircraft is approximated by a section of a conducting paraboloid. This component will contribute (a ) in the range
0 < 0 < 74~. It's contribution is obtained from:
(o) = sec4 9. (.13)
(ii) The main body of the fuselage is approximated by a conductive circular cylinder of length L = 19.72 m and radius a = 1.08 m. This
will contribute in the range 74~ < 9 < 140~. It's contribution
(a2) is determined by using the following expressions:
36
X a sin 0
0c (Q ) = o 740 < 6 < 85~ (6,14a)
2o 2 2 ' 
87~r Cos 0
0
2
2(r/2) =2 L a, for 95~ < e < 140~ (6.14b)
2 X  O 
(iii) Each of the two wings is approximated by a conducting rectangular
plate oriented in the yz plane. Each plate has dimensions W and
L in the y and z directions, respectively. The combined contribution (a3) from the two wings is obtained from:
2
W2L2 2 sin (kL cos 9 )
o3(eo) = 2 sin e (6.15)
2 o (kL cos e )
0
with L = 3.6 m and W = 7.92 m.
(iv) Each of the two tail fins is approximated by a rectangular metal
plate oriented in the yz plane. This combined contribution (a4)
is obtained from (6.15) with L = 4.32m and W = 1.44m.
(v) The two engine ducts in the front are approximated by circular
cavities each having a diameter a = 1.5 m. The scale model indicated that the opening of each duct is onefourth of the complete
2
circular area, Ta. The contributions (05) of the two engine
ducts is obtained from:
2
sin (2ka sine )
5(0 ) = 0.05(ka) 2(6.16)
5 0 (2ka sin 9 )
for 0 < 0 < 84~.
 o 
(vi) The two exhaust ducts, located in the rear of the aircraft, are
modelled by circular cavities each having a radius a = 0.5 m.
Their combined contribution (a6) is obtained from:
37
2
3 2 sin (2ka sin 9 )
06(0 ) = 2 x 0.4(ka)32   2 (6.17)
6 0 (2ka sin O )
0
for 135~ < < 180~
 o 
Note that all linear dimensions are expressed in meters and the calculated
cross sections are obtained in square meters. Also note that shapes and dimensions of the scattering components are assumed such that their scattering
crosssections are polarization independent.
The zcoordinates of the scattering centers of the above components
are: z= 9.36 m, z2 = 0.0, = .7.2 m4 5 + 1.08 m and
Z6 = 9.36 m.
Even after identification of the various scattering components, proper
care must be taken to combine them for a given aspect angle. This is because
the geometry may be such that at some aspect angle parts or all of the scattering from a component may be shadowed by other(s). To avoid the complications due to shadowing effects, we have restricted ourselves to the determination of RCS in the xz plane and proper considerations have been given in
obtaining the cross section expressions given above.
6.5 Numerical Results
Figures 34(a) and 34(b) show the static average, RMS and relative phase
crosssections, o', a' + s and a, respectively, versus aspect angle 6 for the
aircraft obtained at X = 3 and 30 cm. Of course the average cross section
o' stays within the RMS bounds 0' + s at all aspect angles. Over most of the
range a also stays within the RMS bounds; at some aspect angles, o moves
p p
out of the RMS bounds. These results are in general agreement with results
discussed elsewhere [18, 19].
The dynamic cross sections are obtained for the fundamental vibration
mode at w./27r = 6 hz and a wing tip halfdeflection t =o 0 3 cm.
1~
38
iwo sets of dynamic RCS have been obtained: one referred to as
the tipscattering center assumes that the scattering center of the wing is
located at its tip which would experience the maximum displacement due to the
induced vibration; the second set of results, referred to as the midwing
scattering center, assumes that the scattering center of the wing is located
at its center. Figures 35(ae) and 36(ae) show the dynamic RCS as a function
of time and for selected values of the aspect angle 0. Observe that the results are shown over a complete cycle of vibrations at the dominant mode.
Notice that at some aspect angles, the RCS values at X = 3 cm are lower than
those at X = 30 cm; this is due to the fact that those aspect angles are located at or near the nulls in the RCS pattern at X = 3 cm. Generally, the
dynamic results in Figures 35 and 36 indicate that the aircraft vibration induces some kind of fluctuation (or modulation) in its RCS. At most of the
aspect angles, the total deviations in the dynamic RCS values from the corresponding static values appear to be more at X = 3 cm than those at A =
30 cm. The fluctuations appear to be large at selected aspect angles. As a
function of time, the modulation in the RCS for A = 30 cm appears to occur
at the frequency of vibration of the aircraft. For X = 3 cm, the modulation
also contains a component of the vibrating frequency at all aspect angles; in
addition, at longer aspect angles (0 = 35~, and 45~) there exist quite strong
third harmonic components. The location of the scattering center of the wing
at its center or tip does not appear to change the general nature of the
results.
Observe from Figure 35(e) that at 0 = 45~, as a function of time, the
total deviation in the dynamic RCS, at A = 3 cm is about 8 dB. However,
the static results shown in Figure 34(a) indicate that near 0 = 45~, the RCS
varies quite strongly with 0. If it is assumed that aspect angle varies about
0
39
+ 2~ due to reasons other than the induced aircraft vibration, then careful
study of Figure 34(a) near e0 45~ indicates that this may cause about 1 to
5 dB variations. This implies that under such conditions vibrationinduced
modulation would produce about 3 to 7 dB deviations in the dynamic RCS. Perhaps it should be mentioned that low frequency variations in the observed
dynamic RCS of aircraft have been reported in [20,22]. Our results here tend
to indicate that these may occur as low frequency variations in the RCS of the
aircraft due to its vibration induced by air turbulence.
In our scattering model we have neglected the effects of shadowing
by the individual scattering components and of the incident polarization.
The accuracy of the assumed model is satisfactory for the static case [18]
and should be acceptable for rough estimation of the general effects in the
dynamic case. Further study is required to obtain the detailed nature of
the effects of aircraft vibration on its RCS.
40
VII. CONCLUSIONS AND RECOMMENDATIONS FOR FURTHER STUDY
7.1 Conclusions
Three fighter aircraft have been analyzed for aeroelastic response to
gusts and turbulence. The study included the effect of operating conditions
on the modal frequencies and shapes, as well as determination of relative amplitude response of elastic modes.
It was found that airspeed had a moderate effect on frequencies and
modes for all three aircraft. Fuel and armament loads had a large effect,
particularly when carried on the wings (as opposed to fuselage). The one aircraft with a swingwing had dominant fuselage bending at the lower frequencies;
these modes were changed only moderately by the wing position.
Perhaps a more critical issue than the invariance of the modes is
whether the modes are excited sufficiently by gusts and turbulence to allow
observation. Only five percent of the atmosphere contains turbulent patches
with a gust greater than 2 ft/sec. recorded at least every ten seconds. A
fivemode simulation of the symmetric wing bending problem was carried out for
each aircraft, using a 2 ft/sec. sharpedged gust. Each of the aircraft responded with a total elastic wing tip deflection of 3/4inch or less. The
bulk of this response was in the first mode, and response in higher modes was
small.
The only situation which has any promise for identification is the
fundamental (fuselage bending) mode for the Type A fighter/bomber. The
frequency of this case can be mimicked by smaller fighters carrying sufficient stores. Therefore, for success, some unique characteristic of the
mode shape, such as the large tail motion, needs to be exploited.
41
After identifying its dominant scattering components, a theoretical
scattering center model has been obtained to calculate the RCS of a type A
aircraft. Average RCS and relative phase RCS of the static aircraft have
been determined as functions of the radar aspect angle, and for A = 3 and
30 cm. It has been assumed that the radar is groundbased, and the RCS calculations have been performed in a vertical plane such that the shadowing
effects on RCS are minimum. Dynamic RCS of the aircraft has been obtained
by assuming that the appropriate scattering centers experience vertical displacements (in time) produced by the motion of the aircraft undergoing its
fundamental mode of vibration induced by air turbulence. At some selected
values of aspect angles, we have determined the dynamic RCS over a complete
time period of the fundamental mode.
With the assumed scattering model, the dynamic RCS of the aircraft in the
noseon direction appears to be independent of the aircraft vibration in the
vertical plane. In other directions (aspect angles), the RCS values appear
to contain amplitude modulations at the fundamental and the third harmonic
of the frequency of the fundamental mode of vibration of the aircraft. Although these modulations are generally found for both X = 30 and 3 cm, those
of the latter wavelength appear significant enough to be observable.
The significant finding of the study is that the motion of the aircraft induced by air turbulence seems to produce low frequency amplitude modulation of its ambient RCS. From the considerations of the maximum vertical displacements due to turbulence suffered by the wings (or wingtips) of a Type A
aircraft, it appears that such modulations may be observable with a 3 cm groundbased radar system. At the completion of the present study, it is not clear
42
whether such observations could be used to identify the aircraft. Further investigation is needed for this purpose.
7.2 Recommendations
The present investigation should be considered as a preliminary study
of the general problem of identifying an aircraft by its RCS modulations induced
by airframe vibration. Although some of the results of the present study are
found to be significant from this point of view, they are not complete and well
understood. Therefore, to ascertain the potentialities and practical realizability of this method of aircraft identification, the following studies are
recommended.
(i) Obtain the RCS vs. time for a given aircraft in flight.
(ii) Obtain experimentally the RCS modulations for a model aircraft
undergoing a motion simulating that of the fundamental mode
of vibration.
(iii) Investigate the implications of the results obtained in (i)
and (ii) with regard to the identification of the aircraft.
7.3 Unresolved Points
Some unresolved technical points include:
(i) Should the identification be based primarily on random or
deterministic concepts? In the present study, deterministic
ideas have dominated.
(ii) If a random approach is taken, are the newer, nonGaussian turbulence models [23] more appropriate than the von Karman isotropic turbulence model? Although more accurate, the newer
theory will probably not be worth the computational effort.
(iii) How much effort does the longitudinal rigid body pitching mode
have? The socalled short longitudinal mode has frequencies of
the order of one hertz and is felt not to couple into the problem.
/. A
(iv) Will the active control systems of the future couple with gust
and turbulence response? Both the Rockwell Bl and the latest
versions of the Lockheed 1011 have active systems which suppress
elastic modes but may introduce frequencies peculiar to the control system.
7.4 Acknowledgements
The authors have been supported in this study by many suggestions from
Mr. John Lennon (RADC/EEC) and Professor Thomas Senior. Aircraft data were
supplied by Mr. Walter Dunn (ASD/ENFSR) and FACES program assistance by Mr.
Sam Pollock (AFFDL/FBRC) and by Mr. M. A. Ferman (McDonnell Aircraft Company). This help is gratefully acknowledged.
44
VIII. REFERENCES
[1] Ferman, Martin A. (1975), "An Extension of the Rapid Method for Flutter
Clearance of Aircraft with External Stores," vol. I, Theory and Application, McDonnell Aircraft Company, Air Force Flight Dynamics Laboratory
Technical Report AFFDLTR75101, vol. I, November.
[2] Unger, Walter H. (1975), "...vol. II, User's Manual for FACES Computer
Program, AFFDLTR75101, November.
[3] Wells, J. R. (1975), "... vol. III, Programmers' Manual for FACES Computer Program, AFFDLTR75101, November.
[4] Houbolt, J. C. (1973), "Atmospheric Turbulence," Dryden Research Lecture,
AIAA Journal, v. 11:4, pp. 421437, April.
[5] Hardy, K. R. and Ottersten, H. (1969), "Radar Investigations of Convective Patterns in the Clear Atmosphere," Journal of Atmospheric Sciences,
26, pp. 666672, July.
[6] Fujimori, Y. and Lin, Y. K. (1973), "Analysis of Airplane Response to
Nonstationary Atmospheric Turbulence Including Wing Bending Flexibility,"
AIAA Journal, 11:3, pp. 334339, March.
[7] Fujimori, Yoshinori and Lin, Y. K. (1973), "Analysis of Airplane Response
to Nonstationary Turbulence Including Wing Bending Flexibility. Part II,"
AIAA Journal, 11:9, pp. 13431345, September.
[8] Coupry, G. (1971), "Critical Analysis of the Methods Used for Predicting
the Response of Large Flexible Aircraft to Continuous Atmospheric Turbulence," AIAA Paper No. 71342, April.
[9] Roskam, Jan. (1971), Methods for Estimating Stability and Control Derivatives of Conventional Subsonic Airplanes. Published by the author,
The University of Kansas, Lawrence, Kansas, 3.23.3.
[10] Fung, Y. C. (1955), The Theory of Aeroelasticity, John Wiley & Sons, Inc.,
New York, pp. 280282.
[11] Bisplinghoff, R. L., Ashley, H. and Hoffman, R. L. (1955), Aeroelasticity,
AddisonWesley, Reading, Massachusetts.
[12] Hamming, R. W. (1973), Numerical Methods for Scientists and Engineers,
McGrawHill Book Company, Hightstown, New Jersey, pp. 375377.
[13] Bathe, K. J. and Wilson, E. L. (1975), Numerical Methods in Finite Element Analysis, PrenticeHall, Inc., Englewood Cliffs, New Jersey, pp.
322324.
[14] Swerling, P. (1954), Probability of Detection for Fluctuating Targets,
RAND Corporation Report, RM1217, March 17.
[15] Swerling, P. (1968), Radar Target Signatures, Intensive Lecture Series,
Technology Service Corporation, Santa Monica, CA, August 2630.
45
[16] Marcum, J. I. and P. Swerling (1960), "Studies of Target Detection by
Pulsed Radar," IRE Trans., vol. IT6:2, pp. 59267, April.
[17] Nathanson, F. E. (1969), Radar Design Principles, McGrawHill Book Co.,
Hightstown, New Jersey, Chapter 5.
[18] Crispin, J. W. and Siegel, K. M. (1968), Methods of Radar CrossSection
Analysis, Academic Press, New York, New York, Chapters 9 and 10.
[19] Crispin, J. W., Jr. and Maffett, A. L. (1965), "Radar CrossSection
Estimation for Complex Shapes," Proc. IEEE, 53:8, pp. 972982, August.
[20] Skolnik, M. I. (1970), Radar Handbook, McGrawHill Book Company,
Hightstown, New Jersey, pp. 283 to 285.
[21] Crispin, J. W., Jr. and Maffett, A. L., (1965), "Radar CrossSection
Estimation for Simple Shapes," Proc. IEEE, 53:8, pp. 833848.
[22] Olin, I. D. and Queen, F. D. (1965), "Dyf:azci Measurement of Radar
CrossSections," Proc. IEEE, 53:8, pp. 954961.
[23] Pi, W. S. and Hwang, Chintsun. (1978), "A NonGaussian Gust Model for
Aircraft Response Analysis," AIAA Journal, 16:7, pp. 641643, July.
46
IX. TABLES
Table 1
Aircraft Weights
The airplane cases studied follow. In all cases, additional loading is simulated by inertial effects alone.
Type A: 2 different wingsweep configurations, 3 internallyloaded cases
A) 16 deg. 1. e. sweep
1 —1: dry airplane ('light')
gross weight = 44,507 lb.
1 —2: dry wing, 23,327 lb. fuselage fuel ('medium')
gross weight = 71,834 lb.
1 —3: 5,468 lb. wing fuel, 23,327 lb. fuselage fuel ('heavy')
gross weight = 77,302 lb.
B) 72.5 deg. 1.e. sweep
1 —4: dry airplane ('light')
gross weight = 44,507 lb.
1 —5: dry wing, 23,327 lb. fuselage fuel ('medium')
gross weight = 71,834 lb.
1 —6: 5,468 lb. wing fuel, 27,327 lb. fuselage fuel ('heavy')
gross weight: 77,302 lb.
Type B: 3 externallyloaded cases
4 —1: clean airplane, unloaded pylons ('light')
gross weight = 37,704 lb.
4 —2: 2 loaded pylons per semispan ('medium')
total of 4 loaded I/B pylons per airplane (14 M117GP bombs)
gross weight = 49,068 lb.
4 —3: loaded pylons per semispan ('heavy')
total CF 4 loaded I/B and 4 loaded 0/B pylons per airplane
(I/B: 14 M117GP bombs) plus
(0/B: 2 MK81 bombs and 2 LAU 32 A/A FFAR rocket
gross weight = 51,752 lb.
Type C: 3 externallyloaded cases
5 —1: clean airplane, all stations unloaded ('light')
gross weight = 15,265 lb.
5 —2: I/B and tip stations loaded ('medium')
I/B pylon: 50% 150 G. fuel tank
Tip station: AIM98 'sidewinder' missile & launch
gross weight = 17,258 lb.
5 —3: 0/B ANC tip stations loaded ('heavy')
I/B pylon: full 275 G. fuel tank
O/B pylon: BLU27/B(F)
tip station: AIM98 'sidewinder' missile & launch
gross weight = 21,908 lb.
47
X. FIGURES
48
109720
109722
1072 109
I.
40
30
o
069909
'239706
079907
079907
0
099815
q p p
578116
>  o  — 
329 507
N
14
4 trl
u
1)
O
v)
O
pc
20
'224984
Mixed
513280
568209. .
I
I
Wing bending and torsion.. 73681  Wing bending and torsion, v  ,. :" w,,11 w........ I
411690
Fuselage bending
341693
1
o0
(
Fuselage bending
250397 240397
a
a
I
I
I
0
I I If W
SMIN~m / r% P. 
200
400
ouu
U0J
Equivalent airspeed at sea level, V, knots
Fig. 1. Modal frequencies of aircraft type A in flight. Weight = 44, 507 lb. (Dry airplane, 16 1. e.
sweep, symmetric modes.)
40
069906
049906
069906 04990
30
573276
329 503
561781
0 Jo
0  a
189803
57 58 58
C)PI~,,
N..
418241
Kp~
Is_,
20
756318
Wing bending and torsion
6 0 1
A
355179 Fuslag beding 1
C). 71r —_   ~ : ~ —~  r "      T —
3 55179 Fuselage bending 124489
uw  m . —I
421V689 
10
Fuselage bending
41.198,
200298 Fuselage bending 240297
I
I
I
I
I
~'~A ~J~r~%an*ap~i~lsa~sr~~h ~ ~ m~11~~L~~~i~~ —r~~s~yi~a ;ul~L; ~BI~lrR 1~g~~p~fWI~Ba~Y A — a ar~
200
400
6 0f.
800
(Ji pivalelit airspeed at sea level, V, knoi
>'.LJai"~ f ~t, type A in 'light, Weight:71, 4 lb. (Dry wing, full fuselage
fual J e &W;ap, syr nmetrcIK modes. N
40
30
059907
109907
000
533279
494078
p c 
_ ~ 
un
1 59905
, ____
049820
586056
  ,..~..;........
0
— 7.. Ol
N
0):j
cr,
a)
1 4 
20
10
25942 5
n /
471187
Fuselage bending
36b49U
  1
db 0 b C    ==lI
D ~ ~  _r~0 855114 Wing bending and torsion 776215
* * *. a  2 _
 521883
Fuselage bending
492284
210298 Fuselage bending 250297
a
I
I
I
I
I
I I i III..... . a
60 80
0
0
200
400
600
800
Equivalent airspeed at sea level, V, knots
Fig. 3. Modal frequencies of aircraft type A in flight. Weight = 77, 302 lb. (Full fuel load, 16 1. e.
sweep, symmetric modes.)
i
I
Burn off
Fuselage fuel
40
109722
No_
Burn off
Wing fuel
04990 6 
561781
189803
418241.6079 13
T099815
N
ti4
30
20
. 1%
329507
513280
Wing bending and torsion
109907
494078
049820
259425
362490
77621 5
492284
250297
I. I
568 209~ ""~~~~~~  —~   7  
Fuselage bending
Fuselage bending 
124489,!
10
124489
7I
411989
240297
8 
2440397
0 5p 00c
Fuselage bending
10, 000
1 5, 000 20,000 2
I] I
i
G9,i. i
I
30., 000
Winr.g dry
t Full fuel. load
Fiuel load,, lb.
500 knots  575 mph,:i, i...:g fuel l.oad for arcraft type A at Y0 knots. (16~ I.e. sweep, symmetric
V " K CiK.
109720
i69906
0 5990'
69909
573276 533
329503
3 0 
1 30239706 329__ 15C;. ^  —— 8  58(
578116
7 56318
^ 20 224984 Wing bending and torsion 47
736810 Fuselage bending 3551 l
C i, 42 689
I 411690 Fuselage bending
10 ':
" 'T __________' "  —— ^3?) — 2
250397 Fuselage bending
30, 000
209000
0 o10, 000
Fuel load, W, lb.
Fig. 5. Ground vibration frequencies for aircraft type A with varying fuel load. (160 1. e. sweep.)
Fig. 5. Ground vibration 11eque4
I 
1z.
60 5(,5114
10298
293688
40
'U
IN
C
239705
805329
293689
0 0 a  f
269604
 % 81522 —
81 5228
    c A  ~
30
Irl
0~
Q)!j
k
538 503
)  —— ~0....... —/   
528 50 5
~DI    p
0
481886
Fuselage bending
462086
 ,.   
~~  — a
864031 Wing bending
 p     "
353'138
0
I O
m l GoIL ~ D1DC ~I ~ L~_  m m C Iyp — M I —.661175 Wing bending and fuselage bending 621078
250497 Fuselage bending 21(
)498
0 "00 200
I
I
a
I
I
— b~IIF IYycLgyl  — 1 ill 1Aige ~ 9 1 I — 9rh~ — 1 UI
300 400 500 600 700 800
Airspeed, V knots
eq4
0
vfte~ A in flght. Weight 44, 5&7' ~tb, (Dr,, airplane, 72., 5 ie
_ 1gI
 C.
~~~5 vet:. &<w<I
40
249616
279601
db Ah db All'. ap

292293
 — o
282194

30
825513
0 0  He
795915
N
r(
0
O
Q
cr(
0 o — 159 5o
159527
30
633669 Wing bending and fuselage bending
a RP  4m 4p
 654065
O 903427
893627 Wing bending
C 0
I

10
low low w 
691471
Wing bending and fuselage bending
711369
0
o{
190298 Fuselage bending 180298
I
I
I
I
I
I
I
I
* 5 U a l
0
100
200
300 400
Airspeed, V, knots
eq
500
600
7(UU
tUU
Fig. 7. Modal frequencies of aircraft type A in flight. Weight = 71, 834 lb. (Drying, full fuselage fuel
= 23, 327 lb, 72. 5 1. e. sweep, symmetric modes.)
40
339220 329221.........   __ o _....o 303987
30 930935 940834
^ 139814 189809
20
2 482584 Fuselage bending 50288
q 883531 Wing bending 883533
1 ~ — ff  —ftI~  ePC~~II —~ ^^.:iC)L — ~4~ ft~ ~
711669 Wing bending and fuselage bending 791659
180298 Fuselage bending i 70298
100 200 300 400 500 600 700 800
A.ir peed, V, knots
eq:ig. s. I;al fr. f Iquerc.s of.ircrft t iYpe A in fligWbt. 'Weight = 77, ^: Ib. (Fully fueled, 72.5 1. e
s.,,eep, symre: tri c  ordes )
I
40'
30
4 a)
44
U
a)
a)
04 cr'
(1
w4
20
10
Fuel load, W, LD. % Wing dry Fu
Fig. 9. Modal freencies for aircraft type A with varying fuel at00 knot (72 e sweep
symmetric modes.)
40
I
I
8249
I292
616
293
>513
2 30
I
30
JUl.X
339220
303987
Q30935
1 39,.214
482584
883531
711669
180298,f.14
1+4
m
a)
4
u
r
(1)
'iI
cr
0);_1
'4;
11
N,
0
0
C I
20
10
538503
481886
I
__j
Fusela e bending
I,633669
269
m
9 3 6 
864031
Wing bending.........
I
~~~~~~~ .. s y
661175 Wing bending and fuselage bending
%049 7 Fuselage bending
I!
68936271

4
W
691471
^  ,,_.. 
190298
a
f
I
10, 00( 2, 000 30, 000
Fuel load, W, 1b.
'g,. i <, (;,;  'or aircraft Aype A with varyi~g, fuel load. (72. 1. e. sweep,
235779, 175681
2 3 5 — 1 75
40
~
379307
409108
  >
db k.
377851
358146
N 30
^
>a
0
 20
^41
(
149904
> _ 379305
337557 Wing torsion 368245
627807 Wing and torsion 5980 04
627807 Wing bending and torsion 598004
(
A/iT vAd
74 5144
645r53 5 53
841 86491 5
864912 Wing bending
I
I
I
I
I
I
I * * la a a a
0 O
)
200
400
600
800
Equivalent airspeed, V, knots
eq
Fig. 11. Modal frequencies of aircraft type B in flight. Weight  37, 704 lb.
fueled, symmetric modes.)
(No pylons, partially
40
30
20 (
10
0
(
102796
112596
Ak
174985
114986
0 0    , ~ —  FPI O
488708 lw 508607. ..
1T63294 ~223292
W Wing bending and torsion — 657603
62780
Mixed 6864 36
6 FT...
923714 Wing bending 873932
844 332
874423 Wing bending
0
I
I
I
I
I
I
I
_qyt;6%~~gl;.llAjyrarWUr.Y .C a/~I. uc~~pi  —— ~~  —~ —~L — 7sracsacCI Ai.PJFanirpl C  pPI 318PiPllFI Bwa I)s s BY II  I C
0 200 400 600 800
E~quivalent airspeed, V, knots
eq
Fig. 123. NIodal frequencies of aircraft type B in flight. Weight = 49, 068 lb. (Four pylons per wing
'wth'# to lE(R racsF, i, 364 Ib. armament, syrrmetric modes.)
40
30
045286.. 065583
u 389114 
O 20 103095
602 329501
I v0 — O
 507838 Mixed 50 
1778
10 I Wing nding and torsion
8450 23 Mxx
~ 795331
864621 Wing bending
0  *  ' — MI. ~ I, I   r 
0 200 4
Equivalent airspeed, V, knots
eq
Fig. 13. Modal frequencies of aircraft type B in flight. Weight 51, 752 lb. (Four pylons with tM
MER per wing, 14, 048 lb. armament, symmetric modes.)
O10
40
30
10
4 inb~oard
pylon s
, I 4 r, ri n i, + c, IQ%7 ri, rn i f r I r, m o,11, f s. I
40
1022796
w 4i
30
20
I11
04E,286
389114
063 19
149904
337 557
84502 3
864621I
0
W, 00lb. r e t. (S y mym e tric m o e )
Fig. 15 Ground vibratiofl frequencies for aircrf ye$wt ayn ra
60
c I,. I
1,. to r iorn
269606
r 
— G 0~LLo  U~~ 11~I~ I,~
I
 14W
50
129902 wing torason. 'Ok339406
  n
r.
— i  A I  I
1 277462
wing torsion
279130
— 2  — p
401'm
wing bending and torsion
73680?'
4.4
ON
X —
II,.+>1
301in
931 534
wing bending
80245t
' U _ ___ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ ___ __ _ _ _ _ _ _ _ _ _ _
4r U7 
20
775237
933705
Ipb  P
wing bending
8 bd46n 8
wing berd
lmr —  5;.111, Flutt
Mode
IW
10
 2o0496 f l pgebending
270496 fuselage bending
— oo
220497
L. _I
I
a
a
a:.~JsuClhPuln*~;ad,  W I I,~ag BL I~
A
I
a
0
200
I I I
400
0U0
800
Equivalent airspeed at sea level, V, knots
e q
c1& A r o. eic for aircraft type C in flight. Weightl, 15, 265 lb. Internal fuel
only (liiJihh).
40
30972501 wing bending 972601
30
532681 fuselage bending 502782
U
o '  
20 972010 wing bending 972209
) — 0 
903229 wing bending 883432
286471 wing torsion and fuselage bending 297658
10 725641
73 12 69 5251 wing bending and torsions 904208
746706
667410 wing bending and torsion Flutter in Mode (g=0. 03)
0 I II II.II..I,.. l
0 200 400 600 800
Equivalent airspeed at sea level, V, knots
eq
Fig. 11 Modal frequencies for aircraft type C in flight. Weight 17, 258 lb. (Symmetric modes.)
20
1 5'
N
'4'
I
i
a
943308
0 a   0 0 0 
342391 fuselage bending
OM  ) ~ —.0 
332392
wing bending
I
N
i
943308
2 59705
wing torsion
379209
OL .. lw.  ~
10
462286 fuselage bending 442188
 
694258
nmixed
584965
k
L
I  Ak  & INk AM  W a    a
It 0 4& 8
  
83219 wing bending 3_5___6
N — — p  
am n 17 3 It I fn
OQ k f'7Cm
 r s Ylrl r
 v Z 1 U Wig UDIlnL1gi 7 c f
5830 wng torsion 139238
5 2 8 03 0 wing torsion 1 392 38
Flutter
in 1st
Mode
(g=O. 03)
0
I
).200
w a,.K1<42 ff 0.X
a
I
I
I
AWxm 94veMIM10
I
(
400
I
600
800
Equivalent airspeed, V, knots
eq
:1
r 1.., ( P, r  1... I,  . I I, !.
r,... ,;  ft t Tr, n Cr in flight. Weight 21. 908 lb. (Symmetric modes.)
60o!
269606 Wing to:;ion
501 
4
339406
279130
736802
Wing torsion
Wing torsion
Wing bending and torsion
40
4
N
'4ii
>1
u
0'
QU
cr
Q)
IL4
301
802455 Wing bending
874615 Wing bend.
% 972601 Wing bending
V 502782 Fuselage bending
> 972209 Wing bending
~ 883432 Wing bending
2 0 894605 Wing bend.
220497
Fus. bend.
10
297658
725641
904208
746706
Wing torsion
Mixed
Wing bending
Wing bending and torsion
%943308 Wing bending
V 332392 Fuselage bendin
~ 379204 Wing torsion
422188 Fuselage bendirio
O 584965 Mixed
A 943506 Wing bending
D 981707 Wing bending
o 139238 Wing torsion
I
I
I
a
I
I
I
0
Is I  I I p  L   zls    L 1 I B  P 
0
1000
200C
3000 4000 5
Armament weight on pylons, lb.
000
6000
7000
8000
Fig. 19 Modal frequencies of airplane type C in flight at 500 knots. (Symmetric modes.)
601Om
2 239705
50 
1 " CQar
I L ) 7 7V L?77462
815902
40
00
O
L.
>,
cr
l^
30o
931534
775237
933705
20
( 97250]
V 532681
0> 972010
9 903229
286471
9 695251
a 736712
o 667410
10
0
) 270496
<, 943308
V 342391
o 259705
a 462286
o 694258
o 835219
972110
0528030
I
I
I
I
I
I
I
I
A AI
1000
2000
3000
4000
5000
6000
7000
8000
A:i iLarnient weight on pylons, lb.
PFi. 20 Ground vibration frequencies for aircraft type C with varying fuel and armament load.
17 5681 "Optimal" mode tracking
RMS error  22.8
RMS error  18. 3
40
112596
tN
Or
sq.1
4 
30
20
065583
438914
103095
329501
508516
617718
10
318051
795331
1 r nr i
0
0 5,000 10,000 l, UUU
Armament weight, W, lb.
Fig. 21 Automated mode tracking attempt for aircraft type B at 500 knots. (Symmetric modes. A
rework of data in Figure 14.)
69606 Wing torsior)
Wing tobrsion
2 Wing bend.
torsion OPTIMAL" mode trackiing
RMS error = Z3.1.\ ~ si~"PlA~ oetakn
30
972601 Wing bending
RMS error  20.2
o 1 802455 Wi benrg /
50332392 Fuslage be
20497 Fbus. ebend76 nd5 Wing torsi Wing tors
102 422188 Fuselage bei
o 20 Wing
Wing bend. 746706 Wing bending & toro 943506 Wing bendinr
bending
10 2c 422 1878 Fuselage bWing bend. 746706 Wing bending & torsion 943506 Wing bendi981707 Wing bendini
139238 Wing torsior
1,
7,d 3_
y
II
r"r1Jn
0
L.~
0 1000 2000 3000 4000 5000 6000 7000 8000
Armament weight on pylons, lb.
Fig. Z2 Modhi frequencies of airplane type C in flight at 500 knots. (Mode tracking "experiment"
witt frequency data. Synnmmetric modes.)
60
C(REF)
B(RE A(RE F)
B (pa.tiailly a cr."5ed)
C (Partially1
armed)
A Pc.. i,
fueliedI
50
40
(Fully
armed)
A! (FtullG; ft eled )
C (Fully
J
30.
f
1 0
0 10, 000 20, 000 30, 000 40, 000 50, 000 60, 000 70, 000 8
Armament weight, W, lb.
Fig. 23. Composite relation between modal frequencies and total aircraft weight at 500 knots.
(Reference aircraft have no external stores.) (Symmetric modes.)
000
Figure 24(a). Fundamental mode of aircraft type A with wing
fully forward (16~ 1.e. sweep). 494 knots at
sea level. Medium weight = 71,834 lb. Verticat displacement of wing. f  5.98 hz
   r~~~ L. +
u in 4mA
I Mr &A on_&  L.Sh o md lL   A A — A"t ^^r
m
0. 100. 150. 200. 250. 300. 350. 400.
LLIJ
Ld
UI
N
(D
o~
STI
I, IN,
A MEDM, WING
ZD, 493.6 KT MD 1
M 
W   . FT's a c
Figure 24(b). (cont.) Torsional rotation of wing. I
0
a:,
0.
ft
CD
z
0m 1
0N
100.1
300.1
400.,
Fy MEI1
STEN7 IN7
A MEDMFWIN6
*0. 1~
~_II __
' Figure 24(c).
(cont.) Vertical displacement of fuselage.
LLi
Cr)
U
40.
20.'
0.S
STI,INLET
I
EXHAUST
I
DUD a1 6K y 1
IN 200A MI
Figure 25(a). Fundamental mode of aircraft type A with wing fully }
swept (72.5~ I.e. sweep). 498 knots at sea level.
I edium weight = 71,834 lb. Vertical displacement
[ of wing. fl = 6.03 hz.
*, ^& r "~ ~~ 1 — — + 4
50. 100. 150. 200. 250. 300. 350. 400.
ILJ T i Nr A MESWWING ZD,498.4KTrMDl
LL
CQ 4.
N
Z3
12.
Figure.125(b).
Fiur 2(b. (cont%.) Torsional rotation of wing.
C0CD1
z%
II
0 2 
onij
0a.0
SI~
— + i i UI .0
00" 11" 0 0
I? A s F I 0i
IMD 1
100 11
i Figure 25 (c). (cont.) Verti(
i
cal displacement of fuselage.
LJ
LL
1
LJ
(D
L
40. +
L  i jLL i i
INLET I
l L I I I,. I I I I I a
*i,..Lti tr
EXHAUST
1000..4KT, MD1
0.... L   .  ... 
9 a a
S
STI,7 INr
200.
A
XTI a V I r I , Ia I I I —T
00. 6l.
M W FUS, ZD,
4 I 91
800
498
20.
 —CC CI CIC — — ~  —L __ __ __
Figure 26(a). Fundamental mode of aircraft type B. 533.5 knots
at sea level. Medium weight = 49,068 lb. Vertical displacement of wing. f = 6. 70 hz.
I X
ULJ
LLU
L 20.I
(D 10."
H PYLON I i PYLON
3 1?
0.
I
I
L
pi.LI1
o +200. 250. 300.,WING W7. 433.5KTr MD1
rr
`~t%
10.
i Figure 26 (b). (cont.)
I
Torsional rotation of wing.
Ut
H
0~
CD
z
1. f
1 2
0.0
s1
I,,.. A i I?; I N? t6B ME~?W I N 0 3T, 4; %TD 1K
___ __ __ ___
' Figure 26(c).
(cont.) Vertical displacement of fuselage.
_ ____,I
I INLET I EXHAUST
I I
I I
0.
100.
— o.00. 700.
433
433.5KTr MD 1
LLJ
LU
LL0%
I
N
V)
Z, IN,
B MEDM,
4.
8.
10.
12.
2:
0
FC)
S
Q)
CO
vi4
a
44
' —4
0
H0)
S
(N
N
2:
0
2JI
a
C0
(N
vi4
a
C0
C0
S..
LUL
()
84b
z
%..
I
S. '
0
a
114,
I
S
iliii CQZ
9NIM I
Figure 27(a).
Fundamental mode of aircraft type C.
sea level. Medium weight = 17,258 lb.
displacement of wing. f1 7. 46 hz.
483 knots at
Vertical
z
0 
".4
Ii4
a
rn0
6Aii
HQC
S a
N '4
a a
Lii
a
GIVH'(LO~I 9NIMA
Figure 27(b). (cont.) Torsional rotation of wing.
82
I
X
LJ
1I
I
I
I
I9
it
I
/~
J*

LL
z
6
0
IZ
0
0
I
l33'aOz 3sn]
Figure 27(c). (cont.) Vertical displacement of fuselage.
83
14
12
sea level
10
8
/ 40,000 ft. altitud
4)
O
U
0 2 4 6 8 10
Elapsed time, t, sec.
Fig. 28. Sharpedged gust response for rigid type B aircraft. Gust vertical velocity = 2 ft/sec. Aircraft weight = 54, 611 lb.
e
84
a
u
ui
(n
NS,,
a
LL
0
a
CY)
4*.039:
Cf)
Fu
0
i
uj
In
a
V4
r"I
a
u
Lli
co
Li
a
a
a
CD
co
(10:DI
CD
0 LLJ
4 Z:
4
b*.:D
C)
a
0
a %.dp
0 C5 6
1 lll) 3 v 1 C4,9 1 a
a
0
Jli —9NIA
C)
a
C)
Figure 29. Elastic response to sharpedged gust., air f t ype A.
85
a
LUi
(I)
a
HLL
N
C~)
a
N
0
aLi
(a,
a
Lf) u
L U
'4 (n
LUj
'" i4
D
II
C
[ii
H
(D
LO)
a
0
6 a
C C OL
a
0
6
iNIW9OVldSIO dIlr9NIM
Figure 30. Elastic response to sharpedged gust, aircraft type B.
86
a
LUI
(JO)
NS.
LL
N
0
J
CD
0
UY)
0
(N
LOU
zsu
C)
a
U)
0
aS
0 
CI
0
0
~N2J4WDOVIdS I
dJli9NIA
Figure 31.
Elastic response to
sharp.edged gust., aircraft type C.
87
H.
LI)
tr%)
PEAK GUST VELOCITY
2 FT/SEC
ff H.
C!q
LA) H.
O00
rt Id
0*
0_
(0
H.
0
CF2
(0
C)
(0
to%
z
I
0.1000+
0.001ef
e0 0o0s+
C
a
A
000001i'=
et
2
Iv
e, 4, 
G"
v
so.
LOWER FREQIJENCY.ILIP4!T ON POWER SPEC~TRUM CHZJ
RIGiD,ODY PLUNGING RESPONSE rO CONTINUOUS
TUR~BULENCE
x
Figure 33. Aircraft coordinate system used for RS calculation
Figure 33. Aircraft coordinate system used for RCS calculation
89
4~CD
o 1 1i0
N)
CDr
w C~)
o<<
zo0
tHLOL
C(2j,
6) 6
(El
C 'W Os9)
90
60.
50.
40.
WAVELENGTH = 30.0 CM.
6
Or)
_Jr —
UJ a
c21~
" it
0 0
LJ (r)
O L
30.
20.
10.
o.
1 0.
50.
100,
200.s
VIEWINGANGLE
CDEG. 3
Figure 34(b).
STAT I C RADARSCATTER I NG
CROSSSECTION
AIRPLANE TYPE 'A'
97.
8.7.'
STATIC. DYNAMIC
30.0 CM
VIEWING ANGLE =
5 DEG.
61
5.
tbJ
J
Ui03
ma
UlJ cf)
D,.
4.
3.0 CM
ovn! & U T A^. INTINA IL
STATIC
2  I I — I IO0. 0.02 0.04 O. c 0.08 O010 0.12 0.14 0. 16.0
TIME CSEC]
OVER ONE VIBRATION CYCLE
DYNA I C RADARSCATTER ING CROSSSECTION
FiL uIrce " (a)
1.
AIRPLANE TYPE 'A'
VIEWING ANGLE = 15 DEG.
0.
3.0 CM
(f) r%.LJ a
ui Z:
sa
IL) O)
00W
LLJQ.J
0.. J........_ STATIC
— 0.02.04 0.06  0.10.1 0.4 06 3 0 02 a. 04 0. 06 0 08 O. 10 a 12 On 14 Om 16
0.
1.
1.
30.0 CM
TIME CSEC)
OVER ONE VIBRATION CYCLE
Figur 35(b). DYNAMIC RADARSCATTER I N CROSSSECTION
I
AIRPLANE TYPE 'A'
VIEWING ANGLE  25 DEG.
V) rLJ a
0co
O ~%.
2.5&
2.0!
1.5 1.0
08.5 
' Ca  __ _ ....STATIC
— DYNYAMIC
30.0 CM
3.0 CM.. —.    < — STATIC
d DDYNAMIC
0a I  ;4^  —~"h   — +~( .i  — I
O0 O0.02 0.04 0.06 0. 08 0.10 0.12 0.14 0.16
TIME CSEC)
OVER ONE VIBRATION CYCLE,.~, )q. J\I",'A, h C RAf R SCATTER I NG CROSSSECTION
3.
AIRPLANE TYPE 'A'
VIEWING ANGLE a 35 DEG.
2.
) OC
uiLJ
Q<~
2.
STATIC
— C30.0 CM)
STATIC
— C3. O CM)
2.
2.2I  i —i i  —   a i —I —ai —
0.0 002 0.04 0.06 008 0.10 0.12 0.14 0.6
0.0 0.02 0.04 0.06 0O. 0 0.10 0.12 0.14 O. 16
TIME CSEC]
OVER ONE VIBRATION CYCLE
DYNAMIC RADARSCATTERINO CROSSSECTION
Figure 35(d).
16.
AIRPLANE TYPE 'A'
VIEWING ANGLE = 45 DEG.
0 CM)
14.
12..J
LLJ E
03
L.) C
Q~.
u3 La
10.
N0
0'
8.a
0.0
0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16
TIME (SEC)
OVER ONE VIBRATION CYCLE
DY.I T C' RADARSCATTER I NG CROSSSECT I ON
Fiasirp i fpc^
9.
AIRPLANE TYPE 'A'
VIEWING ANGLE a 5 DEG.
MIDWING SCATTERING CENTRE
8.
7.
6.
STATIC, DYNAMIC
30.0 CM,,O
s0
() d"'.J S
) C3
l o 4 *
3.0 CM
DYNAMII
3.'
3.            — STAT I C,.
0.0 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16
TIME CSEC
OVER ONE VIBRATION CYCLE
DYNAMIC RADARSCATTER ING CROSSSECTION
c
Figure 36(a).
i
AIRPLANE TYPE 'A'
VIEWING ANGLE w 15 DEG.
flI0o.".VING SCATTERING CENTRE
1.1
0.
3. 0 CM.J a
uicr)
M S
0.
c
I  a I IJ 0. 02.0 OoC O6.C 8 010. a12 0. 14 0. 16
 0 .l.. 0  * — a    STATI C
30.0 CM DYNAMIC
4.1'
'DYNAMIIC
TIMlE
OVER
CSEC)
ONE VIBRATION
CYCLE.1
1"Y'NAtil I.. '5 1; .
RAFJARS CATTER I NO RSSETO
#r...ROS(7 SECT I ON
  jp..q     — WArMd=ZS —
_  _ _ —'ar  
  STDYNAMTIC
AIRPLANE TYPE 'A'
VIEWING ANGLE " 25 DEG.
MIDWING SCATTERING CENTRE
30.0 CM
2.51
2. 0
1.5t
en)
LLJ E
C]
C) O
Jr co
0C0L
LUJO'
1
a
0.0
0.(
3.0 CM. —.   . . STATIC
 DYNAMIC
 .I  —.... — 1  I A  I
D 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16
TIME
OVER
CSEC)
ONE VIBRATION CYCLE
Figure.36(c). DYNAM I C
RADARSCATTERING
CROSSSECTION
I
f
t
AIRPLANE TYPE 'A'
VIEWING ANGLE * 35 DEG.
MIDWING SCATTERING CENTR,.J a
LLJ Z
or:
5 a
oc O
LLJ cr
2.
2.
~ Q —STATI C
(30 CM)
— STATIC
C(3 CM)
C
0
C30 CM)
DYNAMIC
( 3 CM)
0. 0
0n.02 0a.04 0n.06 Oa OC2 01 0
0. 12 0. 14 0. 16
OVER ONE VIBRATION CYCLE
RAUAP,SCATTERlN6 CRO""~3SECTION...,, I U Y ill\',Il  If
'I. g u i t' — ) t "I
l' j . i  %.I
16.
AIRPLANE TYPE 'A'
VIEWING ANGLE a 45 DEG.
MIDWING SCATTERING CENTRE
14.
12.
0
1*j
UV)
LLJ a
in
LI W
0Ld0
10.
8.40
0.0
0.02 0.04 0.06 O0.8 0.10 0.12 0.14 0.16
TIME CSEC]
OVER ONE VIBRATION CYCLE
Figure 36(e). DYNAMIC
RADARSCATTER I NG
CROSSSECT I ON
APPENDIX
BILIGA '"lA'
I 0 7.
,, 'A'
, y  " " 0 C, Z A 1? ' "r, 1 *,, 0 L. 0   ,. i I 14
J N l!ITR. Tf 0? IC I GAN STUDY F`R U. S. AIl LO CE
lEERENCES PAE FOR:
1) ATMOSPHERIC TURBULENCE
2) METHODS FOR CALCULATING AIRCRAFT RSESONSE TO TU2RBULENCE
3) VIBRATION CHARACTERISTICS OF SPECIFIC AIRCRAFT SUCH %S F4, F1 )4
F1 11
4) EFFECTS OF AGEING ON VIBRATION PROPERTIES OF AIRCRAFT
W. J. ANDERSON
SANJAY CORREA
10 OCTOBER 1977
ADAMS, M.S. AND GRANTHAM, W.D.,"ANALYTICAL STUDY OF EFFECTS OF
SEVERE TURBULENCE ON FLIGHT MOTIONS OF A TYPICAL SUBSONIC JETTRANSPORT AIRPLANE," NATIONAL AERONAUTICS AND SPACE ADMINISTRATI^'N.
LANGLEY RESEARCH CENTER, LANGLEY STATION, VA., REPT NO: NAS
ATND5573, L5990, DEC 69.
ADVISORY GROUP FOR AEROSPACE RESEARCH AND DEVELOPMENT, "EFFECTS
OF SURFACE WINDS AND GUSTS ON AIRCRAFT DESIGN AND OPERATION," REPT.
NO: AGARDR626, NOV. 1974
** THE THIRD PAPER ON WIND SHEAR MAY BE USEFUL FOR RADAP i.D.
AHARRAH, R. C.,"MANEUVERABILITY AND GUST RESPONSE PROBLEMS
ASSOCIATED WITH LOWALTITUDE, HIGHSPEED FLIGHT," ADVISORY GROUP
FOR AEROSPACE RESEARCH AND DEVELOPMENT. PARIS (FRANCE)., REPT NO:
AGARD556, OCT 67.
AIKEN, WILLIAM S. JR AND LEAN, D., "FLIGHT IN TURBULENCE," ADVISORF
GROUP FOR AEROSPACE RESEARCH AND DEVELOPMENT PARIS (FRANCE),
REPT NO: AGARDBCP140 NOV 73
"AIRPLANE STRENGTH AND RIGIDITYFLIGHT LOADS," MILITARY SPECIFICATION MILA8861, MAY 18, 1960. AERONAUTICAL STANDARDS GROUP.
ALBANO, E. AND RODDEN, W.P., "A DOUBLET LATTICE METHOD FOR
CALCULATING LIFT DISTRIBUTIONS ON OSCILLATING SURFACES IN SUBSONIC
FLOWS," AIAA JOURNAL, VOL. 7, NO. 11, NOV. 1969, P. 2192.
ANDREWS, W. H., ROBINSON, G.H. AND LARSON, RP. R.,"EXPLORATORY
FLIGHT INVESTIGATION OF AIRCRAFT RESPONSE TO THE WING VOPTEX
WAKE GENERATEr PY JET TRANSPORT AIRCRAFT, NATIONAL AERONAUTICS
AND SPACE ADMINISTRATION. FLIGHT RESEARCH CENTER, EDWARDS, CALIF.,
REPT NO: NASATND6655, H671, MAR 72.
ANGELINI, JEANs,"ESURE DE LA TURBULENCE ATMOSPHERIQUE A TRES
BASSE ALTITUDE ET GRANDE VITESSES (MEASURE OF ATMOSPHERIC TUPBULENCE AT VERY LOW ALTITUDE AND GREAT SPEED). ADVISORY GROUP FOR
AERONAUTICAL RESEARCH AND DEVELOPMENT. PARIS (FRANCE), iEPT
NO: AGARD441, APR 63.
ANON, "CHARACTERISTICS OF ATMOSPHERIC TURBULENCE NEAR THE
GROUND. VARIATIONS IN SPACE AND TIME FOR STRONG WINDS (NEUTPAT.
ATMOSPHERE)," ESDU DATA ITEMS N 75001 JUL 1975, 31 P.
ARNOLDI, R.A., "UNSTEADY AIRFOIL RESPONSE," NASA SPEC PURL
207 (BASIC AERODYNAMIC NOISE RESEARCH) JULY 1415, 1969,
P. 24756.
103
6 1
62ASHBURN, E. V. s, WACO, D, E AND MITCHELF A 7, "OV E`O'ElMENT63 OF HI.1GH, ALT"ITUDE CLEAR AIR TURBULENCE MODEL3,' A R l03CE ZLiiTT
604 DYNAMICS LABORATORY, WRIGHTPATTERSON AFB, OHIlO, AFFDLT&R0'9793,33
65 NOV. 1969.
66
67 ASHBURN, ET A.L,"HIGH ALTITUDE CLEAR AIR TURBULENCE MODELS FOR
68 AIRCRAFT DESIGN AND OPERATION,"1 LOCKHEEDCALIFORNIA COMPANY,
69 AFFDLTR6879, JUL 68.
70
7 1 ASHBURN, E.V.,, WACO, D.E., AND MELVIN, C.A., "fDEVELOP~m N T O F
72 HIGH ALTITUDE GUST CRITERIA FOR AIRCRAFT DESIGN." AIR FORCE
73 FLIGHT DYNAMICS LABORATORY, WRIGHTPATTERSON AFBs OHIO,
74 AFFDLTR~7O101, OCT. 1970. L
7 5
76 ATNIP, F.K. AND GAULT, J., "ANALYSIS OF GUST VELOCITIES FO)R
77 APPLICATION TO AIRCRAFT DESIGN,'# INTERNATIONAL CONFERENCE ON
78 ATMOSPHERIC TURBULENCE, COMP.ILATION OF PAPERS, THE ROYAL
79 AEROINAUTICAL SOCIETY, LONDON, ENGLAND, MAY.
80
81 BAARSPULI M. AND GERLACH, O.H.,r"CALCULATION O,,F THE PESPONSCE
82 OF AN AIRCRAFT TO RANDOM ATMOSPHERIC 'TURBULENCF. PART 2  (M
83 METRIC NOTIONS," TECHNISCH E HOGESCHOOt. DELFT (NETHERLAND4. DEPT.
84 OF AERONAUTICAL ENGINEERING., REPT HK 139, APR 68.
8 5
86 BANNON, J.K., "TURBULENCE IN THE STRATO$_lPAE9E AND IN THE UPPER
87 TROPOSPHERE," ATMOSPHERIC TURBULENCEH AND ITS RELATION TO AIRCRAFT,
88 ROYAL AIRCRAFT ESTABLISHMENT, FARNBOROUGH, ENGILAND, NOV. 16,
90
91 BARNOSKI, R.L. AND MAURER, J.R., "MEANSQUA~RE RESPONSE OF
92 SIMPLE MECHANICAL SYSTEMS TO NONSTATIONAPY RANDOM EXCITATION,"9
93 TRANSACTIONS OF ASME; SERIES E: JOURNAL OF APPLIED MECHANICS,
94 VOL. 36, NO. 2, JUNE 1969, PP. 22122 7.
95
96 EARROIS, "OA REVIEW OF FRE'NCH W4ORK ON FATIQUE?OR THE IPFRIOD
9 7 19641966, AERON. FATIQUE FEB. 1968, 2339378.
98
99 ~ BATCHELOR, G. K.,"THE THEORY OF HOMOGENOUS TURBULENCE," CAMBFRIIUNIVERSITY PRESS, 195.3, PP. 1417.
BEER., F.P. AND TREVINO, G.,t "ON RESPONSE OF STRUCTURE V>
THROUGH RANDOM FIELD,"l ASMEPAPER 69VIBP38 FOR MEETING MAR 30 APR 2, 1969, 5 P.
FABENNETT, FLOYD V. AND PRATT, KERMIT G.,"CALCULATED RESPONSFN,
llBST COMPARISONS, NATIONAL AERONAUTICS AND SPACE ADMI41STRTif~
OKLANGLEY STATION, VA. LANGLEY RESEARCH CENTER., REPT NO:
NASATR~R69f 19600.
*BERGQUI1ST, RUSSELL R.,"1HEUICOPTER GUST RESPONSE INCLTU))i.
VUNSTEADY AERODYNAMIC STALL EftFECTS,"1 Ull"TED AIRCRAFT CORP, ~TP T F') R
1 4 CONNo SIKORSKY AIRCRAFT DIV, FINAL REPT, MAY 73.
eRMRAN, S., MAC CREADY, P.B. JR., WEBSTIER, A. A_,D W~_L~lIA;lI
17 R.E., '"OPERATIONAL APPLICATIO11N OF A UNIVERSAL TURBULE NC' MS E A1~15'j
SYS'~F,"'EM FINAL REPORT, METEORiOLOGY RESEARCH, ILNC.,f ALTADENA', CALI.; 1 9 REPT N09: NASACR62025, MR.I,6 5FE&3O1, NOV 65.
JI 04
E I S P) l C; O3 a  IN" > 35RN A D Oi 5RF N ', ' F. u g s T? LCADS ON..iG RPAF ES IH TC GL J O URNAL O " THE. AR'N AJUTCAL. SC^:NCES, wOL. 6, JAN. 1951, P?. 3342.
BiSPLINGHOFF, R. L., ASIHLEY, H., AND HALFMAN, R.L., "DYNA yIC
> RESPONSE TO A DISCRETE GUST," AEROELASTICITY, 1ST ED., ADDISONWESLEY, CAMBRIDGE, MASS, 1955, PP. 673679.
) BLACKMAN, R. B AND TUKEY, J. W, "THE MEASUREMENT OF POWER
i SPECTRA," 1ST ED., DOVER, NEW YORK, 1958.
BOONE (AIR FORCE FLIGHT DYNAMICS LABORATORY), HIGH ALTITUDE
CRITICAL ATMOSPHERIC TURBULENCE DATA SYSTEMS, AFFDLTR671, ^AY 67
BOUCHER, R. J., "MESOSCALE HISTORY OF A SMALL PATCH OF
CLEAR AIR TURBULENCE," JOURNAL OF APPLIED METEORALOGY, VOL. 12,
AUG. 1973, PP. 814821
** IT IS POSSIBLE THAT RADAR RETURN FROM C.A.T. IN THE
*I TROPOPAUSE OR BELOW WILL MASK THE AIRCRAFT VIBRATIONAL
** PROPERTIES IMBEDDED IN THAT C.A.T. THE C.A.T. SEEMS TO
** OCCUR IN REGIONS OF TEMPERATURE INVERSION AND HIGH WIND
** SHEAR (IN THE VERTICAL PLANE).
BOUJOT, J., "A LINEAR CONTROL OF SYSTEMS WITH RANDOM INPUT 
APPLICATION TO GUST RESPONSE CONTROL," OFFICE NATIONAL D ETJUDES
ET DE RECHERCHES AEROS PATIALES, PARIS (FRANCE)., REPT NO.: ONE
RAP131, 1970.
BOWNE & ANDERSON (TRAVELERS RESEARCH CENTER, INC.), "TAKEOFF
AND LANDING CRITICAL ATMOSPHERIC TURBULENCE (TOLCAT) ANALYTICAL
INVESTIGATIONS," AFFD LTR6823, APR 68, AD 835 232.
EROADBENT, E.G., ZBROZEK, J.K. AND HUNTLEY, E., "A STUDY OF DYNAII(
AEROELASTIC EFFECTS ON THE STABILITY CONTROL AND GUST RESPONSE
OF A SLENDER DELTA AIRCRAFT," ROYAL AIRCRAFT ESTABLISHMENT,
FARNBOROUGH (ENGLAND)., REPT NO: A RCR/M3690, ARC32779, 1972.
BRUNING, G., "STATISTISCHE PROBLEME IN DER FLUGMECHANIK (STATISTIC
PROBLEMS OF FLIGHT MECHANICS)," DEUTSCHE VERSUCHSANSTALT
FUER LUFTUND RAUMFAHRT E V GBERPFAFFENHOFEN (WEST GERMANY),
REPT NO: DVL305, 1969.
BUCCIARELLI, L.L, AND KUO, C., "MEANSQUARE RESPONSE OF A
SECOND ORDER SYSTEM TO NONSTATIONARY RANDOM EXCITATION," TRANSACTIONS OF ASME; SERIES E: JOURNAL OF APPLIED MECHANICS, VOL. 37,
NO. 3, SEPT. 1970, PP. 612616.
BULLEN, N.I., "A REVIEW CF INFORMATION ON THE FPEQUENCE OF
GUSTS AT LO W ALTITUDE," AERONAUTICAL RESEARCH COUNCIL, LONDON,
C. P. NO. 873, 1966. P ON MICROMETEROLOLOGY, D.A. HAUGEN, ED.,
AMER. METEOR. SOC., 165
BURNHAM, J., "AN EXPERIMENTAL CHECK ON THE THEORETICAL
RELATIONSHIP BETWEEN THE SPECTRAL DENSITY AND THE PROBABILITY
DISTRIBUTION OF CROSSINGS FOR A STATIONARY RANDOM PROCESS 4ITH
GAUSSIAN DISTRIBUTION, USING DATA OBTAINED IN MEASUREMENTS OF
AIRCRAFT RESPONSE TO TURBULENT AIR," AERONAUTICAL RESEARCH COUNCIL
LONDCN (ENGLAND), REPT. NO: ARCCP834, SEPT 1963
BUSCH, N.E., 1973: "ON THE MECHANICS OF ATMOSPHERIC TURBULENCE."
105
WORKSHO , AND S.E. LARSEN,, 1972 "5L2ECTRA OF, TURBULENCE P'_
182THE ATMOSPHERIC SURFAC""E LAYER." RISOG REP. NO. 256, 18 20 7.
'13 41 CAMPAZGNA, A.W. AND PRIi3Y0,r fl."Zo "A STU3Y OF STAk3IL'IZATIOlN TECiiT
1 3 5 FOR SMALL, FIXEDWING, REMOTELY PILOTED AIRCRAFT, "#ARMY ELECTRONICS
186 COMMAND FORT MONMOUTH, N.J., REPT NO.: ECOM'4239, AUG 7L4
187
188 CANSDALE, RI. AND HALL, H., "GUST RESPONSE MEASUREMENTS ON?A MO (
18 9 AIRCRAFT,"l ROYAL AIRCRAFT ESTABLISHMENT, FARNBOROUGH (ENGLAND).
19 0 REPT NO.: ARCCP11 13, RAETR69273, 1970
19 1
19 2 CARLSON, E. FRANK, "AN INVESTIGATION OF THE POTENTIAL1. Bl.NEFTTs
19 3 OF DIRECT SIDEFORCE CONTROL FROM A MISSION VIEWPOI.NT," BOEIlN%';
19 4 AEROSPACE CO SEATTLE WASH RESEARCH AND ENGINEERING DIV, PEPT
195 NO: D180175081, 31 JUL 73.
19 6
197 CASE, E.R. "A STUDY OF THE EFFECTS OF C LCOUPLING ON THE
198 LATERAL STABILITY OF AIRCRAFT IN ATMOSPHERICl TURB3ULENCE" TORNT
'199ci UNIV. (ONTARIO). INST. FOR AEROSPACE STUDIES.,. REPT NO.:
200 UTIASTN118, SEP 67
20 1
202 CHALK, CHARLES, "FLIGHT EVALUATICN. OF VARIOUS PH'IGGOID 7iYN P 1IC 
20 3 AND 1/TH 1 FOR THE LANDINGAPPROACH TASKol" C3'&N._r~jlL AERO%%AUTIC'.,AL
2014 LAB., BUFFALO, N~.Y., REFT NO: TCo1K4 DEC 65.
235
205 i CHAN, PAUl. T., O"LOh ALTITUDE PE NE T i AT ION PARAMETRIC STUDYr PARC7
207 II, EFFECTS OF ATMOSPHERIC TURBULENC ]~ LOWi ALTITUDE FLIG.HT. PFIRF'OP'
20~ AERONAUTICS DIV. LINGTEMCOVCUGdT INC. DALLAS, TEXAS, EEPT. NO: LT'
20 9 255100/5R50275t MARCH 1965.
2 10`
2 1 lilCHEN, W.Y., "APPLICATION OF RICE'S EXCEEDANCE STATISTICS Tn
212 ATMOSPHERIC TURBULENCE," AlAA JOURNAL, VOL. 10s, NO. 8, AUG13. 19
2 13 72, PP. 11031105.
214 * SHOWS THAT RICE'S CALCULATION OF EXCEEDENCE STATISTllICS
21 5 DOESN'T REALLY APPLY TO ATMOSPHERIC TURBULENCE BECAUSE
2 1S f) TURBULENCE IS IN FACT STiCNC!2`' eiON GAUSSIAN.
218 CHINTSUN, Hl. AND PI., W.S., "INVESTIGATION O'F!40ORTHRCP >5A\ Wf1'4
~19 BUFFET INTENSITY IN TRANSONIC FLIGHT,"1 NORTHROP CORP., HIAWT HNE,,
CALUf. AIRCRAFT DIV., REPT NO..: NASACR214814, NOV 714
CHRISTOPHER, R..T AND DUNN, J..H I 'NFLUENCE OF AONKRJ
Z1ONGITT UD I NAL A E ROD `N i MI C CH A RAC T E R!T I CS O N T H E P OW E R S PE C T~AI,
RESPONSE OF AIRCRAFT TO1 ATMOSPHERIC TURBULENICE.", AERONAUT Q.
V. 214, PART L4, NOV. 1973, P 28'4294
kZESENTSON, C.C., "f,'N INVESTIGATIONl OF THE POWER SPECTRAL DN1~
OFATMOSPHERIC TURBULEINCE,"1 INSTRUMENTATION LABORATOR"Y  i
REllPORT NO.: 644 5D. 31 MAY 1950.
COLEMIAN, THOMAS L. o PRESS, HARRY AND MEADOW.S, MAY T. j"AN rVLVMJ
OF EFFECTS OF FLEXIBILITY ON WING STRALINS IN ROUGH AIR P.P
ALARGE SWEPTWN AIRPLANE BY MEAN~S OF EXPERIMENTALLY DETER<,NE
FREQUJENCE RESPONSE FUNCTIONS WITH AN AISSESSMEN~T OF RANDJOMPROCESS TECHNIQUES EMPLOYEDr NATIONAL AERONAUTICS33 FID t~PACF
ADMINISTRATION, LANGLEY STATION, VA. LANGLEY RESEkaCH
NO.: NASATRR;70, 1960.
239 COLE ~IAN, T.L AN D STLE,~ "ATNOSPHEPZIC TU.RBULENCE ""EX2TJP.
24+C OBTAIMN.D FROM AIRAgLANE A2LA1N ~ tiA ITUDES~
0 u6
?1,0 0 T FQ ( 7 QO FT FO. R E A A AS O T ALH NO R R
2 EEi.APNER2 II ISA TN D48 jv960:3
COLSON, D. "METEOROLCGICAL ANALYSIS OF 1964 ICAO TU:.33JLENCE
DATAh, WEATHER FUREAU TECHNICAL MEMO, ENVIRONMENTAL SPACE AND
SCIENCE ADMINISTRATION, TDL 14, OCT. 1968.
CONNER (LOCKHEEDCALIFORNIA COMPANY) PRELIMINARY DESIGN STUDY
FOR A HIHICAT VEHICLE AND INSTRUMENTATION SYSTEM, AFFDLTR66100,
) OCT 66, AD 809 829
COUPRY, G., "CRITICAL ANALYSIS OF THE METHODS USED FOR
PREDICTING THE RESONSE OF LARGE FLEXIBLE AIRCRAFT TO CONTINUOUS
ATMOSPHERIC TURBULENCE," AIAA PAPER NO. 71342, APRIL 1971
** IT IS CLAIMED THAT SPANWISE VARIATIONS IN TURBULENCE
** LENGTH CAUSE ENOUGH CANCELLATION OF LIFT AS TO SMOOTH
** OUT THE PREDICTED RIDE. FOR THE PURPOSES OF RADAR
** MODULATION BY ELASTIC MODES, THIS IS IMPORTANT BECAUSE
** IT MEANS THAT SIMPLER THEORIES ("CYLINDRICAL" WAVES)
W * WILL OVERPREDICT THE AIRCRAFT RESPONSE. NEVERTHELESS,
** THERE IS A SCALE FACTOR INVOLVED, I.E. THE LENGTH OF
** COHERENCE OVER THE WINGSPAN AND FOR FIGHTER
** AIRCRAFT THIS SCALE MAY BE LARGE ENOUGH TO ALLOW A
** CYLINDRICAL WAVE ASSUMPTION. EVEN FOR AN AIRCRAFT AS
** LARGE AS THE CONCORD, THE SPANWISE EFFECTS ONLY REDUCE
** PEAK RESPONSE BY A FACTOR OF TWO. FOR FIGHTER AIRCRAFT
** THE ERROR DUE TO THE CYLINDRICAL ASSUMPTION MUST BE
** ABOUT 10%.
COUPRY, GABRIEL, "PROBLEMES DU VOL EN TURBULENCE." (PROBLEMS
OF FLIGHT IN TURBULENCE," INT COUNC OF THE AERONAUT SCI (ICAS),
9TH CONGR. PROC. HAIF A, ISR, AUG 2530 1974 V 2: STRUCT. MATER,
DYN, PROPUL. DES, NOISE AND POLLUT P 561574.
COUPRY, G., RAPID EVALUATION OF THE STATISTICAL CHARACTERISTICS
OF AN AIRCRAFT IN ATMOSPHERIC TURBULENCE, FRANCE. OFFICE NATIONA.L
D ETUDES ET DE RECHERCHES AEROSPATIALES, CHATILLONSOUSBAGNEUS.,
REPT NO.: TP256/1965/, 1965.
COX, R.A., "COMPARATIVE STUDY OF AIRCRAFT GUST ANALYSIS PPOCEDURES$
A ERON J V. 74, N. 718, OCT. 1970, P 80713
CROOKS, ET AL (LOCKHEED CALIFORNIA COMPANY), HIGH ALTITUDE
CLEAR AIR TURBULENCE, AFFDLTR65144, SEP 65, AD 474 616
CROOKS, W.M., HOBLIT, P.M., AND PROPHET, D.T., "PROJECT HICAT.
AN INVESTIGATION OF HIGH ALTITUDE CLEAR AIR TURBULENCE," AI.
FCECE FLIGHT EYNAMICS LABORATORY, WRIGHTPATTERSON AF3, OHIO,
AFFDLTR67123, NOV. 1967.
CROOKS, W.M., HOBLIT, F.M., AND MITCHELL, F.A., "PROJECT HICAT.
HIGH ALTITUDE CLEAR AIR TURBULENCE MEASUREMENTS AND METEOROLOGICAL
CORRELATIONS," AIR FORCE FLIGHT DYNAMICS LABORATORY, WRIGHTPATTERSON AFB, OHIO, AFFDLTR 68127, NOV. 1968.
CROSS, A.K., T38 DYNAMIC RESPONSE GUST LOADS COMPARISON BFTWEEN
FLIGHT TEST AND ANALYTICAL RESULTS, NCRAIR DIV NORTHROP
CORP, HAWTHORNE, CALIF., REPT NO.: NOR60306, IAR 64
DIEDERICH, F.W., "THE RESPONSE OF AN AIRPLANE TO RANDOM ATMOSPHERIC
107
301 DISTURBANCES," REPT NO. 1345, 1958, NACA: SUPERSEDES TN 3910, N\CA.
302
303 DIEDERICH, F.W., "THE DYNAMIC RESPONSE OF A LARGE AIRPLANE
304 TO CONTINUOUS RANDOM ATMOSPHERE, J.A.S., VOL. 23, OCT. 1956.
305
306 DONALDSON, C. DUP. AND SULLIVAN, R.D., "THE APPLICATION OF
307 INVARIANT MODELING TO THE CALCULATION OF ATMOSPHERIC TURBULENCE,"
308 AFFDL TR71168, JAN. 1972, AIR FORCE FLIGHT DYNAMICS LAB.,
309 WRIGHTPATTERSON AIR FORCE BASE, OHIO.
310
311 DONELY, P., "ATMOSPHERIC TURBULENCE AND THE AIR TRANSPORTATION
312 SYSTEM, "PROCEEDINGS, INTERNATIONAL CCNFERENCE ON ATMOSPHERIC
313 TURBULENCE, LONDON, ENGLAND, ROYAL AERONAUTICAL SOCIETY, 1971,
314 PP.14. DRYDEN, H.L., "A REVIEW OF THE STATISTICAL THEORY
315 OF TURBULENCE," TURBULENCE, EDITED BY S.K. FRIEDLANDER AND L.
316 TOPPER, INTERSCIENCE, NEW YORK, 1961, PP. 115150.
317
318 DUTTON, J.A., THOMPSON, G.J., AND DEAVEN, D.G., "THE PROBADILI.
319 STRUCTURE OF CLEAR AIR TUEBULENCESOME OBSERVATIONAL RESULTS
320 AND IMPLICATIONS," CLEAR AIR TURBULENCE AND ITS DETECTION,
321 EDITED BY Y. PAO AND A. GOLDBERG, 1ST ED., PLENUM, NEW YORK,
322 1969, PP. 183206.
323
324 DUTTON, J.A., AND H.A. PANOFSKY^i, 970: CLEAR AIR TURBULENCE;
325 A MYSTERY MAY BE UNFOLDING. SCIENCE, 167, 937944.
326
327 DUTTON, J.A., AND DEAVEN, D.G. 1969: "A SELFSIMILAR VIEW OF
328 ATMOSPHERIC TURBULENCE." RADIO SCI., 4, 13411349.
329
330 DUTTON, JOHN A. PROBABILISTIC DETERMINATION OF AIRCRAFT RESPON
331 TO TURBULENCE AT LOW ALTITUDES, AERONAUTICAL SYSTEMS DIV
332 WRIGHTPATTERSON AFB, OHIC, DEPUTY FOR ENGINEERING, TECHNICAL
333 REPT. MAY 68NOV 67, OCT. 68
334
335 EGGLESTON, JOHN M. AND PHILLIPS, WILLIAM H., "THE LATERAL BRES
336 OF AIRPLANES TO RANDOM ATMOSPHERIC TURBULENCE,' NATIONAL AER)NA[T7TC
337 AND SPACE ADMINISTRATION, LANGLEY STATION, VA., LANGLEY
338 RESEARCH CENTER., REPT NO.: NASATRR74, 1960.
339
340 EMERNBERGER, L.J., "METEOROLOGiCAL ASPECTS OF HIGH ALTITUDE
341 TURBULENCE ENCOUNTERED BY THE XB70 AIRPLANE," PROCEEDINGS, THI 9)
342 NATIONAL CONFERENCE AERCSPACE METEOROLOGY, NEW ORLEANS, AMERICAAi
343 METECROLOGICAL SOCIETY, 1968. PP. 515522..4 4
345 EHERNBERGER, L.J., "ATMOSPHERIC CONDITIONS ASSOCIATED WITE
346 TURBULENCE ENCOUNTERED BY THE XB70 AIRPLANE ABOVE 40,000 VFEET
34' ALTITUDE," TN D4768, 1968, NASA.
>EH EHERNBERGER, L.J., AND LCVE, B.J., HIGH ALTITUDE GUST.ir CELERT
IO ENVIRONMENT AS EXPERIENCED BY A SUPERSONIC AIRPLANE, NATIONA i
35% AERCNAUTICS AND SPACE ADMINISTRATION. FLIGHT RESEARCH CENTER,
2 t EDWARDS, CALIF., REPT NO: NASATND7868, H836, JAN 75.
353
354 EHLERS, H.L., "TECHNICAL CONSIDERATIONS IN THtE DESIGN OF G{ST
355 ALLEVIATION CONTROL SYSTEMS," AUTONETICS REPORT X79)3/301, AN01 iS
356 CA, APRIL 1967.
35 7
358 EICHENBAUM, F.D., "THE APPLICATION OF MATRIX METHODS TO CL.EAR
359 AIR TURBULENCE MEASUREMENT," AIAA PAPER 66967, BOSTON, MAS:.,
360 1966.
108
I
2 ICHEA ' j M^t FD. D A GI GZ OE'iAL TLHEORY OE AIRCR AFT RESPONSE
TC i$tE 'EDIMEAS#ISNAL TU RBULECE,' JOURNAL O. A:RCRAFT, VOL 8,
4 NC. 5, MAY 1971, PP.353360.
* A DETAILED ThEORY TO PREDICT SYMMETRIC AND ANTISYMMETRIC
** RESPONSE TO 3D TURBULENCE. USES ASSUMPTIONS OF HOMO7 ** GENEITY, STATIONARITY, ISCTROPY AND TAYLOR'S HYPOTHESIS.
9 EICHENBAUM, FREDERICK D., EVALUATION OF 3D TURBULENCE TECHO NIQUES FOR DESIGNING AIRCRAFT, LOCKHEEDGEORGIA CC MARIETTA*AIR
FORCE FLIGHT DYNAMICS LAB. WRIGHTPATTERSON AFB, OHIO, FINAL
2 REPT. 1 OCT 7315 APR 75, JAN 75.
3
et EICHENBAUM, FREDERICK D., RESPONSE OF AIRCRAFT TO THREE DI5 MENSIONAL RANDOM TURBULENCE, LOCKHEEDGEORGIA CO MARIETTA, TECHNICAL
6 REPT. JUL 71MAR 72, OCT 72.
EICHENBAUM, F.D., "NEW METHOD FOR COMPUTING THE DYNAMIC RE3 SPONSE OF AIRCRAFT TO THREEDIMENSIONAL TURBULENCE," AIAA/ASME 10
S STRUCTURES, STRUCTURAL DYNAMICS & MATLS CONFERENCE — TECH PAPERS
FOR MEETING, NEW ORLEANS, LA, APR 1416, 1969, P. 8494.
ELDERKIN, ET AL. (BATTELLE MEMORIAL INSTITUTE, PACIFIC NORTH
WEST LABORATORY), TAKEOFF AND LANDING CRITICAL ATMOSPHERIC TURBULENCE (TOLCAT)  EXPE RIMENTAL INVESTIGATION, AFFDLTP70117,
MAY 71, AD 885 321.? ELDERKIN, ET AL. (BATTELLE MEMORIAL INSTUTUDE  PACIFIC NORT
HWEST LABOR ATORY), TAKEOFF AND LANDING CRITICAL ATMOSPHERIC TfU
BULENCE (TOLCAT)  EXPERIMENTS AND ANALYSIS, AFFDLTE71172,
APR 72, AD 750 131.
ENDLICH, R M. AND MCLEAN, G.S., "EMPIRICAL RELATIONSHIPS
BETWEEN GUST INTENSITY IN CLEARAIR TURBULENCE AND CERTAIN
METEOROLOGICAL QUANTITIES," JOURNAL OF APPLIED METEOROLOGY, VOL.4,
APRIL 1965, PP. 222227.
** AN ATTEMPT TO PREDICT MODERATE OR SEVERE TURBULENCE FROM
** MEASURABLE ATMOSPHERIC QUANTITIES, E.G. THE PRODUCT OF
** WIND SPEED AND TURNING OF THE WIND WITH HEIGHT, OR VERTICAL
** SHEAR OR RICHARDSON'S NUMBER. A FREQUENCY OF OCCURENCE
** GREATER THAN 50X CAN BE PREDICTED WITH THESE OBSERVABLES
** (NONE OF THE MEASURED QUANITIES CAN BE MEASURED BY RADAR,
** HOWEVER).
ENDLICH, B.M. AND MANCUSO, R.L., "THE TURBULENCE CLIMATOLOGY
OF THE UNITED STATES BETWEEN 20,000 AND 45,000 FT. ESTIMATED FRCO
AIRCRAFT REPORTS AND METEOROLOGICAL DATA," CONTRACT AF19
(628)5173, JUNE 1968. STANFORD RESEARCH INSTITUTE, MENLO PARK, CA.
EPPS, J.B., LIBERTY, S.R., FERRY, D.K. AND SEECAT, R.H.. "OUTPUT
ACAPTIVE DYNAMIC MODEL FOR ESTIMATING TURBULENCE." MIDWEST SYMP
ON CIRCUIT THEORY, 16TH, PROC, PAP, UNIV OF WATERLOO, ONT,
APR 1213, 1973 V.1, PAP VII. 4, 10 P.
ETKIN, B., JOHNSTCN, G.W. AND TEUNISSEN, H.W. "MEASUREMENTS OF
TURBULENCE INPUTS FOR V/STOL APPROACH PATHS IN A SIMULATED PLANETARY EOUNEARY LAYER." TORONTO UNIV INST AEROSP STUD UTIAS REPT
NO 189, JUL 1973, 90 P.
ETKIN, B., "THEORY OF THE FLIGHT CF OF AIRPLANES IN ISCTROPIC
109
4i21 TURBULENCE  REVIEW kbiD ET~lSI0N," AEVISORY GROUi? ZOR AERONAUTICAL
2.2 RESEARCH AND DEVELOPMENTs 2ARIS, (FRANCEW),, RhT.NO AGARD2372,, A73?R.
4213
424 FICUTER, D., CALCULATION OF THlE FREQUENCY RESPONSE OF THE
42 5 ELASTIC AIRPLANE'S REACTIONS TO VERTICAL GUSTj.S AT INCOMPREZSSTELE
42 6 FLOW, DEUTSCHE VERSUC HSANSTALT FUR LUFT UIND RAUIFAHRL. OVER427 PFAFFENHOFEN (WEST GERMANY). INSTITUT FUER FUGMECHANIK.,, REEPT NO:
42 8 DVL821, DLRFB69040 JAN 69
429
4 30 FIREBAUGH, J.M., "EVALUATIONS OF A SPECTRAL GUST M~CDEL UJSlNG
43 1 VGH AND VG FLIGHT DATA,"1 J. AIRCRAFT, 4:6, 518525s, NOVDEC 1967.
432 * AN EXCELLENT OVERVIEW OF THE RESPONSE TO TURBULENCE
433 * PROBLEM. GIVES GUST INTENSITY PARAMETERS, FLIGHT TIMl`;.
434 * IN TURBULENCE AS FUNCTIONS OF ALTITUDE. MUCH EXPERIMENTAL
4 3 5 DATA ARE GIVEN, BUT FOR A RATHER OID FLEET OF C130,
43 6 L* 749, L188 AND B720B AIRCRAFT.
437
4 38 FRANKLIN, J.A., "TURBULENCE AND LONGITUDINAL FLYING QUALITIESI`
439 NASA CONTRACT REPT CR1821, JULY 1971.
440
44 1 FRICK, J.K. AND JOHNSON, W., OPTIMAL CONTROL THEORY 1TNV1EST1 442 GATION OF PROP ROTOR/WING RESPONSE TO VERTICAL GUST, NA1IO0NAL
44 3 AERONAUTICS AND SPACE ADMINISTRATION. AMES RL>E3)ARCH CENTEF,<)FT
444 FIELr, CALIF., REPT NO: NASkTMX6 L2'k, SEPT 74.
445
446 FUJIMORT, Y. AND LIN, Y.K., "ANALYSI11S OF AIRPLANE FESPONSE
44 7 TO NONSTATIONARY ATMOSPHERIC 'TURBULENCE INCLUDING WING BENDING
44 8 FLEXIBILITY," AIAA JOURNAL, VOL. 11, NO. 3j, ~1ARCH 1973, PP. 3314
44 9 339.
4 50
451 FUJIMORI, YOSHINORIa, AND LIN., Y.K.j, "ANA laY IS OF AIRPLANE
452 RESPONSE. TO NONSTATIONERY TURBULENCE INCLUDING WING"` BENDING FEI
453 BILITY. PART Ile" AIAA JOURNAL, V. 11, NO. 9,j SEPT 1973, PP. 1343 454 * IHIS PAPER IS NEEDED TO SAKE THE PREVIOUS ONE BY FUJIMORI
455 * AND LIN IMPORTANT. HERE IT IS SHOWN THAT SUDDEN ONSET OF
45 6 STATIONARY RANDOM FORCING CAN' CsAUSE 28% YIORE ACCELERATION
457 * AT THE AIRCRAFT C.G. THAN STATOA1:1RY RAN3OM FOR"'ING.
45 8 PERHAPS THIS CORRECTION FACTOR SHOULD BE APL2LIED IN
459 * DESIGN SOMETHING LIKE A SHARPEDGED GUST.
FUJJIMORI, YOSHINORI, "'ShEAR AND MOMENT RESPCINSE, OF ath'~ A~~
PLN5WNT ONTTONARi TURBULENCE." AIAA JOURNAL VOL. ~,4 NO. 11, NOV 1974, PP. 14591460.
FUJIMOBIj, Y.,r SHEAB AND MOMENT RESPONSE OF THE AIR6 ~?LALNE WING TO NONSTRTICNARY TURBULEINCEj, NATIONAL AEROSPACE,
LAL.w TOKYO (JAPAN) v REPT NC: NALTR 40 4T, JAN 75.
FULLER, J.R.,o RICHMONDa, L.D. ET AL., "CONTRIEN1MTIONS T ki'
DEVELOPMENT OF A POWERSPECTRAL GUST DESIGN PROCEDUBE FOih &v IA AJ
CRAFT," BOEING RENTON, FAAADS54v JAN. 1966.
FULLER, J.R.j, ##A PROCEDU~RE FOR EVkLUA.LI4G Ah C~S ~ T i
TTION S OF CO0NT I NUOU S 'TU R BU LEN CE ON A I PP LA NE L~R SON SET3, J IF
OF AIRCRAFT, VOL. 5,v NO. 1, JANFEB 1968, PP. 49b
**'7 A FAIRLY EASIC APPROACH AT PROVIDING IN LH INTO D
**EFFECTS IN RESPONSE TO TURBULENCE.
44 9 FU NG s Y. C., A N I N TRODU CTIO N TO T HE T HEO0R Y O,)F A ERGE L AS7UJ" VT,,I~
4 8 01 WILEY, NEW YORK$ 1955.
I110
FUNA, Y13C2 S.ATISTICAL ASPECT CF DYNA~MIC LOAD," JOURNAL CF
AR SG ATICL SCIENCES, VOL. 20d MAY 1953,?P. 31 7330
PUNGI Y.C., AN INTRODUCTION TO THE THEORY OF ELASTICITY.
DOCVER, NEW YORK, 1969, PP. 280281.
GAULT, LOW ALTITUDE ATMOSPHERIC TURBULENCE LOLOCAT MIDTERM
TECHNICAL DATA ANALYSIS, (THE BOEING COMPANY), SEGTR6735,
AUG 67, AD 820 880.
GAULT, J.D. AND GUNTER, D.E., JR., "ATMOSPHERIC TURBULENCE
CONSIDERATIONS FOR FUTURE AIRCRAFT DESIGNED TO OPERATE AT LOW
ALTITUDES," JOURNAL OF AIRCRAFT, VOL. 5, NO. 6, NOV.DEC. 1968,
PP. 574577.
* VERIFIES THE VON KARMAN MODEL OF THE POWER SPECTRUM FOR
** ATMOSPHERIC TURBULENCE GIVES SOME ADVICE ON LENGTH SCALES
** OF TURBULENCE FOR SEVERAL MODELS.
GAULT, J.D., "LOW ALTITUDE ATMOSPHERIC TURBULENCE ANALYSIS
METHODS, " CANADIAN AERONAUTICS AND SPACE JOURNAL, VOL. 13, NO.
7, SEPT. 1967, PP. 307314.
GAULT, ADDITIONAL RESEARCH OF LOW ALTITUDE TURBULENCE DATA,
(THE BOEING COMPANY), AFFDLTR71150, SEP 71, AD 739 875.
GENERAL DYNAMICS, SAN DIEGO, CALIF. CONVAIR AEROSPACE DIV,
"CONTROL POWER CRITERIA FOR STATICALLY UNSTABLE AIRCRAFT," REPT
NO: CASDNSC76003, NOV 76.
GERLACH,O.H., VAN DE MOESDIJK, G.A.C. AND VAN DER VAART, J.C.,
"PROGRESS IN THE MATHMATICAL MODELLlNG OF FLIGHT IN TURBULENCE,"
FLIGHT IN TURBULENCE, AGARD CP140, 1973, PP 5.15.38
GIESING, J.P., STAHL, B., AND RODDEN, W. P., "ON THE SEARS
FUNCTICN AND LIFTING SURFACE THEORY FOR HARMONIC GUST FIELDS,"DOUIGLAS PAPER 5368, MARCH 1969, DOUGLAS AIRCRAFT CO; ALSO JOURNAL
OF AIRCRAFT, VOL., NO.3, MAYJUNE 1970, PP. 252255.
** THIS WORK APPEARS TC HAVE BEEN MOTIVATED BY THE EXPENSE
** OF THE DOUBLET LATTICE METHOD FOR CALCULATING UNSTEADY LOADS
** DOE TO HARMONIC GUSTS. BECAUSE A GUST OF ARBITRARY PROFILE
4* REQUIRES A WIDE HARMONIC CONTENT TO DESCRIBE IT, MANY
** rISCRETE FREQUENCY CALCULATIONS WERE PREVIOUSLY REQUIRED,
** PARTICULARLY BECAUSE THE SEARS FUNCTION IS SO RAPIDLY VARYING.
** BY TRANSFORMING THE ORIGIN (WHERE THE GUST VELOCITY HAS
** "ZERO PHASE ANGLE") TO THE LEADING EDGE, THE SEARS FUNCTION
** S SUITABLY TAMED SO THAT INTERPOLATION IS POSSIBLE.
GOBELTZ, J., LABORATORY FLIGHT SIMULATION WITH FREEFLI';HT
MODELS, KANNEkR (LEO) ASSOCIATES, REDWOOD CITY, CALIF., REPT NO:
NASATTF17124, AUG 76.
GOGOSHA, OREST R. AND MORIARTY, THOMAS E., THE RESPONSE OF A
HOVERING V/STOL AIRCRAFT TO DISCRETE IURBULENCE, REPT NO: SGC/EE/
677, JUN 67.
GOSSARD, E.E., J.H. RICHTER AND D. ATLAS, 1970: INTERNAL WAVES
IN THE ATMOSPHERE FROM HIGH RESOLUTION RADAR MEASUREMENTS.
JOURNAL GEOPHYS. RES., 75, 3 5233536.
111
54 GVIFEIN, C. JR AIND LAAjGNEj, A. H4., THEE2R LTO OF THF. SCAT
~42 TERING CROSSSECTIONS 0F THE DISTURBED T.NDEX QF REFFACT720N A.ND
0 THE ACCELETRATION INCREME~NT OF A CONVENTIONAL" AllZCRAFT DUE T C
544 CLEAR AIR TURBULENCE, TEXAS UNIV AUSTIN ANTENNAS AND PROPAG.AT; ON1011
54 5 LARTNO P28t 28 MAY 68.
546
547 GUNTER, ET 4L., LOW ALTITUDE ATMOSPHERIC TURBULENCE LOL1OCAT
548 PHASES I AND II, THlE BOEING COMPANY, ASDTR6912, FEI3 69,, AD
549 853 299.
550
551 HALL ER, P~.L. A ND P EL OUDBET, R. P. J R PAkR A MET RIC S TU DY O F B3 C
552 ACCELERATION RESPONSE TO IURBULENCE AND CCMPARISONS WITHi FLI(;IiT
553 DATA, AUGUST 1967  AUGUST 1968, GENERAL DYNAMICSFORT WORTH,71
554 TEX.,v REPT NO.: NASACR66699,, NOV 68.
556 HAMEL, P., ON THE EFkECT OF GUSTS AND CROSSWIND ON THE DY557 NAMIC RESPONSE OF AIRCRAFT. ESTABLISHMENT, FARNBOROUGH (PN~3LAND))
558 REPT NO: RAELIBTRANS1524, OCT 70.
559
56U HAMEL, P. GUST EFFECTS ON THE DYNAMICS OF kIRCRAFi DURING
55 6 1 LANDING APPROACH, NATIONAL AERONAUTICS AND SPACEAYIiATFN
562 WASHINGTON, D.C.,f REPT NO.: NASATTF12751, MAY 71
563
564 HAMMOND, J.K., " ON THE EP ~&E AND MULjTIDEGRfp, OF
565 FREEDOM SYSTEMS TO NONSTAT&l 1.~Ai~fl IM7) X t.TA.OS ORN
566 0F SOUND AND VIBRATION, VOL. 7, 196a, 3 393 4 16.
567
56`8 HARDY, K.R. AND OTTERSTEN K* "RADAR INVESiTI,(2AT.1IONS 0?7 CYI56 9 VECTIVE PATTERNS IN THE CLEAR ATMOSPHERE," JOURNAL OF ATMOSUFNP.tC
570 SCIENCES, VOL. 26, JULY 1969, PP. 666672.
571 * TWO TYP ES OF CLEAR AIR CONVECTIVE PATTERNS A&R OBSERVED AITH
572 * RADARs, A SMALL DOUGHNUT TYPE AND A BERNARD TYPE. T HlE FFIR ST
573 * TYPE IS 1~3 KM IN DIAMETER AND SEVERAL HTINDRE"D M~ETERS IN HIEIHT
57 4 AND PERSISTS FOR 2030 AINUTES. THE SECOND TYPE IS 5""0 KM
5 7 **l IN DIAMETER AND 1 2 KM IN HEIGHT.
576
577 EIARRINGTON, CHARLES A. IIA1, DE.L" OF C"lf,)NTBOL SYSTEM TO
578 SThB~LILIZE THE AFT FUSELAGE OF A B 52 BOMBER 'LeI THE PRESENC"T, O)F
5 7 '9 A RANDOM WIND GUST, AIR FORCE INST OF TECH, WR`AGPIT?ATT~lfSO)N, AF93,
~8OOHIO SCHOOL OF ENGINEERING,. liEPT NO: G"E/'ZE/7L4Ml5,r MAR 74.
32HILDRETH, ET AL. HIGH AILJITUDE CLEAR A~IR TURBUlLvENCE, L0CTh T)
CALIFORNIA COMPANY, ASDTDR634440, SE? 63, AD ~421 857.
HINZEv J.0.,v TURBULENCE., AN INTRCDUCTION TO ITS MECHAN IS1 AUU)
THEORY, MC GRAWHILLt NEW YORK, 1939,r P. 147.
fiOBLIT* F.$4., PAULs, N.,p ET AL.,q "DEVELOPMENT OF POIE?, F&,
TRAL GUST DESIGN PROCEDURL FOR CIVIL AIRCRAFT," LOCKHEED CA L F.
~,j FAAArS53a, JAN. 1966.
HOUBOLT, J. C., "ATMOSPHERIC CATURBULENCE",, DtEYDEN aESEtjRflCr!
LECTURE, AlAA OCURNALs, VOL. 11, NO. 4, APRIL8j 1973.1,P. 2I4
GOOD SUMMARY OF TURBULENCE.A II J Y,!1. Z INCLUDEFS flTKL DF7PI'T LO
9"FOR ORIGIN OF TURBULENCE, VON KAVMAN,'S  AIEsT ~), C 2WT
5 9 SPECTRA FOR ISOTJROPIC TURBULENCEv AND zRATI "5OF
q 7 *CCCURRENCE OF VARTOtJS SIZ1Z25 AND) VELOCITY TNTFNUTTTFJ"_ OF
TURBULENCE PATCHES. EIlPHASIZES FANOOM INP~UT F OR 01EaS.IG N.
591 * * AND SFIG WS 'T.; EQ UIV AL.EXCE BET', —, E"N?A.ND OM 2X'"`CT 1 AMIO','N D E S TCN,
It 0 01** LAWS AND GU.;i) DESIO2 LATE. __T IM'f>S:'tCRA"T `
1r TiJR3Pi: T PCnS '7 O'?H TII,; " 1,.00, O40,000 FT:i`NGE.
2
3H0 OLT^ u DESIG HA;UAL 1"OR V E'TICTAL GUSTS BASED ON
POYEE SECTRAi T CHNIQUi ES APFDLT '70 106, T EC. 1970, AIR FCRCE
FLIGHT DYNAMICS LAB., WRIGhTPATTERSON AIR FORCE EASE, OHIO.
7 HOUBOLT, J.C., "THE ART Of DETERMINING GUST FREQUENCE RESPONSE
FUNCTIONS," PRESENTED AT THE 31ST AGARD STRUCTURES AND MATERrALS
PANEL MEETING, TONSBERG, NORBAY, OCTNOV 1970.
)
1 HOUBOLT, J.C., "MATHEMATICAL MODELING AND RESPONSE EVALU'ATION
FOR THE FLUCTUATING PRESSURES OF AIRCRAFT BUFFETING," ADVISOrY
GROUP FOR AEROSPACE RESEARCH AND DEVELOPMENT, REPT. NO: AGARDR630o JULY 1975
HOUBOLT, J.C. "GUST DESIGN PROCEDURES BASED ON POWER SPECTRAL TECHNIQUES," AFFDLTR6774, AUG. 1967, AIR FORCE FLIGHT DYNAMICS LAB., IRIGHTPATTERSON AIR FORCE BASE, OHIO.
S?OUBOLTo J.C. "ON RESPONSE OF AIRPLANES IN A 3DIMENSIONAL
GUST FIELD, " REPT 161, JULY 1971. AERONAUTICAL RESEARCH ASSOCIATES
OF PEiNCETON INC., PRINCETON, N.J.
HOUBOLT, J.C., "AIRCRAFT RESPONSE TO TURBULENCE INCLUDING
WAKES," AIRCRAFT WAKE TURULENCE AND ITS DETECTION. PLENUM PRESS,
NEW YORK, 1971.
HOUBOLT, J. C., "ON THE RESPONSE OF STRUCTURES HAVING TULTIPLE
RANDOM INPUTS," WGL JAHRBUCH (FREDERICK VIEWEG UND SOHN, BRAUNSCHWEIG, GERMANY, 1957), PP. 296305; ALSO PAPER DK 533.6.013.08,
517.512 (1957).
HOUBOLT, J.C. AND SEN, A., "CROSSSPECTRAL FUNCTIONS BASED
ON VON KARMAN'S SPECTRAL EQUATION," CR2011, MARCH 1972, NASA.
HOUBOLT, J.C., STEINER, R., AND PRATT, K.G., "DYNAMIC RESPONSE
OF AIRPLANES TO ATMOSPHERIC TURBULENCE INCLUDING FLIGHT DATA
ON INPUT AND RESPONSE," TR R199, 1964, NASA.
HOUBOLT, JOHN C., "PIELIMINARY DEVELOPMENT OF GUST DESIGN PROCEDURES BASED ON POWER SPECTRAL TECHNIQUES." VOLUME I. THEORETICAL
AND GENERAL CONSIDERATICNS, AERONAUTICAL RESEARCH ASSOCIATES
Of PBINCETON, INC., N.J., REPT NO.: ARAP83VOL1, JUL 66,
AND VCLUME II. SUMMARY OF POSSIBLE PROCEDURES, REPT. NO: ARAP83VOL2,
MARCh 1966.
HOUBOLT, JOHN C., "EFFECT OF NONUNIFORM SPANWISE GUSTS (" AIRCRAFT VERTICAL RESPONSE," AERONAUTICAL RESEARCH ASSOCIATES '?
PRINCETON, INC, N.J., REPT NC: ARAP209, JAN 74.
HOUBOLT, JOHN C.o "ON THE RESPONSE OF AIRPLANES IN A THREEDIMENSIONAL GUST FIELD," AERONAUTICAL RESEARCH ASSOCIATES OF PRINCETON,
INC., N.J., REPT NC: ARAP161, NOV 72.
HOUBOLT, JOHN C. AND WILLIAMSON, GUY G,, "SPECTRAL GUST RESPONSE
FOR AN AIRPLANE WITH VERTICAL MOTION AND PITCH," AERONAUTICAL
RESEARCH ASSOCIATES OF PRINCETON INC NJ, REPT NO: ARAP256, NOV 75.
HOUBOLT, JOHN C. AND WILLIAMSON, GUY, "A DIRECT TIME HISTORh' STUDY
113
C61 OF THE RESPONSE OF AN AIRPLANE TO NONSTA7'IO'NF~R`N URBUJLENCE04
662 AERONAUTICAL fRESEj'.jARCHi ASSOCIATES OF PRXNIC.ETLON ILNC N.J. *AT11 7?CC2
6 31 FLIGHT DYNAMICS LAB., WRIGL!TPAT TERSON AFE3 iL. RLP~7 N'o:
b64 ARAP230, JAN 75.
66 5
666. HOWELL, L.J.o AND LIN, Y~.K., "RESPONSE OF FLIGHT VEHICLES 7')
667. NONSTATIONARY ATMOSPHERIC TURBULENCE," AIAA JOURNAL, VOL. 9,
66 8. NO0. 11, NOV. 1971, PP. 22012207.
66 9 A STUDY OF PLUNGING MOTION DUE TO ONSETA OF A PATCH OF TUDflLENC6 70 U ITH EXPONENTIALLY GROWING PROFILE OF [EXP(AT)EXP(BT) 1
671 * CHARACTER. CAN BE MADE TO GIVE A RAPID OR SLOW ONSrlET O F A
672 * STATIONARY RANDOM LOADING.
67 3
6 74 HOWELL, L.J., "RESPONSE OF FLIGHT VEHICLES TO NO'NSTATION r R Y
675 RANDOM ATMOSPHERIC TURBULENCE," PHd.D. DISSERTATION, FEB. 19471,
676 UNIVERSITY OF ILLINOIS, URBANA, 1LL.
677
678 HUNSAKER, J.C. AND WILSON, E. B., "REPORT ON BEHAVIOR OF AERO~
679 PLA NE S I N G UST S" R EPT. 1, 19 15, NAC A.
680
681 HUNTER, PA. A, "TURBULENCE EXPERIENCE IN A R QKVNE OVE RA T ION$,
682 MEETING ON AIRCRAFT RESPONSE TIO TURBULENCE, LAM(,LFY, IVA., r NSAf
683 1968, PP. 20.120.1 M.
684
685 HUSTON, W. B. AND SKOPINS~I, H~., " Ot3P~iLl'iY AND FIREQ~l ENCY
686 CHARACTERISTICS OF SOME FLIGSHT BUFFET LTiS* 73,15, AA
687
688 HWANG, CHINTSUN, KAMBERG, B.D. AND Pl, W.S. AND CROSS, A. K~.,
689 CALCULATICNS ON PROVEN TRAINER AND FIGHTER AIRCRAFT FOR THE
690 VERIFICATION OF A GUST CESIGN PROCEDURE,"1 NORAi17.R DIV NORTHRCP CCiU?
691 HAWTHORNE CALIF, REPT NO.: NOR 66149, JUL 66.
692
693 HWANG, C. AND PI, W.S., "T{NOI UFE FHVOFO N RTMP,
694 F5A AIRCRAFTs" ADVISORY GROUP FOR~ AEROSPACE RESEARCH AND DEVELOLP2
695 PARIS (FRANCE), REPTL. NC: AGIAE~DR624, SEPT. 1974
696 B* UFFETING IS A RELATIVELY ~iiGl3 I?REQTJENCY PHECNOMENON, AT 50200
697 * IT DOES EXCITE RIGID BODY TRAN3L.4&'lI0"N AT THIFSE FEQUENCS.'lEj3.
698
919 ~II, J.M, AND SIDWELL, K.W.o "EVALUA~LCION OF UNSTEkafJY AE'3YNMl~l1(
700 FORC`_ES AND DYNAMIC RESPONSE OF FLEXIBIE AIRCRAFT STRUJCTURE C
CONTINUOUS TURBULENCE I I2~OI LGT"PO~D!SO A
0 ~8TH STRUCTURES, STRUCTURAL DYNAMICS AND MATERIALS CONFE[XENCL", VSPRINGSo CA, MARCH 2931 19607, PP 380390.
**THE AUTHORS POINT OUT 'ThAT AERiODYNAMTC COUPLING of Tr82
**MAIN WTNG ON THE ST.ABIL IZER' IcS' IMPORTANT FO9F L2XTBL~
** CDY MODES. '"HE FLLEXIBLE' BODY MODES USEB IN ITHE STU D Y
ARE iMIE 4AT(URAL VIBRATION MODES. THE THEOREITICAL STUDY
**WORKS HARD ON THE BCX METHOD FOR SUPERSONI1C FLOW.
INGRAM, C.T. AND EICHENBAUM, F?.D., "A COMPA RISON O0F (> I
FLIGET TEST MEASURED AND THEORETILCAL VERTICAL GJST RESPONSlv4
JOURNAL OF AIRCRAFT,. VOL. 6, NOV.DEC. 1969, PP. 532~53o.
IVERSEN, J.D. VN ~3ERNSTENS,"YAI 7I iULAT1AJ ~JF
CRAFIL UNDER TLHE EFFECT CF VOLTEX WAKE TURVU'LENC;.~ A.VN ~S 0 LI
CALCUL ANALOGIQUE, V 1th N. 3, JUL 1972s P 136 I'.
dJffNSON, C. E. ANV9 SMill, L'jJ.R., "FlJTTER NA SAN'D
7j TESTING OF THEE F/C/D/E A C.'.RAFT CARRYING MK '4 GR MK 32 S '
i 4~,C ON Til MJF0 TB OA BD W I NG S TA ILT&S,w MC DO N ko7F L L A I aC RA FT c '), 1~ ~T'. C U1,S3
14
I NO., INiL BE'r. JUNAUG 72.
2
3 3JONES, G.I. J,ONES J, k., AND,ONSOCN, K. R., "LOW ALTITUDE
A iMOSPHERIC TURBULENCE IOLOCiT PHASE III INTERiM REPORT," AIR
FCCE `,SY!TEMS COMMAND TECH. REPT AFFOLTR6963, VOLS. I AND IT,
OCT., 1969, WRIGHTPATTERSON AIR FORCE BASE, OHIO.
7
i3 JONES, J.G., "SPEED RESPONSE OF AN AIRCRAFT CONSTRAINED TO FLY
3 ALONG A STRAIGHT PATH IN THE PRESENCE OF TURBULENCE AT LOW
) ALTTUDE," AERONAUTICAL RESEARCH COUNCIL (GT. BRIT.)., SEP 67.
1
2 JONES, J.W., MIELKE, R.H., JONES, G.W., ET AL., "LOW ALTITUDE
3 ATMOSPHERIC TUBBULENCE, LOLOCAT PHASE III," VOL.1, PT. 1 DATA
4 ANALYSIS, AFFDLTR7 010, NOV. 1970, AIR FORCE FLIGHT DYNAMICS LAB.,
WRIGHTPATTERSON AIR FORCE BASE, OHIO.
7 JONES, R.T., "THE UNSTEADY LIFT CF A WING OF FINITE ASPECT
RATIC," REP T. 681, 1940, NACA.
3
] JONES, G.W., JONES, J.i., AND MONSON, K.R., "INTERIM ANALYSIS
1 OF LOW ALTITUDE ATMOSPHERIC TURBULENCE (LOLOCAT) DATA," AI?
2 FORCE SYSTEMS CCIMAND TECH. REPT ASDTR697, FEB., 1969,
'3 WRIGHTPATTERSON AIR FORCE BASE, OHIO.
S KAYNES, I.W., "A SUMMARY OF THE ANALYSIS OF GUST LOADS RECORDED
BY COUNTING ACCELEROMETERS ON SEVENTEEN TYPES OF AIRCRAFT,"
7 ADVISORY GROUP FOR AERO SPACE RESEARCH AND DEVELOPMENT, PARIS
B (FRANCE), REPI NC: AGARDf605, DEC 72.
3
KAYNES, I.W., "AIRCRAFT CENTRE OF GRAVITY RESPONSE TO TWODEREN1 SIONAL SPECTRA OF TURBULENCE, ROYAL AIRCRAFT ESTABLISHMENT,
2 FARNEOROUGH (ENGLAND)., REPT NO: ARCR/M3665, RAETR69271, 1971.
3
4 KONRAD, T.G., 1968: THE ALIGNMENT OF CLEARAIR CONVECTIVE.,
5 PROC, INTE RN. CONF., CLOUD PHYSICS, TORONTO,, 539543.
5
7 KONRAD, T.G., AND R.A. KilOPFLI, 1968: "RADAR OBSERVATION OF
3 CLEARAIR CONVECTION OVER THE SEA. PROC. 13TH RADAR METEOR. CONF.,
) BOSTON, AMER. METEOR. SOC., 262269.
1 KUSSNER, H.G., A CCMPARISON OF METHODS USED IN FLUTTER RESEARCH,
2 ADVISORY GROUP FOR AEROSPACE RESEARCH AND DEVELOPMENT PARIS
3 (FRANCE), REPT NO: AGARD592, AUG 72.
4
KUSSNER, H.G., "DAS ZWEIDIMENSIONALE PROELEM DER BELIEBIG
3 BE^EGTEN TRA FLACHE UNTER BERUCKSICHTIGUNG VON PARTIALBEWEGUNGEN
1 DER FLUSSIGKEIT," LUFTF AHRTFORSCHUNG, VOL.17, 1940., PP. 355361.
3 LAPPE, U.O., "A PRELIMINARY EVALUATION OF THE F100 ROUGH RIDER
) TURBULENCE MEASUREMENT SYSTEM," NATIONAL SEVERE STORMS LAB.,
1 NORMAN, OKLA., REPT NO: IERTMNSSL36, OCT 67
2
3 LATZ, ROEERT N., "KC135 POWER SPECTRAL VERTICAL GUST LOAD ANA4 LYSIS, VOLUME I. DETAILED ANALYSIS AND RESULTS," BOEING CO RENTON
WASH AIRPLANE EIV, REPT NO: D618252VOL1, JUL 66
7 LEE, J., "PLUNGINGMCDE RESPONSE OF AN IDEALI7ED AIRPLANE TO
3 ATMOSPHERIC TURBULENT GUSTS." J SOUND VIB., V.44, N. 1, JAN. 8,
3 1976, P. 4762.
)
115
78 LICHTENSTEINs J.H., 9CG~iiIJTED LATERAL RkTE AND ACC.ELDRATIGN
782 POWER SPECTRAL RESPONSE Of C'ONVENTIONAL AND SO A I RP1.A N ES `0
i a31 ATMOSPHERIC TURBULENCEo," NATA"ILONAL AERCNkUTICS AND SPACE AD.011iNI~84STRATION. LANGLEY RESEARCH CENTEi~, LANGLEY STATION, VA., RELI T NO:
785 NASATND8022, L10018, DEC 75.
786
787 LICHTENSTEINo J.H.,r "COMPUTED LAIERAL POWER SPECTRAL DENSITY
788 RESPONSE OF CONVENTIONAI AND STOL AIRPLANES TO RANDOM ATMOSPHERIC
789 TURBULENCE," N4ATIONAL AERONAUTICS AND SPACE ADMINISTRATION.
790 LANGLEY RESEARCH CENTER, LANGLEY STATION, VA., REPT NO:
791 NASA9END7444, L9035, MAR 74
792
793 IIEPMANN, H.W., LAUFER, J., AND LIEPMANN, K., "ON THE SPECLArR r 
7 94 OF ISOTROPIC IURBULENCE,." TN 2473, 195.1, NACA.
795
796 LIEPMAN* H.W., "ON THE APPLICATION OF STATILSTICAL CONCErTS,
797 TO THE BUFFETING PRCBLEM,"f JOURNAL OF THE AERONAUTICAL SC~IENCES,
798 VOL. 19, DEC. 1952, t1P P. 793800. UIN, Y.,~., PROBALISTI1C
799 THEORY OF STRUCTURAL DYNAMICS," MC G.RAWHILLs, NEW YORK, 1967.
800
801 LIN, Y. K., "TRANSFER MATLRIX REPRESENTATION OF FLEXIBLE AIV i I
802 I"N GUST RESPONSE STUDY," JOURNAL OF AIRCRAFT7 VOL. 2,r N(O.2,r io'AiCff
303 APRIL 1965 PP. 116121.
804
805 LOYNESs, R.M., "ON THE CGNICEPT OF TlHE SE1U FOR NONSTATIONA
806 PROCESSES,"~ JOURNAL OF ThE ROYAL STATI S T 1C A1. SC I ET;Y, E.fV
807 30, 1968,. PP. 120
808
809 LUMLEY, J.L. AND PANOFSKY,, H. A., "THE S3TRUCTURE OF AT 1M0SHF:BRf.
$310 TURBULENCE," EDITED BY B.E. MAdSHAK, VOL. X11, LNTIERSCIENCE,
811 NEW YORK, 1964.
$12
813 MAC PHERSCN, 3.1. AND MORRISSEY, E.G., "STRATOSPHERIC T7JRBULE14
814 AND TEMPERATURE GRADIENTS M'EASURED BY AN RB57F," NATIONAL
815 RESEARCH COUNCIL OF CANADA, OTTAWA, LR 551, OCT. 1971.
817 MC CLOSKEYs, ET ALL, "'STATI STICAjLa AN~ALYSTLS OF LOLOCAT TURT13ULFNI
P DATA FOR USE IN THE DEVELOPMENT OF REVISED GUTCRTRI,
9 UNIVERSITY OF LAYTON RESEARCH INSTITUTE, AFFDLTPF71291 A." 723d
19 "'0 139, APR 71.
MICELC... "CALCULATION OF THE RESPONSE COF AFIVV
AIRCRAFT TO TURBULENT AIR AND A.CiAIO IH LGTMAUF
ET,"THE AERONAUTICAL JOURNAL, VOL. 72, O 88 PI 1 96 8
KMITCHELL., C.G.B., "ASSE~SSMENT OF THE ACCURACY OF GUSTL Ff57T'7?4
CALCULATIONS BY COMPEARISON WITH EXPEFIMENISff" 3 AIPCRAFTw V
N C. 2, MARAPR 197 0, P. 11725.
W 0 ~~MONSON, ET AL, "LOW ALTITUDE ATMOSPHERIC TURBULENCE, 'FC
LOLCCAT PHASE TIII," INTERIM REPOERT, THE BOEING COMPANY, AFFD?.!L~
TB6963, VOL. It VOL. Ile AD 861 911, AD864 273, OCT 9L,;34 MULLANS, R.E. AND LEMLEY, C.E., "BUFFET DYNAMIC LOADS D'T I
SONIC MANEUVERSt" MCDONNELL AIRCRAFT CO, ST. LOUIS., MO., 1 A I
I REPT. MAR'70DEC 71, SEP 72.
8 3 L4 N E L SOCNv POBE RT C., "TH E R E SPOCNS E O F A I RC RA FT ENC JU11N PTR 7~33
83 9 CRAFT WAKE TURPBULENCE, ",IR FORCE FLIGHT DOYNAMICS!AB, WPIGPT — 2 A
84 ") TEFRSCN AFB, OHIO, REPT Nu:,4 AiFLTb7429,, JUN 74.
NELSCNt BC.., "CDY2IAMIC bEhAVIGOR CF AN A.iRCAAFT ENCOtUNTEi ING
AIRCEAFT WAKE TURBUILENCE," J AIRC. V. 13, NO. 9, SEPT' 1976, P.
NEULS, G.S., MAIER, H.G., LERWICK, T. R., ROBE, E.A., AND WEBSTER,
I.J., "OPTIMUM FATIQUE SPECTRA," AERONAUTICAL SYSTEMS DIV.,
V., WRIGHTPATTERSON AIR FORCE BASE, ASDTR61235 (APRIL 1962).
NEWBERRY, CLIFFORD F., "INTERACTION OF HANDLING QUALITIES,
STABILITY, CONTROL AND LOAD ALLEVIATICN DEVICES ON STRUCTURAL
LOADS," ADVISCRY GROUP FOR AEROSPACE RESEARCH AND DEVELOPMENT,
PARIS (FRANCE), REPT NO: AGARD593, JUL 72.
NORTH AMERICAN AVIATION INC, COLUMBIS, OHIO, "TURBULENCE STUDY
OF A TRANSONIC WIND TUNNEL AND AN ANALYSIS AND TESTS OF AIRCRAFT
RESPONSE TO TURBULENCE," REPT NO: NA63H636, 1 OCT 64.
NORTON, PAUL SHERIDAN, "THE DETERMINATION OF THE DYNAMIC RESPONSE OF A SMALL SWEPT WING JET FIGHTER TO ATMOSPHERIC TURBULENCE
USING THE POWER SPECTRUM METHOD OF ANALYSIS," MASTER'S THESIS,
DEC 67.
CEHMAN, W.I., "PRELIMINARY STUDY OF AIRPLANE AUTOPILOT RESPONSE TO ATMOSPHERIC TURBULENCE," NASA SPEC PUBL 270 (PROC CONF
ON AIRCRAFT SAFETY AND OPERATING PROBLEMS), HAMPTCN, VA, V. 1,
MAY 46, 1971, PAPER 24, P. 32334.
0' HARA, F. AND BURNHAM, J., "THE ATMOSPHERIC ENVIRONMENT,
NOW AND FUTURE," THE AERONAUTICAL JOURNAL, VOL. 72, NO. 690, JUNE
1 S68.
ONO, K., SCTOZAKI, T., TAKEUCHI, K. AND YAMANE, K., "AN OBSERVATIOP
ON SPANWISE DISIRIBUTIOCN OF VEUTICAL ATMOSPHERIC TURBULENCE,"
ROYAL AIRCRAFT ESTABLISHMENT, FARNBORCUGH (ENGLAND)., REPT NO:
RAELIB TRANS1820, BR47555, JAN 75.
CNO, K. AND YAMANE, K., "AN EXPERIMENTAL INVESTIGATION ON VERTICAL
GUSTS AND THE AIRPLANE RESPONSE," NATIONAL AERASPACE LAB., TOKYO
(JAPAN)., REPT NO: NALTR89, 1965.
OTTERSTEN, H., 1969: "ATMOSPHERIC STRUCTURE AND RADAR BACKSCATTERING IN CLEAR AIR." RADIO SCI., 4, 11791193.
PAGE, C. H., "INSTANTANEOUS POWER SPECTRUM," JOURNAL OF APPLIED
PHYSICS, VOL. 23, JAN. 1952, PP. 103106.
PANOFSKY, H.A., 1969: "INTERNAL ATMOSPHERIC TURBULENCF T BUILL.
AMER. MET EOR. SOC., 50, 539543.
PARKINSON, R.C.H.: KELLY, D.W., "A DYNAMIC ANALYSIS OF %EROPLANES
ENCOUNTERING VORTEX WAKE TURBULENCE," SYDNEY UNIV. (AUSTRALIA).
DEPT OF AERONAUTICAL ENGINEERING., REPT NO: ATN7301, JAN 73.
PCHELKO, T.G. AND VASiL'YEVA, G.V., "TURBULENCE IN A CLEAR
SKY," TR. GIDRCMETEROL. NAUCHNOISSLED, TSENT. SSSP, NO. 7, 1967.,
PP. 3015.
PECKHAM, C.G., "A SUMMAtY OF ATMOSPHERIC TURBULENCE RECORDED
BY NATO AIRCRAFT," ADVISORY GROUP FOR AEROSPACE RESEARCH AND
117
901 DEVELOPMENT, NEUILLYSU RSEINE, FRANCE, AGARD,58671, SEVT, 1971.
902
0o3 PEELE, El AND STEINER, P., "SIMPLIFIED MET;OD OF ES. TATrNG THE
904 RESPONSE OF LIGHT AIRCRAFT TO CONTINUOUS ATMOSPHERIC TURBULENCE,"
905 J AIRCRAFT, V. 7, NO. 5, SEPTOCT 1970, P. 4027.
906
907 PERROCHON, J., "STUDY OF ATMOSPHERIC TURBULENCE AT VEFY LOW
908 ALTITUDE, " ADVISCRY GROUP FOR AERONAUTICAL RESEARCH AND DEVELOPMENT.
909 PARIS (FRANCE)., REPT NO: AGARD440, APR 63.
910
911 PETERSEN, E. L., "A MODEL FOR THE SIMULATION OF
912 ATMOSHPERIC TURBULENCE," JOURNAL OF APPLIED METEOROLOGY,
913 VCL. 15, JUNE 1976, PP. 571587
914.
915. PETRAKIS, JCHN AND MILLER, NELSON, "RESPONSES OF SMALL RIGI D X
916 CRAFT TO DISCRETE AND CCNTINUCUS GUST ANALYSIS," PHASE I, NATTONAL
917 AVIATION FACILITIES EXPERIMENTAL CENTER ATLANTIC CITY, N. J.,
918 J* FEDERAL AVIATION ADMINISTRATION, WASHINGTON, C.D. SYSTEMS
919 RESEARCH AND DEVELOPMENT SERVICE., REPT NO: P AANI7444, DEC. 75.
920
921
922 PHILIPS, W. H., "GUST ALLEVIATION," NASA SPEC PUTBL 258 (PER923 FORMANCE AND DYNAMICS OF AERCSPACE VEHICLES), TROY, N.Y., 1971
924 PAPER 8, P. 50553.
925
926 PHILLIPS, W. H., "STUDY OF A CONTROL SYSTEM TO ALLEVIATE AIP927 CRAFT RESPONSE TO HORIZONTAL AND VERTICAL GUSTS," NATIONAL AFRO928 NAUTICS AND SPACE ADMINISTRATION. LANGLEY RESEARCH CENTER, IANGLEY
929 STATION, VA., REPT NO: NASATND 7278, L8844, DEC 73.
930
931 PI, W. S," AND, HWANG, C., "A NONGAUSSIAN MCDEL FOR AIRCRAFT
932 RESPONSE ANALYSIS,"AlAA JOURNAL, VOL 16, NO. 7, JULY, 1978,
933 PP. 641642.
934
935 PIERSOL, A.G., "INVESTIGATION OF THE STATISTICAL PROPERTIES
936 OF ATMOSPHERIC TURBULENCE DATA," TR MAC 2803207, 1969, MEASURE937 MENT ANALYSIS CORP., MARINA DEL REY, CALIF.
938
939 PINSKER, W. J., "THEORETICAL ASSESSMENT OF THE GENERAL STABILI'
940 AND GUST RESPCNSE CHARACTERISTICS OF STOL AIRCRAFT," ROYAL
94" AIRCRAFT ESTABLISHMENT, bEDFORD (ENGLAND). AERODYNAMICS/FLTiiT
942 DEPT., REPT NC: ARCR/M3686, RAET R71028, FEB. 71.
9435
944 PORT, W.G.A., "HIGH ALTITUDE GUST INVESTIGATION," ROYAL ArERONA
c4J5 ESTABLISHMENT, FARNEOROUGH, ENGLAND, AERO 2341, NOV. 1949.
o46 PRATT, K.G., "RESPONSE OF FLEXIBLE AIRPLANES TO ATMOSPiiERIC
 T 3PR ATT, K.G., "RESPONSE OF FLEXIBLE AIRPLANES TO ATMOSP?5i R.C
4,9 TURBULENCE IN PERFORMANCE AND DYNAMICS OF AEROSPACE VEHICLES,".0 NASA SP258, 1971, PP. 439504.
952 PRATT, K.G., "A REVISED FORMULA FOR THE CALCULATION OF GUS'
953 LOADS," TN 2964, 1953, NACA.
9514
%55 PRESS, H., "AN APPROACH TO THE PREDICTION OF THE FPIQE NCY
956 DISTRIBUTION OF GUST LOADS ON AIRPLANES IN NORMAL OPERATIONS,'"
95 NACA, TN 2660, 1952.
'945)8
959 PRESS, H., MEADOWS, M.T., AND HADLOCKI, I A REEVALATIAT(IN
960 OF DATA ON ATMOSPHERIC TURBULENCE AND AIRPLANE GUST LOADS FOR
118
1 APPLICATION IN SPECTRAL CALCULATIONS," NACA.EPT 1272 (1956).
2
3 PRESS, H., "ATMOSPHERIC TURBULENCE ENVIRONMENT WITH SPECIAL
$4 EFBEENCE TO CONTINUOUS TURBULENCE," AGARD 115, APRILMAY 1957.
5
6 PRESS, H., AND MAZELSKY, B., " A STUDY OF THE APPLICATION OF
7 POWERSPECTRAL METHODS CF GENERALIZED HARMONIC ANALYSIS TO GUST
8 LOADS ON AIRPLANES,' REPT 1172, 1954, NACA.
9
0 PRESS, H. AND TUKEY, J.W., "POWER SPECTRAL METHODS OF AJALYSIS
1 AND THE IR APPLICATION TO PROBLEMS IN AIRPLANE DYNAMICS," AGRBD
2 FLIGHT TEST MANUEL, VOL. IV, PT. IVC, (1956).
3
4 PRITCHARD, F.W., EASTERBROOK C, CC, MC VEHIL, G. E., "SPECTAL
5 AND EXCEEDANCE PROBABILITY MODELS OF ATMOSPHERIC TURBULENCE
6 FOR USE IN AIRCRAFT DESIGN AND OPERATION," AFFDLTR65122, AIF7 FORCE FLIGHT DYNAMICS LABCRATORY, NOVEMBER, 1965.
8
9 PUCCINELLI, L., "CCMPARISONS BETWEEN ANALOGICAL AND NUMERICAL
0 METHODS FOR STUDYING THE RESPONSE OF AN AIRCRAFT TO GUSTS.
1 CONFRONTI FRA METODI ANAL OGICI E NUMERICI PER LO STUDIO DELLA PIS
2 POSTA DI UN VELIVOLO ALIA RAFFICA," PCLITECNICO DI MILANO (ITALY).
3 IST. DI INGEGNERIA AERCSPAZIALE., REPT NO: P UBL97, 1970
4
5 RANKINE, ROBERT R. JR AND LEONDES, CORNELIUS T., "AIRPLANE YAW
6 PERTUREATIONS DUE TO VERTICAL AND SIDE GUSTS, J AIRON, V. 9,
7 N94, APR 1972, P. 3163 17.
8
9 REEVES, P.M., JOPPA, R.G. AND GANZER, V.M., "A NONGAUSSIAN MODEL
O OF CCNTINUOUS ATMOSPHERIC TURBULENCE FOR USE IN AIRCRAFT DESTGN,"
1 WASHINGTON UNIV., SEATTLE., SEPT NO: NASACR2639, JAN 76.
2
3 REITER, E.R., 1969: "THE NATURE OF CLEAR AIR TURBULENCE: A FERVIEW.
4 "CLEAR AIR TURBULENCE AND ITS DETECTION," NEW YORK, PLENUM
5 PRESS, 733. REPORT OF THE NATIONAL COMMITTEE FOR CLEAR AIR TUR6 BULENCE TO THE FEDERAL COORDINATOR FOR METEOROLOGICAL SERVICES
7 AND SUPPORTING RESEARCH. U.S. DE PARIMENT OF COMMERCE, DEC. 1966.
8 AIMOSPHERIC TURBULENCE IN SEVERE STORMS AND CUMULUS CLOUDS,"
9
O BEITER, E.R, "NATURE AND OBSERVATION OF HIGHLEVEL TURBULENCE
1 ESPECIALLY IN CLEAR AIR," INSTITUTE OF THE AEROSPACE SCIENCES, IAS
2 PAPER NO. 6381, PRESENTED AT THE IAS 31ST ANNUAL MEETING, NEW YORK,
3 NEW YORK, JAN. 2123, 1963
4
5 RHYNE, R. H. AND STEINE", R., "PCWER SPECTRAL MEASUREMENT OF
6 ATMOSPHERIC TURBULENCE IN SEVERE STORMS AND CUMULUS CLOUDS,"
7 TN D2469, 1964, NASA.
B
9 RICE, S.O., "MATHEMATICAL ANALYSIS OF RANDOM NOISE," BEZ L SYSTEf
D TECHNICAL JOURNAL, VOL. 23, NC. 3, JULY 1944, PP. 282332,
1 AND VCL. 24, NC. 1, J AN 1945, PP. 46156.
2
3 RICH, M. J., JEPSON, W. D. AND BUFFALANO AC, C."STRUCTURAL DY4 NAMIC RESPONSE OF LARGE LOGISTIC V/STOL VEHICLES," TECHNICAL DCC5 UMENTARY REPT., JUN 62F EB 64, APR 64.
6
7 RICHE, S.O., "MATHEMATICAL ANALYSIS OF RANDOM NOISE," BELL
8 SYSTEM TECHNICAL JOURNAL, VOL. 23, 1944, PP. 283332; ALSO VOL.
9 24, 1945, PP. 46156.
3
119
102 1 ROBERTS, J. Be., "STRUCTURAL FATIQUE UNDER NONSTATIONAiRY RhND0M
102 2 LOADING,"l JOU&,AL OF MECHANICAL ENGINEERING SCIENCE, VOL. Et
'~023 NG. 4, 1966,r PP. 3921405.o
1024
1025 RYAN, J.P.s, BEEENS, A.P.j, ROBERTSON, A.C., DCMINIC, R.J., AND
1026 ROLLE, K.C., "1MEDIUM ALTITUDE CRITICAL ATMOSPHERIC TURBULENCZE
1027 (MEDCAT) EATA PROCESSI'NG AND ANALYSIS," AFFDLTR7182, JULY,
1028 1971, WRIGHTPATTERSON AIR FORCE BASE, OHIO..1029
103 0 SAWDY, D. T., "ON THE TWODIMENSIONAL ATMOSPHERIC TURBULENCE,
1031' RESPONSE OF AN AIRPLANEa," KANSAS UNIV., LAWRENCE., REEPT NO: "TASA1 032 CR911161, 1966.
103 3.1034 SCHAENZERs G.r "THE INFLUENCE OF COUPLED NONSTATIONARkY GUSTS
1035 ON LOINGITUDINAL AIRCRAFT MOTION,"1 DEUTSCHE FORSCHUNGS, UND y;E?
1036 SUCHSANSTALT PIER LUFT  UIND RAUM4FAHRwt, BRUNSWICK (WEST GERMINY).
10637 INST. FUER FLIJGFUEHRUNG., REPT NO: DLRFB6965, JUIN 69.
*1038
1019 SEARS, W. R. AND SPARKS, 13.0., "ICN THE REACTION OF AN ELkSTIC
lb~4O WING TO VERTI1CAL GUSTS,"l JOURNAL OF THE AERONAUTICAL SCIENCES,
'1041 VOL. 9, 1941, PP. 64 67.
10 42
1.04 3 SEARS,. W.R.,"4SOME ASPECTS OF NONSTA'T c;[ AROL 3
11.044 AND ITS PRACTICAL APPLICATIONS," JOUT. Of THE AERONAUTICAL
1045 SCIENCES, VOL. 8, NO. 3, 1941, PP. 104108..1046
* 1047SHINOZUKA, N. AND YANG, J. N., "PEAK STRUCTURAL RESPONSE TO NO10
1048 STATICNARY RANrOM EXCITATIONS." J SOUND VIBR* V. 16a, NO. ~4, JUNE 22,.1049 1971,w P. 50517..1050
1051 SHINOZUKA, M., "RANDOM PROCESSES WITH EVOLUTIONARY POWER,"1
105 2 TECH. REP! 4, SEPT., 1969, COLUMBIA UNIV.
10o53
1054 SIDWELL# K., "A METHOD FOR THE ANALYSIS OF NONLINEAFITIES TN
1 055 AIRCRAFT DYNAMIC RESPONSE TO ATMOSPHERIC TURBULENCE," NATIONAL
1 056 AERONAUTICS AND SPACE ADMINISTRATION. LANGLEY RESEARCH CENTER,
105 7 LANGLEY STATION, VA., REPT NO: NASA TND8265s L10L487, NOV 76.
"0)58
'1O SKELTON, GRANT 2.,i "INVESTIGATION OF THE EFFECTS OF GiUSTS ON
1O'U V/STCL CRAFT IN TRANSITION AND HOVER," HONEYWELL INC ST PAUL MN
RESEARCH DEPTs REPT NO: 12060FR1, OCT 68.
C)SMETANA, F. 0. AND CARDEN, R. K., "AN ANALYTICAL STUDY OF H
it) 4 PONSE OF A CONSTANTATTITUDE AIRCRAFT TO ATMOSPHERIC TURBUL1ENCE,
1 06 5. NORTH CAROLINA STATE UNIV., RALEIGHo REPT NO: NASACR220~4,t M A F,7U
I b, 6 DURING LANDING APPROACH," NATIONAL AERONAUTICS AND) SPACE ADMNTSTSR.A
SNYDER, C. T., "ANALCG STUDY OF THE LONGITUDINAL RESPO3 OI F
06 9 A SWEPTWING TRANSPORT AIRPLANE TO WIND SHEAR AND SUSTAINED GUSTS
1070 DURING LANDING APPROACH,"l NATIONAL AERONAUTICS AND SPAC%.E ADMITNISTRA~
07 I TION. AMES RESEARCH CENTER, MOFFETT FIELD, CALIF., REPT NO:
1.012 NASA'N —4477, APR 68.
1 07 3
~4014SPEAKMAN, JERRY D.,. BONFILI, HUBERT P.,v HILLE, HAROLD K. kND
I 0 7. JOHN N N, "CREW EXPOSURE TO VIBRATION IN THE F4C AIRCRAFT D'IRING
1076 LOWALTITUDE, HIGHSPEED FLIGHT,"f AEROSPACE MEDICAL RBSEURCH iltB,zl
o0 7 7 WRIGHTPATTERSON AFB, OHIO, REPT NO: AMRLTR7099, JAN 71.
1078
10 79
1i08 0 SPILLANE, K.T., "THE WINTER JETSTREAM OF AUJSTR~ALIA AND 17 —'Q
I 20
1.U.. S L A L,GAZ iNE VOL. i, F S 96 6,
3
4 SPIE, JAiES K. "VALIDATION OF N ~ GUST DESIGN PROCEDURES FOP: IL~[TARY TRANSPORTS," LCCKHEEDGEORGIA CO MARIETTA, fEPT NO:
i LG73ER0153, NOV 73. STEINER, R., "A REVIEW OF NASA HIGH ALTITUDE
47 C'LEAB AIR TUREULENCE SAMPLING PROGRAMS," JOURNAL OF AIRCRAFT, VOL.
3 3 JAN. 1966, PP. 4852.
J
STEINER, RCY, "tA REVIEW OF NASA HIGHALTITUDE CLEAR AIR
I TURBULENCE SAMPLING PROGRAMS," J. AIRCRAFT, VOL. 3, NO. 1,
FEB. 1966, PP. 4852
* A GOOC REVIEW OF CLEAR AIR TURBULENCE UP TO 1966. SEEMS
** TO OVERSIMPLIFY A LITTLE, BUT HAS SOME GOOD CURVES FOR
** PROBABILITY OF EXCEEDING GIVEN GUST VELOCITIES PER MILE
~* TRAVELLED. GIVES ESTIMATES FOR TURBULENT PATCH SIZE.
STENTON, 1. E., "ANALYTICAL STUDY OF THE RESPONSE OF A CCONSTANTATTITUDE AIRCRAFT TC ATMOSPHERIC TURBULENCE." NASA CONTRACT
REPCR1621 AUG 1970, 121 P.
STENTON, T. E., "THEORETICAL FREQUENCY RESPONSE FUNCTIONS AND
POWER SPECTRA OF THE XB70 RESPONSE TO ATMOSPHERIC TURBULENCE,
NORTH AMERICAN ROCKWELL CORP., LOS ANGELES, CALIF., REPT NO:
NASACR1621, AUG 70.
SWAIMN, ROCERT L. AND CONNORS, ALONZO J., "EFFECTS IF GUT VELOCITY
SPATIAL DISTRIEUTIONS ON LATERALDIRECTIONAL RESPCNSE OF A VTOL
AIRCRAFT," AIR FORCE FLIGHT DYNAMICS LAB WRIGHTPATTERSON AFB,
OHIO, REPT NO: AFFDLTR6793, JUN 67.
SWANSON, R., "PRACTICAL FATIQUE LOCADINGS FOR AERONAUTICAL
STRUCTURES," AIAA PAPER N. 64568.
TAYLOR, J., "BUFFETING TURBULENCE," AGARD MANUAL ON AIRCRAFT
LOADS, PERGAMON, NEW YORK, 1965, PP. 245260.
TAYLOR, 3., "RELATIVE FEEQUENCY CF OCCURENCE OF DIFFERENT
NORMAL ACCELERATIONS AT THE CENTRE OF GRAVITY OF AIRCRAFT IN
TURBULENCE," ROYAL AIRCRAFT ESTABLISHMENT, FARNBOROUGH, (ENGLAND),
REPT. NO: RAETR71169, AUG. 1971
THEISEN, J.G. AND HAAS, J., "TURBULENCE UPSET AND OTHER STUDIES
ON JET TRANSPORTS," JOURNAL OF AIRCRAFT, VOL. 5, NO. 4, JULYAUG
'i968, PP. 344353.
THEODORSEN, T., "GENERAL THEORY OF AERODYNAMIC INSTABILITY
AND THE MECHANISM OF FLUTTER," REPT 496, 1935, NACA.
VAN ATTA, C. W. ANE CHEN, W.Y., "STRUCTURE FUNCTIONS OF TURBULENCE IN THE ATMOSPHERIC BOUNDARY LAYER OVER THE OCEAN," JOURNAL
OF FLUID MECHANICS, VOL. 44, 1970, PP. 145159.
VANDERVAART, J. C., "THE IMPULSE RESPONSE METHOD FOR THE CALCULATION OF STATISTICAL PROPERTIES OF AIRCRAFT FLYING IN RANDOM
ATMOSPHERIC TURBULENCE", TECHNISCHE HOGESCHOOL, DELFT (NETHERLANDS).
DEPT CF AEROSPACE ENGINEERING., REPT NC: VTH197, NOV 75.
VERDON, JOSEPH M., STEINER, ROY, "RESPONSE OF A RIGID AfRCRAFT
TO NONSTATIONARY ATMOSPHERIC TURBULENCE." AIAA J, V. 11, NO. 8,
121
1141 AUG. 1973, PP. 10861092.
114. ** THIS PAPER EXTENDS EABLIER WORK ON RESPONSE TO NONSTATiO'ARYE
1143 ** TURBULENCE BY ALLOWING A MORE GENERAL MODULATING ENVELOPE? OF
4 044 ** THE RANDOM VELOCITY FIELD. THIS WAS MOTIVATED BY EXPERI'ENTAT.
1145 ** RESULTS WHICH DID NOT AGREE WITH PREVIOUS THEORY. IT DOES
1146 ** IMPROVE THE RESULTS, BUT IS SOMEWHAT OF A CURVEFITTING
1147 ** APPROACH, SINCE THE MODULATING SIGNAL IS ABSTRACTLY CHOSEN
1148 ** AS A SINE WAVE MULTIPLIED BY A STEP FUNCTION. THE PAPER
1149 ** ONLY CONSIDERS PLUNGING OF A RIGID AIRCRAFT.
1150
1151 VINNICHENKO, N. K., PINUS, N. Z., AND SHUR, G. N., "STUDY OF
1152 CLEAR SKY TURBULENCE IN THE STRATOSPHERE," TRUDY TSENTRALNOY
1153 AEROLOGICHESKOY OBSERVATORII, FIZIKA SVOBODNOY ATMOSFERY, NO. 100,
1154 1970, PP. 8698.
1155
1156 VON KARMAN, T., "PROGRESS IN THE STATISTICAL THEORY OF TURBH1157 LENCE," TURBULENCE CLASSIC PAPERS ON STATISTICAL THEORY, INTER1158 STATE PUBLISHERS, NEW YCBK, 1961, PP. 162173.
1159
1160 VON KARMAN, T. AND HOWARTH, L., "ON THE STATISTICAL THEORY
1161 OF ISCTROPIC TURBULENCE," PROC. ROY. SOC., VOL. CIXIVA, (LON3DOt)
1162 PP. 193194 (1938).
1163
1164 WACO, DAVID E. "VARIATICN OF WT:LJENCE WITH ALTITUDE
1165 TO 70,000 FT," J. AIRCRAFT, VOL. 13, NO. 12, DEC. 1976, PP. 981986
1166 ** A CONCISE REVIEW OF EXPERIMENTAL MEASUREMENTS OF TURBULENCE.
1167 ** SUMMARIZES ALL RESULTS FOR PERCENTAGE OF TIME IN FLIGHT
t168 ** AT TURBULENCE LEVELS ABOVE O.08G (2FPS) REPEATED EXCURSIONS.
1169 ** ALSO GIVES RULES FOR RATIO OF MODERATE TO LIGHT TURBULENCE
1170 ** WHEN OVER VARIOUS TERRAIN. SHOWS HOW DEFINITION OF
1171 ** TURBULENCE IN G'S AFFECTS PERCENTAGE OF FLIGHI DISTANCE
1172 ** DENOTED AS TURBULENT.
1173
1174 WAIKINS, C. E., WOCLSTON, D. S., AND CUNNINGHAM, H. J., "A
1175 SYSTEMATIC KERNEL FUNCTION PROCEDURE FOR DETERMINING AERODYNAITC
1176 FORCES ON OSCIILATING OR STEADY FINITE WINGS AT SUBSONIC SPEEDS,"
1177 TR R48,1959, NASA.
1178
179 WEBER R. N. F., "THE SYNOPTICAEROLOGICAL CCNDITIONS FOR THE
114 8OCCURRENCE OF CLEAR AIR TURBULENCE, 12TH ORGANIZATION SCIENTITIFQJE
1 i ET TECHNIQUE IN TERNATICNALE DU VOL A VOILE, CONGRESS, ALPINE,
(82 TEX., 1970, PP. 366, 423425
4 WILLIAMS, D.A., "MEASUREMENT OF THE SYMMETRIC RESPONSE OF THE
Mta. S. 760 PARIS AIRCRAFT TO ATMOSPHERIC TURBULENCE, COLLEGE OF
l E: AERONAUTICS, CRANFIELD (ENGLAND). REPT NO: COAAERO211, 1969.
'Ja WILSON, R. J., LOVE, B. J., AND LARSCN, R. R, "EVALSUATL DIO
1i39 OP EFFECTS OF HIGH ALTITUDE TURBULENCE ENCOUNTERS ON THE X370
10 AIRPLANEw NASA TND6457, JULY 1971.
i92 WITHERS, DOUGLAS R. JR., "THE INFLUENCE OF FOLL, PITCH, AND
e93 YAW RATE PERTURBATIONS ON THE ALPHABETA STABILITY ENVELOPE OF
1 194 THE E4D AIRCRAFT," AIR FORCE INST OF TECH, WRIGHTPATTESSON AFB,
1195 OHIO, SCHOOL OF ENGINEERING, REPT NO: GAE/MC/75D10, JAN 76.
S19 7 WOODS, J. D., 1969: "ON BICHARDSCN'S NUMBER AS A CRITEPIN F P ^
1<.8 LAMINAR TURBULENT TRANSITION IN THE OCEAN AND ATMOSPHERE. PA.O
1199 SCI., VOL. 4, PP. 12891298.
1200
122
1 YASUE, ~M~, A SL' U D 1 0`~ cU ST S PC N SE i~ A c?2L>T
2 C 3U 31SNG FL IGHiT, O MA 3, AC iIU~S1ETTS IN33T. 0F TECH1., CAMBRIDGE. Ai2RC3 E LtSTIC AND STgUCTUR ES PES~ ARCH L A3L REPT NO: N ASA C R 137517,
4 ASL.LTR17410 AUG 714.
o YFF#, J., "RATIONAL CALCULATION OF DESIGq GUST LOADS IN RELATION
7 TO PBESENT AND PROPOSED AIRWORTHINESS REQUIREMENTS,." ROYAL
8 NETHERLANDS AIRCRAFT FACTORIES FOKKER., AMSTERDAM.,, REPT NO: F'CK9 K66, 1973.
0
1 YOST, JAMES D., JACKSON, WAYNIE B., AND SALTER, L.,"TMPROVED
2 METHCICS OF ATMOSPHERIC TURBULENCE PREDICTION FOR AIRCRAFT DESIGN
3 AND OPERATION." JOURNAL AIRCR 9, NO. 14, APR 1972, PP. 266272.
S ZBROZEK, J. K., "THEORETICAL STUDY OF THE ROLLINkG EESPONSE
SOF AIRCRAFT TO TURBULENT AlR, ADVISORY GROUP FOR AERONAUTICAL PEISEARCH AND DEVELOPMENT, PARIS (FRANCE)., REPT NO: AGARD373,
3 APR 61.
ZBORZEK, J. Ke, "THEORETICAL STUDY OF THE ROLLING3 RESPONSE
OF AIRCRAFT TO TURBULENT AIR, AERONAUTICAL RESEARCH CC)UNCIL (GIT.
3RIT.), REPT NO: ARCR +MTNAERO2753, APR 61
ZBOIRZEK, J. K., "ATMOSPHERIC GUSTS, PRESENT STATE OFTE AIT
AND FURTHER RESEARCH," JOURNAL OF THE ROYAL AERONAUTICAL S OC IET Y,
VOL. 69, NO. 649, JAN. 1965.
ZBORZEKO J. Ka, "THE RELATIONSHIP BETWEEN DISCRETE GUST AND PO)WER
SPECTRA PRESENTATIONS OF ATMOSPHERIC TURBULENCE, WITH A SU,\3IGSTED)
MODEL OF LOWALTITUDE TURBULENCE,"l AERONAUTICAL RESEARCH COUNCTL
R & M. 3216 (MARCH 1960).
FILE
123
b1 4o It 4.1 4. I& * 1* I& * * 'A * * 4. 4, 4. 4. * *.&')&A * ..4 4.& A 4..4.4.4.4.0 4. w& 4..4. 4..L & 4.4. 'k& *:.44..4.4..44. 4. 4.4.4.4. &4 &.&.& 1 L. ,,J..&. & 4.4.4.4.4.4 4. 4.