47th AIAA Aerospace Sciences Meeting Including The New Horizons Forum and Aerospace Exposition
5 - 8 January 2009, Orlando, Florida
AIAA 2009-65
Effects of Turbulence on Bank Upsets of Small Flight
Vehicles
Peter Lissaman
Da Vinci Ventures, Santa Fe, New Mexico, 87505, USA
Flight vehicles of different sizes exhibit different responses to turbulence, particularly as a
function of wingspan. This report exercises an Excel code, TURBANK, to calculate the
stochastic bank characteristics of a vehicle excited by atmospheric turbulence. The lateral
responses in ground level turbulence of ten representative vehicles, ranging in size from the
130 ft wingspan Boeing 707 through birds and small UAVs to a micro UAV of ½ ft wingspan,
are calculated and discussed. Vehicles of less than one foot wingspan exhibit excessive bank
response to turbulence. The code will be a tool for determining the factors involving lateral
disturbances, which is a critically important flight characteristic for small UAVs.
Nomenclature
b
g
m
F
V
S
µ
=
=
=
=
=
=
=
=
span
acceleration of gravity
mass
Froude Number, V2/2gb
speed
wing area
relative mass, m/ Sb
air density
I. Introduction
A
NYONE who has observed a raven, storm tossed in the turbulence downstream of a craggy cliff, will have
noted that the bird is swept into extreme angles of bank, often to wings vertical attitudes. One marvels at the
skill and sensing ability by which the bird, with a few lusty sweeps, contrives, apparently effortlessly, to return to
level flight. And one who has flown a small model airplane of less than half a foot wingspan will also have noted
that, as with the raven, normal atmospheric turbulence can roll it into a vertical bank which, in this case, usually
presages a crash, since the passive stability system of the model cannot handle these severe upsets.
Indeed, the great pioneer of flight, Otto Lilienthal, was bedeviled by turbulence upsetting his glider, for which
his only lateral control was by swinging his legs to one side to regain wings level. This is dramatically shown in the
first figure, a photo from his book, Bird Flight as the Basis of Aviation1 The photograph was made by Ottomar
Anschutz, and taken at Sudende in September, 1894. It shows a vigorous leg sweep to the left, to counteract a right
wing down attitude.
He experienced many crashes, and tenaciously recovered from all these upsets, except the last. The photo,
copied below, is prophetically, and sadly, captioned by Otto: “A Dangerous Position”. In a 1896 flight he could not
regain wings level after a turbulent disturbance, and fell to his death from a modest 45 ft height.
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Copyright © 2009 by Peter Lissaman. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission.
Fig.1 Otto Lilienthal: “A Dangerous Position”
Unfortunately, the small scale model airplanes must battle through full size turbulence! Small air vehicles look
like large ones, but are subject to the same turbulent fields, so, as might be expected, there are significant response
differences. Fundamentally, the small vehicle responds to smaller scale turbulence, and its response is different due
to the obvious difference in the dynamic scaling of mass and size between large and small aircraft. Birds fly in the
same turbulence fields, but are much less affected by turbulence. This is primarily because they have no vertical
stabilizing surfaces, can attenuate gusts by voluntary wing flexure, and have a superb animal sensing, response and
control system. This permits them, like the aerobatic Corvus Corax (the American Raven), to “ride the turbulence”
with abandon.
There is extensive interest in small Unmanned Air Vehicles (UAVs) for many defense and civil functions. These
will always be exposed to atmospheric turbulence, ubiquitous in the sky, especially near the ground in wind.
Sometimes this can be avoided, as with the Gossamer Condor, by flying only in fair weather, but often unexpected
turbulence happens, or a mission must be performed, in spite of weather conditions.
A technical and quantitative understanding of the lateral response of small aircraft is required so that performance
in turbulence can be predicted and designs can be developed to avoid catastrophic events.
.
II. Factors Involved
A. Aerodynamic
For flight in a turbulent field, one half the turbulent energy is unsymmetrical with respect to a wing, creating roll
moments that cause bank. The other 50% of the energy causes heave and pitch, involving vertically up- and
downwards motions, depending on the disturbing input and its resonance with the aircraft modes. This longitudinal
response is similar to driving a road with crosswise corrugations. There will be coupling according to the vehicle
speed, wheelbase and suspension characteristics, but no rolling. This wings level loading is important for flight
vehicles, and can cause critical loads in a wing structure, but does not directly contribute to catastrophic instability
as do the lateral effects. Only the lateral modes will be dealt with here.
The lateral analysis involves the full three component equation description of the vehicle lateral motion, defining
roll, yaw and sideslip in the usual Newtonian equations of motion. One can distinguish between the latter two terms
by noting that yaw is the rotation of the vehicle about its vertical axis, as indicated on a compass, while sideslip is
the sideways motion of the aircraft relative to the airflow, the inclination of the flow to the vertical plane of
symmetry of the vehicle. For primitive flight tests one can use as a sideslip indicator a string attached near the nose
of the vehicle and streaming along a marked line on the vertical axis of symmetry. Historically, this has been called
a “yaw string”.
Much of the lateral dynamics of vehicle are determined by the aerodynamic stability derivatives, that are functions
only of the vehicle configuration (airlines) and not of the inertia, that is weight, size or speed. The derivatives are
essentially purely geometric factors. The two inertial factors that affect the vehicle response are the Relative Mass
and the Froude Number. Relative Mass is a dimensionless number, defined as µ = m/ Sb where m is the mass,
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the air density, S the wing area and b the span. It characterizes the mass of the vehicle relative to its size. This
quantity varies quite widely, for a Boeing 707 in landing configuration it is about 8, for a raven it’s about 2 while for
the Gossamer Condor, a very exceptional flying machine, it is about 0.04. Naturally, the lower the relative mass,
the lighter the vehicle seems with respect to aerodynamic forces, so the more it is at the mercy of the vagaries of the
wind. The Gossamer Condor had the lowest µ of any known vehicle. In a 1979 presentation to the Royal
Aeronautical Society the present author noted that the Condor is so big and light, and the air mass effects so large,
that the apparent inertia ratio in roll (apparent mass/ real mass) for the Condor is significantly below that of any
conventional flight vehicle and, in fact, about the same as that of an insect, the dragonfly. The Condor is indeed,
loath to roll by pilot roll inputs,– an advantage in many respects.
The other inertial term is the Froude Number, F, defined as the F = V2/2gb where V is the speed and g the
acceleration of gravity. The number F characterizes the speed, or kinetic energy, of the vehicle relative to its size.
The inertial scaling numbers, µ and F are coupled by the lift coefficient, CL, in the relationship, µ = CL F. Since
most of the vehicles in the low level flight mode studied in this paper operate at lift coefficients of about unity, the µ
and F values are roughly the same. A primary dimensional factor related to the response is the span of the vehicle
relative to the spanwise length of the dominating disturbing turbulence. This is analyzed below.
It is clear here physically that long wave turbulence will not cause much roll effects, while very short wave
turbulence will tend to balance out across the span. The largest disturbance will come from waves having a length
of about one half the span, so that there is a maximum vertical updraft on one wing tip cooperating in roll with one
in the opposite direction on the other. This effect is illustrated in Figure 2 which shows the aerodynamic rolling
moment for turbulence of a given scale to wingspan. It considers a lateral wave of a given spanwise length and
shows its effect on wings from zero to large spans. It is seen that only wings with a span about equal to the turbulent
wave length will experience significant roll effects.
ROLL
MOMENT
WING SPAN/TURB. WAVE LENGTH
Fig. 2 Effect of wingspan on rolling moment
The other effect controlling roll is resonance with the lateral modes of the vehicle. There are normally three: first,
the Spiral Mode, an aperiodic long time-scale motion that may be stable or not, but operates very slowly. It is
named after the legendary “Death Spiral” that occurs for instability in this mode, which if uncorrected will
eventually cause a vehicle to enter an increasingly steep spiral dive with catastrophic consequences. Spiral
instability is associated with a relatively large vertical tail, hence its other name – “tailspin”.
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Second, the Dutch Roll Mode, is a stable mixture of yaw and roll causing a wallowing lateral motion, where the
wingtips to describe an ellipse in vertical plane. Named in the early days of flight dynamics, it has a fancied
resemblance to a Dutch boy skating along a canal, moving and swaying from side to side. It is this mode that causes
discomfort to passengers and poor tracking for gun aiming or observable sighting.
The third mode is the Roll Damp Mode, aperiodic and of very short time scale, which essentially garauntees that
the wings will rapidly damp any roll input, so that, for example, the vehicle responds rapidly and without overshoot
to pilot aileron inputs.
In gust stability analysis it is convenient to use wave number rather than frequency. Wave number is not an
elementary vibration concept, so a few words are in order. Wave number is the reciprocal of wavelength, for
example, a wave of 4 ft in length has a wave number of ¼ per foot, which would be written as 0.25/ft.
Atmospheric turbulence is described in terms of wave number; the waves sit there, frozen, doing their thing, and any
frequency a vehicle perceives is created by the speed with which it traverses this wave system.
For frequency, two definitions are used. One may use , indicating radians per second or n, indicating cycles per
second. The former is used in mathematical analysis to avoid a profusion of 2 ’s; for example, most engineers
remember centrifugal acceleration as 2R. The straight frequency, n, in Hz, is used for engineering reports, because
that’s what is usually measured. An identical distinction occurs in wave number measurement, where one can
describe the radian wave number or the cycle wave number. For theoretical analysis it’s more convenient to use the
radian wave number definition.
The streamwise modes can be seen in the transfer function plot for a typical small UAV (Vehicle # 6, the AV
Pointer HLUAV) shown in Fig. 3. This is plotted as a function of wave number. A high wave number implies that
there are a lot of wiggles in a foot. The wave number abscissa here is the logarithm of the radian wave number per
semi span
RESPONSE TO STREAMWISE WAVES
12
SPIRAL
10
TRANSFE
8
6
DUTCH ROLL
4
ROLL DAMP
2
0
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
-2
LOGWAVE # SEMIS SPANS
Fig. 3 Effect of streamwise wave number on rolling moment
The spiral mode, at very low wave number has strong gain, but the turbulent energy at this wave number is quite
low, so no significant response occurs. The Dutch Roll mode is normally significant. The wave number value - 0.1
on the scale near the Dutch Roll resonance represents 0.79 rads/semispan so this means that the wavelength here is
about 2 /0.79 semi spans per wave, and the vehicle span is 9 ft so the Dutch Roll excitation occurs for waves of
about 33 ft wavelength in the streamwise direction.
These responses have different implications for vehicles of different configurations and dynamic scales. Their
magnitudes are strongly affected by scale and the proportions of the lateral surfaces of the vehicle, especially the
dihedral and the size of the vertical tail, and the disposition of mass in the direction of the wingspan. An
understanding of the interaction of the various airframe aerodynamic factors can indicate design proportions that can
significantly modify these modes.
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B. Turbulence
The turbulence level by which the vehicle is excited drives its response. Results depend on the model of
atmospheric turbulence assumed. In general, for atmospheric turbulence out of ground influence, the vertical
turbulence can be well represented by the 2-D von Karman spectrum, called 33. The turbulence is taken as
stationary, homogeneous, isotropic, Gaussian and frozen – this sounds very restrictive, but they are not bad
assumptions! The shape of the spectrum is a function only of the length scale of the turbulence. This scale can be
thought of as approximately equal to the wavelength of the strongest eddies. The intensity of the turbulence is not a
function of length scale, but of the process exciting the turbulence. So we require a turbulence scale, relating to the
generating process and a turbulence intensity value, relating to the magnitude of the energy put in. Good models,
supported by the experimental literature, are available for both of these.
For turbulence in the vicinity of the ground, a more complicated interaction occurs. Here turbulence is generated
mechanically by the wind blowing over ground roughness, and is far from isotropic. The streamwise disturbance
created by flow over a rough surface occurs as a windwise turbulence component, causing forwards and backwards
perturbations with respect to the mean wind speed. The cross stream horizontal turbulence is created by these
streamwise terms squishing sideways according to continuity, while the vertical turbulence undergoes the same
squashing process as the horizontal flow but its magnitude is suppressed by the presence of the ground. For a
typical case the streamwise, cross flow and vertical turbulence rms values are in the ratio 1: 0.8: 0.5. For nonisotropic turbulence it is customary to use the isotropic formulation for the two dimensional spectrum, using the
appropriate level of vertical turbulence.
At about 1,000 ft above ground level the influence of the ground vanishes and the turbulence approaches isotropy,
with rms values in all directions the same.
It is the vertical turbulence term, 33, that concerns us. The 2-D power spectrum for this has the characteristic
“volcano” shape, where the low wave number energy is very small, the maximum contribution occurs at about the
characteristic length scale, and the energy then rapidly decreases with increasing wave numbers. The low energy
levels in the small wave number area are fortunate, since it assures that the highly upsetting, low frequency, spiral
response range will not be strongly excited by turbulence in this scale. This is shown in Fig. 4 for two dimensional
vertical turbulence at a scale of 30 ft. The figure is axisymmetric about a vertical axis, but appears “squarish” here
because it is plotted on loglog scale, where a circle looks like a rounded square.
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TURBULENT INTENSITY
6
5
4
3
2
1
S25
S2
S21
0
S19
S17
S15
S13
S11
S9
S7
S5
SPANWISE WAVE #
STREAMWISE
WAVE #
S3
S1
Fig. 4 Turbulence intensity for 30 ft scale
An interesting picture of what low level turbulence does is shown in Fig. 5. Taken from Watkins, and Vino2, it
shows the long bubble formed by the wind blowing a soapy fluid film through a large hoop. The photograph has
been stretched in the vertical to illustrate effects. This is a vivid pictorial representation of turbulence at about 7 ½ ft
from the ground in a light breeze.
The natural flyers are well aware of the unfortunate destabilizing effects of turbulence. Butterflies stop flying, and
start walking, at wind speeds of about 3 ft/sec, gnats and midges at 6 ft/sec, while bees, beetles and swallows are
grounded at 18 ft/sec. Ravens, like hardcore surfers, revel in wild winds and stormy weather, and seem to enjoy
cavorting in turbulence and strong winds.
Fig. 5
The World’s Biggest Bubble. Guinness Book of Records, 1998
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An analysis of the lateral modes has been made. This involves contributions from most of the aircraft
aerodynamic and mass terms to provide the transfer function for excitation by streamwise and cross stream
turbulence. The details are not elaborated on here since this is a well-known but tedious analysis.
From the aircraft characteristic lateral equation the streamwise stochastic transfer function can be calculated.
This is combined with the spanwise transfer function to produce the general transfer function, a function of spanwise
and streamwise wave energy distribution. This must then be combined with the turbulent excitation to calculate the
power spectrum of the response.
A general model for atmospheric turbulence, using the v. Karman spectrum has been developed. This checks
well with the measured data for low level turbulence.
The specific turbulence model for the cases calculated and listed in Section IV below is for a scale of 30 ft, and
a vertical rms intensity of 3 ft/sec. This turbulence level would occur about 30 ft above ground level for a ground
roughness of about 3.5 ft. This corresponds to woodland forests and light urban built structure in a wind of about 14
ft/sec. This wind level occurs frequently, representing a speed of about 9 ½ mph, or Force 3 on the Beaufort Scale -what was described by Admiral Beaufort in 1806 as “a gentle breeze” in “which leaves and small twigs are
constantly in motion, and wind extends light flags”.
The turbulence exciting spectra is then convoluted with the vehicle transfer spectra to generate the response
spectrum, a function of spanwise and streamwise wave number of the turbulence, using a code, TURBANK,
developed for this purpose. From this the rms bank value can be calculated as well as the characteristic wave
number of the response. The latter is used to estimate the number of cycles experienced during any given time
period of exposure to the turbulence. A typical response spectrum is shown in Figure 6. This is drawn for a typical
Micro AV (MAV), the Megatech Avion, described in Section IV, which has been calculated to have very excessive
bank response – implying it is prone to large bank angles and upsets in turbulence.
BANK RESPONSE SPECTRUM
10mTURB LENGTH SCALE, VEH.# 8
RMS 44 DEG FOR 1 m/s TURB
0.7
0.6
0.5
0.4
0.3
1
0.2
7
13
19
SPANWAVE#/SS
0.1
25
31
S25
S19
S16
S13
S7
S10
S4
S1
S22
0
37
STREAMWAVE#/SS
Fig. 6 Response spectrum for Micro AV Avion
The volume under this peaky surface represents the rms bank angle. It can be seen that the response is strong
near the spanwise wave number at which the vertical spanwise turbulence waves couple with the span. For the
streamwise effects, it is noted that energy is received for a wide band of streamwise wave numbers. There is no
strong resonance near the Dutch roll frequency.
The TURBANK code was exercised to determine the rms bank characteristics of ten of vehicles, each having
characteristics of significance for this study. The ten vehicles chosen were selected to provide insight into the
effects of turbulence on real aircraft and birds. The rationale of selection is given below.
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IV. Vehicles Analyzed
Since this study involves unknown effects for which the author had no previous experience and could find no
information on, it is useful to conduct a pilot study to analyze a set of vehicles of demonstrated known performance,
to obtain some insight into their response to turbulence. Each has something to tell us about the problem. The
vehicles are described below, with the reasons for their choice.
Vehicle #1 Boeing 707, Model 720. This aircraft is typical of a large jet transport in the landing configuration.
It flies through ground level turbulence fields on landing and take off, as must all aircraft. As expected, calculations
show it to be impervious to the turbulence levels used in the present calculations.
Vehicle #2 Gossamer Condor. This eccentric aircraft is exceptionally light and large, with no vertical tail. Like
all human powered vehicles, it suffered serious lateral control deficiencies in its early versions, and required about
12 months of flight test, crashing and diligent modification to fix. As the author experienced, all the numerous
crashes were caused by lateral problems of wing dropping due to turbulence and inadequate lateral control. The
author actually crashed this vehicle during a flight, but was luckier than Lilienthal. For the Condor configurational
development theoretical lateral stability analyses were developed by the author, and coupled with extensive flight
test and “good sense” lateral design. Serendipitously, the final version proved excellent with respect to the lateral
modes. The Condor was never flown in winds exceeding a few miles an hour (Force 1, Beaufort).
Vehicles #3, #4 Fieseler Fi. 167 Storch (Stork) and Cessna 305A Bird Dog. These are both low speed military
observation/liaison aircraft, intended to fly operationally at speeds below 50 mph in the nappe of the earth. The
Storch featured in many dramatic low speed escapades by the Luftwaffe, while the Bird Dog served the same
mission for USMC and USA in Vietnam. The Storch was famous for its low speed handling. During acceptance
trials in 1937 Ernst Udet, Technical Director of the Luftwaffe, and a test pilot with a distinguished WW I Jagdstaffel
record, “hovered” the Storch over a fixed ground point for about an hour. This must have involved butting into a 45
mph headwind, where, even with a relatively smooth ground, the vertical turbulence might have been about 6-9
ft/sec.
Vehicle #5 Lilienthal 1896 monoplane, designated the Normalsegelapparat. This is the vehicle in which
Lilienthal experienced an uncontrollable bank in turbulence, and fell to his death. He had been making successful
glides in aircraft of this type for three years, so the configuration could not have been excessively sensitive to bank
upsets in turbulence.
Vehicle #6 AV Pointer FQM-151A. This vehicle, in service with the US military, has an excellent reputation
for low speed, docile flight. It can be flown with the minimum of pilot training. In operation it is hand launched and
climbs rapidly out of ground turbulence, while it lands by dropping from about 50 ft almost vertically in the deep
stall mode, so it is not much exposed to ground level turbulence.
Vehicles #7, #8 The Family Corvus. Enter the birds! The great American Raven (Corvus Corax) and its smaller
cousin, the Jackdaw (Corvus Monendula) have been analyzed. Both birds spend a great deal of time in turbulence,
which they handle with aplomb, and appear to enjoy “surfing the gusts”. The present analysis assumes a rigid
airframe, improbable for these intelligent creatures, but indicates that, even with no avian corrective actions, the
vehicle is not susceptible to gusts.
Vehicle #9 Megatech Avion. This is a very small commercially available R/C electric biplane that uses optic
link control technology. The advertisements state it can be flown indoors or out. The author has test flown this
vehicle and found it exceedingly susceptible to bank upset in outdoor flight, even at dawn, when the ambient wind
appears close to zero.
Vehicle #10 Micro Air Vehicle M1. This is a hypothetical very small MAV, laid out by the author to assess
the effect of size on the lateral response. The M1 looks just like a miniature airplane – it has a conventionally
proportioned and located wing, fuselage and a three component tail. The current analysis shows that it is certainly
not an ideal configuration for this size of air vehicle!
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V. Results
The expressions for bank are integrated in the usual fashion through the wave number spectrum for spanwise and
streamwise waves according to the intensity defined by the von Karman spectrum. This provides the rms value of
bank angle for each vehicle when excited by the common turbulence field. In general terms, the rms bank angle
varies from values below 100 to about 450. This does not seem like a very wide range of response.
Calculations were made for the same turbulence, namely 3 ft/sec vertical intensity at scale length of 30 ft. This is
typical for a light breeze over rough terrain.
At first appearance, the small vehicles, at rms bank levels of 440, are only about 4 times as much affected as the
Pointer at rms bank of 110. But this is very deceptive. Because of the statistical quality of the response, an
exceedance of about 2 required to reach wings vertical (2 x 44o ~ 900) in Vehicles #9, #10 will occur after about 150
seconds, while for the Pointer the wings vertical bank requires an exceedance of about 8 (8 x 11 o ~ 90 o), which will
take a long time to occur, in fact millions of seconds.
This is a stunning illustration of the pathological non-linearity of probabilistic events; where for a small vehicle
with an rms bank of only four times higher than that of the Pointer, the probability of an upset for the smaller vehicle
is a million times higher.
Table I shows the results of the calculations. The last column gives the calculated exposure in seconds (time in
turbulence) for the vehicles to assume a 900 bank with a given likelihood of 85%. The same situation for a
probability of about 95% requires about 4 times as long exposure. It is noted that the extreme non-linearity of
stochastic probability events drastically separates the aircraft, so that they fall into two distinct classes. The results
provide useful insights. The key result of the analysis is the two final columns showing rms bank in degrees and
seconds of flight before catastrophic wing drop. It is seen that only the two small vehicles #9 and #10 show any
extreme bank tendency. Vehicles #1 through #8 will not fall off on a wing in modest turbulence, where-as Vehicles
#9, #10 are essentially certain to do so. Flight tests conducted by the author with Vehicles #2, #6 and #9 support the
calculations.
VEHICLE
TYPE
SPAN
FT
SPEED
MPH
MU
RMS
BANK
DEGREES
FR
EXPOS.
TIME
SECS
VEH#1
BOEING
131
164
8.3
6.9
4
.
>10^9
VEH#2
CONDOR
96
11
0.04
0.04
6
.
>10^9
VEH#3
STORCH
47
59
2.5
2.5
7
.
>10^9
VEH#4
BIRD DOG
36
73
4.9
4.9
8
.
>10^9
VEH#5
LILIENTHAL
25
26
0.82
1.0
12
.
>10^9
VEH#6
POINTER
9
26
1.5
2.6
11
.
>10^9
VEH#7
VEH #8
VEH #9
VEH#10
RAVEN
JACKDAW
AVION
MAV M1
4.6
1.9
0.62
0.33
20
22
12
17
2.1
5.7
5.0
25.1
3.0
8.1
7.1
31.4
7
10
42
44
.
.
.
.
>10^9
>10^9
148 .
116 .
Table I General features and lateral response of vehicles analyzed
VI. Conclusion
The vehicle performance shown in Table I indicates that a wide variation of relative mass, from about 7 to 0.04,
has no significant effect on bank upset event, a surprising result. The table indicates that the dominant discriminant
for bank characteristics is the wingspan, and for spans less than ½ ft there is likely to be a high undesirable bank
response. An analysis can now be made of methods of making these small vehicles stable in bank. The code
developed here will make it possible to examine a range of configurations to determine how to avoid bank upsets
with small vehicles, and the extent to which this is possible.
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Conclusions are listed below:
1. A method of describing lateral performance and calculating transfer functions for turbulence in spanwise and
streamwise directions has been developed.
2. A procedure for estimating appropriate turbulence properties has been developed.
3. A method of combining lateral performance and exciting turbulence to estimate rms bank angle has been
developed.
4. Items 1, 2, 3 above have been incorporated into a robust computer code, TURBANK, that runs rapidly and
effectively on Excel.
5. Ten representative flyers have been analyzed to predict their lateral response.
6. Exercise of TURBANK indicates that conventional configurations of less than ½ ft span are very susceptible
to lateral disturbances due to turbulence
7. Modification of the aerodynamic and mass features, and incorporation of active lateral damping or directional
gain can likely alleviate the above problems with small vehicles. Practical gust attenuation systems can be
designed using the code
8. Very small flight vehicles with satisfactory turbulence performance will not look like miniature airplanes
References
1
Lilienthal, Otto, “Bird Flight as the Basis of Aviation” 1889. Translated by A.W. Isenthal 1911. Reprinted by Markoski
International Publications, Hummelstown, PA, USA, 2001.
2
S. Watkins and G. Vino, “The Turbulent Wind Environment of Birds, Insects and MAVs”. School of Aerospace,
Mechanical & Manufacturing Engineering, RMIT University, Melbourne, Australia, Dec. 2004.
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