NASA Technical Reports Server (NTRS) 20010097310: A Sensor-Independent Gust Hazard Metric

13 Pages·0.69 MB·English

by  NASA Technical Reports Server (NTRS)

AIAA 2001-4135
A Sensor-lnd.ependent Gust
Hazard Metric
Eric C. Stewart
NASA Langley Research Center
Hampton, VA
AIAA Atmospheric Flight Mechanics Conference
August 6-9, 2001 / Montreal, Canada
For permission to copy or to republish, contact the American Institute of Aeronautics and Astronautics,
1801 Alexander Bell Drive, Suite 500. Reston. VA, 20191-4344
AIAA 2001-4135
ASENSOR-INDEPENDENT
GUST HAZARD METRIC
Eric C. Stewart*
NASA Langley Research Center
Hampton, VA 23681-2199
Abstract I measured gust amplitude innegative direction,
ft/sec
A procedure for calculating an intuitive hazard
A+ measured gust amplitude in positive direction,
metric for gust effects on airplanes is described. The
A'+
hazard metric is for use by pilots and is intended to
--, g's
replace subjective pilot reports (PIREP's) of the
w,
turbulence level. The hazard metric iscomposed of 3
2
numbers: the first describes the average airplane measured gust amplitude in negative direction,
response to the turbulence, the second describes the
A'_
positive peak airplane response to the gusts, and the
--, g's
third describes the negative peak airplane response to
w I
the gusts. The hazard metric is derived from any time
history of vertical gust measurements and is thus Ar estimated gust amplitude required to produce
independent of the sensor making the gust lg acceleration for a computational interval r,
measurements. The metric is demonstrated for one g's
simulated airplane encountering different types of gusts (7+).
maximum measured gust amplitude in positive
including those derived from flight data recorder
measurements of actual accidents. The simulated direction using a computational interval of r
seconds (figure 3), g's
airplane responses to the gusts compare favorably with
the hazard metric. minimum measured gust amplitude in negative
direction using a computational interval of r
Nomenclature
seconds (figure 3), g's
maximum estimated gust amplitude in positive
A non-dimensional gust amplitude, g's
direction using a computational interval of r
dimensional gust amplitude over computation
seconds (figure 3), g's
interval r, ft/sec
minimum estimated gust amplitude in negative
Ar non-dimensional gust amplitude over
direction using a computational interval of r
seconds (figure 3), g's
computational interval r, -- g's
w1 acg change in acceleration at the center of gravity
A" (positive upward), g's
measured gust amplitude in positive direction,
ft/sec aaft change in acceleration at the aft passenger
*Aerospace Engineer, Senior Member AIAA cabin (positive upward), g's
0.n running standard deviation of acgover a
Copyright © 2001 by American Institute of
computational interval of 4 seconds, g's
Aeronautics and Astronautics, Inc. No copyright is
asserted in the United States under Title 17, U.S. 0.n average value of o"nover reporting interval,
Code. The U.S. Government has a royalty-free g's
license to exercise all rights under the copyright 0"4.0 standard deviation of vertical gust velocity
claimed herein for Government Purposes. All
over a 4-second computational interval, fps
other rights are reserved by the copyright owner.
-l-
American Institute of Aeronautics and Astronautics
conditions. The (unbuckled) victim is usually thrown
0"4.0 standard deviation of non-dimensional vertical
to the ceiling when the airplane momentarily
gust velocity over a4-seconds computational
experiences less than 0g's vertical acceleration. The
0"4.0 most severe injuries occur when the acceleration returns
interval, --, g's
to normal positive values and the victim falls back to
wI
the floor or, worse yet, on the seat backs or arm rests.
r computation interval (also called rise time), Usually the only damage to the airplane isconfined to
0.25, 1.0, and 4.0 seconds in example the airplane interior and is caused by the impact of
W airplane weight, Ibs unsecured objects and people with the cabin ceiling and
overheads.
wg vertical gust velocity (positive upward), fps
One approach to reducing the turbulence
p density of air, slug/ft 3 accident rate is to develop new or improved turbulence
warning and avoidance sensors such as enhanced
V true airspeed, fps airborne radars or iidars, reference 2. However, a
S wing area, ft2 clearer definition of the turbulence characteristics that
cause the accidents is needed so that the new sensor
t time, seconds
outputs can be made to accurately reflect these
CL, _ lift curve slope, per radian characteristics. Past turbulence metrics have had one or
more deficiencies. For example, the turbulence metric
wt gust amplitude of a step input that will cause a
described in reference 3 is a measure of the eddy
dissipation rate, an "average" meteorological parameter
1g acceleration ( 2_p VSCL., _), fps
unknown to most pilots. The metric described in
HM composite hazard metric, reference 4 is a running average of the square of the
vertical gust velocity. Neither metric is a direct
[HM,_ HM+ HM_ ], g's ( Read as
measure of the peaks of dangerous discrete gusts that
"' HMo ' g's continuous turbulence, with are of primary interests to pilots, reference 5. In
addition, these metrics do not discriminate between
peaks to plus' HM÷ ' g's and minus ' HM_ '
positive gusts and the more dangerous negative gusts.
g's") Finally, since both are measures of only turbulence
HM,. hazard metric for peak gusts using a characteristics, they need to be multiplied by the
computation interval of r seconds, g's appropriate airplane transfer functions to translate them
into more useful information for pilots flying different
HMr_.k peak hazard metrics HM÷ and HM_,
airplanes at different airspeeds inthe same turbulence
g's field. This isnot to say, however, that the average
HM÷ component of composite hazard metric due to value of the turbulence isof no interest. For the
peak positive gusts, g's majority of airline operations in turbulence, the
turbulence has a relatively low level and appears to be
HM_ component of composite hazard metric due to
more or less continuous. Therefore, any metric that is
peak negative gusts, g's useful in all conditions must reflect the "average" value
HM,_ component of hazard metric for sigma level of of continuous turbulence as well as the peaks of the
discrete gusts.
turbulence, g's
The primary purpose of this paper is to define
the discrete-gust components of the hazard metric as a
Introduction
function of the first-order, fundamental parameters that
determine airplane gust response. A procedure for
The National Aeronautics and Space
calculating the numerical values of these components of
Administration has initiated the Aviation Safety the hazard metric from measurements of vertical gust
Program to reduce the aircraft accident rate by 80% in velocities is discussed. (The method of measuring
l0 years. One part of the program is aimed at reducing these velocities isbeyond the scope of this paper). The
the injuries and deaths caused by extreme turbulence composite hazard metric, which also includes an
encounters. Airline experts report and the analysis of average component for continuous turbulence, is
Flight Data Recorder (FDR) data indicate that these intended to replace Pilot Reports (PIREPS) which are
extreme events are caused by large, discrete gusts in the subjective, airplane-dependent estimates of turbulence
vertical direction, reference 1. The typical gust intensity as described in the Aeronautical Information
encounter that induces serious injuries lasts only a few Manual (AIM), reference 6. Since the present metric is
seconds and issurrounded by relatively calm based on the characteristics of turbulence that are the
-2-
American Institute of Aeronautics and Astronautics
rootcausoef airplane turbulence response, itcan be gusts. In addition, reporting the turbulence levels in
used as the basis for developing sensor-dependent knots (or other velocity units) would require the pilot to
hazard metrics. mentally translate those numbers into a projected
response of his airplane at the current airplane
Theoretical Basis configuration and flight condition. Although a similar
mental translation is currently required of pilots for the
above-mentioned tower-reported wind conditions, a
Previous work, reference 7, has shown that the
more useful hazard metric would automatically
rise time of discrete gusts as well as their amplitude
translate the gust velocities into response units such as
affects the theoretical severity of a gust encounter. For
g's. This translation could be easily accomplished with
example, if an airplane gradually encounters a given
existing on-board computing capability and parameters
amplitude gust, its response is much smaller than if the
already available on the airplane's data bus such as the
airplane encountered the same amplitude gust in a much
airplane's weight, airspeed, and altitude. The
shorter period of time. (The rise time isequal to the
turbulence could then be displayed to the pilot on
spatial dimension of the gust divided by the true
his/her console message center as (for example): "Two-
airspeed of the encountering airplane. In the
tenths g continuous, with peaks to plus five-tenths and
description of the hazard metric algorithm below, the
minus eight-tenths g's." This is the type of hazard
"computation interval" is equal to the rise time). There
metric described herein. It actually consists of three
is another class of parameters describing the
characteristics of the encounter airplane that affects the numbers, HM,,, HM+, and HM_, but will be
airplane response, but these parameters are readily referred to in the singular.
available on the data bus of most modem commercial There is another desired characteristic of the
airliners. hazard metric that is implicit in the above discussion.
That is,the hazard metric is defined over arelatively
Desired Characteristics of Hazard Metric long period of time and reported at the end of this
period. This is desirable from the pilot's standpoint
because of his limited capability to process large
A measure of the potential gust hazard to
volumes of data. It is also desirable from the standpoint
airplanes (hazard metric) that is intuitively obvious is
of data transmitting and receiving bandwidths
needed. For example, a metric similar to the wind
requirements. That is, the datalink capacities on
direction and magnitude information an airport traffic
commercial airliners will limit the frequency that
controller gives to a pilot approaching an airport would
turbulence information can be reported or received. If
be useful. In-flight turbulence could be reported as:
bandwidth were not a factor, the complete time history
"Five knots continuous with peaks to plus 10 knots and
minus 15 knots." The value of the continuous of gust velocity measurements could be applied to an
turbulence can be a simple running calculation of the airplane-specific, configuration-specific, transfer
function on every airplane. This approach would
standard deviation (sigma) of the vertical gust velocity
and is related to ride comfort more than safety. It, provide a more exact prediction of the airplane's
therefore, is not the focus of this paper and the NASA's response than the approximate response function
incorporated in the present hazard metric.
aviation safety program, but is included for
completeness. The sigma value of the vertical velocity
is closely related to the cube root of the eddy Algorithm Description
dissipation rate calculated in the in-situ turbulence
algorithm described in reference 3. The cube root of Since this is a description of a sensor-
independent hazard metric, it isassumed herein that a
the eddy dissipation rate (in meters2/3/second) is more
time history of the vertical gust velocity is available.
meaningful to meteorologists, and the sigma level of
The method used to make these measurements is not
the turbulence (in knots or other velocity units) is more
considered; see reference 2 for example measurements.
meaningful to pilots as a measure of the continuous
Only the translation of these assumed gust velocities
turbulence and ride comfort.
into a meaningful metric for pilots isdiscussed. The
For the large discrete gusts that cause
complete algorithm, shown in figure 1,is described in
accidents there may be no consistent relationship
detail inthe following discussion. The first part of the
between the sigma value of the turbulence and the peak
algorithm is the calculation of the sigma component of
values. The peak values of the gusts are the metrics of
the hazard metric described by the upper leg of the flow
interest to pilots from a safety standpoint, reference 5.
But for the peak values to be of real value they must diagram. The sigma level 0''40 (t) is calculated for a
also reflect the rise time or the spatial extent of the fixed interval of time. The preliminary suggested
3
American Institute of Aeronautics and Astronautics
computatioinntervaflorthiscalculatioisn4seconds
amplitudes Ar(t) to approximate the airplane response
althougthheexacitntervaisl notimportasnitncethe
valueswillbeaverageladteroverthemuchlonger to different gust rise times. The result of this
reportingintervalT.heinstantaneosuigsmalevels calculation is HM, (t), the estimate of airplane
response due to gusts with lengths corresponding to r =
0''40 (t) in ff/sec are divided by wI to produce the non-
0.25, 1.0, and 4.0 seconds. The equation used was
dimensional sigma levels 0"4.0(t), in g's. The first
component of the hazard metric for the sigma
turbulence is simply the average value of the 4-second
HM_ = -A,(t)/ 2, (2)
running sigma level 0-4.0 over the reporting interval
(suggested length of 2 minutes).
where
-4r = 1+ r with r = 0.25, 1.0, and 4.0. (3)
HM o = 0---4o. (I)
^
The second part of the algorithm is the calculation of The equation for A ris an approximation for the l-g
the peak components of the hazard metric described by acceleration contour presented in figure 11of reference
the lower leg of the flow diagram. The first step inthis 7. Further research may be needed to define a more
leg is the calculation of the incremental gust amplitudes representative equation for the whole commercial fleet.
as illustrated in figure 2. The word "incremental" The last step in the process is to determine the
should be emphasized in the preceding sentence. The maximum and minimum values of HMr to produce
incremental amplitudes are calculated relative to the
instantaneous value of the vertical gust velocity at the the peak hazard metric components, HM+ and
beginning of each computation interval. The figure HM.
shows calculations at two different measurement times
t_and t2. At each measurement, three least squares
HM + = (HM ,)max and
lines containing 0.25 seconds, 1.0 second, and 4.0
HM_ = (HM, )ram (4)
seconds of data are calculated from the wg values
supplied from the turbulence sensor at some given data
rate. (For example, 100 samples, second). Only the It should be noted that the dimensional sigma
slope of these lines is of interest since itis only the level 0-'4.0(t) and the gust amplitudes .,zl_(t) may be
slope, and not the intercept, that affects the gust
useful to meteorologists for producing various weather
response of the airplane. The values of the slopes for
products. However, the emphasis here is on a hazard
each line are kept in separate bins for each computation
metric for pilots for use in the cockpit in place of
interval (rise time), r, (0.25 seconds, 1.0 second, and 4.0
current PIREP's.
seconds inthe above example). These three bins
A graphical depiction of the logic involved in
contain all the instantaneous values over a fixed interval
calculating the peak components of the hazard metric is
of time (preliminary suggested reporting interval is 2
presented in figure 3for an assumed example. As can
minutes). The values in each bin over the 2-minute
be seen from figure 3, the lines of constant +/- 1g
interval are then multiplied by their respective
acceleration (corresponding to equation (3)) reflect the
computation interval (0.25, 1.0, or 4.0 seconds inthe
fundamental characteristic that larger gust amplitudes
example) to produce the incremental gust amplitudes in
are required to produce the same acceleration level for
the units of velocity--see typical incremental gust
longer rise times. The figure also illustrates the logic
amplitude Al#0(tl) for the measurement at t = tI in for calculating values of the peak hazard metric
figure 2. The dimensional gust amplitudes A_ (t) in components HM , and HM_ .
For the present example of three rise times, the
ff/sec are then divided by w1 ,the level of a step-input
6 peak non-dimensional gust amplitudes inthe
vertical gust that will produce an acceleration of 1g, to
reporting interval can be compared with their
produce the non-dimensional gust amplitudes A, (t) in corresponding values on the lines of constant +/- 1g
g's. acceleration. The positive gust amplitude that is largest
The next step in the calculations for peak hazard metric relative to its corresponding value on the +lg line will
components isto scale the non-dimensional gust be the "reported" positive peak hazard metric
component. A similar interpretation can be applied to
4
American Institute of Aeronautics and Astronautics
thenegativpeeakcomponenOtf.courseth,ese
with a relatively large value because it includes the first
operationasreactuallycarriedoutinthealgorithmby
4 seconds of the data in figure 4. When o-4.0is non-
equation(1s)thru(3)forHA[+ and HM_. In the
dimensionalized by wI and then averaged over the 14
example shown in figure 3,(A+)10 isthe largest seconds of available data, the sigma hazard metric
component is about twice the averaged simulated c.g.
relative positive gust, and (A)40 isthe largest
acceleration (1.18 g's compared to 0.62 g's), figure 5.
relative negative gust. Thus, the sigma hazard metric component does not
For this paper, a distinction is made between
correlate well with the simulated response for a discrete
positive and negative gusts since negative gusts are gust. This result was expected since the sigma hazard
considered more dangerous because they can cause
metric component is designed for low-level continuous
people to rise offthe floor or their seats. However, turbulence and not discrete gusts. In addition, it should
further research may indicate that only the largest
be remembered that for this example, the averaging
absolute peak hazard metric (or only the negative
time for HM,_ was only 14 seconds rather than the
hazard metric) is needed. The sigma hazard metric
component will probably be necessary no matter which suggested 2minutes for an operational algorithm. If2
peak hazard metric component is used. minutes of flight data were available, the averaged
The three rise times used in this paper values o'-n--and HM,_ would probably be much smaller
correspond to different spatial dimensions of the
than in this calculation because of the apparent limited
turbulence depending on the true airspeed of the
spatial extent of this particular discrete gust. In fact, if
airplane. For a typical cruise speed of 800 ft/sec, the
the averaging interval (reporting interval) were much
corresponding spatial dimensions are 200 ft, 800ft, and
3200 ft. The present values of rise time are preliminary longer, o'---_and HM,, would approach zero even
and further research may be needed to establish final though there are very dangerous peaks in the gust.
values. In addition, more than three different values of These peaks are captured by the peak hazard metric
rise time could be used for finer rise time resolution or components described next.
a wider range of rise times. The dimensional gust amplitudes, A' 's, for
the peak components of the hazard metric are also
Simulated Cases presented in figure 4. The largest (absolute)
dimensional gust amplitude for this discrete gust is for
the 4-second rise time. However, the calculations
Sample calculations were made to illustrate the
application of the hazard metric using the preliminary shown in figure 5 indicate that when the amplitudes are
values of the defining parameters. The one exception to adjusted for the response characteristics of the airplane
the suggested preliminary values isthe 2-minute (using equation (3)), the resulting hazard metric for the
reporting interval because the data did not exist for that 1.0-second rise time has the largest values (+1.29 g's
length of time. In these calculations, various gust and -2.50 g's). These values compare reasonably well
shapes were used as input to the longitudinal math to the largest simulated accelerations at the center of
model for the 140,000 lb transport airplane described in gravity of 1.73 g's and -1.87 g's. Although the
reference 7. The simulated airplane responses to these comparison might be improved by using different rise
times, the comparison for other gust profiles might be
gust shapes were then recorded and the maximum and
minimum accelerations at the center of gravity were degraded. A large variety of gust shapes must be
determined. The hazard metric was, on the other hand, examined to see which rise times, etc give the best
calculated solely from the input gust shapes and the overall correlation. Continuous Turbulence Example
gust parameter w1as described above. The results of
Continuous Turbulence It is instructive to examine the
these calculations are shown in the following figures.
characteristics of the 3 hazard metric components for
The simulations were run using atime increment of.01
continuous turbulence. The dimensional parameters for
seconds. The effect of the values of the time increment
Dryden turbulence (sigma level = 30 fps and
on the comparison was not investigated.
characteristics scale length of 1750 feet) are shown in
Discrete Gust Example The results of the calculations figure 6. The 4-second running sigma level, o'40 is
for a gust profile derived from the flight recorder relatively constant as itshould be for continuous
measurements of an actual accident are presented in turbulence. In addition, the sigma hazard metric
figure 4. The gust profile is representative of a discrete
component, HM_, compares favorably with the
gust that causes accidents. The 4-second running sigma
averaged sigma simulated acceleration, o', ,(I.47 g's
calculation of the vertical gust velocity, o'40, begins
-5-
American Institute of Aeronautics and Astronautics
/
and 1.29 g's respectively in figure 7). This result was to
accelerations in the aft cabin, _,a,a }t,,,ak ' are shifted
expected since the sigma hazard metric component was
designed for continuous turbulence such as this. larger absolute values especially for the Dryden
turbulence. This result isto be expected since the
The 3 peak amplitude traces ( A'25, Ai0,
airplane's rigid-body pitching motion and the structural
A'4o in figure 6) show that this part of the algorithm response tend to increase the acceleration at the aft
cabin compared to the acceleration at the center of
effectively filters the gust velocities with the longer rise
gravity. But as mentioned earlier, the high-frequency
times corresponding to longer filter time constants. For
accelerations due to the structural mode are not as
this turbulence, the peaks of the incremental gust
likely to cause passenger injuries as are the lower rigid-
amplitudes are practically equal for rise times of 0.25
body accelerations, reference 7.
seconds and 1.0 seconds while the gust amplitudes for
The sigma component of the hazard metric is
the 4.0-second rise time are much smaller. When the
compared to the simulated sigma acceleration at the
dimensional amplitudes arc adjusted for the airplane
center of gravity in figure 10. As expected the
response, the peak hazard metric components
agreement is good for the Dryden turbulence but poor
for the 0.25-second rise time are the largest, figure 7,
for the discrete gusts. This result is the opposite of the
rather than those for the 1.0-second rise time for the
result shown in figure 8. Thus, these two figures show
discrete gust example. This result reflects the high
that the sigma component and the peak components
frequency content of the Dryden turbulence. The final
complement each other for different types of
values for the peak hazard metric components are +4.71
turbulence. It should be emphasized that the above data
g's and -3.09 g's. These values do not compare as
are for simulated airplane responses. As shown in
favorably with the simulated peak c.g. accelerations
reference 7,the actual airplane response in the NTSB-
(2.59 g's and -3.26 g's) as did the previous values for
reported data were sometimes much larger than the
the discrete gusts. However, more examples are needed
simulated responses. The reason for this discrepancy
to draw firm conclusions. Another noticeable
was most probably due to either transients when the
difference in the calculations in figure 7 isthe high
auto-pilot disconnected or out-of-phase inputs by the
frequency (3 Hz) response inthe acceleration at the aft
pilot. No hazard metric will probably ever be able to
cabin location. This response isdue to the first-
predict the response of every pilot to an unexpected
fuselage-bending mode being excited by the high
turbulence upset.
frequency components of the Dryden turbulence. The
present hazard metric does not account for structural
Concluding Remarks
responses, but as shown in reference 3high frequency
accelerations are not likely to cause passenger injuries.
A quantitative hazard metric for airplane
Collected Results: Twelve additional gust wave shapes turbulence response has been described. The metric is
were investigated in addition to the two examples intuitively and is intended to replace the subjective,
shown above. That is, mountain rotor wave shapes airplane-dependent Pilot Reports (PIREPS) in current
with 4different amplitudes and gust lengths were use. A procedure for calculating the metric has been
simulated using the expression described in reference 7. described and demonstrated using preliminary values
Two additional discrete gusts from actual airplane for the fixed parameters defining the metric. The
accidents were simulated, as were four l-cosine gusts, metric has been applied to simulated discrete and
and two additional Dryden turbulence fields with continuous gust encounters and has been shown to give
different sigma levels and scale lengths. The results of reasonable results. That is, the discrete gusts are
these calculations are summarized in figures 8-I0. The adequately described by the "peak" components of the
agreement between the peak hazard metric components, hazard metric, and continuous turbulence is adequately
figure 8, isacceptable for most of the gust shapes with described by the "sigma" component of the hazard
the poorest agreement for the continuous Dryden metric.
turbulence as expected. Generally, the largest The fixed parameters defining the hazard
disagreement is in a conservative direction; that is, the metric need to be more thoroughly checked before the
peak hazard metric over-predicts the actual hazard metric is operational. The metric should also be
accelerations. compared to actual airplane responses (rather than
Although the hazard metric presented here was simulated responses as was done here) for several
encounters of real turbulence by instrumented airplanes.
designed to predict the acceleration at the center of
gravity, a comparison of the peak hazard metric The correlation is expected to be useable for most
components and the acceleration at the aft passenger modem transport airplanes. The defining parameters of
cabin are compared in figure 9. The biggest difference the final hazard metric will be a compromise for
between figures 8and 9 is that the simulated different gust shapes/flight conditions/airplanes/etc.
-6-
American Institute of Aeronautics and Astronautics
Theparametethrsatneedtobeoptimized/ascertained
. Soreide, David C., et al "Airborne Coherent
are: Lidar for Advanced In-Flight Measurement
(1) The number of rise times inthe "peak" (ACLAIM) Flight Testing of the Lidar
hazard metric component calculations (3 Sensor," 9thConference on Aviation, Range,
in above example) and Aerospace Meteorology [for American
(2) The values of the rise times over which Meteorological Society], Sept I1-15, 2000.
the peak gust amplitudes are calculated . Cornman, Larry B, et al. "Real-Time
(0.25, 1.0, and 4.0 in above example). Estimation of Atmospheric Turbulence
(3) The best relationship between gust Severity from ln-Situ Aircraft Measurements."
amplitude and rise time for adjusting the Journal of Aircraft, Vol. 32, No. 1,January-
dimensional gust amplitudes of airplane February 1995
response (equation (3)). . Chan, William; Lester, Peter F., and Bach,
(4) The time interval over which the metrics Ralph E.: " Wingrove Parameter: A New
are averaged and reported (2 minutes Turbulence Metric" Journal of Aircraft Vol 33,
preliminary suggested value). No. 2, March-April 1996.
(5) The number of peak hazard metric values . Bass, Ellen J., et al. "Pilot Decision Aid
that need to be reported. That is, whether Requirements for a Real-Time Turbulence
both positive and negative hazard metric Assessment System" The Tenth International
components need to be reported (as in Symposium on Aviation Psychology.
above example) or is the largest absolute Columbus, Ohio, May 2-6, 1999.
metric or the negative metric sufficient. . Jeppesen Sanderson Training Products.
(6) The effect of spatial or temporal Federal Aviation Regulations/Aeronautical
resolution (data rate) of the vertical gust Information Manual 2000. Jeppesen
measurements. Sanderson Inc.
. Stewart, Eric C., "A Study of Airline
Passenger Susceptibility to Atmospheric
Turbulence Hazards," AIAA Paper 2000-
References
3978, August, 2000.
. Fuller, J.R., "Evolution of Airplane Gust
Loads Design Requirements," Journal of
Aircraft Vol. 32, No. 2 March-April 1995
-7-
American Institute of Aeronautics and Astronautics
O'4.0(t)
,IAverage t H(gM's)
Running RMS _1 (g's)
computation interval=,4 seconds reporting Interval -2minutes
A/C .S CL_
d.. / /
b_,I t Combine
HM=[HM a HM+
[Notr_rt ol
Jlgodthm]
figure 3
/ figure 2 1 IC(_gsI_lACdjus"tfP°r °_°" [HM+'HM-
-_[ IAnmcrpelmiteundteaslAI_tms_[ -W- I MinimumMaximum(g.'s)
r=O1S, 1,0,4.0 seconds
reporting interval - 2minutes
Figure 1. Flow diagram of hazard metric calculation.
Measurement
att =tI Least Squares line
_ (t1)',_
IA //_ r=4.00 ^.
Vertical I_A ' r=1'_OOk'_ J _'/ "_ J_V___ ._
gust velocity, fps V- '_ [----_ :i_,,-l- _ --_'tJ V X "- Time
" "\
I _"................ Al"°(t1) )
I (typical}
I
Measurement
at t =t2 Least Squares line
I /aa(t2) r=l.00
r =0.25 :_ _, /
Vertical
oo
gust velocity, fps
I
Figure 2. Illustration of incremental, dimensional gust amplitude calculations.
-8-
American Institute of Aeronautics and Astronautics
(A+)1.0
For HM+= _'--_" 0
example
shown (Ao)4.0
HM.=-
Maximum relativevalue
'...... _ ® (_'+)4.0
A I ,_ I
(1,(A'+) 1.0)___
1 constant+1gacceleration
1.0
('_+).25
A, 0 I I I ,,._
non-dimensional
,2.S 1,0 4,0
('_J.25 r,seconds
-1.o ® (_'J1.o
' A '
, ® ( J4.o',
_I _nimum relative value
constant-1 gacceleration
(4,(_.)4.0)
Figure 3. Graphical depiction of the terms involved in thepeak values of'the hazard metric.
, i i i i i i
2°°t i_' i
Wg,r-ps2ooo_I i ,
I I L I I I I
1°° I , , ! ! ' T ! '
o,_.o ,fps 50_--'_'__ , i i ,
01 i I i
200,I , , ! , !
AC25 •fPs 0_
-200 I i I , I I I i I
2001 ........
A_.O, fps 0 " :..... : " "
-200 J , , , i , i , ,
200 .........
A4.0 , fps 0
- 200 ' ' ' K , , J , J
0 2 4 6 8 10 12 14 16 1'8 2O
Time, seconds
Figure 4. Incremental, dimensional gust amplitudes and running SIGMA for a discrete gust
9
American Institute of Aeronautics and Astronautics