Frequency of occurrence of atmospheric gusts and of related loads on airplane structures


Material Information

Frequency of occurrence of atmospheric gusts and of related loads on airplane structures
Series Title:
Alternate Title:
NACA wartime reports
Physical Description:
31 p., 8 leaves : ill. ; 28 cm.
Rhode, Richard V
Donely, Philip
Langley Aeronautical Laboratory
United States -- National Advisory Committee for Aeronautics
Langley Memorial Aeronautical Laboratory
Place of Publication:
Langley Field, VA
Publication Date:


Subjects / Keywords:
Airframes   ( lcsh )
Aerodynamics -- Research   ( lcsh )
federal government publication   ( marcgt )
bibliography   ( marcgt )
technical report   ( marcgt )
non-fiction   ( marcgt )


Summary: A number of samples of flight acceleration data taken by the National Advisory Committee for Aeronautics under a variety of operating conditions were evaluated to determine the total frequencies and the frequency distribution of atmospheric gusts. The samples include 1748 hours of operation by several airplanes of the domestic airlines of the United States, a Martin M-130 airplane of the Pacific Division of Pan American Airways System, and the Boeing B-15 airplane of the Army Air Forces. These data are supplemented by V-G records, so that more than 9,000,000 miles of operation are represented. Samples taken on an Aeronca C-2 airplane at low altitude in the turbulent air of the earth's boundary layer are compared with similar samples taken on the Lockheed XC-35 airplane at high altitude within cumulus-congestus and cumulo-nimbus clouds. Similar data of German origin have been reanalyzed and included for comparison.
Includes bibliographic references (p. 25-26).
Statement of Responsibility:
by Richard V. Rhode and Philip Donely.
General Note:
"Originally issued November 1944 as Advance Restricted Report L4I21."
General Note:
"NACA WARTIME REPORTS are reprints of papers originally issued to provide rapid distribution of advance research results to an authorized group requiring them for the war effort. They were previously held under a security status but are now unclassified. Some of these reports were not technically edited. All have been reproduced without change in order to expedite general distribution."

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University of Florida
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All applicable rights reserved by the source institution and holding location.
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November 1944 as
Advance Restricted Report 4IA21

By Richard V. Rhode and. Philip Donely

Langley Memorial Aeronautical L.toratory
Langley Field, Va.
P.O. BOX 117011

.. NACA.
& : -. .. ,

NACA WARTIME REPORTS are reprints of papers originally issued to provide rapid distribution of
advance research results to an authorized group requiring them for the war effort. They were pre-
viously held under a security status but are now unclassified. Some of these reports were not tech-
nically edited. All have been reproduced without change in order to expedite general distribution.

L 121

a ....,

Digitized by the Internet Archive
in 2011 with funding from
University of Florida, George A. Smathers Libraries with support from LYRASIS and the Sloan Foundation

Ii: -7






By Richard V. Rhode and Philip Donely

A number of samples of flight acceleration data
taken by the National Advisory Committee for Aeronautics
under a variety of operating conditions were evaluated to
determine the total frequencies and the frequency dis-
tribution of atmospheric gusts. The samples include
1748 hours of operation by several airplanes of the
domestic airlines of the United States, a 1'.irtin M-150 air-
plane of the Pacific Division of Fan American Airways
System, and the Boeing B-15 airplane of the Army Air Forces.
These data are ',.innlenimnted by V-G records, so that more
than 9,000,000 miles of operation are represented. Samples
taken on an Aeronca C-2 airplane at low altitude in the
turbulent air of the earth's boundary la-yer are compared
with similar samples taken on the Lockheed XC-55 -ir:.-lane
at high altitude within cumulus-congestus and cumulo-
nimbus clouds.

Similar data of German origin have been reanalyzed
and included for comparison.

It was concluded that the distribution of gusts
within turbulent regions of the earth's atmosphere
follows a substantially fixed pattern regardless of the
source of the turbulence. The total frequencies are
therefore governed by the total length of flight path
in rough air, and operating conditions determine the
total frequencies only by affecting the ratio of the
length of flight path in rough air to total length of
the path. Gust-load frequencies were found to be
inversely proportional to airplane size.

It was further concluded that the gust frequencies
can be applied with small error to- the estimation of
stress frequencies in the primary structures of airplanes.
The results of the analysis are applicable to the fatigue

NACA ARR No. L4121

testing of the primary structure of the airframe and to
the estimation of the probability of encounterin- gusts
of excessive intensity within any stated period of


The trend in airplane design toward higher wing
loading, higher seed, and larger size and consequently
toward mi her rean stresses and greater severity of loads
on the structure has resulted in a growing appreciation
b," desi-gners of the -otential icortoance of fatigue in
'he primary structure and of te necessity for designio
on the asis of fatigue strength for limited "life
expectancy." reference 1, for exarlje, displays a great
deal of concern about the fatigue life of airplane
struck tures.

Life exe,-ctancy is governed not only by fatigue but
also by- 'Pbe probability of occurrence of single quasi-
static loads of such high mragitu:e as night endanger
the structure directly. This problem nas bean made
more acute by the overloading of airplanes due to
wartime traffic demands.

An obvious prerequisite for control of fatigue
strength and for the determination of the probability
of single large loads is flight data that show the
frequency of occurrence of loads or stresses in the
structure correlated with the many factors that influence
the frequencies. In the flight operations of trans-ort-
type airplanes the principal source of structural loads
and stresses is atmospheric turbulence, and iosU of the
required flight data annm cable to transncrt air-lanes
may be obtained by measurements of the loads or stresses
during cruising flight in rough air.

Kaul (reference 2) and ?Trise (reference 3) have
presented data on rte win;-load listcries experienced
by a number of airplanes both unde s.necial test condi-
tions in ro-.i' t air and in so-i 6.b3 hours of cruising
flight on several branches of '"e Deutsche Lufthansa.
Kaul obtained results b means of an accelerometer located
near the ce ter of -r:.vit of' 'e airplane and Freise,
by means of a strain gage counted on a chord member of a
wing spar near the wing root. The results were expressed
In references 2 and 3 in terms of applied wing load.


The INACA has from time to ti-ne collected data
similar to these presented by KIaul and Freise. These
data include acceleration measurements from 1320 hours
of the early operations of the domestic airlines of the
United States, 313 hours of :M:scellaneous cross-country
flying by the LBoing B-15 airplane, a 115-hour round-
trip flight between Alameda, Cslif., and Hons ln-, China,
by a L'artin Mi-130 airplane of Pan American Airways System,
and two special gust investigations in the vicinity of
Langley Field, Va. Data taken with the NACA V-G recorder
(reference 1.) during some 8,500,000 miles of airline
o.,-rations are also included to take into consideration
the rare gusts of great intensity that are not normally
encountered during the takin: of samples of limited
scope. In the present paper these data are analyzed and
compared with the German data of references 2 and 5
to establish a broader basis for the determination of
the frequency of loads resulting from atmospheric gusts.

1. "L3' A-)D .II'.7 CLATURE

An acceleration increment normal to chord of wing,
g units

weight of airplane

S wing area

a slope of lift curve

po mass density of air at sea level

VaO/2 equivalent airspeed

U., effective gust velocity

K relative alleviation factor

c mean wiing chord

F total frequency, total number of occurrences of
a phenomenon in a sample

f frequency, number of occurrences of a phenomenon
within a class interval

NACA ARR No. L4121

fr relative frequency (f/F)
kay average gust interval, average distance along
flight path in turbulent air between
significant gusts

L oath of operation, total length of flight path
for any considered scope of operation

R oath ratio, ratio of length of flight nath in
turbulent air to oath of operation

The class interval is the range between two values
of a measured quantity within which measurements of like
value are grouped (or classed) for the purpose of tabula-
tion offrequencies. I-. class mark is the definitive
value, or midvalue, of a class.


In most investigations of atmospheric turbulence
conducted by the NACA, the acceleration response of
airplanes to the gusts has been utilized in the measure-
ment of atmospheric turbulence. Although much of the
philosophy underlying the concepts involved in the use
of acceleration response in the measurement of turbulence
has not been published, some basic considerations are
discussed in references !. to 6. These considerations
lead to the relatively simple concept of an "effective
gust velocity," which has been selected as the basic
attribute or independent variable to which the statistical
analysis best applies. T1heef"ective gust velocity is
defined by the relation

poaKUeVI 1/2
An = (1)

The relative alleviation factor K allows for the
velocity of the al.r-lane normal to the flight oath caused
by application of acceleration during the finite time of
action of the gust. The factor K is given as a function
of the .t--G loading in figure 1. 1The derivation of this
curve, which takes into consideration the lag in transient
development of lift and the gust gradient, is attributable

NACA ARR "o. L1121

to the authors but has not been published. The curve
in figure 1 is rart of the American design requirements
and has been published as figure 11(a) in reference 7.
Although derived at a relatively early date when little
information on gust gradients was available, the rela-
tionship described by the curve has remained in excellent
agreement with suosequently obtained flight data ar.-d with
advances in the theory of unsteady lift.

SCOPE OF ", .1. .:F3

Extent of operations

Domestic airlines.- Acceleration records for
1520 h.:,_rs, zr -. 1.45,000 miles,of fli'-:t were
obtained during the early daTs of r -:c rt operations
on the domestic airlines of the U--ted States. The
data were taken during routine scheduled operations
over a period cf about 2 years. average operating
altitude was about L000 feet above sea level. The
airplanes on which the measurements were made included
the foll(-.'.ing tynes: Ford 5-AT, Fokker P-10-A,
Boeing 40-E, and Boeing 80-A. 1-~ routes flown covered
most sections of the 17ited States and represent all
types of climate and topography in this country. The
data from these early domestic-airline or-rations are
referred to subsequently as "s-,.le 1." The charac-
teristics of the airplanes and a summary of the operating
conditions for all the c2.rles are -iven in tables I
and II, respectively.

A large number of acceleration records were obtained
later on the domestic airlines. These records represent
4l2,1- '-5 hours, or about 7,000,000 miles, of routine
tra..spct operations by Boeing B-1-.7, Doi- ls DC-2,
and Do.'las DC-S airplanes on several airlines covering
most sections of the Tr'ted States. The data from these
later domestic operations are called samples 2, 5, and 4
for the B-247, DC-2, and DC-3 airplanes, respectively.
(See tables I and II.)

Alameda to Hon- Konr,.- Records were taken with a
number of instr" .M.'.s riin r a round-trip flight in
June 1958 from Alameda, Calif. to :l ..w:, China
by a MIartin .7-130 airplane of 7 : American Airways
System. The average altitude was about 10,000 feet

6 1A.A ARR ":. 14121

and the flying time was 11-5 hours, corresponding to
17,000 miles of flight. The data from this flight
are called sample 5.

Records of acceleration covering 12,252 hours, or
about 1,520,013. miles, of .routine operations with
.,artin ?I-130 and Boeing .-51 airplanes are included
in the analysis for the route from Alameda to Hong .-'ong.
The data from these operations are called E-_.:-..le c.

Boeing --15 airplane.- Records of acceleration
were T, :-:.. c:. _. --~' -Troila-e during 315 hours, or
about b1,000 miles, of miscellaneous flying incl-~ing
a number of cross-country fli ts ove-r various sections
of the Uni .:' States and one round trip to the 2-:-'.
Canal Zone. These fli-' ts were nade between '-.vember 1953
and June lL0. The average altitude of the operations
was about 5000 feet. The data are subsequently called
sam-le 7.

XC-55 airnlane.- The Army Loclheed XC-55 aIrolaAe
was o...'..... ... ,'.cinity of La :.ler Field, Va. durL"'
an investigation of atmospheric turbulence in the
suimiers of lLl and 1042. n!easureirents of acceleration
and airspeed were taken onl-- d.-2-c'.. fli ht through rough
air, mostly within cumulus-congestus and cumulo-nimbus
clouds. The surveys were made at various altitudes up
to 54,000 feet. Only two samples 'rom these surveys
are included in t' e analysis. One of these s.-r:le:s
(sample 8) was selected at random '_?.' the several sets
of data; the other sample (sv.ple 9) represents the
roughest fli t.

Aeronca C-2 airrlane.- An Aeronca C-2 airplane was
flown 7 .: .' ..Ttion irn .107 of turbulence at
very low altitudes in the earth's boundary layer. A
sample (s-,.o'-)le 10) was selected at random fr:-". the
complete data and is incAl--f' hers for

Anparatus and Limit.tions

o'mnestic airlines (early orerations).- In the early
trans' -: Ui c ,s '-nl-- "- "-; 'n re,-cords were
obtained. T'-,.- record .s were .,,..- with commercial vibra-
tion recorders that '1 been re': .t into acclerometers
by the -,CA. --se accelerometers recorded ,.ainst time
on a waxed-raner disk about 4 inches in diameter. The
instruments wvere arr :. .--.d to make ome revolution of the


disk in several hours. The time scale was therefore
cramped and only the moderate and the large values of
acceleration could be counted.

As the airspeed was not recorded, effective gust
velocities were evaluated on the basis of the known
cruising speeds of the airplanes.

Although the slopes of the lift curves were known
from available data, the wing loadci-:ls of the airplanes
as flown were not usually known. Effective gust
velocities were, therefore, evaluated on the basis of
the assumption that the airplanes were flown at normal
gross weight. This assumption leads to somewhat
conservative values, as the airplanes were usually
flown at less than normal gross weight.

Domestic airlines (recent operations).- In the more
recent domestic trans-ort operations, both acceleration
and airspeed were recorded by means of NACA V-G recorders,
which are described in reference 4. These instruments do
not record against time; the accelerations are registered
vertically on a small smoked-glass plate while the values
of airspeed are recorded horizontally. The record is
an envelope of the maximum and minimum values of accelera-
tion against a scale of airspeed. The small accelerations
are illegible within the envelope and only the larger
values of acceleration that project beyond the envelope
of the small values can be counted.

No assumption as to airspeed is required with the
NACA V-G recorder, as the instantaneous value of airspeed
associated with any observed acceleration is given by
the record.

As in the case of the early transrorts, the wing
loadings of the more recent transport airplanes as
flown were not known exactly. It was determined,
however, that a reasonable approxi:'..tion of the average
operation weight was 85 percent of the normal gross
weight; this value was used in the evaluation of effective
gust velocities.

Alameda to Hong Kong.- During the round-trip flight
between Jl..ia.ed:a and Eorng Kong of the M-130, the airplane
was equi-:;-ed with an NACA V-G recorder, an NACA recording
accelerometer, an :-CA airspeed recorder, and several

17.AA ARR 'To. $1121

NACA scratch-recording strain ;:'es. Both the accel-
erometer and the airspeed recorder recorded the measured
quantities --.ainst time with a scale sufficiently open to
er'mit detailed evaluation of :'ie records. The strain
gages also recorded against time, .but the motion was of
an intermittent character so that all the strain peaks
could not b'e counted. Only one strain gage operated
satisfactorily throughout the fli ht. Many of the strain
values could, however, be correlated with the accelera-
tion measurements.

During the fliZht an observer operated the instru-
ments and a complete log of time s.-ent in rough air,.
total time, airnlone weight, and other pertinent detail
was kert. The records therefore remnit a complete and
accurate evaluation -f the frequencies of effective gust

Except for the records taken on this round-trip
fli-'It, all records of acceleration and a'lrbs?=. taken
on the Alaneda-Hon Kong route were made with NACA V-G

3-1- air1lane.- The B-15 airplane was equipped with
an .C' rsCo:'di : accelerometer and an NACA airspeed
recorder havi'n- t-e time scales sufficiently open to
rer-mit detailed evaluation of the records. A n'.imbsr
of NACA and EVL t'pe scratch-record.-- strain -.L-ges
were ir-stalled on shear and chord members of a wing spar
at two stations alc:i- the span. The DYL type ,-aces
recorded continuously gl.."st time, and a count of 'he
strain reakss is possible alth-: such a count has not
been made. As in the case of the ro-.5-trip fli" :t to
Hc',-.g Vong by the M,-150airplane, the strain records are
used herein only to show the relationship between a
number of measured strains and accelerations.

DurinT the fli__-ts of the 3-15 airplane, an observer
opera-: ?, the instruments and kent a complete log of time
spent in rough'~ air, total time, airplane weight, and
other pertinent quantities. TL:' record's from these
fli:gts therefore w'ermit a comnlete and accurate
evaluation of the frequencies of effective gust velocities.

YC-35 alirnlane.- The XC-35 airplane was equipped
with -r: 7 in accelerometer and an ...A air-
sneed recorder set to aive an onen time scale. The records
obtained are amenable to detailed evaluation. .he

NACA ARR ?o. 14121

operating wei'-~ts for all flights are known, and effec-
tive gust velocities can be completely and accurately

Aeronca C-2 airplane.- The Aeronca C-2 airplane
was alic fitted ,ith an '.'.CA recording accelerometer
and an '.,CA airsoeed record-er, and the operating weights
are accurately known. Detailed evaluation of effective
gust velocities is possible from the records.



method d of Count

The metl-od of counting frequencies used herein
was dictated largely "- the type of record available
for analysis and by the quality of the records. Only
the records from the KACA accelerometer -ermitted
detailed examination, but even with those records it
was necessary for Oractical reasons to confine the count
to single max'.-i'ums and mir'ni.nis, or :-aks, between any
two consecutive intersections of the record line with
the lg reference level. This method of count neglects
the minor oscillations superimposed on those counted.
Kaul (reference 2) emolo-ed a similar method of count,
and in this respect the German ar the American data
are comparable.

From the records for sa:-rle 1, in which the time
scales were cramped, L] fron the records taken with
NACA V-G recorders it was not Dossible to determine
whether the acceleration returned to or crossed the
lg reference level after the attainment of a maximum
or minimum value. In these cases, therefore, the
evaluation was made by counting the acceleration peaks
standing out fro.:, the envelopes of the small accelerations.

Since, except for the '.'- data, it was considerably
more convenient to count accelerations directly than to
convert accelerations to effective -ust velocities prior
to the count, the conversion was made for relatively
short sections of each 3.a-rle on the basis of mean air-
speeds for these sections. In this way lar e errors in
airsoeed were avoided and the small- deviations of the
airspeed from the selected means were of no great

:Tm-CA ARR :-o. LL 21

Class Intervals

The intervals for the classification of frequencies
were chosen at about the smallest values consistent with
the accuracy of the several acceleration measurements -
namely, about 0.1g. For a number of reasons the
intervals x-ere not always quite the same. This fact is
of no consequence for, in any event, since the accel-
eration values were convenientl- converted to effective
gust velocities after ths count was made, the class
intervals expressed in terms of effective gust velocity
would not remain equal for the various samples -_ cause
of differences in air-lane characteristics and airspeed.
The class intervals, expressed in terms of :-'3t velocity,
corresponding to to'e actual evaluation are given in
table III.

Threshold Values of Acceleration

and E'ffective G'Just Velocity

In counting the frequencies in the lowest class
(that is, tle class containing the s allest values of
acceleration), t"-e result depends upon the minimum values
that can be observed. On the records from the .ACA accel-
erometer, variations "n acceleration attributable to
gusts as small as 0.02g can be ccovenientl- observed,
and all greater values can therefore be counted.
limit of acceleration for which the count can be made is
termed herein the "threshold value" of the acceleration.

On the V-3 records and the records from the con-
verted sco, ercial recorders used in c;t:.."i .t sample 1,
the threshold values of acceleration were rather high
because of the limitations of the instruments orev. ously

7Te threshold values for the samples are -.1ven in
terms of effective gust veloci': in table III.

!ative-- ._"* :.,.: ncy Listri ,:tion

I-e frequencies f and t-. tot -" f: .-uencies F of
the fsts fcr the 10 samples are liven in table ITII as
counte wi'tln the selected cla;s intervals a,.1 to the
thresuol: values of effective ,7ust velocity.

NACA ARR o. 14T21

In order to arrive at the broadest and most rational
view of gust-frequency distribution, all data were
plotted in the form of relative-frequency polygons
(reference 8). The polygon of relative gust frequencies
is a graph of the ratios f/F = fr for the different
classes plotted at the respective class marks on a scale
of effective gust velocity. Since the shape of such a
pol --o. is dependent upon the size of the class interval
and upon the class mark of the lowest class within which
the count is made, pol 7g..s for the different samples
can be cocoared only w] en plotted for a co.xnon class
interval and for a common lowest class. In order to
place all the data on a comparable basis, a common
class interval of 4.5 feet rer second, the largest of
the class intervals for which count was made, was chosen.

Since samnle 5 and samples 7 to 10 have about the
same small threshold value falling within class 1,
relative-frequency rolvgons for these samples can be
plotted immediately after conversion to the common class
interval. The 'ol.:'.r. for samples 5 and 7 are shown
in figure 2; the ,ol .-ics for samples 8 ;:n" 10, in
figure 5; and the pol-yin for sample 9, in figure 4. A
reference polygon, "relative distribution A," is shown
in these figures to facilitate comparisons.

In constructing polygons from the remaining data,
samples representing generally similar operations were
combined. The combination of these samples, which
include the V-G data, was performed in such manner as to
bring the relative frequencies of the rarer lar-..e gusts
into a proper relationship with the other data. The
basic assumption involved in the process was that, for
data covering a large scope of operations, the relative-
frequency distribution follows a single pattern. The
validity of this asswurtion is discussed in a later

In the case of samples 1 to 4., all of which
re-cresent domestic transport operations, none of the
data extended to low values of ei.>'ctive gust velocity
for reasons previously given. The total frequencies
for these samples are, therefore, relatively smaller
than the total frequencies for the more refined samples
because of the omission of the frequent low-value gusts.
In order to bring the relative-frequency 'olygon for the
combined samples 1 to 4 into nri --er relationship with
the polygons for the more co'".olte samples, it was

NACA ARR Ho. 14121

necessary first to estimate the frequencies of the
missing low-value gusts and the corresponding total
frequencies. For this purpose a mean relative-frequency
distribution from samples 5, 7, 8,and 10 was assumed to
represent the missing low-value gusts of sample 1, which,
of the combined samples 1 to )-, had the lowest threshold
value. With this as3"mption, the total frequency of
sample 1, including the frequencies of the lower classes,
was estimated to be 1,600,000 gusts for the 1320 hours
of operation.

The freq-u-ries of sample 2 were then reduced by the
ratio of the path of operations of sample 1 to the path
of operations of sample 2 (table IV). Similarly, the
frequencies of samples 3 and 4 were reduced to correspond
to the path of operations of sample 1. The sum of the
reduced frequencies within each class of samples 2, 5,
and ). was then added to sample 1 to obtain the polygon
for the combined samples 1 to 4.

In combining samples 1 to L a precaution was
necessary in regard to class 6 because of the following
considerations. After conversion of sample 1 to class
interval )4.5, the highest class in which data fell was
class 6. This class is the lowest in which data from
the V-G records fell. Thus, frequencies were available
from all samples of the combination only in this class.
In arriving at a combined frequency for class 6, two
rDossible methods could have been used; namely, either
the reduced frequencies from samples 2, 3, and 4 could
have been averaged with the frequency of sample 1, or
the most reliable sample could have been used without
inclusion of the less reliable samples. The second
method was actually used and the frequency for class 6
was taken frc'. sample 1 since the obscuration of some
class 6 acceleration peaks within the V-G envelopes of
sjcoles 2, 3, and 4 made these data less reliable for
this class.

The frequencies for samples 5 and 6 were combined
in a manner similar to that in which samples 1 to 4
were combined. In this case, however, it was
unnecessary to estimate a total frequency for sample 5,
as the threshold value was comnnarable to the threshold
values of the other comnolete saminles. Also, inasmuch
as th]e hit:,hest gust-induced acceleration for both
samples was recorded within bhe rather limited scope
of sample 5, this one value was assigned a frequency
of unity for the combined sanles.

NACA ARR No. 14121

Polygons for the combined samples 1, 2, 5, and 1
and for the combined samples 5 and 6 are shown in
figure 2.


Relative-Frequency Distribution

Significance of ar'ols sramrles.- The relative-
frequen' '. Tio.n f. t: a '. ie of data does not
necessarily represent general average conditions. For
instance, the frequency distribution of sample 5 is not
representative of average conditions because of the
occurrence in sample 5 of one of the most severe gusts
ever experienced on the Pacific Division of the
Pan American Airways System. Even without other samples
for comparison, this fact mizht have been suspected from
the form of the relative-frequency polyg. for sample 5
in figure 2, which shows a sudden break to large values
of Ue. Sample 9 1s another case tl:at is not repre-
sentative of average conditions, because this sample
was obtained during the roughest of a considerable
number of flights made during a special investigation
of turbulence within cumulus-congestus and cumulo-nimbus
clouds. For sample 9, as can be observed from a com-
oarison of the polvygon in figure l with the other
polygons in figures 2 and 5, the frequency distribution
indicates relatively high proportion of gusts of high

In contrast to the "fullness" of the frequency
distributions for samples 5 and 9, the frequency distri-
bution for sample 7 shows relatively low proportion of
gusts of high intensity. This result is in line with
the conditions of operation, according to which regions
of high turbulence were avoided as far as possible so
that greater weight was given the frequencies of the
smaller gusts.

Since the conditions governing samples 5, 7, and 9
are known to give rise to more or less extreme frequency
distributions, a sample representative of average condi-
tions applicable to large scooe of operations would be
expected to lie somewhere between the extremes. Probably
the most representative of the samples containing
detailed data in the lowest classes are samries d and 10,


w-ich were selected at random from a considerable mass
of data. The relative-frequenc polrsc.-is for these
sainles (fig. 3) may be observed by comparison with
figures 2 z:nd a to lie between the -olygons for
samples 7 and 9 and inside the end point of the pol'gon
for sample 5.

The combination of samples 1 to 4 and of samples 5
and 6 in the manner described greatly extends the scope
of the data applicable to the respective operating con-
ditions represented. 7T' combined samicles are thus more
true than any single small sample in the sense that the
influence of accidental occurrences, such as the encoun-
tering of an unusually. strcn: * in sa-'le 5, is sub-
merged in the mass of data; that is, acci--:.ntal occur-
rences of this :ort occur in sufficiently large number
within a samrle of large scope that they become more
truly representative of the average conditions. Fig-
ure 2 shows t'-is effect clearly; the combined sa'nrle
5 and 6 and the combined samnole 1 to L have relatively
uniform distributions lying between the extreme distri-
butions of saur.les 7 and 9.

For comparison with the 7. r nles presented herein,
distribution pol'--"".s of TUe have been constructed
from Eaul's data wit- a class Interval of 4.5. It may
be seen from flure 2, which shows the envelopes of the
nolvgons for .aul's data, t'-at the German and the
American results are in very good :.ireement.

Influence of airnlane characteristics and source
of turbulence.- It 1s evident from the preceding dis-
cussion Ta-f the major discren.-sies between the fre-
quency distributions for the various sanmrles can be
accounted for largely by accidental occurrences during
the operations. '."-n the scope of the s::nr.les is
sufficiently increased to be representative of avercie
operating conditions, these accidental influences are
not so strong and the frequency distributions tend to
fall into the same pattern re .:. of the source
of the data. The results therefore indicate that
individual gusts in 'irbulent regio-is of the atmosphere
are distrib uted on the whole in a fixed manner irrespec-
tive of Yhe location of the turbulent re-ions and of the
source of the turbulence.

figure 3 -.-rE'.,er illustrates the similarity of
distribution for di fervent samples. Sam-le 3 was

"ACA A-? No. L4 121

obtained at high altitude within cumulo-nimbus and
cumulus-co.; estus clouds and represents turbulence
havin'i its origin in thermal convective processes.
Sample 10, on the contrary, was obtained at very low
altitude in the absence of thermal effects and the
turbulence arose from the shearing of the wind in the
earth's boundary layer. tUotwithst ,'_.g these con-
siderable differences in the aerol: -cal conditions,
the f:-euency distributions are nearly the same and they
are also in close agreement with those from other sources.

Another point, most clearly evident from samples S
and 10 but also evident from the other data, is Jhat
the distribution of turbulence as measured is largely
independent of airplane size a.-. other air lane charac-
teristics. '- close similarit-" of the distributions
for sample 8 (obtained with the Lockheed XC-55 airplane),
sample 10 (obtained with the Aeronca C-2 airplane),
and the sanoles from the airline operations indicates that
the basic assumptions and concerts underlv-r." the gust-
load formula (equation (1)) are correct.

Influence of disturbed motion of airplane in
c a r-: s t -o -

istics apply on the average, in coGt..n -'-
turbulence the frequency d istributicun a : to
contain abnormal .r.euencies in 1,e 'iher classes
unless precautions are taken to eliri:nate the effect of
disturbed and controlled motions of tLe airplane. In
the flight from which sample 9 -;;as derived, which was
the :u.h2st of a l .er number of flights throu'_.
cumulo-nimbus clouds, the airplane motion was con-
siderably disturbed from the desired str,*' t -th,
so that the gyroscope of one of the flight Instruments
was at times put out of action (reference 9). Under
these circumstances the airplane was subject to moderate
acceleration fluctuations of lo-g period u--- which the
short-neriod accelerations due to the turbulence wer3
superimposed. .'.:-n the count was made in the descri' ed
manner chosen for the -:neral analysis, abnormally high
values of effective gust velocity were ascribed to the
various Irequencies and the pol-- on appeared full
(")g. )-. '.Ten the count was made with res-ct to the
variable litum caused by the disturbed motion rather
than with respect to the ig datum, the frequency distri-
bution conformed more nearly to the distributions of the
other samples. The corrected olygon retained a certain


degree of fullness, however which may be ascrib'ed to
actual greater frequencyT of the more severe gusts.

differences between two nol--Ions like those shown
;n fig-ure 4- provide means of evaluating the effect of
the disturbed motion on the frequenc'r of applied loads.
The data given here apnly specifically to the char-
acteristics of the XC-35 airplane and cannot be safely
applied to other cases. This fact is of small concern,
because large disturbed notions are rarel- encountered
in normal operations, so that such effects as are shown
in figure would hardly be noticeable in a sample
representing large scope of operations.

Factors Governing Estimation of Total '"i-luencies

Average and standard i.ust intervals.- The fact
that t:!-+ eq., L. ,ist. ouct'J flSov for samples of large scope indicates that the total fre-
quency is proportional to the distance flown within tur-
bulent regions. Conversely, tihe average soacing between
gusts is inversely proportional to the distance flown.
In order to provide a useful basis for estimating the
total frequencies of significant 'gusts (namely, those
causing measurable acceleration of an airplane), the
term "aver i-- i st interval I a is introduced. This
ter is defined as the average distance along a flight
rath in turbulent air between significant g:usts. NurIer-
ical values of Xav have been derived from the total
frequencies of samples 5, 7, 3, 0, anw 10 and are given
in table IV. In evaluating Xay the actual oath lengths
in rough air, which are also given in table IV, were
divided by the total frequencies.

The aver~'-- gust interval Aay is plotted a :ir1t
mean wing chord in figure 5. The dependence of Xay
on airplane size is evident, although the exact nature
of the relationship is not entirely clear from the
figure. The avera., gust interval for the four samples
shown in figure 5 1s 11 chord lengths. 2: Is value may
be used to estimate total fir uency .hen the path lenr,,th
in turbulent air and the airplane size are known.
Although t2e points on figure 5 do not fall on a stri.1,.t
line, they could probably be made to do so by suitable
correction. Fi,:ur 6 of reference 10, for example,

NACA ARR No. I-121

shows a marked tendency for average gust interval to
increase with gust intensity; corrections for this effect
would raise the point for sample 7 and lower the point
for samples 8 and 9.
Path ratio.- Tn order to estimate the total fre-
quencies- 'o actual operating conditions over a long
period of operations, it is necesrvr: to know something
about the percentc:je of the total flight path that falls
within regions of turbulence or about the actual total
frequencies that occur within total paths of operation
of large scope. Information on the relative period of
operation within turbulent regions is given in table IV
*for samples 5 and 7 in terms of the path ratio R. The
total frequencies are

F = 5280 -


p 5230 (2)

when L is in miles, ky, is in feet, and T is in

Although the path ratio is not known for the other
samples to which such a ratio is applicable, the total
frequency of samnle 1 is estimated at 1,600,000 gusts
to a threshold value of Ue = 0.3 foot per second in
the manner -reviously explained. Because this total
frequency applies to a nath of o-erations of 145,000 miles
and because the mean chord was about 10.5 feet, R is
anproximatelv 0.24 from equation (2).

O-eratinr conditions.- The path ratio and therefore
the total gust frequency for any path of operations
manifestly will depend on the operating conditions. A
feeder-line transport operating overland at low altitude,
for example, would be expected to encounter a greater
percentage of turbulent air than an airplane operating
at high altitude above the mechanical turbulence near
the ground and above most of the convective clouds.
Although the operating conditions are important in
defining total frequencies, the data available at this
time are too sketchy to permit correlations between

NACA ARR No. 14121

total frequencies and the factors composing the operating

In order to -ermit estinations of total frequencies,
all available pertinent data including those fr:-m German
sources have been assembled in table V. The first four
sets of German data in table V have been based on the
data of reference 3. Owing to tna fact that Freise
presented frequencies for noncontiguous classes, the
total frequencies given were obtained by multiplication
of the frequencies counted by Fraise by 2.5, which is
the ratio of the interval between class marks to the
interval within which the original count was made. Th7
path ratios from thle German data :ere estimated by7
application of equation (2).

In applying. t7e data of table V to the estimation
o4 total frequencies, some Judgr-ont will have to be used
to ensure that values of rath ratio most nearly repre-
senting the operating conditions are used. It will be
noted that oath ratios range from about 0.006 to 0.24,
with an aver, t value of aoout 0.1.



Choice of 3ust-rr:quenciy Distribution

T' relative-fr-quency polygons representing the
available data permit some latitude in the selection
of a fre'- -ncy distribution to be applied in a design
problem. Choice of a conservative gust-frequency dis-
tribution for use in estimations of stress frequency
depends upon the relative significance of the small
and large stresses in the problem 1nder analysis. If
the problem is to determine the probability of occur-
rence of large stresses in excess of the strcnath of
the structure at the design limit load, a more con-
servative estate will result fr:' the selection of a
freque:nc, distribution having relatively high frequencies
at the hi,':r values of effective gust velocity. For
other oses, the selection of a distribution having
the higher frequencies at the low effective *.:ust
velocities may give a more conservative estimate. Two
li'miti-' relative-frequency polAyons, A and B, representing

NACA ARR 'To. IJ$121

the approximate limits cf the data are shown in fiij 7'" 6.
Polygon A has previously' been used as "relative distri-
bution A" to facilitate comparison of the data shown in
S, r ..s 2 to 4. For some nurooses siummation curves, or
olives (reference 8), are "'.ore convenient representations
of frequenc, distributions than frequency nolygons.
Tnit s3ummation curves corresoon~dng to rol --',-13 A and B
of figure 6 are therefore given in figure 7.

Relation between Effective Gust Velocity

and Stress in the Structure

Direct application of the gust-frequency distribu-
tion ard the total frequency by means of equation (1)
with the usual design assumption of static load will
yield approximately correct values of stress frequency.
There are, however, several phenomena that modify the
actual stress frequencies fro:"' the stress _rq.uencies
estimated in this sirmnrle manner. Those phenomena

(1) Superposition of uncounted s:all gusts on the
larger gusts counted

(2) Distribution of *-ust velocity across the s:.-'.

(5) Dynamic response of the structure

Uncounted sumerimposed gusts.- As previously men-
tioned, che minor real:s in the acceleration records
were not ordinarily counted unless they occurred as
single phenomena between two consecuti ve intersections
with the Ig datum. A special total count of these neg-
lected peaks was made in one case -'.-., a clean-cut
record without reference to the exact 'agnitudes of the
acceleration increments or to the acceleration level at
which the- occurred. It was found that the number of
these small sunerTirnosed neaks was about twice the total
frequency counted in the rmanner adopted for the -neral
analysis. '--.ese ._ -r 'osed :: -.ks w-ere irregular in
shape, sequence, and time or p-lace of occurrence. 7he
magnitudes of'the -superimposed acceleration peaks with
respect to the adjacent acceler-ation levels were small
and did not in any case exceed a value corresponding to
AUe = -.5 feet per second. T- great majority of these
peaks were-near. the threshold value of 0.3 foot rer second.


Discussion of the reason for the consistently
small magnitude of the superimposed peaks is beyond
the scope of this paper, as the question of the rela-
tionship between gust intensity and gust dimensions
and the question of the probability of superposition
of randomly distributed gusts are involved.

Kaul (reference 2) reports a similar count of
superimposed peaks from a record of wing-tip deflection.
Kaul irmlied that the acceleration records did not
contain such neaks and that the extra seaks counted
were due to damped vibration of the wing structure
after disturbance b-r the individual musts. The ratio
of the number of extra breaks to the number counted
with respect to the ig datum was, however, about 2 -
a result that is in agreement with the authors' count
of the extra acceleration peaks. It seoms probable,
therefore, ti-at some additional acceleration peaks due
to superimposed ;usts an' some acceleration peaks due
to vibration response of the wi g-fuselage system were
actually counted in both cases.

So far as the mere question of gust frequency
is concerned, without regard to surerposition, these
additional small neaks may be placed in class 1. The
inclusion of such s Mall peaks in a fatigue test, however,
cannot -roperly be effected on the basis of this simple
classification. If the su-ernosition of the additional
small peaks is felt to influence the fatigue strength
to an important degree, the phenomenon of superposition
must be taken into account. The superposition may
perhaps be pictured sufficiently well for ap-lication
to fatigue tests by imaginingl te periods of the
various stress cycles to be proportional to the
amrlitude. Further, assume the cycles correspondin-
to the basic gust frequency distribution to be applied
without suoeroosition. Finally, superimcoose the
additional small cycLes on the basic cycles of class 2
and of the i- -'.r classes, distributing the additional
small neaks uniformly along the time scale to determine
the numbers to be sunerimnosed on each basic cycle.

actual annlication of sneerimposed cycles in
fatigue testing is a 1f'ficult matter and requires
either the construction and use of a family of summation
curves with mean stress as a parameter or the construc-
tion of a complex fatigue machine with which the small

NACA ARR No. L4121

cycles can be superimposed on the larger cycles. The
derivation of the summation curves would require that
the basic stress cycles be considered as square waves
for tle purpose of establishing a finite number of mean
stress values, and the acbual testing would involve the
difficulty of occasionally holding the mean stress levels
at very high values while the small cycles were being

Distribution of gust velocity along soan.- The
distribution~ -' ust ..el' :' 1 t.,- 1 -i of a wing
is not alwa-s uniform, so that the usual assumption of
uniform distribution leads to some error in estimation
of stress frequencies from the gust frequencies. The
results of the gust investi-ation with the XC-35 air-
nlane indicate the various t --cal srnunise distribu-
tions that actually occur and the frequency of each
t -r, If desired, further refinement of the stress
frequencies can be made from these data, which are
reported in reference 11.

D-ynamic response of the structure.- Owing to the
flexibility of wing structures, accelerations caused by
gusts will not be the same at all points along the
span. The accelerations at the wing tips will be
somewhat greater than and out of phase with those at
the fuselage. Some calculations pertaining to two
typical large airplanes (reference 12) and tests in
the Langley gust tunnel indicated that the maximum tip
acceleration at about 200 miles per hour was about
twice the acceleration at the fuselage and occurred
earlier than the fuselage acceleration. The wing
oscillation in these cases damped out in 1 to 2 cycles.
The effect of such d-.nmic action is to cause, at the
outer portions of the wing primary structure, super-
imposed stress cycles with a maximum amplitude about
10 percent of the static stress for the uniformly
distributed gust.

Because the natural period of wings increases
almost in direct proportion to the wing linear dimensions
and because the size of gusts to which airplanes will
respond also increases as the airplane sizo, the ratio
of natural period to period of application of load
remains about constant for constant flight speed. The
dynamic response of the structure would, therefore,
aprear not to increase with airplane size.

iL.C.A ARR No. L4121

If desired, the additional frequencies of the small
dynamic stresses at the outer portions of the wings can
be included in the same manner as the uncounted super-
imposed gust frequencies.

Experimental evidence.- Some test results from
the s t. -: v : T-.t -i: i .:.n m:ieasurements on the -.-150
and the B-15 airplanes are shown in figures 8 to 10.
C :r> active stress frequencies cannot be shown, but the
fi ,jr-s illustrate the degree of agreement between peak
stresses as measured and as would be calculated by the
usual assumption of static load for the corresponding
measured accelerations.

For the Y-150 airrlane (fig. 8) a datum stress
increment corresonding to application of a load factor
of 1 was determined b7 taking the difference between
stress while in level flight in smooth air and stress
while at rest on the water. Correction was made for
wing weight. The niot therefore indicates the agree-
ment between gust-induced stresses as measured and
gust-induced stresses as determined b7 multiplication
of the datumS stress by the measured acceleration. The
distribution of the points along a line of 1'50 slope
indicates excellent agreement; this result and the lack
of scatter beyond the limits of error denote lack of
serious dynamic response of the structure.

The results shown for the 8-1.5 airplane in fig-
ures 9 and 10 are given simpnly as plots of measured
stress against measured acceleration because a datum
stress increment was not measured. The stress-load
relationships shown are, however, substantially linear;
this fact, together with virtual a absence of scatter
ber-Dn] the limits of error, shows absence of serious
dynamic response.

These results indicate that, with the exception
of the small uncounted superimposed stress peaks, the
stress fr-equencies of the primary wing structure will
be given with sufficient exactness, for all practical
ourroses, by arnlication of the gust frequencies through
equation (1) and the usual assumption of static load.

\.'vi1+ion t- 'urfrce.r.- The gust-frequency
data '1 "-:'. '.- -.. .,,-- t r _-Ty anplicable to tail
surfaces. Some unpublished flight data on the relative
,--."..tudes of effective gust velocities on wings and

NACA ARR No. Lkl21

tail surfaces indicate, however, that a rough approxi-
mation of the tail-load frequencies might be obtained
by utilizing the gust frequencies given here and by
multiplying the values of effective gust velocity by 1.6
for the vertical tail surfaces and by 0.5 for the
horizontal tail surfaces.


Available flight data are sufficient to indicate
that the distribution of gusts within turbulent regions
of the atmosphere follows a substantially fixed pattern
which is independent of the source or cause of the
turbulence. The average Interval between gusts causing
measurable airplane response is about 11 chord lengths,
and the total frequency of significant gusts in any
stretch of rough air is therefore the length of the
flight path in rough air divided by 11 times the mean
wing chord.

The total gust frequency to be -xpected during
the operating life of an airplane depends upon the
operating conditions, which determine the ratio of
path length in roi-,: air to the total path of o-.era-
tions. Information on the path ratio as a function of
operating conditions is sketchy at this time and
should be supplemented by further measurements. From
the available information, the average path ratio for
a variety of operating conditions is about 0.1, although
individual values vary between about 0.006 and 0.24.

The available data on gust frequencies permit
anproximate determination of stress frequencies in
the primary structures of airplanes due to gusts.
These frequencies anoear to describe adequately, for
many design purposes, the stress conditions for
transport-t-',e airplanes in flight. S-'r-lementary
information on stresses in secondary members of the
structure and on the additional frequencies of small
stresses in the primary structure resulting from dynamic
structural response and nonlinear lateral gust distri-
bution is desirable. This information will have to be

24 NACA ARR I'. L121

obtained. by stress measuirements correlated with airplane
size, dead-weight distribution, and other factors.

Langley -Jemorial Aeronautical Laboratory
National Advisory Co:mmittee for Aeronautics
Lanrleyr Field, Va.



1. Bland, Reginald B., and Sandorff, r-ul E.: he
Control of Life Expectancy in Airplane Structures.
iero. Eng. Review, vol. 2, no. 8, Aug. 19i53,
Pp. 7-21.
2. Kaul, Hans '.: Statistical Analysis of the Time and
Fatigue Strength of Aircraft "ing, Structures.
YACA T 'To. 992, 19411.

3. 7.':eise, Heinrich: Spitzennwerte und :.ufiIgkeit von
B6enbelastungen an *erkehrsfl, .eu-on. Jahrb. 1933
der deutschen Versuchsa-istalt rdr Luftfahrt, E. V.
(Berlin-Adlershof), pp. 210-224.

4. Rhode, Richard V.: Gust Loads on Airplanes. SAE Jour.,
vol. 0i., no. 5, March 1957, po. 31-36.

5. Rhode, Richard V., and Lundquist, EUn--me E.: Prelimi-
nary Study of Apnlied Load Factors in E.m1py Air.
NACA T7: No. 5714, 1931.

6. Donely, Philip: Effective Gust Structure at Low
Altitudes as Determined r'- the Reactions of an
Airplane. NACA Ren. :~I. 692, 19 0.

7. Anon.: Airplane Airworthiness. Pt. 0O of Civil Aero.
Manual, CAA, U. S. Dept. Commerce, Feb. 1, 19!1,
p. .2-2.

8. Rietz, H. L.: Frequency Distributions Averagss and
Measures of Dispersion (Elementary methods) .
Ch. II of Handbook of Mathematical Statistics,
H. L. Rietz, ed., Horvzton 'ifflin Co., 1924,
pp. 20-55.

c. Plight Research Loads Section: XC-35 Gust Research
Project Bulletin No. 5 C"rerations near Cold
Front on August 12, 1941 Maximum Gust Intensities.
i'7.1. RB, April 1942.

10. Moskovitz, A. I.: XC-35 Gust Research Project
Ealletin No. 8 Analysis of Cust Measurements.
NACA RB No. L)D22, l1 4.

26 NACA ARR No. LT4I21

11. --oskovitz, A. I.: XC-35 Gist Research Project
Bulletin No. 7 Preliminary Analysis of the
Lateral Distribution of Gust Velocity along the
Span of an Airplane. NACA RB, March 194.5.

12. Pierce, Harold 3.: Dvnrmilc-Stress Calculations for
Two Pirnlanes in Various Gusts. I'."A ARiR,
Sept. 1941.

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NACA ARR No. L4121

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< 0 0 4) 0N U' e' 0'I l U

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me H 00 0 0 0 1
0 I 0 0' 0 0 0 0 0 0 C5
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7 .1.

_ ,-7:-_-4-{--I-I' i.---;:-:-- _f-- -
^ ^ ^ ^ ;^ ;S|;^-^-------:= ..... ,_ .-- _4_-- 4--1--:-->--1---4

+ ----1 5 i :-

4 -:-f -----t ... .
:-- ------ .- ------
.. .... ~-- ".'- ---'-"'r --- --
:i! :' -: 4:A:
..7 __.,- J_ ._-

I .. .
w- ._O t .:i

Fig. 1

NACA ARR No. L4121

-40 -30 -0 -/0 0 /0 20
Effective gust velocity fps

40 50

Figure 2.-Polygons of relative-frequency distribution of e",.' gust






Sample 7. B-/5_ Sample 5:- -/30 airplane ,
arplone m/scel round f0rp / A "0, 1to
-Kaul/s data

Pe/lti/ve ditrl Samples 5 and 6r
burton A R\ A- .' and B-3/4
o'rpl/nes, A/ameda
t/o // w K-ong,1V-G
________ ____ \^ data included
,Sampl/es / to 4 : Domestic transports\ |_



Fig. 2

NACA ARR No. L4121

r fiuarnbaey aola/a/





a ga


iz Q

Figs, 3, 4

NACA ARR No. L4121



(fl) U9) C/

0 0 1

Fig. 5



cr .

z L..



- I -


.4/ ,adS, /S6 a^d Av
^^^^ / ,11J^// ISW7& 0&7CJ,9W


11 9



NACA ARR No. L4121

Figure 6. Relaive -frequency polygons
defitnng approximate limi/s a' samples.

Fig. 6

NACA ARR No. L4121 Fig. 7

NACA ARR No. L4121 Fig. 8

|------- on a a-----------

0 1 Os'sa6' U/0,7

-NACA ARR No. L4121

Figs. 9, 10

I0 o







3 1262 08106 620 0

, ..--'Y OF FLCRoDA
,. TS 1 p7,1 ET
,".(. S 11707

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