Tolefson, H B

English

NASA Technical Reports Server

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NATIONAL ADVISORY COMMITTEE 
FOR AERONAUTICS a _ 
TECHNICAL NOTE 
No. 1628 ’ 
AN ANALYSIS OF THE VmTION WITH ALTITUDE OF EFFECTIVE 
GUST VELOCITY IN CONVECTIVE-TYPE CLOUDS 
By H. B. Tolefson 
Langley Memorial Aeronautical Laboratory 
Langley Field, Va. 
Washington 
June 1948 
https://ntrs.nasa.gov/search.jsp?R=19930082296 2020-06-17T21:09:30+00:00Z
TECENI~AL NOTE NO. 1628 
ANANALYSIS OFTHEVABIATIONWITHALTCTTJDE OF EEEECTIVE 
GO-ST VTZOCITY W C-m-Tppp: CLCUDS . 
By H. B. Tolefeon 
Available gust-velocity data for convective-type clouds at various 
altitudes are analyzed to determine the variation with altitude of the 
effective gust velocity. These data include about loo0 tiles of record 
distance at altitudes up to 34,000 feet in the vicinity of Langley Field, 
Va., and 6700 miles of record distance at altitudes up to 26,000 feet in 
the vicinity of Orlando, Fla. 
The aualysis indicates that the distribution af effective gust 
velocities is roughly equal at various altitudes within convective-type 
clouds. The nmiber of gusts of a given intensity encountered per flight 
mile at different altitudes within convective-type clouds would, there- 
fore, be essentially equal. Ccmsideration of these results for altitudes 
below 34,000 feet indicates that similar results would apply to convective- I 
I type clouds within the troposphere at altitudes above 34,000 feet. 
. moDuc~oN 
The results obtained from routine collections of gust data with the 
V-G recorder (reference 1) aud from special investigations such as thotie 
described in reference 2 have provided the basis for specifying the 
present desigu gust load requirement of a 3CK foot per second effective 
gust velocity where K is the relative alleviation factor (reference 3). 
Whereas this requirement has been found to be satisfactory for flight 
operations up to moderate altitudes, the present trend toward higher 
operating altitudes has raised the question of the proper gust velocity 
to be used in the design of high-altitude airplanes. The requirement of 
reference 3 has been felt to be overly ccnsemative for high-altitude 
operations so that high-altitude airplanes will suffer a severe Weight 
penalty. 
As a tentative solutim to the problem of proper selection of design 
. gust velocities at various sltitudes, reference 4 proposes the use of a 
desigu gust velocity of constant equivalent airspeed for altitudes up 
to @,OOO feet. For higher altitudes a linear variation with altitude d 
w 1 design gust velocity from the value prescribed for 25,000 feet to 60 per- cent of that vslue at 'jO,OCO feet is proposed. The reduction in desigu 
2 NACA TN No. 1628 
gust velocity at altitudes above 25,000 feet in this proposal is based on 
estimates of the munt of convective-type clouds at various altitudes. 
These estimates indicate that the amount of rough air and, consequently, 
the total number of gusts decrease at the higher altitudes. In order to 
obtain a final solution, more complete-information on the gust-velocities 
in rough air as a function ofaltitude and on the amount of rough air at 
various altitudes is required. 
In the present paper, the variation of effective gust velocity in 
convective-type clouds with altitude is investigated. Data obtained 
during 1941 and 1942 at altitudes up to 34,000 feet and data.obtained mere 
recently from the Thunderstorm Project (reference 5) at altitudes up to 
26,000 feet are utilized forthis purpose. Consideration is given in 
analyzing the results both to data for the range investigated and to 
extrapolations of the data to higher altitudes. 
SCOPE OF DATA 
Gus-t-velocity data for altitudes up to about-34,000 feet were 
obtained by the IUCA from 35 flights in the vicinity of Langley Field, Va., 
during the spring and Sumner months of 1941 and 1942 (reference 2). It 
was intended that successive surveys of cumulus congestus snd cum.alo-nimbus 
clouds would be made at decreasing altitudes during the period of maximum 
convective activity. Frontal activity was of importance aa a cause of 
the turbulence encountered on only a few of the flights. About 12 percent 
of the total record mileages were t&en at altitudes of 30,000 feet or 
greater; about one-half of the records at these altitudes were t&en in 
thunderstorms, with the remainder taken in cirrzls clouds or clear air in 
the vicinity of the tropopause. A summary of the number of traverses 
made with the airplane and the distances traveled during recording ofgust- 
velocity data within various altitude renges is given in table I. 
Additional gust-velocity data for altitudes from 6000 feet to 
26,000 feet were obtained from operations made during the summer of 1946 
of the Thunderstorm Project at Orlando, Fla. (reference 5). These data 
were taken during simultaneous traverses of a cumulus congestus or a 
cumulo-nimbus cloud by two to five fighter airplanes at different altitude 
levels. The clouds were caused primarily by surface heating since frontal 
activity was present in the vicinity of Orlando on orJ.y two of the 
38 flight CIBYS. The number of traverses and the distances traveled during 
turbulence recordings at the various altitudes surveyed by the airplanes 
are summarized in table I. 
NACA TN No. 1628 
EVALUATION OF DATA AND IRBUZCS 
3 
The records taken during 1941 and 1942 have been previously 
evsluated in reference 2 for effective gust velocities by use of the 
formula:' 
VlnW 
ue = 
PoaVeSK 
in which 
ue effective gust velocity, feet per second 
Aa acceleration increment, g units 
W. weight of airplane at time acceleration increment was experienced, 
p0UIldfl 
PO air density at sea level, slugs per cubic foot 
a slope of lift-coefficient curve corrected for Mach number 
effect, per radian 
'e equivalent airspeed of airplane, feet per second 
S wing area, square feet 
II relative alleviation factor taken from figure 9 of reference 3 . 
The results of this evaluation for different ranges of altitude are ah- 
as frequency distributions in table II; The gusts in the lowest altitude 
range (altitudes from 0 to 5000 ft) of reference 2 were omitted from 
table II because a relatively small emount of data was obtained at those 
EiLtitudes. The data in the interval of effective gust velocity from 0 
to 4 feet per second were also omitted from table II since all gusts in 
that interval could not be evaluated, and the data in this interval do 
not represent a com@ete count. The average number of miles per gust for 
each altitude range, obtained by dividing the record distances of table I 
by the respective total gust frequencies, is also shown in table II. 
The records obtained from the Thunderstorm Project were evaluated 
in a similar manner with.the exception that only the maximum positive 
and negative effective gust velocities above a minimum value of about 
4 feet per second for bath 3000 feet of each traverse were computed. 
The gust-velocity distributions given in table III for the Thunderstorm 
Project are, therefore, not strictly comparable to the distributions for 
4 NACA TN NO. 1628 
the 1941-42 data but represent-distributions of the maximums over short 
space intervals rather than distributions of all gusts abov8 a 4 foot- - 
per second threshold. The Value6 Of miles per gust Of tab188 n arki III- 
are not comparable for similar reasons. 
In order to smooth out-minor irregularities in the data, P8arson 
type III probability curves were fitted to the frequency distributions 
of tables II and III by standard statistical methods (reference 6). 
The curves for the two sets of data are shown in figures 1 and 2. Tests 
for "goodness of fit" indicate that the curves give a satisfactory 
representation of the data. 
In view of the differences cited in the methods of obtaining the 
frequency distributions for the two sets of data, the use of the term 
"probability" with reference to figures 1 and 2 has different m%nings. 
For figure 1, the term probability used herein indicat8s the relative 
frequency with which the given values of effective gust velocity will be 
exceeded within the vsrious altitude renges. For figure 2, the term 
probability indicates the ratio of the number of 3000-foot intervals in 
which a given effective gust velocity will be exceeded to the total 
number of such intervals at the respective altitudes. 
For ease in interpreting the results, the probability curves of 
figures 1 and 2 haV8 been referred to a mileage scale in the following 
manner: If P is the relative frequency with which a given value of-- 
gust velocity will be exceeded within an altitude range, then that value 
will be exceeded, on the average, once in l/P gusts. The average number 
of miles in rough air that must be flown to encounter a gust equal to or 
. greater than the given value then equals l/P multiplied by the average 
number of miles per gust as taken from tables II and III. These results 
for the various altitude ranges of the two sets of data are shown in 
figures 3 and 4. This reduction of-the data from the Thunderstorm Project 
does not yield actual mileage values because only a limited number of the 
largest gusts were evaluated. The values Obt&?38d, however, are a measure 
of the flight miles end may, therefore, be used for making comparisons 
between the Thunderstorm-Project data for different altitudes. No direct 
comparison between the Thunderstorm-Project and 1941-k' mileage values 
can be made. 
DISCUSSION 
An inspection of figure 1 indicates that the data for altitudes 
above 10,000 feet form a family of curves distinct from the data below 
10,000 feet. This observation Is confirmed by application of the Chi- 
squared test (reference 7) to the frequency distributions of table II, 
which indicates that-no significant-differences exist between the 
. 
NACA TN NO. 1628 5 
distributions for the altitude intervals above 10,000 feet. These distri- 
butions, however, ar8 significantly different from the distribution for 
the altitude interval below 10,000 feet. It may also be seen from 
figure 1 that variations of only about 22 feet per second occur between 
the values of effective gust velocity which would be exceeded at the 
various altitudes above 10,000 feet for a given probability value. Since 
these variations are within the range of precision of the effective-gust- 
velocity computations (reference 2), it would appear that the distribution 
of gust velocities in convective-type clouds at the various altitudes 
above 10,000 feet is roughly equal. 
The disagreament noted between the data for altitudes above and 
below 10,000 feet in figure 1 can be accounted for by a consideration of 
the flight procedure and the test conditions during the 1941-42 investi- 
gation. As has been previously indicated, the cloud surveys were usually 
begun at the higher altitudes with the cloud in its pe& stage of develop- 
ment. In some instances where large clouds were being investigated, the 
available record time was consumsd during traverses of the upper parts of 
the clouds so that no gust velocity measuremen-& were obtained at the 
lower altitudes within the clouds. In other instances, the cloud under 
study had dissipated to a considerable extent by the time the lower 
altitudes were reached and the remaining record -time was consumed during 
flight through smsll clouds at altitudes below 10,000 feet or in regions 
of clear air turbulence in the vicinity of these clouds. Hence, because. 
of equipmsnt limitations, the 1941-42 data for altitudes below 10,000 feet 
were taken under conditions of lower turbulence with a resulting decrease 
in measured gust intensities. 
The probability curves of figure 2 for the data obtained from the 
ThunderstormProject form a family of curves similar to those discussed 
for the 1941-42 data. Tests for si~ificant differences between the data 
for the various altitudes also indicate no si@ficant differences from 
6000 to 26,000 feet. The variation in effective gust velocity between 
the differant altitudes for any probability value Is less thank2 feet 
per second. These results confirm the findings of the 1941-42 tests that 
the distribution of gust velocities in convective-type clouds is roughly 
equal at any altitude within the range of the data. 
The preceding results are further illustrated by the mileage curves 
of figures 3 and-k. Itwillbe notedfromfigure 3 thatwhenthe curve 
for the altitude interval fr& 5000 to 10,000 feet is neglected, the 
variations in the average number of miles in convective-type clouds that 
must be flown at the differ&t altitudes to encounter a gust equal to or 
greater then a given value are less than .a ratio of 3 to 1. The curve 
for the lowest altitude interval is neglected because the data are not 
repres8ntative of the conditions surveyed at the higher altitudes. The 
slight tendency for the mileage values for the altitude interval from 
30,000 to 34,000 feet in figure 3 to increase at the higher gust veloci- 
ties results from the fact that this sample of da.-& includes an appreci- 
able number of miles of flight in clear air and cirrus clouds in the 
6 NACA TN No. 1628 
vicinity ofthe tropopause with only a few large gusts being encountered. 
Suitable corrections for this effect on the mileage values would probably 
tend to lower the points for the higher gust velocities so thatdiffer-. 
ences between aXl curves would be less than a ratio of 2 to 1. Figure4 
also indicates that the differences Fn the mileages are in the ratio of 
about 2 to 1. Differences ofthis order are not considered significant 
for desigu purposes. 
Since convective-type clouds have been observed to extend to alti- 
tudes considerably above the altitude range of the present data, the 
question of extrapplatiug the data for clouds at higher altitudes within 
the troposphere appears pertinent. For any probability value in 
figures 1 and 2, the scatter in effective gustv8iocities between the 
various altitudes has bean noted to be only k2 feet per second, or within 
the limits of-accuracy of the data. This distribution with altitude of 
points about a line of constaut~fective gust- velocity would indicate 
that the most suitable extrapolaticm of the data would be a contFnuatim 
of the line to the higher altitude. 
Further evidence on the question of extrapolation may be obtained 
by cross-plotting frcra figures 3 aud 4 to determine the variatim with 
altitude of the effective gust velocity for equal miles flown in 
convective-type clouds. The remi+ts am shown in figure 5 for mileag86 
that were selected to FnClUd8 the higher and most Critical gusts from 
airplane design considerations. 5ese~r8sul.ts indicate that, for given 
miles of flight in convective-type clouds, the variation with altitude of 
effective gust velocity is only about-f2 feet per second when the lowest-- 
altitude interval of the 1941-42 data is neglected. The absence of 
scatter beyond the limits of error of the data together with the linear 
relationship indicated in figure 5 denote that extrapolation of the data 
for convective-type clouds within the troposphere.wouJ,d be a straight- 
line continuation of the constant effective gust velocity. 
CONCLUDING REMARKS 
Available flight data for altitudes up to 34,000 feet in convective- 
type clouds indicate that-the distributions of effective gust velocities 
measured at the various altitudes are roughly equal. The gust experience 
per flight mile within convective-type clouds, therefore, varies to only 
a small extent at different .Ll.titudes. The UnifOIVIity Of the gust- 
velocity distributions for the altitude range covered-by the tests indi- 
cates that these results could be extrapolarted above 34,CDp feet for 
convective-type clouds that are within the troposphere. 
Langley Memorial Aeronautical Laboratory 
National Advisory CommItWe for Aeronautics -1 
Langley Field, Va., March 17, 1948 
NACA TN NO. 1628 7 
1. Rhode, Richsxd V.: Gust Loads on Airplanes. SAFi Jour., vol.. 40, 
no. 3, March 1937, pp. 81-88. 
2. Moskovitz, A. I.: XC-35 Gust Research Project - Analysis of Gust 
Measureqents. NACA RB No. L4D22, 1944. 
3. Anon.: Airplane Airworthiness. Civil Aero. Manual 04, CAA, U.S. Dept. 
Commerce, Ju'ly 1, 1944, sec. O&.ZL2l, p 25. ' 
4. Anon.: Proposed 1947 Edition of AirworbhFness (AIR) Standards and 
Recommended Practices. Ibc 30314IR/18l, vol. III of Final Report 
of Airworthiness Div., Sec. Sessian, Prov. Int. Civil Aviation Org. 
(Montreal, Canada), March 1947, sec. 3.3.1.4.1. 
5. Tolefson, Harold B.: Preliminary halysis of NACA Measurements of 
Atmospheric Turbulence within a Thunderstorm - U.S. Weather Bureau 
ThunderstormProject. EiXCA TN No. 1233, Mezch 1947. 
6. Peiser, A. M., and Wilkerson, M.: A Method of Analysis of V-G Records 
from Transport Operations. NACA ARR No. L5J&, 1945. 
7. Kenney, John P.: Mathematics of Statistics. Pt. II. D. Van Nostrand 
Co., Inc., 1939, PP- 164-1’11. 
NACA TN NO. 1~628 
l 
NUMBER OF TRAVIERS~ AND RECORD MILEAGES 
ATVARIOUSALTITUDES 
5,000 to 10,000 89 
10,000 to 15,000 44 
15,000 to 20,000 37 
20,000 t0 25,000 21 
25,000 t0 30,000 29 
30,000 to 34,000 18 
To-i&La 
Thunderstorm-Project tests 
6,000 84 1032 
Xl,000 120 1548 
16,000 117 1717 
21,000 93 1371 
26,000 71 1044 
Totals 485 6712 
4. 
- 
NACA TN NO. 1628 
l 
TABLE II 
FREQUENCYDEEDUTIORSOF ~GUSTVELOCITYANDMILES 
PER GUST AT VARIOUS ALTITUDES FROMlgb42 TBI'S 
Altitude 
w 
\ 
'e 
@I=4 
4 to 8 
8 to 12 
12 to 16 
16 to 20 
20 to 24 
24 to 28 
28 to 32 
32 to 36 
36 to 40 
Totals 
Miles per 
gust 
I Frequency of gusts 
5,000 
to 
10,000 
1322 
351 
70 
15 
2 
2 
1762 
.140 
10,000 
to 
15,000 
571 
233 
89 
29 
8 
: 
936 
9139 -139 .158 .2lo -257 
15,000 
to 
20,000 
760 
335 
129 
48 
15 
z 
1 
1 
20,ooo 
2$00 
354 
198 
’ 109 
~ 2 6 
1 
1 
~ 724 
25,000 
3o;oo 
4-49 
274 
;z 
15 
6 
3 
30,000 
34;:oo 
4% 
10 ’ NACA TN No. 1628 
. 
. 
TAB- III 
FRK8lXXCYDIE3TRIE3UTIONS OF -GUSTvELocITYAND 
MILES PER GUST AT VARIOUS ALTITUDXS FROM 
Altitude 
w 
\ 
‘e 
(fPd 
4 to 8 
8 to u 
12 to 16 
16 to 20 
20 to 24 
24 to 28 
28 to 32 
32 to 36 
36 to 40 
Totals 
Mlles per 
gust 
T- 
6,000 11,000 
1165 
535 
163 
53 
15 
4 
1 
1822 
z!z 
98 
28 
9 
3 
1936 3020 
0534 l 513 
Frequency of gusts 
16,000 21,000 
1851 
751 
273 
121 
44 
z 
1 
1 
3053 2345 
-563 -585 
26,000 
1556 
.671 
c 
NACA TN NO. 1628 ll 
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RACA TN NO. 1628 
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w.- - /pm 
---f/6,W 
- -2~000 
- -- -26;m i 
NACA TN No. 1628 
6000 
---e--/(&(-JO - 
--- /@Do 
---2&zo - 
-- - 2t5000 
lTACA TN Ro. 1G28 
v 
25 -30 35 
NACA m NO. 1628 15 


An analysis of the variation with altitude of effective gust velocity in convective-type clouds

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