Data comparison for falling sphere experimental measurements on atmospheric densit

Smith, L. B.

English

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DATA FROM FALLING SPHERE EXPERIMENTS INCLUDING
COMPARISON TESTS BETWEEN DIFFERENT SYSTEMS*
Lawrence B. Smith
Sandia Laboratories
Albuquerque, New Mexico
SUMMARY
A discussion is given of the falling sphere program conduc-
ted by Sandia Laboratories. The 30 experiments conducted between
October 1964 and June 1969 are categorized according to their
results. The results from a series of comparison tests made in
May 1968 between a variety of systems used to measure density are
also discussed with emphasis on possible system errors. It is
concluded that more effort needs to be expended to determine the
size of errors arising from drag coefficient uncertainties and
velocity and acceleration measurements.
INTRODUCTION
The falling sphere program at Sandia started in October 1964
with units provided by the U.S. Navy from a discontinued program
at Kwajalein. Since that time we have conducted 30 such experi-
ments mainly launched from Kauai, Hawaii, but also from Johnston
Atoll and Tonopah Test Range, Nevada. This system uses the 66-cm
diameter passive sphere designed an_ developed by Peterson, et.
al., at the University of Michigan. _ Although there are 3 spheres
per Nike-Cajun payload, it has not been possible to obtain simul-
taneous data from all three because of a lack of precision radars.
Thus at Kauai the NASA FPS-16 man-in-space radar at Kokee has
been our primary tracking unit. Contiguous to the Sandia launch
site is the Navy Bonham Air Landing Field which has a number of
less precise radars and usually one MPS-25. Position data from
radars other than the FPS-16 or MPS-25 have not been usable for
density calculations, although I do hope to combine their output
with the other tracks for study on atmospheric dispersion. In an
operation the Kokee unit is requested to track the first sphere,
the MPS-25 to follow the second, and an MPS-26 or equivalent to
track the third.
From October 1964 through June 1969 we have conducted 30
falling sphere experiments. The results have been:
*This work was supported by the Atomic Energy Commission.
257
https://ntrs.nasa.gov/search.jsp?R=19700009278 2020-03-17T01:25:46+00:00Z
21 experiments where density, temperature, and wind data were
obtained from at least one sphere
3 experiments where radars did not acquire sphere (all three
at Johnston Atoll)
5 experiments with improper sphere inflation
i experiment with radar computor malfunction
Of the 5 spheres listed as improperly inflated, 2 were ejec-
ted at too low an altitude as a result of rocket or payload mal-
function, and the other 3 showed slow fall rates indicating under-
inflation. As with most sphere experimenters we verify the fall
rate versus altitude of each sphere with a mean from many observa-
tions. Underinflation was also implied by the fact that these
spheres were from a new group whose shelf life had not been veri-
fied. A check of the remaining units in the group indicated
several with less than the original 8 grams of isopentane.
In the 3 experiments where the FPS-16 radars did not acquire
any spheres, the problem was believed to be operator and not sen-
sor related. With all 3 the radar operators were inexperienced
in sphere operations. A signal-to-noise ratio of greater than
i0 db is usually observed. A description of these operations and
a compilation and analysis of the data from 15 of these experi-
ments is provided by reference 2.
CD
P
SYMBOLS
drag coefficient
mathematical technique for checking sphere inflation
density
%
%
root-mean-square range error
root-mean-square angle error
COMPARISON TESTS
On May 16, 17, and 23, 1968, a series of 14 individual rocket
systems were launched from Kauai on a closely coordinated sched-
ule. The purpose was to measure atmospheric density by several
different techniques and compare results. The following schedule
was maintained •
258
4-I
,--4
E_
qJ
0
0 r-_
! !
0 c_l
0 0
cO 0
00 00
0 0 0 0 0
0 ,-'4 0 _ 0 0 _
I I I I i I I I
c_I cf_ c_ o_ c_ Cxl c_
,-4
0 _ r'_ 0 o'_ 0 0 0
o'_ ,--4 _ _ o_ co 0 0
u'_ 0 -..-l" _ _ 0 0 ,--I
0 0 ,--I _ ,.--I ,...4 ,-_ _--I
0
0 0 0
I I _-_
l b'_ l !
J C_l 0 0
00 c_
0 u-_ u'_ 0
_--_ '--_ -,1" 0
,-.I ,.-I ,-.I ,.-I
oo oo 00 00
O_ _ O_ O_
,-{ ,--I ,--I ,.-q
4-
o_
,._
0 0
"a "a "O
0 ,.-I 0 ,--I ,--I 0 0 0 0 0
I I I I
259
In the above: the Arcasonde and the passive and instrumented
falling spheres are operational systems. The ionization gage pay-
load on a Nike-Tomahawk contains 3 cold cathode and one hot
cathode gage. The 02 absorption experiment used photometers _-
board a N_ke-Tomahawk to observe the attenuation in the 1600 A
and 1216 % lines of the solar spectrum on both ascent and descent.
This system included an automatic pointing system (ACS). The 02
profile with height was converted to mass density by assuming a
N2/Op rate of 4 to I. The ram and static pressure system was the
stanHard instrumented probe on a Nike-Apache. Pressure inside
the probe was measured by Metro-Physics thermocouples and rela-
ted to ambient pressure across the shock wave from wind tunnel
tests on this probe geometry.
Figure I shows observations of density taken over a 4 hour
time interval by the instrumented sphere, the passive sphere, the
radiosonde and the Arcasonde. Between 72 and 95 km the sphere
data differ by as much as 30 percent. Results on the second day
are indicated in Fig. 2 where measurements by the optical and the
probe pressure techniques are also included. At these altitudes
quoted uncertainties in the optical data are of the order of ± 20
percent and those of the probe data are i0 to 15 percent with the
greater uncertainty in these probe results on the positive side.
In Fig. 2 data from other systems fall between the density pro-
files from the instrumented sphere as a lower limit and the pas-
sive sphere as the upper limit. Except for the region above i00
km all measurements indicate a notable similarity in their varia-
tion with altitude. Above i00 km the sphere data diverge signifi-
cantly. Between 70 and i00 km comparison with the other measure-
ments is not conclusive because of the large error bars. Below
about 60 km, comparison between passive sphere, pressure probe,
Arcasonde, and radiosonde shows very good agreement. All dif-
ferences are less than i0 percent, a result which can easily be
attributed to small time and space variations. Such variations
have been observed by a variety of other sounding techniques in
most of the altitude region between 30 to ii0 km.
Passive sphere experiments 154-110 and 154-111 indicated normal
flights on the basis of their fall rate versus altitude as shown in Fig. 3
and on the basis of their acceleration and velocity on an expan-
ded altitude scale as shown in Fig. 4. A k check as suggested
by Engler J was also made on both flights at the altitud_ of
acceleration maximum. The results of 1.6 and 1.2 x I0 -_ m -I
were well within the limits proposed by Engler for slightly lower
altitudes. It is thus assumed both Sandia spheres were properly
inflated. No such checks were made on the AFCRL sensor but the
experimenter expressed confidence that the sphere inflated
proper ly.
260
In an attempt to at least indicate the reason for the ob-
served density differences in the sphere data, comparisons be-
tween pertinent parameters from four sphere flights are
listed in Table I. The four flights consisted of two instru-
mented spheres (IS) and two passive spheres (PS). Differences
between the two types of systems are given as percent difference
in density but as absolute difference (zl)in other parameters.
TABLE I
Launch 2300 and 0015 LST on 16 and 17 May 1968
Altitude
km
Density
gm/cm3 x i0 _ Mach No. Reynolds No.
IS PS D ff IS PS A IS PS A
99
95
90
85
8O
75
0.6 0.8 -25
1.2 1.0 20
2.9 3.9 -24
7.2 7.0 3
16.6 20.3 -18
37.1 47.7 -22
4.9 3.3 1.6
5.2 3.1 2.1
5.5 3.5 2.0
5.6 2.9 2.7
5.6 2.6 3.0
5.4 1.6 3.8
17 35 18
33 46
86 203 117
209 270 61
578 765 187
1090 1070 20
Drag Accwl.
CD m/sec z
IS PS _ IS PS A
Fall Speed
m/sec
IS PS A
99
95
90
85
8O
75
1.6 1.9 0.3
1.4 1.8 0.4
1.2 1.3 0. i
i.i 1.3 0.2
1.0 1.2 0.2
1.0 i.i 0.i
0.2 -4.9 5.1
0.4 0.7 0.3
0.8 10.3 9.5
2.0 19.0 17.0
4.4 32.6 28.2
9.6 17.0 7.4
1417 951 466
1443 964 479
1472 945 527
1499 873 626
1519 702 817
1525 427 1098
261
Launch i000 and ii00 LST on 23 May 1968
Altitude
km
Density
gm/cm 3 x
IS PS
109 Mach No.
D_ff IS PS A
Reyno ids No.
IS PS A
i00
95
90
85
8O
75
0.4 0.5 -19 4.9 1.6 3.3
1.5 1.3 15 5.2 2.2 3.0
2.0 3.4 -41 5.5 2.1 3.4
6.6 9.2 -28 5.6 2.2 3.4
!
15.4 18.8 -181 5.7 1.8 3.9
34.2 42.3 191 5.4 1.3 4.1
14 12 2
33 65 32
86 98 12
209 297 88
508 465 43
1092 766 326
Drag Acc_l.
CD m/sec L
IS PS A IS PS A
Fall Speed
m/sec
IS PS A
i00
95
90
85
8O
75
1.6 2.4 0.8
1.4 1.6 0.2
1.2 1.5 0.3
i.i 1.3 0.2
1.0 1.2 0.2
1.0 1.0 0.0
0.2 -8.5 8.7
8.9 -5.9 14.8
4.1 -2.1 6.2
1.8 6.2 4.4
0.8 i0. I 9.3
0.4 10.8 10.4
1411 520 891
1446 568 878
1474 605 869
1500 598 902
1522 517 1005
1529 374 1155
For the altitude region of interest the spheres are in transitional flow
between continuum and free molecular flow. The literature shows quite a
variance or scatter of the drag coefficient data in this regime and accordingly
this parameter is the most readily suspected as the cause of the differences.
The Sandia program uses University of Michiganl derived drag tables which
are based on measurements by Ashkenas4 and May5 for the transitional
region and on measurements by Goin6 in the subsonic region. From Mach
2.5 to 4 these coefficients are considered independent of Mach number. The
AFCRL coefficients were taken from measurements by Sims7 and Aroesty.8
These appear to be quite independent of Mach number although this is not so
stated by the authors.
262
If drag coefficient uncertainties are not the fundamental
cause of the differences, the problems must be in the determina-
tion of velocity and acceleration since the only other parameters
are area and mass and both are carefully measured. The passive
sphere depends upon position versus time coordinates provided by
the radar to determine velocity and acceleration.
At the time of this writing no empirical data were available
on the magnitude of radar tracking errors in the i00 km region.
However, if the results quoted by Engler3 can be extrapolated to
the 80- to 100-km layer, the contribution to the density from
radar tracking errors is less than 3 percent. This estimate re-
suited from a comparison of densities calculated from two inde-
pendent FPS-16 radar tracks of the same balloon. The validity of
this extrapolation is enhanced by the fact that Engler's data
show the variation increases with decreasing altitude. Thus the
maximum difference in densities was found in the 50-60 km layer
rather than in the higher 60-70 km layer implying it may be
less above 80 km. Also, the difference was nearly independent
of the type of smoothing. A similar experiment for altitudes
between 80 and ii0 km is to be conducted at White S_nds this
month.
An attempt was made to compute the effect of tracking errors
by generating a fictitious set of position data which incorpor-
ated random radar errors. The regular computer program then
used these fictitious data to compute new accelerations and ve-
locities from which new densities were calculated for comparison
with the real time data. Each new coordinate was generated by
a Monte Carlo process that algebraically added to the real time
range and angle value the product of a random number and an
assumed RMS radar error. The random numbers were taken from a
normal distribution with zero mean and unit standard deviation.
The above technique was tried with 2 sphere experiments
with results as shown in Table II. Although errors frequently
quoted for a well maintained FPS-16 are o k = 0.I mil in angle
and oR = 5 meters in range, the tabulated results are based on
more conservative errors as given. Each coordinate was assumed
to be independent of the others and no correlation was assumed
between the measured parameters or with themselves, i.e., range
error was not assumed to depend on distance or angle to target,
etc.
Table II shows the percent deviation in density as computed using random
number generation of sphere position data relative to densities obtained from
original real time data. Radar errors are given as RMS percent for
e = angle error in degrees and R = range error in meters. Apogee altitudes
for experiments 154-110 and 154-111 were 144 km and 152 km, respectively.
263
TABLE II
Altitude
km
I00
99
98
97
96
95
94
93
92
91
90
<90
Percent deviation in density
154 - ii0
_e-0.001 ° and aR = 10m
Experiment
154- i ii 154- ii0 154- i ii
1.9
-0.i 4.5
3.1 II.0
-0.5 3.8
-2.6 3.4
-2.8 3.6
-3.0 2.2
-2.2 3.7
-0.8 2.2
0.6 1.6
0.7 1.2
<I <0.6
_e = 0.00050 and aR = 10 m
0.2 -4.7
0.4 -2.3
-0.4 7.6
0 -1.5
-0.6 0
-0.2 0
-0.4 0.5
0.2 1.2
0.2 0.7
-0.2 0.2
0 0.3
-<0.2 s0.4
On the basis of Table II random radar tracking errors are
generally less than 3 percent. It is, of course, possible that
a fixed bias causing errors may exist. However, in view of the
excellent equipment and operating personnel at the NASA Kokee
site it appears unlikely that these real time coordinate data
were so skewed.
One other possibility exists. The velocity-position data
from the instrumented sphere reduction is obtained from integra"
tion of the telemetered acceleration measurements. The begin-
ning altitude results from a radar track while each subsequent
position and sphere velocity is a sum of previous values. An
error in each such determination would be cumulative with an
unknown magnitude.
264
CONCLUS IONS
The comparison tests described in this paper have shown
that the falling sphere technique provides atmospheric data in
good agreement with other systems from 30 to about 70 km. The
technique is also capable of altitudes much above 70 km although
these tests indicate the errors in density so derived may be as
great as 20 to 30 percent, significantly greater than the usual
5 to I0 percent error quoted. It is not apparent what causes
such errors nor is it apparent whether they are unique to one
of the two types of spheres described here or if they result from
an accumulation of several small errors.
The literature provides a variety of drag coefficient data
for the transitional region. One highly desirable product of
this conference would be to standardize such data so that sphere
experimenters would at least have a common input. The new tech-
nique of computing coefficients by a Monte Carlo calculation
shows promise and could be used.
Additional studies are needed on the accuracy of radar
tracking and the possibility of cumulative errors in the velocity-
position data from the instrumented sphere.
265
REFERENCES
la
•
•
o
Peterson, J. W., W. H. Hansen, K. D. McWatters, and G. Bon-
fanti, "Falling Sphere Measurements Over Kwajalein," J.
Geophy. Res., 704477-4489, 1965.
Smith, Lawrence B., "Observations of Atmospheric Density,
Temperature, and Winds Over Kauai," SC-RR-68-523, Sandia
Laboratories, August 1969.
•
Engler, Nicholas A., "Development of Methods to Determine
Winds, Density, Pressure, and Temperature from the Robin
Falling Balloon," Contract AF19(604-7450), University of
Dayton Research Institute, 1962.
Ashkenas, H. I., "Sphere Drag at Low Reynolds Numbers and
Supersonic Speeds," Jet Propulsion Laboratory Research Sum-
mary, No. 36-12, Vol. i, 1962.
May, A., "Supersonic Drag of Spheres at Low Reynolds Numbers
in Free Flight," J. Applied Physics 28, 910-912, 1957.
•
•
So
Goin, Kennith L., and W. R. Lawrence, "Subsonic Drag of Sphere
at Reynolds Numbers from 200 to i0,000," AIAA Journal 6,
961-962, 1968.
Sims, William H., Rarefied Gas Dynamics,
Academic Press, New York (1969)•
Vol. i, p. 751,
Aroesty, J., "Sphere Drag in a Low Density Supersonic Flow,"
University of California Tech. Rept., HE- 150-192, Berke-
ley, 1962.
266
AI.i.I
n
l--
,..J
110
100
9O
8O
70
6O
5O
4O
I
AFCRL
SANDIA
RAOB
ARCASONDE
I I I I
• • • 16MAY 1968 2300 LST
0 o 0 17MAY 1968 0015 LST
• • • 16MAY 1968 2027 LST
• • • 16MAY 1968 2130 LST
o
O
30 I I mJ__ I I
0.6 0.8 1.0 1.2 1.4
(PlP62 USSA )
Figure 1.- Atmospheric density measurements on May 16-17, 1968, at Kauai, Hawaii, with the data normalized to
the 1962U.S. Standard Atmosphere (USSA). (Data listed as AFCRLand Sandia pertain to falling spheres of the
instrumented and passive type, respectively.)
267
II--_l--' I-I- I.i I--I_
- t t
fii r,i,l ,iiI _m_,l rII rII r II
xO • I<D_ @
xO 4 I_-_
I.ii!
I I I I I I I
I I I I I I I
( W)i ) 30n1117v
E
o:
v
- ,._;
N
o_J
E
d
i
u-
268
lO
SPHERE RELATIVE VELOCITY
_E
l.LI
C:3
m
i--
.-I
4O
154-110 o
154-111 x
30 I I I
20 40 60 100 200
RELATIVE VELOCITY (M/SEC)
Figure 3.- Fall rate data from passive sphere experimentson May 17, 1968. (The two parallel segmented
straight lines include the mean and ± one standard deviationof the fall rates from 12 previous sphere
flights.)
269
100
90
80
,,,i,..
_E
70
l-,-
i
I--
,...I
60
5O
0 100 200
I I
/
300
I
I I I
-6 -2-+0 4
VELOC
X
X
ACCELERATION
154- 110x • x APOGEE 144KM
154- 111OOOAPOGEE 152KM
400 500 600 700
I I I I
VELOCITY ( MISEC )
I ! I
8 12 16
ACCELERATION( M/SEC
800 900 1000
! I I
I I 1 I
20 24 28 32
2 )
Figure4.- Accelerationand velocitycurvesfor two spheresreleasedat 144and 152km over Kauaiin May 1968.
270


Data from falling sphere experiments including comparison tests between different systems

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