| ,,:! .. ti':
j.FREE-FLIGHT MEASUREMENTS OF AERODYNAMIC HEAT TRANSFER
TO MACH NUMBER 3.9 AND OF DRAG TO MACH NUMBER 6.9
OF A FIN-STABILIZED CONE-CYLINDER CONFIGURATION
By Charles B. Rumsey
Langley Aeronautical Laboratory
Langley Field, Vg^ CAWSD TO IAWLIN
UNIVERSITY OF FLORIDA AAMMOUSCB ,
t:1DOCUMENTS DEPARTMENT NrnCTiV DATEs FEMBUAHt S 1960
S20 MARSTON SCIENCE UBRARY
VI lP0, BO-X 117011
ESVILLE, FL 32611-7011 UAFE. DOCUNE,,
TiMe mnteral contains I rmation affecting the Natioa Defense of the United States within ti M meniag
?ol o e esplznge laws, TlUBe 1, U.S.C., Secs. 70S anr 79, ULe tranmilsson or revelaSllo of which n a3y
m er i o an aanthorixed person I prohblbllted by la.
a NATIONAL ADVISORY COMMITTEE
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NACA RM L55G28a
NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
RESEARCH MEMORAI IDUM.
FREE-FLIGHT MEASUREMEDIi'S OF AERODYNAMIC HEAT TRANSFER
TO MACH i-MIEBER 5.9 AND OF DRAG TO MACH NI~IJU.E.R 6.9
OF A FIN-STABILIZED CONE-CYLIIIDEF: CONFIGURATION
By Charles B. Rumsey
Aerodynamic-heat-transfer measurements have been made at a station
on the 100 total angle conical nose of a rocket-propelled model at flight
Mach numbers from 1.4 to 3.9. The corresponding values of local Reynolds
number varied from 18 x 106 to 46 x 106 and the ratio of skin temperature
to local static temperature varied from 1.2 to 2.4. The experimental
data, reduced to Stanton number, were in fair agreement with values pre-
dicted by Van Driest's theory for heat transfer on a cone with turbulent
flow from the nose tip.
Drag coefficients were measured on the heat-transfer model and on a
similar fin-stabilized cone-cylinder model of fineness ratio 21.4 at sev-
eral Mach numbers between 2.5 and 6.9. Values of Reynolds number based
on body length were between 4 x 106 and 225 x 106. Estimated values of
total drag coefficient, based on computed component drags, were in good
agreement with the measurements at Mach numbers of 2.75, 5.75, and 6.0
but were approximately 20 percent higher than the measurements at Mach
number 6.9. A reduction in measured drag coefficient occurred as Mach
number decreased from 6.5 to 6.3 with corresponding Reynolds numbers
based on body length of 29 x 106 and 14 x 106, respectively. The reduc-
tion in drag coefficient is attributed to growth of the laminar boundary
layer over the body, and the measured change agrees reasonably well with
the theoretically computed change in friction drag coefficient..
A current program of the Langley Pilotless Aircraft Research Division
is the development of its rocket test technique to enable free-flight
testing at Mach numbers well into the hypersonic range. This program is
the result of an obvious need for data in this Mlach number range for use
in the development and evaluation of theory and in the design of high-speed
missiles and airplanes.
NACA RM L55G28a
The first two models in this program, which were exploratory in
nature, reached Mach numbers of 5.0 and 5.6 and skin-temperature measure-
ments at a single station on the nose of each model were obtained. These
aerodynamic heating data have been presented in reference 1. A further
step in the program was the flight test of a model to Mach number 6.9.
Reported herein are measurements of skin temperature at a station on the
nose of this model. Although the skin-temperature instrument failed at
Mach number 3.9, and before maximum skin temperature had been reached,
the limited data obtained are presented because of the scarcity of heat-
transfer data at the high stagnation temperatures and Reynolds numbers
corresponding to free flight at these Mach numbers.
Also reported herein are measurements of drag coefficient obtained
from the model tested to Mach number 6.9, and from the model previously
tested to Mach number 5.6 (model 2 of ref. 1). Drag data from these two
tests are complementary since the model configurations were similar.
Aerodynamic heat-transfer data measured on the conical nose are pre-
sented in the form of local Stanton number for the local Mach number
range 1.4 to 3.7. The corresponding Reynolds numbers based on conditions
just outside the boundary layer at the measurement station and length
from the nose tip ranged from 18 x 106 to 46 x 106.
Total drag coefficients for this fin-stabilized, cone-cylinder con-
figuration were obtained at several Mach numbers between 2.5 and 6.9 and
at Reynolds numbers, based on body length, between 4 X 106 and 225 x 106.
The flight tests were conducted at the Langley Pilotless Aircraft
Research Station at Wallops Island, Va.
A area, sq ft
a absolute deceleration, ft/sec2
AL telemetered drag deceleration, ft/sec2
CD drag coefficient, D/qs
CH local Stanton number, h/CppyVv
Cp specific heat of air at constant pressure, Btu/slug-F
NACA RM L55G28a CONFIDENTIAL 3
cw specific heat of wall material, Btu/lb-F
D drag, Ib
g gravitational constant, 32.2 ft/sec2
h local aerodynamic heat-transfer coefficient, Btu/sec-sq ft-F
J mechanical equivalent of heat, 778 ft Ib/Btu
K thermal conductivity of air, Btu-ft/sec-oF-sq ft
I axial distance from nose to skin-temperature-measurement
L axial body length, ft
M Mach number
Pr Prandtl number, Cpp/K
Rv local Reynolds number, pyVV/1
RL free-stream Reynolds number, PoVoL/o
Q quantity of heat, Btu
q dynamic pressure, lb/sq ft
RF recovery factor, Taw -
S maximum body cross-sectional area, 0.267 sq ft
T temperature, OR
t time from start of flight, sec
V velocity, ft/sec
W weight of model, lb
P Stephan-Boltzmann constant, 4.8 x 10-13 Btu/sec-sq ft-R4
E ratio of emissivity of skin to emissivity of black body
4 CONFIDENTIAL NACA RM L55G28a
e angle between model longitudinal axis and horizontal, deg
p density of air, slugs/cu ft
p density of wall material, lb/cu ft
T thickness of wall, ft
7 ratio of specific heats of air, 1.4
p viscosity of air, slugs/ft-sec
aw adiabatic wall
o undisturbed free stream ahead of model
v just outside the boundary layer
MODELS AND TESTS
The general configuration and pertinent dimensions of the two test
models, designated models 1 and 2, are shown in figure l(a). Drag meas-
urements from model 1 (which is model 2 of ref. 1) and drag and heat-
transfer measurements from model 2 are the subjects of this report. Fig-
ure l(b) is a photograph of model 2.
The body, which was similar for both models, was a cone-cylinder of
fineness ratio 21.4. The conical nose had a total angle of 100, was
40 inches long, and was constructed of Inconel skin approximately
0.05 inch thick except for the tip which was made of steel, hollowed out
as shown in figure l(a), and welded to the skin at station 6. On each
model the exterior surface of the nose skin was highly polished and the
surface roughness was approximately 5 microinches root mean square as
measured by a Physicists Research Co. Profilometer. The cylindrical body
which housed the sustainer motor was rolled from sheet steel.
Four steel fins were welded to the body at the base. The plan form
of the fins was the same on both models but the fin thickness and
NACA RM L55G28a
leading-edge shape differed as shown in figure l(a). The thickness at
the root was 0.2 inch on model 1, 0.5 inch on model 2, and tapered line-
arly to 0.1 inch at the tip on each. The leading edge of the fins on
model 1 consisted of a 5 included angle wedge with the edge rounded to
a 0.05 inch radius. The leading edge of the fins on model 2 consisted
of a 450 included angle wedge 0.06 inch thick followed by a 40 half-angle
A total-pressure tube on a pylon having a double-wedge-profile was
mounted at the front of the cylindrical body of model 1 as shown in fig-
ure l(a). The total-pressure measurements are extrinsic to this report
and the tube is mentioned only because it constitutes a difference in
configuration between models 1 and 2.
A four-channel telemeter was carried in the nose of each model. The
telemeter was protected from the high temperatures reached by the skin
during flight by a radiation shield which consisted of a second Inconel
cone located approximately 1/4 inch inside the exterior skin.
Measurements of skin temperature, drag deceleration, thrust acceler-
ation, and total pressure were telemetered from model 1. The skin tem-
perature, measured at station 22.5 on this model, was reported in refer-
ence 1. The drag accelerometer measurements are reported herein. Thrust
acceleration and total pressure were measured in order to obtain velocity
in case of a radar tracking failure.
The telemeter in model 2 transmitted measurements of a skin temper-
ature pickup, a drag accelerometer, a thrust accelerometer, and a trans-
verse accelerometer. Results from the skin temperature and drag measure-
ments are reported herein. Thrust and transverse accelerations were
measured to provide velocity data in case of failure of the radar tracking
unit and to aid in the analysis in case of a structural failure. (Neither
Skin temperature was measured on the conical nose of model 2 at sta-
tion 31 by means of a resistance-type temperature pickup cemented to the
inside surface of the skin. The resistance element consisted of a plati-
num wire 0.0005 inch in diameter and approximately 11 inches long. The
construction and accuracy of the instrument are described in reference 2.
(Also see section on "Accuracy.") There were no attachments to the nose
skin which would contribute to the thermal capacity of the skin and affect
its temperature. Although the temperature pickup failed before the model
reached maximum velocity, data were obtained at Mach numbers up to 5.9.
NACA RM L55G28a
Propulsion and Test Technique
The models were launched at elevation angles of about 700. Model 1
employed a two-stage propulsion system consisting of a JATO,
2.5-DS-59000 booster rocket, which drag separated at burnout, and a
Deacon sustainer motor, carried within the model, which ignited at a pre-
determined time after booster separation. The Mach number was 2.9 at
booster separation, and the maximum Mach number of 5.6 occurred at sus-
Model 2 employed a three-stage propulsion system consisting of two
M5 JATO boosters (which are similar to the JATO, 2.5-DS-59000 rockets)
and a Deacon sustainer motor. Figure l(c) shows this model and its
boosters on the launcher. The first booster accelerated the combination
to a Mach number of 1.4 and drag separated at burnout. The second-stage
booster and the model, which were held together by a locking device,
coasted upward for a predetermined time until the second stage booster
ignited and accelerated them to Mach number 3.9. Chamber pressure of the
firing booster released the locking device allowing the booster to drag
separate at its burnout. After another predetermined coast period, the
sustainer motor ignited and accelerated the model to the maximum Mach
number of 6.9.
Velocity and altitude data were measured by means of CW Doppler radar
and SCR 584 tracking radar sets, respectively. Velocity and altitude data
for model 2 were obtained beyond the range of the radars by integration of
the telemetered drag accelerometer measurements. Atmospheric and wind
conditions were measured by means of radiosondes launched near the time
of flight and tracked by an AN/GMD-1A Rawin set.
The flight conditions of Mach number and Reynolds number for models 1
and 2 are shown in figure 2. The solid sections of the curves are the
power-off portions of the trajectories during which the drag of the model
was measured. Test conditions for the aerodynamic heat-transfer measure-
ments on model 2 are given in figure 3 which presents time histories of
the skin temperature, altitude, and Mach number of the test trajectory.
An expression for the time rate of change of heat within the skin
can be written
dQ= dT hA aw dTA (1)
S= PWCWTAdT = hA(Taw Tw) ETwA (1)
NACA RM L55G28a
Solving for the heat-transfer coefficient gives
-w -t + ET
h = (2)
This equation neglects radiation losses from the skin to the inner radi-
ation shield and heat absorbed by the skin from solar radiation. However,
the term representing heat radiated externally from the skin PeTw is
much larger than these and was itself neglected since it was less than
2 percent of the aerodynamic heat transfer at times for which heat-
transfer coefficients are determined. Also neglected in equations (1)
and (2) is the heat flow along the skin due to conduction which is esti-
mated to be less than 1 percent of the aerodynamic heat transfer.
Equation (2), neglecting the radiation term, was used to compute
heat-transfer coefficients from the skin-temperature measurements from
model 2. The values of skin temperature and the rate of change of skin
temperature with time were obtained from the measured data. The thick-
ness of the skin T at the temperature station was measured, and pw,
the density of Inconel, was known. The variation of specific heat of
Inconel with temperature is given for the present temperature range in
reference 1. The remaining quantity Taw was computed from the equation
T =RF(Tso Tv) + T (3)
Values of RF were determined from the usual turbulent relation
RF = Pr1/ with Pr based on skin temperature. Values of Tv were
obtained from the conical flow tables (ref. 5) with the cone angle and
free-stream conditions of Mach number and temperature known. Stagnation
temperature was computed from the energy equation
Cp dT (4)
NACA RM L55G28a
tiLing into account the variation of specific heat of air with tem-
perature. Values of the integral in equation (4) were obtained from
table 1 of reference 4. At a Mach number of 4 in free flight, stagna-
tion temperatures computed from equation (4) are only about 5 percent
lower than values computed from the relation
Tso =TO + M2) (5)
which assumes Cp of air to be constant. The resulting difference in
Taw, as obtained from equation (3), is only slightly greater than 3 per-
cent. However, the values of h computed from equation (2) can be
affected by much more than 5 percent, depending on the value of T,,
since the denominator of equation (2) is Taw Tw. For the conditions
of the present test, computation of Tso with the assumption of con-
stant Cp (eq. (5)) would have resulted in lower experimental values
of h. The values would have been lower by an amount varying from less
than 1.5 percent at the lower skin temperatures to about 15 percent at
the highest skin temperature.
After determining h, the local Stanton number CH = h was
computed. The specific heat of air at Tv was obtained from reference 5.
Values of velocity and density just outside the boundary layer were
obtained from the conical flow tables (ref. 3) with cone angle and free-
stream conditions of Mach number, temperature, and density known.
Drag data were obtained from the telemetered measurements of the
drag accelerometer and also from differentiation of the CW Doppler velocity
record. Values of total drag coefficient were reduced from the telemetered
drag-accelerometer data from the relation
CD D W AL
qS g qS
where AL is the telemetered drag deceleration in feet per second squared.
The weight of the model and the reference area were known, and q was
computed from the velocity and altitude time histories and radiosonde data.
NACA RM L55G28a
Computation of the drag coefficient from CW Doppler velocity data
requires that the flight-path angle 0 be known. The relation is
C = (a g sin e)
where a is the rate of change of velocity obtained by differentiating
the velocity time history. Values of 6 were obtained by measuring the
slope of the flight-path trajectory as recorded by the SCR 584 tracking
For model 1 and for model 2 through the time of peak Mach number,
the measurements of Mach number are accurate within 0.01, the maximum
probable error in Reynolds number is within t2 percent, and the maximum
probable error in CD is within 5 percent. The accuracy of the meas-
urements for model 2 decreased during the final coast after maximum
Mach number because of the increasing altitude and range of the model.
At the limit of the trajectory where the accuracy is poorest, the maxi-
mum probable error in Mach number is within 0.1, the maximum probable
error in Reynolds number is within about 7 percent and the maximum
probable error in CD is believed to be within t20 percent. The
maximum probable error in the skin-temperature measurements made on
model 2 is within 2 percent of the full-scale range of the instrument,
which was 16000 F. This results in a maximum probable error in Tw/Tv
of 5 percent at the maximum temperature measured.
RESULTS AND DISCUSSION
Aerodynamic Heat Transfer
The skin temperatures measured at station 31 on the conical nose of
model 2 are plotted against time in figure 3 along with the Mach number
and altitude conditions of the test. The aerodynamic heating and cooling
of the skin was moderate until firing of the second-stage booster at
11.4 seconds; after which time, the skin heated rapidly. The maximum
rate of rise of skin temperature was 2500 F per second. The skin tem-
perature had reached 7000 F when the pickup failed.
According to the theory of reference 6, the aerodynamic heat transfer
on a cone with turbulent boundary layer from the nose is a function of the
C.OUT i DEli'TItL
NACA RM L55G28a
local Mach number just outside the boundary layer, the local Reynolds
number (based on length from the nose) and the ratio of wall temperature
to local static temperature. In the present tests, these parameters all
vary with time and their individual effects cannot be isolated. The
measured heat-transfer rates, as indicated by Stanton number, are there-
fore presented as a function of time in figure 4 for the latter part of
the test, when the aerodynamic heating was strong. Also plotted on the
same time scale are the variations of local Mach number, local Reynolds
number based on length from the nose tip and the ratio of wall tempera-
ture to local static temperature. Van Driest's theory (ref. 6) for a cone
with turbulent boundary layer has oeen used to estimate CH for these test
conditions and the results are plotted for comparison with the measured
The agreement between the measurements and theory is fair, the
greatest difference occurring during the last 0.6 second of the test (from
15.8 seconds to 16.4 seconds). Here the measurements are about 20 percent
higher than the theory; this is believed to be a greater difference than
can be attributed to inaccuracies in the measurements. From the present
limited data, it cannot be determined whether this disagreement, and the
lesser disagreements apparent at earlier times, are due to inaccuracy of
the theory or to unaccounted-for test conditions which may have existed
such as laminar flow on the nose of the conel, or a nonuniform skin tem-
perature distribution ahead of the measurement station.
In order to estimate the temperature at the measurement station
through the time of maximum Mach number, a computation was made using
the theoretical heat-transfer coefficients predicted by reference 6.
Turbulent boundary layer from the nose tip and an emissivity factor E,
equal to 0.2 (based on ref. 7) were assumed. The computed temperature
time history is shown in figure 3 by the curve labeled "estimate."
Although the previously noted disagreements between measured and theo-
retical heat-transfer coefficients are apparent in the slightly different
trends of the respective curves, the effect on skin temperature is small
up to the time of failure of the temperature pickup.
1Measurements higher than the theory might be explained by the pres-
ence of a laminar boundary layer over part of the cone length ahead of the
measurement station, in which case the Reynolds number based on turbulent
flow length would be less than Rv. For time 16.2 sec, where maximum dis-
agreement occurs, a theoretical value of CH based on a turbulent Reynolds
number of 15 x 106 would be in agreement with the measurements. This would
indicate laminar flow to a Reynolds number of about 26 x 106, since Rv is
39 x 106. However, because specific knowledge of the transition point
location is lacking, this explanation cannot be verified.
C1':r I DEIJTIkL,
C'[ITF IDEN TI AL
NACA RM L55G28a
As previously stated, there were small differences between the fins
of models 1 and 2, and model 1 carried a total-pressure probe. However,
a computation of the effects of these differences at M = 3.75 showed
that the drag coefficients of the two models would differ by less than
2 percent. Therefore, the drag data from the two models are considered
to be for a single configuration.
The measured drag coefficients are plotted as a function of Mach
number in figure 5. The data between Mach numbers of 2.5 and 5.0 were
obtained from model 1 during the coasting period after booster separa-
tion. The two higher Mach number groups are from model 2; the group
between Mach 3.5 and 5.9 corresponds to the coasting period after sepa-
ration of the second-stage booster, and the data between Mach numbers
of 6 and 6.9 corresponds to the coasting after maximum Mach number. No
satisfactory data were obtained from model 1 after maximum Mach number
because of a structural failure. Both Doppler and telemeter data are
shown in the two lower Mach number groups. Only telemeter data were
obtained for the highest Mach number group since model 2 was beyond the
range of the Doppler radar after maximum Mach number.
Estimated values of CD for Mach numbers of 2.75, 3.75, 6, and 6.9
are also shown on figure 5. The values were obtained by computing the
component drags. The measured Reynolds numbers and estimated skin tem-
peratures were used in the computation of friction drag. The pertinent
data and the component drag values along with the references refss. 8 to
11), used in their estimation, are given in table 1. At Mach numbers 2.75,
3.75 and 6.0, the computed values of CD are in good agreement with the
measured values. At a Mach number of 6.9, the computed value is higher
than the measurements. The reason for this difference is not understood.
The computed value of CD at Mach number 6.9 is higher than that
at Mach number 6 because a turbulent boundary layer was assumed at Mach
number 6.9 (RL = 88 x 106) and a laminar boundary layer was assumed at
Mach number 6 RL = 4 x 106). The experimental values of CD decreased
by about 0.056 as the Mach number decreased from 6.5 (R = 29 x 106) to
6. (RL = 14 x 106). Since changes in the other drag components are
negligible, this decrease is attributed to a reduction in friction drag
as the laminar boundary layer covers progressively more of the body.
Values of friction drag coefficient were computed for the model at M = 6.5
and at M = 6.3 assuming a transition Reynolds number of 14 x 106 laminarr
flow over the entire body at M = 6.5). The difference in the computed
values was 0.042; this value is reasonably close to the measured change.
NACA RM L55G28a
Aerodynamic heat-transfer measurements have been made on the coni-
cal nose of a rocket-propelled model at flight Mach numbers from 1.4 to
3.9. The local Mach number, which is the Mach number just outside the
boundary layer at the measurement station, varied from 1.4 to 5.7. The
corresponding values of local Reynolds number varied from 18 x 106 to
46 x 106 and the ratio of skin temperature to local static temperature
varied from 1.2 to 2.4. The experimental data, reduced to local Stanton
number, were in fair agreement with values predicted by Van Driest's
theory for heat transfer on a cone with turbulent flow from the nose tip.
Drag coefficients were measured on two similar fin-stabilized cone-
cylinder models at several Mach numbers between 2.5 and 6.9. Values of
Reynolds number based on body length were between 4 X 106 and 225 x 106.
Estimated values of total drag coefficient, based on computed component
drags, were in good agreement with the measurements at Mach numbers of
2.75, 3-75, and 6.0 but were approximately 20 percent higher than the
measurements at a Mach number of 6.9. A reduction in measured drag coef-
ficient occurred as Mach number decreased from 6.5 to 6.3 with corre-
sponding body length Reynolds numbers of 29 x 106 and 14 x 106, respec-
tively. The reduction in drag coefficient is attributed to growth of the
laminar boundary layer over the body, and the measured change agrees
reasonably well with the theoretically computed change in friction drag
Langley Aeronautical Laboratory,
National Advisory Committee for Aeronautics,
Langley Field, Va., July 26, 1955.
NACA RM L55G28a
1. Rumsey, Charles B., Piland, Robert 0., and Hopko, Russell N.: Aero-
dynamic-Heating Data Obtained From Free-Flight Tests Between Mach
Numbers of 1 and 5. NACA RM L55Al4a, 1955.
2. Fricke, Clifford L., and Smith, Francis B.: Skin-Temperature Telem-
eter for Determining Boundary-Layer Heat-Transfer Coefficients.
NACA RM L50J17, 1951.
3. Staff of the Computing Section, Center of Analysis (Under Direction
of Zdenek Kopal): Tables of Supersonic Flow Around Cones. Tech.
Rep. No. 1, M.I.T., 1947.
4. Keenan, Joseph H., and Kaye, Joseph: Thermodynamic Properties of Air
Including Polytropic Functions. John Wiley & Sons, Inc., 1945.
5. Woolley, Harold W.: Thermal Properties of Gases. Table 2.10, Nat.
Bur. Standards, July 1949.
6. Van Driest, E. R.: Purbulent Boundary Layer on a Cone in a Supersonic
Flow at Zero Angle of Attack. Jour. Aero. Sci., vol. 19, no. 1,
Jan. 1952, pp. 55-57, 72.
7. Boelter, L. M. K., Bromberg, R., and Gier, J. T.: An Investigation of
Aircraft Heaters XV The Emissivity of Several Materials. NACA
WR W-19, 1944. (Formerly NACA ARR 4A21.)
8. Van Driest, E. R.: Turbulent Boundary Layer in Compressible Fluids.
Jour. Aero. Sci., vol. 18, no. 5, Mar. 1951, pp. 145-160, 216.
9. Klunker, E. B., and McLean, F. Edward: Effect of Thermal Properties
on Laminar-Boundary-Layer Characteristics. NACA TN 2916, 1953.
10. Love, Eugene S.: The Base Pressure at Supersonic Speeds on Two-
Dimensional Airfoils and Bodies of Revolution (With and Without Fins)
Having Turbulent Boundary Layers. NACA RM L53C02, 1953.
11. Moeckel, W. E.: Experimental Investigation of Supersonic Flow With
Detached Shock Waves For Mach Numbers Between 1.8 and 2.9. NACA
RM E50DO5, 1950.
NACA RM L55G28a
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NACA RM L55G28a
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NACA RM L55G28a
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NACA RM L55G28a
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NACA RM L55G28a
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UNIVERSITY OF FLORIDA I
DOCUMENTS DEPAR TMvENT
120 MARS T IAJ SCIEN'CE LIBARy
GAINESVILLE, FL 32e f-?0j I- U- ,
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