drag coefficients of several bodies of revolution at transonic and supersonic velocity.pdf
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ASD-TDR-63-663
DRAG COEFFICIENTS OF SEVERAL BODIES OF REVOLUTION AT TRANSONIC AND SUPERSONIC VELOCITY
TECHNICAL DOCUMENTARY REPORT No. ASD-TDR-63-663
SEPTEMBER 1964
AF FLIGHT DYNAMICS LABORATORY RESEARCH AND TECHNOLOGY DIVISION
AIR FORCE SYSTEMS COMMAND WRIGHT-PATTERSON AIR FORCE BASE, OHIO
Project No. 6065, Task No. 606503
(Prepared under Contract No. AF 33(616)-8310 by the Department of Aeronautics and Engineering Mechanics,
University of Minnesota, Minneapolis, Minnesota; H. G. Heinrich, Sheldon R. Hess, and Gunar Stumbris, Authors)
;XTL75« .114414 1964
When Governmei any purpose other procurement opers responsibility nor ment may have foi ings, specification! otherwise as in a corporation, or cc or sell any patei
other data are used for litely related Government lment thereby incurs no the fact that the Govern-,y supplied the said draw-egarded by implication or r or any other person or sion to manufacture, use, iy way be related thereto.
Qualified requesters may obtain copies of this report from the Defense Documentation Center (DDC), (formerly AST1A), Cameron Station, Bldg. 5, 5010 Duke Street, Alexandria, Virginia, 22314,
This report has been released to the Office of Technical Services, U.S. Department of Commerce, Washington 25, D. C., in stock quantities for sale to the general public.
Copies of this report should not be returned to the Research and Technology Division, Wright-Patterson Air Force Base, Ohio, unless return is required by security considerations, contractual obligations, or notice on a specific document.
400 - November 1964 - 448-11-302
LINDA HALL LIBRARY
3 3690 00566 1391
FOREWORD
This report was prepared by the Department of
Aeronautics and Engineering Mechanics of the University of
Minnesota under USAF Contract No. AF 33(6l6)-8310. This
contract was initiated under Project No. 6065, Task No.
606503. The work was administered under the direction of
the Recovery and Crew Station Branch., AF Flight Dynamics
Laboratory., Research and Technology Division. Mr. Rudi J.
Berndt and Mr. James H. DeWeese were the project engineers.
The work accomplished under this contract was
sponsored jointly by QM Research and Engineering Command.,
Department of the Army; Bureau of Aeronautics and Bureau
of Ordnance,, Department of the Navy; and Air Force Systems
Command,, Department of the Air Force, and was directed by
a Tri-Service Steering Committee concerned with Aerodynamic
Retardation.
Individuals who have contributed significantly to
the project are: Mr. J. G. Ballinger., Principal Engineer,,
Rosemount Aeronautical Laboratories, and a number of graduate
and undergraduate students of the Institute of Technology
of the University of Minnesota.
X
ABSTRACT
The drag coefficients of several bodies of
revolution which are significant for the purpose of aero
dynamic deceleration were measured In the transonic flow
regime and at supersonic speeds of Mach numbers 4 and 5.
This technical documentary report has been
reviewed and Is approved.
Theron J. Baker Vehicle Equipment Division AF Plight Dynamics Laboratory
111
NDAIIALLLIBR KiffStg C%s Mi
TABLE OP CONTENTS
Page
Introduction 1
Models, Facilities, and Instrumentation . . . . 2
A. Models 2 B. Wind Tunnels 2 C. Drag Balance 2 D. Flow Visualization 6 E. Pressure Measurements 6
Results 7
A. Drag Coefficients at Transonic Speeds . . . 7 B. Drag Coefficients at Supersonic Mach
Numbers 9 C. Detailed Discussion of Test Results . . . . 9
1. Ogive Cylinder 11 2. Sphere 14 3. Circular Flat Plate 14
Conclusions 18
Appendix I - Representative Flow Photographs. 19
Appendix II - Test Data 31
Appendix III - Description of the Drag Balance System 39
List of References 42
iv
LIST OP ILLUSTRATIONS
Figure No Page
1. Wind Tunnel Models (Ogive Cylinder, Skirt Hemisphere, Sphere) 3
2. Wind Tunnel Models (Cone, Circular Flat Plate, Hollow Hemisphere, Guide Surface Parachute) 4
3- 1.6-inch Diameter Sphere Installed in Transonic Wind Tunnel 5
4. 1.2-inch Diameter Ogive Cylinder Installed in Supersonic Wind Tunnel 5
5. Drag Coefficients of Several Bodies of Revolution at Transonic Speeds 8
6. Drag Coefficients at M^ =4.01 and 5.01' . . 10
7. Variation of Drag Coefficient with Fineness Ratio for Ogive Cylinder at Moo = 2.64 12
8. Drag Coefficient of an Ogive Cylinder . . . . 13
9. Drag Coefficient of a Sphere 15
10. Drag Coefficient of a Circular Flat Plate . . 16
11. Shadowgraph of 1.2-inch Diameter Ogive Cylinder at M^ = 1.215j Wake Total Pressure Rake at X/D = 2.75 20
12. Shadowgraph of 1.2-inch Diameter Skirted Hemisphere at Moo = 1.278 20
13- Shadowgraph of 1.6-inch Diameter Sphere at Machoo = 1.217; Wake Total Pressure Rake at X/D = 4.5 21
14. Shadowgraph of 1.6-inch Diameter 45° Half-Angle Cone at Moo = 1.217; Wake Total Pressure Rake at X/D = 4.5 21
15. Shadowgraph of 1.6-inch Diameter Circular Flat Plate at Moo =1.215 (Head Shock Hidden from View); Wake Total Pressure Rake at X/D = 4.5 22
v
Pa Shadowgraph of 1.6-lnch Diameter Hollow Hemisphere at Moo = 1.210 (Head Shock Hidden from View); Wake Total Pressure Rake at X/D = 4.5 . . . . . . 22
Shadowgraph of, 1.6-inch Diameter, Guide Surface Parachute Model at Moo =1.224 (Head Shock Hidden from View);. Wake Total Pressure Rake at X/D = '4.5 23
Schlleren Photograph of 1.2-inch Diameter Ogive Cylinder at Mfc> = 4.01; Wake Total Pressure Rake at X/D =4.5 . . . . . . . . . 23
Schlieren Photograph of 1.2-inch Diameter Ogive Cylinder at Moo = 5-01;. Wake Total. Pressure Rake at X/D = 0.5 . . . . .. • • • . 24
Schlieren Photograph of 0.5625-inch Diameter Skirted Hemisphere at Moo = 4.35 . . 24
Schlieren Photograph of. 1.6-inch Diameter Sphere at Moo = 4.01; Wake Total Pressure Rake at X/D = 2.0 . . . . . . . . . . ' . . . . 25
Schlieren Photograph of 1.6-inch Diameter Sphere at M^ = 5.01; Wake Total Pressure Rake at X/D = 0.5 . ;. . . . . . . . . . . . . 2 5
Schlieren Photograph of 1.6-inch Diameter 45° Half-Angle Cone at M B =4.01 (Separated Flow in Base Region); Wake Total Pressure Rake at X/D = 4.46 . . . . .. ., . . . . . . . 26
Schlieren Photograph of 1.6-inch Diameter 45° Half-Angle Cone at M^ =5.01; Wake Total Pressure Rake at X/D =2.0 26
Schlieren Photograph of 1.6-inch Diameter 45° Half-Angle Cone at M^ =5.01 (Separated Flow in Base Region); Wake Total Pressure Rake at X/D = 2.0 . . • • • 27
Schlieren Photograph of 1.6-inch Diameter Circular Flat Plate at M^ =4.01 (Separated Flow in Base Region); Wake Total-Pressure Rake at X/D = .0.5 . r . . . . . . .'•;.-,.. . . . 2 7
vi
No Pa
27. Schlieren Photograph of 1.6-inch Diameter Circular Plat Plate at Moo = .5.01; Wake Total Pressure Rake at X/D = 0.5 28
28. Schlieren Photograph of 1.6-inch Diameter Hollow Hemisphere at Moo = 4.01; Wake Total Pressure Rake at X/D =2.0 28
29. Schlieren Photograph of 1.6-inch Diameter Hollow Hemisphere at Moo = 5-01; Wake Total Pressure Rake at X/D = 0.5 29
30. Schlieren Photograph of 1.6-inch Diameter Guide Surface. Parachute Model at Moo = 4.01 (Separated Plow in Base Region); Wake Total Pressure Rake at X/D = 0.5 29
31. Schlieren Photograph of 1.6-inch Diameter Guide Surface Parachute Model at Moo = 5.01; Wake Total Pressure Rake at X/D = 0.5 . . . . 30
32. Variation of Drag Coefficient of Ogive Cylinder with Preestream Mach Number . . . . 32
33. Variation of Drag Coefficient of Skirted Hemisphere with Freestream Mach Number . . . 33
34. Variation of Drag Coefficient of Sphere with Preestream Mach Number 34
35- Variation of Drag Coefficient of 45° Half-Angle Cone with Preestream Mach Number . . . 35
36. Variation of Drag Coefficient of Circular Plat Plate with Freestream Mach Number . . . 36"
37. Variation of Drag Coefficient of Hollow Hemisphere with Preestream Mach Number . . . 37
38. Variation of Drag Coefficient of Guide Surface Parachute Model with Freestream Mach Number 38
39. Drag Balance (Photograph) 40
vii
L I S T OF SYMBOLS
Cp. = drag/q^ S = drag coefficient o
S = projected area, D v /4
D = maximum body diameter
L = overall body length
L/D = body fineness ratio
Mffl = freestream Mach number
P = wind tunnel stagnation pressure
q = freestream dynamic pressure
Re = P V D / H = Reynolds number (based on maximum body diameter)
X = distance downstream from body base
viii
I. INTRODUCTION
Numerous investigations of the aerodynamic drag of
relatively slender, low drag bodies have been conducted, but
little information is available on the drag characteristics
of relatively blunt bodies. In problems of aerodynamic
deceleration, however, the blunt, high drag bodies are very
important. Knowledge of their drag characteristics is
especially necessary when their application as decelerators
for other bodies is considered.
Therefore, a study is being made at the University
of Minnesota whose overall objective has been identified as:
"Investigation of Wake Effects on the Behavior of Parachutes
and Other Retardation Devices Behind Large Bodies of
Revolution at Subsonic and Supersonic Speeds." To investigate
these wake effects it is necessary to know the drag character
istics of the related bodies in undisturbed flow. Since such
knowledge is not generally available, a series of tests was
conducted as part of the general program to determine the
freestream drag characteristics of the various bodies. This
report presents the results of these tests in the transonic
and supersonic flow regimes, while similar results for sub
sonic flow are given in Ref 1.
Manuscript released by the authors August 1962 for publication as an ASD Technical Documentary Report.
1
I I . MODELS, FACILITIES, AND INSTRUMENTATION
A. Models
The following seven bodies were included in the test
program: A. Ogive cylinder (2.5 caliber tangent nose,
fineness ratio = 4.5)
B. Skirted hemisphere
C. Sphere
D. 45° half-angle cone
E. Circular flat plate
P. Hollow hemisphere
G. Guide surface parachute model
The general shapes and dimensions of these seven
bodies are shown in Pigs 1 and 2.
B. Wind Tunnels
The tests were conducted in the wind tunnels of
Rosemount Aeronautical Laboratories. Transonic tests were
made in the 12 x 16 inch continuous flow, induction type wind
tunnel. Supersonic experiments were conducted in the 6 x 9
inch continuous flow supersonic wind tunnels. Detailed
descriptions of these facilities are presented in Ref 2.
Typical model installations in the transonic and
supersonic tunnels are shown in Pigs 3 and 4 respectively.
The enlarged portion of the model support sting which can be
seen in these photos houses the drag balance.
To reduce the total number of tests needed in the
overall program, a pressure survey of the wake regions of
the various bodies was combined with the drag measurements.
Therefore, a total pressure rake was located at various down
stream positions (as shown in Pigs 3 and 4) in almost all
drag tests.
C. Drag Balance
The drag balance used for these tests is a mechanical-
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PIG 3 . 1.6 INCH DIAMETER SPHERE INSTALLED IN TRANSONIC WIND TUNNEL.
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PIG 4. 1.2 INCH DIAMETER OGIVE CYLINDER INSTALLED IN SUPERSONIC WIND TUNNEL.
5
electrical system whose sensing unit is mounted co-axially
with the model support sting. The drag force acts over the
support sting upon a pair of flexible steel diaphragms. The
deflection of.these diaphragms is transmitted to the core of
a Schaevitz Linear Variable Differential Transformer (LVDT)
which thus gives an electrical signal proportional to the
drag on the model. The output of the LVDT is transmitted
through a control unit to a Brown Variable Span Recorder
which gives a permanent, easily read record of the drag values. A detailed description of the drag balance is given
in Appendix III.
D. Flow Visualization
Observations and recording of flow characteristics
around test models was accomplished by means of shadowgraph
and Schlieren for transonic and supersonic experiments respec
tively.
E. Pressure Measurement
To correct the measured drag values for the presence
of the sting at the base of the body, the body base pressure
and the drag balance internal pressure were recorded. The
base pressure was determined from base pressure coefficients
which were measured by means of the wake total pressure rake.
The exception was the skirted hemisphere model which had a
base pressure tap. The balance internal pressure was measured
directly through an orifice provided for this purpose within
the balance.
The pressure taps were connected by plastic tubing
to Mercury or merriam fluid (sp. g. = 1.05) manometer boards, which were photographed at each test condition.
6
III. RESULTS
The objective of this study was the establishment
of the drag coefficients of the bodies shown in Fig 1 in the
transonic and supersonic flow regime. In addition, repre
sentative flow pictures were to be obtained either by the
Schlieren or shadowgraph method. The drag coefficients will
be discussed in detail in the following pages, whereas the
pertinent flow pictures can be found in Appendix I.
The drag measurements and the flow visualization
were made at the following approximate Mach numbers: 0.6,
0.85, 0.95, 1.05, 1.2, 4.0, and 5.0. A secondary objective
of this study was the establishment of the wake boundaries of
the various bodies. For this purpose, a total pressure rake
was placed behind the bodies under investigation. In the
interest of the wake investigation the rake had to be placed
quite close to the body in several instances, and there is
certainly the possibility that the rake influenced the drag
coefficient of the body. In cases where such a doubt or
possibility existed or appeared likely, the drag coefficients
have been omitted.
A. Drag Coefficients at Transonic Speeds
Figure 5 presents the results of the measurements
on all bodies in the transonic flow regime. The curves show
a somewhat regular and expected characteristic with the
exception of the drag coefficient of the sphere. In the case
of the sphere a strong Reynolds number influence has been
noticed at MQO =0.6, details of which are discussed later
and are illustrated in Fig 9.
More experimental data for the individual bodies
are shown in Figs 32 through 38, Appendix II. These figures
also show experimental points obtained in the supersonic flow
regime.
7
o HOLLOW HEMISPHERE
5.32 < Re x 1 0 5 < 7.08
FLAT PLATE
5.06 < Re X105<6.82
A
45° CONE
4.94 < Re x10 5 <6.70
V
GUIDE SURFACE PARACHUTE
5.03 < Re x 1 0 5 < 6.68
SPHERE
5.38 < R e x 1 0 5 < 7 0 5 SEE FIG 9.
SKIRTED HEMISPHERE
4 .43<Rex10 5 <4.78
_ OGIVE CYLINDER
T3 3.88 <Re X 105< 5.26
FIG 5. DRAG COEFFICIENTS OF SEVERAL BODIES OF REVOLUTION AT TRANSONIC SPEEDS 8
B. Drag.Coefficients at Supersonic Mach Numbers
The results of measurements in the supersonic flow
regime are shown in Pig 6. The indicated points are the
results of an averaging process of a continuous force record
ing obtained from the electric balance.
Figure 6 also indicates the specific location of
the total pressure rake and the form of the wake boundary,
either converging or diverging.
As can be seen from Fig 6, the location of the total
pressure rake appears to be immaterial in view of the drag
coefficient,, . whereas the effect of a converging or diverging
wake boundary appears to be more important. For example,
the 45° half angle cone is shown in Figs 24 and 25, with con
verging and diverging wake boundaries. This may be a Reynolds
number effect because the Reynolds numbers for Figs 24 and 25
are 8,3 x 1CK and 5.8 x 1CK respectively. This rake condition
accounts for the deviation of the drag coefficients in the
order of 10$ as can be seen for the 45° half-angle cone at
Mco = 5 in Fig 6.
In view of these experimental circumstances and under
consideration of information found in literature, an attempt
has been made to establish a drag coefficient of the seven
bodies under investigation, which is considered to be fairly
reliable. These drag coefficients at M^ = 5 and their source
of information are summarized in Table 1. As can be concluded
from Fig 6, the drag coefficients at M , = 4 will vary from
those at Moo = 5 depending on the body.
C. Detailed Discussion of Test Results
Very limited information was found in literature on
the drag characteristics of the skirted hemisphere, 45° half
angle cone, hollow hemisphere, and shapes resembling the
guide surface parachute in the transonic and supersonic flow
regimes. Therefore, the following comparisons are restricted
to a discussion of the ogive cylinder, the sphere, and the
flat plate.
9
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IN BASE REGION
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FIG 6. DRAG COEFFICIENTS AT M»=401 AND 5.01
10
TABLE 1. DRAG COEFFICIENT AT M m = 5 BODY
OGIVE CYLINDER
SKIRTED HEMISPHERE
SPHERE
45° HALF-ANGLE CONE
CIRCULAR FLAT PLATE
HOLLOW HEMISPHERE
GUIDE SURFACE PARACHUTE MODEL
cD
-0.4
0.75 (AT Mo„= 4.4)
0.93
1.1 1.6
-1.7
1.2
SOURCE
FRESENT TESTS AND EXTENSION OF RESULTS
FROM REFS 14 & 15 (FIG g)
PRESENT TESTS (FIG 33)
PRESENT TESTS AND REF 3 (FIG 9)
PRESENT TESTS (FIG 6)
PRESENT TESTS AND REF 3 (FIG 10)
PRESENT TESTS (FIG 6)
PRESENT TESTS (FIG 6)
1. Ogive Cylinder
Most of the results found for similar ogive cylin-.
ders were for supersonic Mach numbers between 1.2 and 3«5J
no comparable results for this body could be found for the
transonic Mach number range.
References 14 and 15 each give drag coefficients
for supersonic Mach numbers for ogive cylinders which are very
similar to the one used in this investigation. In each case
the shape of the ogival nose was the same and the body fineness
ratio, L/D, varied by only +§. Based on the results shown in
Fig 7 , which was extracted from Ref 14, the difference in fineness ratio in this range does not affect the Cj. values. This body, however, has a much sharper nose than the one
under present investigation.
The results of the present study and 'the drag
coefficients from Refs 14 and 15 are presented in Fig 8.
The transonic results from present tests join the results
from Refs 14 and 15 in a satisfactory manner, and therefore
are acceptable. The supersonic results, however, indicate
a slightly higher drag coefficient. Drag coefficients given
in Ref 3 for various projectile bodies indicate that no
11
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significant increase in drag coefficient at these Mach
numbers should be expected.
In view of the new results as well as on the basis
of information obtained from publications, one would expect
Cj. values at M^, = 4 and 5 in the order of 0.4 or slightly
below.
2. Sphere
The results of many investigations concerning the
drag characteristics of spheres have been summarized in Ref 3.
The curve which is presented there for the variation of C^
with Moo is reproduced in Pig 9 together with the results from
present tests. It is noted that for Mach numbers less than
0.75.> the drag curve has two distinctly separate branches.
The lower branch is for Reynolds numbers above critical
conditions while the upper one is for those below the critical
Reynolds number.
The transonic drag coefficient values obtained for
the 1.6-inch diameter sphere tested here agree very well with
the results from Ref 3, except at Moo =1.2. It is noted that
the CD value at Moo = 0.625 falls on the lower branch of the
Cp. curve. The Reynolds number for this test was 5-4 x 10 ,
which is above the critical value. The obtained drag
coefficients agree, in general, satisfactorily with those
found in other publications.
3. Circular Plat Plate
Only a relatively few experimental values for the
drag coefficient of the circular flat plate are available±
with none available in the transonic Mach number range. The
solid part of the CL. versus Moo curve shown in Pig 10 is
identical with a pertinent curve given in Ref 3. The tran
sonic section of this curve which is broken., is suggested in
consideration of the results obtained in this study.
The drag -coefficient value at M^ = 5 agrees with the
results from Ref 3. The test point at Moo = ^ should be
14
15
1.0
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Q5
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IG 6
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9. D
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FF
ICIE
NT
OF
A
SP
HE
RE
25
20 1.5
1.0
0.5
0
_rv-
—
* ^ O
-6 °
o^
^ S
*
o
c J
— R
EF
3,
CH
AP
16,
FIG
18
o P
RE
SE
NT
TE
STS
0.15
0.
2 0.
4 0.
6 0.
8 1.0
M
2.
0 4.
0 6.
0 8.
0 0
0
FIG
10.
D
RAG
C
OE
FFIC
IEN
T O
F A
CIR
CU
LAR
FL
AT
P
LATE
disregarded because it Is known that under these specific
experimental conditions, the form of the wake In the near base region was divergent.
17
IV. CONCLUSIONS
The drag coefficients measured at transonic speeds
for the ogive cylinder, skirted hemisphere, sphere, 45° half-angle cone, circular flat, hollow hemisphere and guide sur
face parachute model are given in Pig 5.
Under consideration of information found in other
publications, the most probable drag coefficients for the seven
bodies involved in this study at a Mach number of 5 are pre
sented in Table 1. It may be assumed that the drag coefficients
related to Mach numbers between the transonic region and the
indicated supersonic Mach number will leave values as indicated
in the respective curves.
18
APPENDIX I
REPRESENTATIVE PLOW PHOTOGRAPHS
19
•• 3- "• 'A* M * ^ / s *
*sw*i i^;)*fcS
^
PIG 11. SHADOWGRAPH OP 1.2 INCH DIAMETER OGIVE CYLINDER AT~ MCD = 1-2-L5; WAKE TOTAL PRESSURE RAKE AT X/D = 2.75
t
I /
PIG 12. SHADOWGRAPH OP 1.2 INCH DIAMETER SKIRTED HEMISPHERE 1 oo ~ 1-278'
20
' . *_*
\ft !'•
FIG 1 3 . SHADOWGRAPH OP 1 . 6 INCH DIAMETER SPHERE AT M ^ = 1 . 2 1 7 ; WAKE TOTAL PRESSURE RAKE AT X/D = 4 . 5 .
11
I
•wi.
PIG 1 4 . SHADOWGRAPH OP 1 .6 INCH DIAMETER 4 5 ° HALF-ANGLE CONE AT M ^ = 1 . 2 1 7 ; WAKE TOTAL PRESSURE RAKE ATX/5) = 4 . 5
21
I
PIG 15. SHADOWGRAPH OP 1.6 INCH DIAMETER CIRCULAR PLAT PLATE AT Mco = 1-215 (HEAD SHOCK HIDDEN PROM VIEW); WAKE TOTAL PRESSURE RAKE AT X/D - 4.5.
PIG 16. SHADOWGRAPH OP 1.6 INCH DIAMETER HOLLOW HEMISPHERE AT Mco = 1.210 (HEAD SHOCK HIDDEN PROM VIEW); WAKE TOTAL PRESSURE RAKE AT X/D =4.5.
22
r
t PIG 17. SHADOWGRAPH OP 1.6 INCH DIAMETER GUIDE SURFACE
PARACHUTE MODEL AT MQO = 1.224 (HEAD SHOCK HIDDEN PROM VIEW); WAKE TOTAL PRESSURE RAKE AT X/D =4.5.
n
•~!:.-l-P.—.W
£.
M * * * > •
PIG 18. SCHLIEREN PHOTOGRAPH OP 1.2 INCH DIAMETER OGIVE CYLINDER AT Moo = 4.01; WAKE TOTAL PRESSURE RAKE AT X/D =4.5.
23
*.-"« »,y 1
* * • ; • % < ^ - ^ *
• , » $!&**
-iff * » • .
• e l * '
*
* ^
- • ^
^
SCHLIEREN PHOTOGRAPH OF 1 . 2 INCH DIAMETER OGIVE CYLINDER AT M AT X/D = 0 . 5
00 5 . 0 1 ; WAKE TOTAL PRESSURE RAKE
SCHLIEREN PHOTOGRAPH OF O . 5 6 2 5 INCH DIAMETER SKIRTED HEMISPHERE AT M = 4 . 3 5 .
00
24
PIG 21. SCHLIEREN PHOTOGRAPH OP : AT Moo= 4.01; WAKE TOTAL
FIG 22. SCHLIEREN PHOTOGRAPH OP AT Moo= 5.01; WAKE TOTA:
.6 INCH DIAMETER SPHERE PRESSURE RAKE AT X/D =2.0.
1.6 INCH DIAMETER SPHERE , PRESSURE RAKE AT X/D =0.5.
25
«*5fc1J
f ••
, » \ - t f ^
PIG 23. SCHLIEREN PHOTOGRAPH OP 1.6 INCH DIAMETER 45° HALF-ANGLE CONE AT M ^ = 4.01 (SEPARATED FLOW IN BASE REGION); WAKE TOTAL PRESSURE RAKE AT X/D = 4.46.
m
FIG 24,
v^g«4«. ".*.,j!. ""''WSij
• • • . r . ' r f ^ ! •*!•.•*!». «•*?••
•"• " i " - " j\* •" • " • " • " " "
'-•. *• • * ^ , ' i * - ' : , •. — * - . . • ' • - » '
.•»,•9R»*ffl.t-,i!iii.-wiv."..- V - !
^ # ^ ; . • • •
SCHLIEREN PHOTOGRAPH OP 1.6 INCH DIAMETER 45' HALF-ANGLE CONE AT Mco = 5.01; WAKE TOTAL PRESSURE RAKE AT X/D =2.0.
26
~vi
• .*".
> • .
• * » « * •
. " . : " • • : . *•
- - •*
SCHLIEREN PHOTOGRAPH OF 1.6 INCH DIAMETER 45° HALF-ANGLE CONE AT M ^ =5.01 (SEPARATED FLOW IN BASE REGION); WAKE TOTAL PRESSURE RAKE AT X/D =2.0.
SCHLIEREN PHOTOGRAPH OF 1.6 INCH DIAMETER CIRCULAR FLAT PLATE AT M ^ = 4.01 (SEPARATED FLOW IN BASE REGION); WAKE TOTAL PRESSURE RAKE AT X/D =0.5.
27
,3m%,
PIG 27. SCHLIEREN PHOTOGRAPH OP 1.6 INCH DIAMETER CIRCULAR PLAT PLATE AT MQO = 5.01; WAKE TOTAL PRESSURE RAKE AT X/D =0.5-
v£«>T.na^:"
*S<*^^^Vw^--* • v
l5V
Ste • i - - •.>.. v v
.'L'.. ?-£•• V~" .
PIG 28. SCHLIEREN PHOTOGRAPH OP 1.6 INCH DIAMETER HOLLOW HEMISPHERE AT M ^ = 4.01; WAKE TOTAL PRESSURE RAKE AT X/D = 2.0.
28
FIG 29. SCHLIEREN PHOTOGRAPH OF 1.6 INCH DIAMETER HOLLOW HEMISPHERE AT MQQ = 5.01; WAKE TOTAL PRESSURE RAKE AT X/D = 0.5.
FIG 30. SCHLIEREN PHOTOGRAPH OF 1.6 INCH DIAMETER GUIDE SURFACE PARACHUTE MODEL AT MQQ = 4.01 (SEPARATED FLOW IN BASE REGION); WAKE TOTAL PRESSURE RAKE AT X/D =0.5.
29
FIG 31. SCHLIEREN PHOTOGRAPH OF 1.6 INCH DIAMETER GUIDE SURFACE PARACHUTE MODEL AT MQQ = 5-01; WAKE TOTAL PRESSURE RAKE AT X/D =0.5.
30
APPENDIX I I
TEST DATA
+-X-+1 LOCATION OF TOTAL
<c ^
PRESSURE RAKE
D
O X /D=0 .5 o 1.5 • 2.0 o 2.75 • NO RAKE FLAGGED SYMBOLS INDICATE SEPARATED FLOW IN BASE REGION
o <y
o
REYNOLDS NO'S
Moo =0.6 Re=3.9x105
1.2 5.2 X105
4.0 4.1 X105
4.4 2.1 X105
5.0 2.7 x10 5
4.0 5.0 6.0
FIG 32. VARIATION OF DRAG COEFFICIENT OF OGIVE CYLINDER WITH FREE-STREAM MACH NUMBER
32
0.9
0.8
0.7
0.6
0.5
C D
0.4
0.3
0.2
0.1
0
FIG 33.
_/
o
.o
a> REYNOLDS NO'S.
Moo =0.85 Re=4.4x10 5
1.28 4.8 x 1 0 5
4.35 2.1 X 1 0 5
0.4 0.6 0.8 1.0 1.2 Moo
^ 1.4^ 4.0 5.0
VARIATION OF DRAG COEFFICIENT OF SKIRTED HEMISPHERE WITH FREE-STREAM MACH NUMBER
33
1.1
1.0
0.9
0.8
0.7
0.6
C D
0.5
0.4
0.3
0.2
0.1
o
1
t 1
/ * \ o D
D
iv
1 _ V ^
<>
r i
0 X/D = 0.5
• 2.0
o 4.5
REYNOLDS N
B
LOCATION OF TOTAL PRESSURE
RAKE
O'S.
1oo=0.6 Re = 5.3x10^
1.2 7.1 x 1 0 5
4.0 3 .6x10 5
5.( D 6.5 >x105
0 0.4 0.6 0.8 1.0 1.2 4.0 5.0 6.0
M<
FIG 34. VARIATION OF DRAG COEFFICIENT OF SPHERE WITH FREE-STREAM MACH NUMBER 34
.4 0.6 0 5.0 6.0 Mc
FIG 35. VARIATION OF DRAG COEFFICIENT OF 45° HALF-ANGLE CONE WITH FREE-STREAM MACH NUMBER
35
1.9-
1.8-
1.7
1.6
1.5 'D
1.4
1.3
1.2
1.1
1.0
0.9
<^
D
D Y LOCATION OF
TOTAL PRESSURE RAKE
M
0 \ ~- 0.5
D 2.0
o 4.5 ® NO RAKE FLAGGED SYMBOL INDICATES SEPARATED FLOW IN BASE REGION REYNOLDS NO'S.
2 0.6 Re = 5.1 x 10s
1.2 6.9 x 10* 4.0 5.1 x 105
4.9 1.5 x 1 0 s
5.0 7.0 x 1 0 s
0.4 0.6 0.8 1.0 1.2 1.4 _L
4.0 5.0 6.0
M,
FIG 36. VARIATION OF DRAG COEFFICIENT OF CIRCULAR FLAT PLATE WITH FREE-STREAM MACH NUMBER
36
0.4 0.6 0.8 1.0
o
V
D
ID — x-*{/-Location of
[ to ta l pres-I sure rake
O \ = 0.5 a 2.0 o 4.5 FLAGGED SYMBOL INDICATES SEPARATED FLOW IN BASE REGION REYNOLDS NO'S Mm=0.6 R G = 5 . 3 X 1 0 |
1.2 7.1 X 1 0 ^ 4.0 4.6 X 1 0 5
'oo •
5.0 6.1 to77xlO^
1.2 M,
1.4 V 4.0 5.0 6.0
FIG. 37 VARIATION OF DRAG COEFFICIENT OF HOLLOW HEMISPHERE WITH FREE-STREAM MACH NUMBER
37
0.4 0.6
_Q_
<y
2i l
u_ v _ * J ^LOCATION OF / TOTAL PRESSURE L_ RAKE
O X/D = 0.5 • 2.0 o 4.5
FLAGGED SYMBOL INDICATES SEPARATED FLOW IN BASE REGION
REYNOLDS NO'S Moo =0.6 Re=5.0x105
1.2 6.7X105 : 4.0 6.3 X105
5.0 7.2X105
0.8 1.0 1.2 Mm
A/ 14 V 4.0 5.0 6.0
FIG 38. VARIATION OF DRAG COEFFICIENT OF GUIDE SURFACE PARACHUTE MODEL WITH FREE-STREAM MACH NUMBER 38
APPENDIX III
DESCRIPTION OP DRAG BALANCE SYSTEM
The drag balance system Includes the balance (the
mechanical portion of the system) and the associated elec
tronic instrumentation. The balance, an exploded view is
given in Pig 39> is composed of: two primary parts, the main
body and the drag sensing capsule. The electronic instrumenta
tion consists of the drag sensing and calibration transformers,
a signal generator., a control unit, and. a recording unit.
The main body of the balance:/:,which is,:3i05 inches
long and 1.55^ inches in diameter> forms the fixed/'^component
of the balance and is rigidly attached to the balance support
sting. In it is housed the drag sensing transformer and its
positioner and also.an internal pressure tap ahd thermocouple.
The Schaevitz Linear Variable Differential Transformer
. (Type 010M-L) is attached to the upstream endrof:5its positioner.
The, other end of the positioner is spring loaded against a cam,
rotation of which provides axial positioning of::the transformer.
The drag sensing capsule, which is 3,102 inches long
and 1.55^ inches in diameter;- is composed of J'a fixed inner
Shell and a floating outer shell. The two shells are coaxially
arranged and are connected'together by two:ring-type steel
diaphragms which provide the spring force for drag sensing.
The inner shell slides onto the inner tube of the main body
and is rigidly attached-to the main body: by a rod which pro
vides adjustment of: :the width of the/slot between the main
body and outer shell of the drag sensing capsule.
The outer shell., which is thus free to deflect the
diaphragms, forms the drag sensing^element. The transformer
core is attached to its downstream end and the test model
sting is rigidly attached by means of an adapter to the upstream
end.
A drag force on the test model causes an axial
displacement of the outer shell of the drag sensing capsule
39
BA
LAN
CE
SU
PPO
RT
S
TIN
G
•EA
LAN
CE
H
OU
SIN
G
MA
IN
BO
DY
TRA
NS
FOR
ME
R
PO
SIT
ION
ER
SLO
T A
DJU
ST
ING
RO
D
TRA
NS
FOR
ME
R C
OR
E
•DR
AG S
EN
SIN
G
CA
PS
ULE
MO
DE
L S
TIN
G A
DA
PTE
R
FIG
39
. D
RA
G
BA
LAN
CE
relative to the fixed main "body. This displacement, which is
proportional to the drag on the model, is measured by the
Schaevitz LVDT. The LVDT is energized by a 10 KC signal
generator and its output is transmitted to a Brown Variable
Span Recorder through the control unit. Since the output of
the signal generator to the LVDT must be constant, the
generator is voltage regulated and is located in a sound
proofed room to isolate it from tunnel noise.
As a displacement of the outer shell of the drag
sensing capsule causes an equal displacement of the trans
former, the transformer gives an output which is proportional
to the drag. The control unit converts this output into
useful recorder information and also extends the recorder
range, thereby permitting measurement of drag over a wide
range without loss of sensitivity. Two other LVDT's, a "Hi"
and a "Lo" at different points on the scale, are used as
calibration transformers. They provide a continuous check on
the accuracy of the system and minimize errors due to
temperature fluctuations.
A linear variation of transformer output with drag,
good sensitivity, and excellent zero return are obtained.
41
LIST OP REFERENCES
Heinrich, H. G. and Haak, E. L. : The Drag of Cones, Plates, and Hemispheres in the Wake of a Forebody in Subsonic Flow, ASP TR bl-587, December, 19bl.
Aeronautical Research Facilities, University of Minnesota, Institute of Technology, Department of Aeronautical Engineering, Rosemount Aeronautical Laboratories, Research Report No. 132., 1956.
Hoerner, S. F.: Fluid Dynamic Drag, published by author, Midland Park, New Jersey, 1958.
Charter's A. C. and Thomas, R. N.: The Aerodynamic Performance.of Small Spheres from Subsonic to High Supersonic Velocities, Journal of the Aeronautical Sciences, Vol. 12, No. 4, pp. 468-476, October, 19^5.
Hodges: The Drag Coefficient of Very High Velocity Spheres, New Mexico School of Mines /RDD/T-b5b, 1949.
May, A. and Witt, W.: Free Flight Determinations of the Drag Coefficient of Spheres, US Naval Ordnance Laboratory, Report No. 2352, 1952..
Kane, E. D.: Sphere Drag at Supersonic Speeds and Low Reynolds Numbers, Journal of the Aeronautical Sciences, Vol. 1», No. 4, pp. 259-270, April, 1951.
Sphere Drag in Rarified Supersonic Gas Flows, Jet Propulsion Laboratory, Research Summary No. 36-5, Vol. II, pp. 10-11, November 1, i960.
Ashkenas, H. I.: Sphere Drag at Low Reynolds Numbers and Supersonic Speeds, Jet Propulsion Laboratory, Research Summary No. 36-12, Vol. I, pp. 93-96, January 2, 1962.
Johnston: An Investigation of the Flow About Cones and Wedges at and beyond the Critical Angle, University of Toronto, Institute of Aerophysics, Report No. 24, 1952.
Drougge: The Flow Around Conical Tips in the Upper Transonic Range, Aeronautical Research Institute of Sweden, Report No. 25, 1948.
The Effect of Nose Shape on Missile Nose Drag, Rosemount Aeronautical Laboratories, Research Report 55, 1950.
42
Stoney, W. E., Jr.: Collection of Zero-Lift Drag Data on Bodies of Revolution from Free Flight Investigations,, NACA TN 4201, January, 195b'.
Walchner, 0.: Systematic Wind Tunnel Measurements on Missiles, NACA TM 1122, March, 1947.
Ferri, A.: Supersonic Tunnel Tests of Projectiles in Germany and" Italy, NACA ACR No. L5H0b, October,
43