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TECHNICAL REPORT RD-77-4
THE AERODYNAMIC CHARACTERISTICS OF WRAP-AROUND
�'FINS AT MACH NUMBERS OF 0.3 TO 3.0
C. Wayne DahikeAeroballistics DirectorateUS Army Missile Research, Development and Engineering Laboratory
US Army Missile CommandRedstone Arsenal, Alabama 35809
15 October 1976
Cleared for public release; distribution unlimited.
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I. qEPORT NUMBER 2. GOVT ACCESSION NO. 3. RECIPIENT'S CATALOG NUMBER
RD-77-4 7)4, TITLE (and Subtitle)
,- TPE OF REPORT & PERIOD COVERED
-z. THE ,kERODYNAMIC CHARACTERISTICS OF WRAP-AROUND Tehnical#-FINS AT MACH NUMIBERS OF 0.3 TO 3.0. 6. PERFORMING ORG. REPORT NUMBER
7. AUTHR(..) 8. CONTRACT OR GRANT NUMBER(&)
C. Wayne TDahRke
9. PERFORMING ORGANIZATION NAME AND ADDRESS 0._ PROGRAM ELEMENT PROJECT, TASK
Commander 4.0. AREAM WORK UNIT NUMBERS
US Army Missile"Command If-1W362303AA214_
Attn: DRSM'tt-RD .- AMCMSC 632303.2140511.05Redstone Arsenal, Alabama 35809 / _ _ _ _ _ _
I1. CONTROLLING OFFICE NAME AND ADDRESS 12. REPORT DATE ---. ,_
Commander/ 15 Octd B76..)US Army Missile Command L-.- UUj,'R OF PAGES
Attn: DRSMI-RPR a_ 6Redstone Arsenal, Alabama 35809 _ _63__ ___
14. MONITORING AGENCY NAME & ADDRESS(If different from Controllind Office) . UIY CLASS. (of thi report)
UnclassifiedISa. DECLASSIFICATION/DOWNGRADING
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Cleared for public release; distribution unlimited.
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IS. SUPPLEMENTARY NOTES
19. KEY WORDS (Continue on reveree side if neceseary end Identify by block number)
Wrap-around finGeometric and flow parametersStatic stabilityDynamic stabilityDrag
20.---A•SrIRACT 'auriftnue Wi reverse eft if nNcweary ead identitfy by block number)
") Results of investigations into many of the geometric and flow parameters
influencing the aerodynamics of wrap-around fins are presented in this report.Particular emphasis is placed on defining static and dynamic roll characteris-
tics between Mach numbers of 0.3 to 3.0. Among the geometric parameters high-
Lighited are fin span, aspect ratio, leading edge sweep, leading edge shape,
finr opening angle, and afterbody geometry. Comparisons of static stability,
dyrinnic stability, and drag are made between the flat and the wrap-around fin.
FOR" •T ~TO, FI•NVSI ~•)EF
DD I JAN 147 EDITIOP oF I NOV 6S IS OBSOLETE UNCLASSI FI ED
SECURITY CLASSIFICATION OF THIS PAGt (LI'en Dara Fntprod)
UNCLASSIFI EDSECURITY CLASSIFICATION Of THIS PAOU(Whan Date Rnfored)
11Block 20 (Concluded)
Problems associated with measurement of wrap-around fin rolling mounts arealso discussed. An overview of the wrap-around fin roll moment characteristicsare presented as an aid for malting estimates and establishing testing tech-niques. This report supercedes RD-73-17.,
ýV U I~ TY CL A!~,If I f) A d 0 - 1 0l A It 1 ,
CONTENTS
Page
I. INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . 3
II. MODELS AND EXPERIMENTAL TEST . . . . . . . . . . . . . 3
III. TESTING TECHNIQUES AND ACCURACY . . . . . . . . . . . . 5
IV. COMPARISON OF WAF TO FLAT FIN STAB~ILITY AND DRAG. . . . 15
V. ROLLING MOMENT COEFFICIENT. ... . . . . . 16
VI. SIDE FORCES AND M'OMENTS .... . . . . . . . . . . 36
VII. OPENING ANGLE . . . . . . . . . . . . . . . . . . . 36
VIII. WAFROLL DYNAMICS.. .. . .. . .. . ... .. 45
IE.E CONCLUS. 0. . . . . . . . . . . . . . . . . . . . . . . . 55
REFEORENCES .. . . . . .. . . .. . . . . . . . . . * . .. . 55
BI L O RI.1 0 0 4 .0 a4 0 0 a 0 0 0 0 0 a 5
-4
1. INTRODUCTION
The wrap-around fin (WAF) may be used in many applications toprovide missile performance equal to flat fins. The WAF has liad limiteduse as stabilizing surfaces, and has been considered for use as controlsurfaces.
One of the main thrust of modern military technology is accuracyimprovement for the most basic form of missilery, the free flightrocket. Both existing free flight rockets and future concepts rangefrom large fixed and/or vehicle launched, to sizes and weights smallenough to be man-portable and shoulder fired. The stabilizing surfacesmay be constrained by physical limitations imposed by rocket motorgeometry and launcher considerations.
The WAF offers a solution for many geometric constraints, and inmany applications can be sized to provide aerodynamic stabilizingcharacteristics equal to flat fin stabilizers. The WAF, however, hasunique aerodynamic characteristics, particularly in roll, that aredifferent from other types of stabilizing devices. The WAF is inherentlyadaptable to tube launched constraints, making it, perhaps, the mostpratical for tube launched rockets.
This report contains a summary of the findings from wind tunnel testsconducted by the US Army Missile Command (MICOM), Redstone Arsenal,Alakbama, with partial support provided by the Air Force Armament TestLabs (AFATL). The ultimate goal is to develop and analytical modelto describe the flow phenomena defining the unique WAF aerodyamicforces; however, at the time, because of the need, it was moreexpedient to define. the characteristics through systematic para-meteric wind tunnel test. The objectiveof this study was to uncovercharacteristics and provide trends that can be used in missile designwhere the anialytical models are not available. The results from thisstudy and other data, such as the Navy III pressure data, should provide
,-. .sufficient information to begin development of an anialytical model.The data herein are presented for comparison of several of the parameters,with importan~t characteristies and trends highlighted, illustratingthose, that have tile most significant effect upon the WAV rolling momentcoef ficient * Problems associated with measurement of WAF roll momentVoofficients usings Conventional techniques are mentioned. In additionto refrences cIted in this report, a bibliography of other WAF docu-
* ~mentcs is included.
I. MODELS ANU EXPENIMNIATAL TEST
* NICOM and Ai'ATL undertook the study of fint; anid afterbodygemetriv effectg on the static rollinig maictit charActeristics of WAV,a.ý cigrood to in the initial plantndng of ;I TTCP vtoperative program.Fiji gteowetry was varied arounid tIL stladIA il al )sown iii
3
, ~~F IM n -w~
*177.
0 , T' T a n e n ý n ' 0%b4 D 0 0 l 0ý1ý
'-' 0 0 v %a o D i m . o - N 1? 1 Uý
o 0 0~N 0 0 a 0 4% 0 0 0 0 0Hý 4C
o Do t
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CNN
'0 aa
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the Arnold Engineering Development Center's (AEDC) 4-T wind tunnel inFigure 1. The models consisted of a 2-caliber secant ogive nose with an8-caliber cylindrical afterbody, including 3 afterbody shapes and finconfigurations. The basic body configuration had a straight cylindricalafterbody (4 inches in diameter) and two alternate afterbody shapesstepped down to a diameter of 3.6 tnches over a length of 7 and 4 inches,
* irespectively, from the base (Figure 2).
The exposed semispan b/2 for the WAF was chosen to be approximatelythe chord length for the arc that encloses a quadrant of tubular bodycross section or 0.707 D (Figure 3 and Table 1). These variations(Table 1) included two larger aspect ratios (same span as standard WAFwith shorter chords of 2 and 4 inches), three additional thicknessratios, four leading edge shapes, seven leading edge sweep angles, onetip alteration, two reduced span fins, one fin body gap, and severalof these fins tested on a step down body configuration (Figure 2).An investigation of fin opening/closing angle for the standard WAF wasconducted for seven opening positions ranging from fully closed to 10Qbeyond the standard fully opened case. Static aerodynamic measurements,including total airframe and individual fin force and moment character-istics, were conducted in three wind tunnel facilities. The majorityof transonic tests were coaducted in the AEDC 4-foot transonic windtunnel 12,3,4,5,61, while the majority of supersonic tests were conductedin che NASA Langley 4-foot unitary plan wind tunnel 17]. Limitedtransonic and supersonic tests were conducted in the McDonnell DouglasAerophysics 4-foot trisonic wind tunnel [8]) In addition, limitedroll damping chikracteristics were conducted in the AEDC 4-foot transonicfacility (9], and both subsoMIc and supersonic free flight tests wereconducted in the Jet Propuls-ion Laboratory (JPL) 20-inch supersonicwind tunnel for the standard WAF configuration and its equivalent planarfin, V9 (Figure 4). Test: variables for the static aerodynamic tests arelisted in Table 2 for the varying geometry tests. In addition to these"MICON/AFATL sponsored tests to specifically study the WAF effects,several projects have considered use of the WAV; 4ome are listed byHolmes IlI and others are briefly mentioned in this report. A morecomplete description of the models and testing conducted by 141COM iscontained in data reports 12,3,5,6,71.
I. TESTING TECHNIQUES AND ACCURACY
There are questions, concerni•g the accuracy and repeatabilityof the rolling momenti coffiient data. Tie magnttudes of the self--idutueed Vo.litlg moment coefficiants of the WAV are ,mall in relation to
ithe si, of tEle coeffioiouts of fins wittl large cants. The only readym isa~ of obrtinting foree data Wi a wind tunuel is with a strain gage611 i. ba.la . Th1 0.tlan1ce1 MUst be sized to meet special, rtequtlremenAts. butit must he capabl)e of handtling thie forcee and moments of the CompletemIdel in the test facility 1to be us,4ed. To obtain sensible rolling
:,merit cOMefficient induced by WAY., wivid tunnel dytiamie pres•atre andfin sizes must be wade largo Withliln practicable limits. Botii Cause
5
o 0 0 0 0 0
¼o o 00 o o o o o
(10 a >ca2
(00
!¼oo 00 0 0 0 0 0
Cz0 00 00 c ol(
00 000000 00 a 0 0 0 00a wcc
(4 a 0
E- 0 00 0 0Q0 0 0 0a0 'dAAC) tQ 0 El 0
T- a ( 0 000A 0 a
0 r0lQ 0,0-Uaa) - .0 an 00
CC C
C3 Aw 0
- 00
00
777 7> --77 .7 -r~r
MODEL INSTALLATION STANDARD CONFIGURATION, 0 =0. a 0
-4i
SWEPT FIN CONFIGURATION
SPLITTER PLATE
Vlgorc 1. WA? uaodct.
V+ -
REAR VIEW LOOKING UOITREAM
1 40.00
31-7
40.00
Xw CONFIGURATION a
02
ALL DIMENSIONS IN INCHES0MOMENT REFERENCE LOCATION
I~Ur 2. ~UWW114d bxkly owo4LX~%Y.
'S
0a
(J0.p1�I- / *� IU. / 4�.]
(II /Ir�
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100
larger aerodynamic loads on the model which result in requirements oflarger strain gage balances. To date, strain gage balances and associa-"ted instrumentation are not ideal for measurement of these small rollingmoments; however, from the available balances one can be chosen thatis optimum for given requirements. A composite plot of rolling momentdata precision is shown in Figure 5. At transonic speeds, the rolling; !. *1 moment gage was large because of the requirements dictated by normalforce and pitching moment loads. As a result the data precision, asquoted by AEDC [3,5], is larger than desirable; however, as shown later,ci the repeatability from duplicate points during the same test and fromseparate entries show that the data are reproducible well within these
precision limits. An attempt was made to measure the cant of each fin"during the transonic testing [2,5]. These measurements of 76 fin instal-lations had a mean cant of 0.011 with a standard deviation of 0.142%,with a quoted measurement accuracy of ±0,1. If all four fins for oneconfiguration have a 0.1i cant, the rolling moment coefficient would be
V 0.004 to 0.010 which is within the quoted (Figure 5) data precision forthe subsonic/transonic test. Because of the uncertainty of the cantmeasurements and the small magnitude of fin cant-induced rolling momentrelative to the data precision, corrections to rolling moment coeffi-cient caused by fin cant are not presented.
0 0.04w•, REFERENCE 141N
4 REFERENCE 13.510.02-
REFERENCE 171EFERENCE 18)
S~-0.02--
0'-0.04
0o 1.0 2.0 3.0MAC41 NO.
V1'i•Fgure 5. WAF rolling momnt data precision.
Several compiri sons were made frow the numerous duplications andother geometric stmilaritite. Figure 6 showe a comparison of the1-caliber chord WAF configuration BIF2 tested on the smooth body withfour malin balaucos aMd iL three different facilities. A separate testJ4] was conducted explicitly to check the rolling moment obtained i.
S .... -11.
J . .-
0.06CONFIGURATION BIF2
0REFERENCE [2] Pt = 2000,RN = 4 x 10 1/ft03 REFERENCE [4 Pt =2600, RN-=S x 106 lift AR 1.3"
uA. 0.04- '~REFERENCE [5 Pt=2600.R= 5 x 106 1/ft tc=ii?1.0r0 t~~i REFERENCEP [7 R=3x;O 1/ft C.C=.
Z ~~ REFERENCE [8] RN = 7x106 1/ft
0.02-C REFERIENCE [81 RN-7x 16 1ftFROM FIN DATA
'U
ONN
MACH NO.
Figure 6. WAF rolling moment coefficient comparisonsfrom several tests, a 00 0 0.
an earlier test (2] at transonic speeds. This test was conducted witha balance that had a 100-inch-pound roll moment gage. Tile normal forceand pitching moment gages were alsc. low capacity, and angle of attackwas restricted to less than% 2'. The m~ain purpose of this test was toobserve tile self-induced WAF rolling moment coefficient at vero angleof attack, and compare these to previously obtained coefficients withtile less sensitive balance. Comparisons of this repeat, Lost are shownin Figure 6 by tile square symbol.
Most models were tested at 00 and 45' roll. angles (Figure 2)throughout thle Mach number range at angles of attack of' -6* to 6. Tileoutcome of thle rolling mnoment coefficient should be the tsamo for anyroll angle at zero angle of attack from it flow and model, syntiietiwviewpoint. Differences between roll position canl Le ittributed to dataiinstrumentation repeatability. Figure 7 shows self-induced WAF rollinigmoment coetticients At zero anigle of, attack throuighout thle Makchnumber range for two roll angles of 0'~ an~d 45*. This does niot ncoss~ar-ily indiciate the precision of thle data, but these resul~ts are typicalof the repeatability of thle data fur both thle transonic and supersonic
12
.BIF16.0.04
0 0 = 0 MAIN BALANCE REFERENCE [2 AND 81 AR - 1.540 = 45 MAIN BALANCE REFERENCE [2AND 81 t/C = 3%
l3 = 0 FIN BALANCE REFERENCE (21 CR/D - 1.00. 0.02 CT/CR 0.75
0
-20
LU -0.02-"0
l Z-0.04p -0.0e
1 -. 0 &o 30
M-CH NO.
Figure 7. WAF roll moment coefficient from main balanceand fin balances, 0 = 0 and 45 degrees.
phases of testing. Tests were conducted for other roll angles duringthe transonic phase, and all results were compatible with those shown
in Figure 7.
"Each fin was mounted on a three component strain gage balance.Total missile rolling moment coefficient was computed from the measuredfin normal force and root bending moment coefficient and compared tothe rolling moment coefficient obtained from the main balance. Typicalcomparisons of the WAF self-induced rolling moment coefficient at zero
"angle of attack for the transonic test are shown in Figure 8. The datamost questionable are the transonic phase, as shown in Figure 5, wherecompariaion between the two methods of obtaining rolling moment coeffi-cient are better than expected.
In addition to the computed rolling moment coefficient from thefour fin panel balances, shown by the flagged symbols (Figure 8), therolling moment coefficient also includes the main balance data for the
TTCP standard WAF Bl Fl. Fin cant variation cn produce roll momentsequally as large as any WAF-induced roll moment observed during alltests, Superimposed on the data of Figure 8 is the roll moment coeffi-cient for a typical tactical prototype fin with incidence (cant) toler-ance of O.l for all four ftns, where the nominal fin incidencewas zero. The overall value-of this analysis is to indicate the
"13
00
04 0
* 0l
w Q)I
0 13
000 0
00 14
000
OV. ~ I 4dL
0IVL AO91N*uzW mDIA"A~o sui *
14 I
10 7
difficulty in obtaining the precise magnitudes that a WAF may exhibitwith flight hardware; however, the trends shown here and those in thefollowing sections are realistic. To obtain the accuracy of themagnitudes desired will require extreme care in model fabrication andsophisticated measurement techniques tailored for precise roll momentmeasurement.
IV. COMPARISON OF WAF TO FLAT FIN STABILITY AND DRAGThe major concern of the effects of WAF has been the self-
induced rolling moment; however, additional comparison of static stabilityparameters was made for a flat fin and the standard WAF. The flat finhad the same total exposed span and projected area as the WAF. Thesetwo fins were tested through the Mach number range of 0.3 to 3.0 on abody of revolution. The normal force coefficient slope at zero angleof attack and the center of pressure are shown in Figure 9 for theflat fin and WAF. Any difference in total configuration staticstability coefficients appears to be within the uncertainty of measure-ment accuracy. Included on the center of pressure data are pointsfrom the JPL free flight bi-planar results at Mach 0.86, 2.0, and 3.03.Similar results were obtained from a comparison of data for the flatfin and WAF tested on a reflection plane at transonic speeds and frombody mounted fin panel data. The flat fin and WAF were also comparedby testing both on a reflection plane (6] (Figure 1, bottom photo) attransonic speeds, Figure 10 shows the basic WAF and flat fin coeffi-cient variations with angle of attack for Mach 0.3 to 1.3. This shows"that the basic lifting characteristic of the WAF is essentially the sameas the flat fin for angles of attack less than t". Figure 11 shows theflat and WAF basic fin lift curve slope at zero 4.,Qle of attack alongwith the longitudinal and lateral center of pressure for the fin ona flat plate and on the body of revolution. The only significantdifference between thle splitter plate data and the data for fins onthe body of revolution is the increase in normal forca coefficient causedy b ody upwash. The upwash factor obtained from the ratio of these two
curvwes ranges from 1.4 to 1.7 through the Mach range of 0.3 to 1.3.This is comparable to tile slender body theory factor of 1.39 for thisf in wtith a body diameter to total span ratio of 0.43.
Drag coefficiean comparisons between the flat and WAF configurations
"are shown on Figure 12. The upper portion shows the drag force coeffi-cient for body alone, the WAF and body, and the flat f t (of equalprojected area to thie WAF) and body. The lower portion shows thesame data with tho body alone, drag subtracted out. The WAF is approx-ima-ely I0% highter, which corresponds to the additional frontal area thatthe WAF hirs becausoe of the. curvature. The other geometric parameters(loading edge sweep, thlickness, leaditng edge shape, and aspect ratio),show their itifluence on drag to be as expected for flat fins with thesame guooetric changes.
f •5
7>" "<
ifAref LD2
r0.2
0.1-
0
1 CALIBERjuD 0 WAF
0 FLAT* j o&L JPL FLIGHT
0
w
MACH NO.
)?igure 9. Comparison of flat and WAV static stability derivatives.
V. ROLLING MOMENT COEFFICIENT
The uwin objective for this study was to investigate theeffects on WAV rolling woment due to the various gemtrie, and flowparameters. Thto variation of rollitig moment Is considered for three,flow parameters: Mach number, Reynolds number, and angle of attack forseveral geometric variations. Peatlterstone and Dalidke 110,.111 hatveshtowni the WAV to have self-induced normal forces at vero angle of It tack.Theo most significant effect With Mach number appears to he at transonic
spees werein eneal, a chainge In sign occurs for roilling miomenit.lit initial studiess, Pentlterstone hans suggested the scelf-indueed force isdirected toward the ceniter of curvature a usncsed n wyfothe center of curvature at supersonic speeds with t~he crossover oecurringclose to Macih 1. This was demonstrated for those- fin configuratitonsOil smooth body With a C /D~ 1.75, with the exception of 0th fin% with
16
JLL
N +r-IM
0
22z
a41
0'aC
4.)
0
U40
UlU
N3i
j ________
0.03 FIN ON SPLITTER PLATEb 0 WAF, F1
ef2 R FLAT,F9~ S
~0.02-
1~ 0.01
0.4
10.2-
01
HL.
0b/2
03
00024O 0.A 0.2 1.0 1.2 .1.4MACH NO.
lVigure 11. Comparisoni of WAI: £in p~allo). to flat 1fit pano3.static stability.
FIN ON BODY0.04j
I0 FLAT, F9
~0.03
0.02
0.4
0.2-
0
0.6
¾j ~0.2J
0** 0. 's
* . MACH NO.
F~igure 11. Concluded.
19
N u.L. 4 L
4 -4
4.4
0 A
aUj
to
-A4
ci -40
maximum thickness t/C = 0.045 F8. This trend exists for fins withrectangular and trapezoidal planforms, for leading edge profile modifi-cation, and for modifications to the root chord (gap fin) and the tipchord. All roll moment coefficients are referenced to the area of body
* 2cross section vD /4, and reference length is the body diameter D. Itis difficult to isolate and illustrate many specific parametric effectswithout pointing out the influence of another parameter. There is alsothe case of the influer'e of Reynolds number which, at this time, isnot clearly shown to be an important parameter with the exception of theotherwise unexplained difference between the crossover point shown bythe JPL free flight data and the results from static test. Grit wasused as boundary layer trips on the body of JPL models, but grit wasnot used on fin leading edges which Mr. Jaffe (JPL) and this authoragree may have been a mistake. The effect of three parameters are shownon Figure 13 for the standard TTCP WAF. The Reynolds numbers vary from
7 to 40 x 106 based on body length for the static test and for the JPL
models was 2.5 x 10 . As can be seen, the effect of R. on smooth and
step-down body, except for JPL, shows differences well within davaaccuracy. Illustrated on this same curve is the variation of rollingmoment with Mach number and the difference of trends with a smooth bodyand a step-down body which may more realistically simulate flight hard-ware hinge recesses. More information will be presented for the Machnumber and body with step-down later in this report.
Other parameters which appear to have lesser influence on the WAFrolling moment are leading edge sweep and fin thickness (Figures 14 and15). The surprising result from the leading edge sweep data is the levelof magnitude, and the trend with Mach number appears very much the sameas the rpetangular fin with the same root chord length. Sweep of theleading edge dtd not show a shift in crossover Mach number as antici-pated. The effect of modifying the leading edge shape is shown in"Figure 16. There is a large change in roll moment, as expected, withthe unsymmetrical leading edge. This may be related to regimes of sub-sonic and supersonic leading edge due to detached and attached shocksover the curved fin, which is neither aii axisymetric body of revolutionor a two-dim•nsional surface. The symmetrical leading edge variationwith included angles of 20.0*, 45.00, and blunt show an effect tran-
* .sonically, but at supersonic speeds is incomplete at this time. NavyWAV pressure data .ill have showit the leading edge pressure differencebetweell the convex and concave side to be larger than any other chord-Wiiv location, except H - 1.3 data which show the largest difference tooccur at aj)proxiwately 312 chord from leading edge. Unfortunately,neither the 200 or blunt leading angles have been tested supersonically.Ho.wevor, as p'eoseuted by Featherstone 1101 , this leading edge pressure-f fect may be atn inlet phenomenon due primarily to fin curvature and notinfluenced signiticantly by leading edge shape or fin thickness..igure 17 presents the rolling moment coefficient for three rectangularplantform WAF's with different churd length, therefore,. haviug different
21
IIT
A . S2 ITANDARD WAF, F1
0.02 4 STEP-DOWN BODY; ! .02- DOef"44 in.
U 0
RN X 106 BASED ON L•*[L 3 40) McDONNELL.
9 -23 McDONNELL
I I SMOOTH BODY 0 17 AEDCx X X , 13 AEDC/McD)ONNELL
0.0210 LANGLEY!i2 0 x . ILAEDCx' XX5 P
0
•"°°0 1.0 30•
MACW NO.
Figure 13. Effect of Reynolds number on zero angle of attackrolling moment coefficient.
aspect ratios. The primary influence seems to be the fin body juncturegeometry and/or boundary layer, which it this case ia fin root chordlength rather than aspect ratio. Aspect ratio was also varied bysweeping the leading edge. The leading edge was swept up to 60' forC /D - 1.75t and a delta planform for CR/D - 1.0. From these variations
it- is shown (Figure 15) that data with like root chord length tend toj look similar and that the effect seen in Fligure 17 may be a subsonic
( ¶ fin-body juncture (chord) length effect.Additional modifications were made to the fin root and tip chord
- .(F1O and F1l, Vigure 3 and Table 1). These were tested only at tran-
sonic speeds and show small effect on rolling moment coefficieet(Figure 18).
One of the most significant changes lit WAF rolling voment coeffi-cient occurs with variatiott of angle of attack. The toll producingforce increases with angle of attack at all Macht numbers ann missileroll orientation and is directed toward the fin away from the fin centerof cuovature. Figure 19 presents the VAF compared to the flat fin &tsupersonic Maclh numbers from the Langley atqd McDounel tests [7.81.
22
LEADING EDGE SWEEP0.06 CT/CR CR/D AR -3
0.02- A0.75 1.00 1.540.00
-0.02_-
--0.06
I-01
FIN THICKNESS2 .0 t/d% CR/D AR
0.0 0 3.0 1.76 0.75A 0.0 AI 1.76 0.75034.6 1.75 0.75
0.02
-1002
OA 0 0.2 0.* 0.6 OA01.0 1.2 i.4 1.0 1.11 Z.02.22.4 U 2.111 .0MACH WO.
14 .ff kcI t 4,tii )adfiktikilb
CR/D= 1.75FiN SYMBOL A ARF1 0 0.0 0.75F14 0 46.9 0.94
oF17 60s.0 1.110
o
N 01.0 2.0 3,0MACH NO.
z
0.05Cr/D= 1.0
I"0= FIN SYMBOL A AR0 *F2 0 0.0 1.30
F18 0 46.9 1.97zF19 0 57.3 2.55
o 0
00"a~
00 -0.05
0~ 1.0 MAHN.2.0 3.0
MAC NO
Figure 15. Effect of fin leading edge sweep aind aspect-rat~o on rolling momient coefficient.
24
LEADING EDGE ANGLE
CRID 1.75 6
0.06-
U- 004 A180 dog -BLUNT
0.2
0-.0
p,0.0 0.2 0.4. 0.6 0le 1.0 1.2 1.4, 1.0 1.81 2.0MACH NO.
UNSYMMETRICAL LEADING EDGEI- 0.10
wCRID 1.75
0.06
4 0-
0
0002040.6 0,8 1.0 1.2 1,4 1.6 18202.2 2.4- 26 2. 3.0MACK NO.
Figur'e 16., Etfoct of leading adpo stlape on: WA1y rolli~I0t %
WAR CR/Du0.06-
LL
U.0.04-
0 0.020.5
z 0.0020 -0.04-a 0.004z
cc 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.0 3.0
MACH NO.
Figure 17. WAF rolling moment coefficient versus Mach No.,
TIP CHORD MODIFICATION0.06
0.02-
ROOT CHORD - BODY SURFACE GAP
0 NO GAPz£ GAPID 0,058
AM
4`0 ().2_ 0'#4 .0G0, 6 1 1.2 1,4 Ile I's"ACH NO.:
Figur;e 18. IEffant o$T mod fyi*ng j~W- root ~and tip ch~ord crossseatioKn oai rvlliujtxg~omont, -a' 0- t/C.. 3 porcent.
._ _ _ .1 . .. ..
LbU
4 w W
2 04 Q1
.1 U
00$4
if 0
44
oa WU
44
00
0 U.14J00~
.40
0000
13)011)AAC .NW N
12
",*1 "2..J
This trend was shown to be essentially unchanged with missile rollattitude with fins of equal exposed span and to a lesser extent atsubsonic Mach numbers [2,3,8]. The rolling moment coefficientsthroughout the Mach number range tested are shown with varying anglesof attack for fins F! and F2 on Figures 20 and 21. Navy ZUNI data havealso demonstrated this phenomenon and it has been shown by Stevens [12]that this driving moment may be a useful design tool for avoiding roll-
yaw resonance problems during missile flight.
The span for all but two WAF's tested had nearly equal exposedsemispans of 0.66 body diameters. These two (F20 and F21) had reducedspans of 0.54 and 0.35, respectively. The zero angle of attack rollingmoments are shown at supersonic Mach numbers (Figure 22). Significantreductions in induced rolling moments occur at Mach numbers above twofor WAF's with spans less than a quarter circle. This suggests thepossibility of tailoring the induced rolling moment variation with Machnumber by varying the fin radius of curvature. This design procedureis only allowed when adequate space exists around the rocket for thefin curvature to depart from the body surface. The variation withangle of ittack and missile roll attitude are shown in Figures 23 and24 for the three spans. There are two significant effects that shouldbe noted. There appears to be much less variation with angle of attackinduced with shorter span WAF (Figure 23); however, at the supersonicMach numbers, roll moment will be dominated by body vortex and span(Figure 24). The interaction is not necessarily unique to the WAF butis related to the relative position of the body vortex core at angleof attack, fin span, and missile roll attitude, where the fin arrange-ment is not symmetrical at angle of attack (e.g., * 22.50).
The step-down body effect is probably the most significant trendthat must be considered in WAF designs requiring a hinge recess and/orbody step-down geometry. The standard WAF is shown on the smooth andstep-down body in Figure 1$. All symmetrical leading edge fins on t!-smooth body show only one crossover point for Mach numbers less than3.0, but the step-down body demonstrated an additional crossover atlow supersonic Mach numbers and is opposite to tihe Featherstone postula-tion that the force at supersonic Mach numbers is dtirected away fromthe WAF center of curvature. Two additional fins that show this areshown in Figure 25. These fins have a 1-caliber root chord; one isrectangular and the other has a 20.6' swept leading edge. Comparisonsof rolling moment coefficient between the smooth and step-down body forfour fin planforms are shown on Figureps 26 and 27. The flow lmechanismthat causes this trend may be the key toward development of supersonic
analytical .. othods.
'0.00.02 Bi~iMACH NO.
0.1.0
0.00 1.7RZ8
0.0 -1.7
-0.04
--0.02
~0.02 .
w 0.00AAAWWk A.
0,001.0520.00
n -0 02EI ii '
cc 0.02
0.00- OO..i-m..OK=OCJXZ)Q0s..o.. 1.00
0.00 -0.750.00 0.U
0.00- 0.5
0.00 0
-0.020 I I I.
-0 -8 -4 -4 -2 0 2 4 6 S 10ANGLE OF ATTACK (dWg
Viguro 20. Variaii~on of WAF r~olling tiouomat coefficient wi~th~aiig1u of attack, All 0.75.
29
Bi F20.00 CCR1.00 MACH NO.
0.00 CRI/D 1.0-02.86
0.00
0.00 - - - )23-0.02
%% 1.~ 1.6
I-0.00
4 ~0.00
0.:0 1.2
:E 1.05-0.04
~0.00
0.00 1.00~0.00 0.000 .
0.00 0.5
0.00
-0.04
40.00
-0.10-10 -8 -4 -4 -2 0 2 4 6
ANGLE OF ATTACK (dig)
Figure 21. Variationi of WA' rolling w1omet~~ cW±effic±itt withanigle of attack* AR 1.33.
30
0.04 0.04
C2 ICR s.
0 0'
-0.041 0.04,
0:02 0.4 0.6 0.8 0 0.2 0O4 0.6 0.8
b/2D b/2D
~ 10.04 0.04M2 M2.0M 3.
0 a 0
-- 0.04 -0.041__
0 0.2 0.4 0.6 0.8 0 0.2 0.4 0.6 0.8
b/2D b/2D
Figure 22. Effects of span on WAF induced rolling moment
SRI/D -1.75.
0.04
ib/2
M L5 0.6
-0.0
>0 cc
0
001
U .4
I.J,
i~a,
>44
I; - "__ _ _ j
0
4C
4rS ,-~rAU143
o O4
* AUm U4.U4
EFFECT OF STEPDOWN BODY ON WAF ROLLING MOMENTCOEFFICIENT, 0, tICR 3 PERCENT, CR/D =1.75
*0.10 BlFl
0 SMOOTH BODY Bi CT/CR1.0.06 STEP DOWN BODY B2
* 0.02
0.00z-0.02
t-.06
i--0.10
81F13
0 SMOOTH BODY 51CTCm07S0.06 a~ STEP DOWN BODY B2
0
0.020.00 A
-0.02
0. 0.2 OA 0. 0.6 1.0 1.2 1.4 1.0 1.6 2.0 2.2 2.4 2,6 2.8 3.0MACHl NO.
Fig1.ure 26. E~ffect of ~aftebody shiape on 14A1 rulling uet
* . 34
Sf
O~..
Ln 0
Sq o
w LI a)
co
10
' I ILU04
z 35) .
Vl. SIDE FORCES AND MOMENTS
It has been suggested [11] that in addition to induced rollingmoments, the WAF causes side force and moment variations with pitchangle of attack. A typical comparison between flat and WAF at supersonicMach numbers is shown as a function of angle of attack in Figure 28.Nothing was observed during this series of testing (Figures 29, 30,and 31) that substantiates the generation of cross derivatives of signi-ficant magnitude over the angle of attack range ±60, contributable to"cruciform WAF at subsonic and transonic Math numbers. Small variationswith angle of attack may have been seen at supersonic Mach numbers asshown in Figure 28. ZUNI data at Mach 3.) are shown to have a similartrend to the MICOM data at Mach 2.86. The step-down body does not showany significant differences in side force or moment with angle of attack
•;, variation.
The same mechanism that causes large roll moment changes withshort span fins at roll orientation and angle of attack (Figure 24) alsoinduces large yawing moments (Figure 32). This trend is not consideredto be unique to the WAF and may be, as expected, a function of rollorientation especially for angles of attack (at supersonic Vach numbers)where body vortex cores rise to the fin tip. Missile roll rate will tendto average out this phenomenon and usually wil.l not prevent a problemin flight. Outside of this effvect, cruciform WAF's do not appear tohave significant cross derivatives except possibly at Mac•li numbers above
--- .2.5. Goometric arrangements of the WAF other than cruciform can beexpected to induce side force/yawing moment variations with angle ofattack and roll, attitude. These would Include; throe-fin configurations:staggered longitudinal conl(igurations; WAV with a .ternate open i ngdirections; and, opening angles other thian tihe fully open as defined inthis report.
VII. OPENING ANGLE
The standard WAF was testod on the smooth body for istvevn.pening/lclosing angles defined as fully open whet% zi line passAes thf bodycenter, the fin pivot point, and tip chord. The fin is fully Closed andconforms to the body surface at 0 139. The rest mittrix is tdiownin Table 3. Host transontic data were obtained At AIim4 II, and aillsupersontic data were obtained at tichontnel 001igl.as Aerophysieot 1aboratory18). Figure 33 shows the modol. with tihrte opening jinges of 0, A'S' aInd90*. Vtn lifft etiven, s (Figure 34) is shiowti for three Mach nmtihlbersover tie range of closing augles tes1ed. ai ftt•'levtiveito"s is defioed":*ll• . as the ritiu of tihe fin% normal, force ait a given tising angle • to the
fit nor"1l force at the fully open cact, 0 - 00.0) The fin centter o!pressure appears to be essentially tnvaruiant with olosing 1ngle akitd 0a function only of Ma30 nuohber as for the lul ly opein ease. A goometrit"fit of vos 2/3 0 is showit in vowpari %•,oti i the fill lift oftfect iveness.Figure 35 shuws the zuero angle of aLLack rolling auwleut varI4Lloti with
36
0 J-
A U4
U4
c-i
.4U
0o0Lii
4v-I
3WJ 0
374
0.2 B1F2MACH NO.
0.0 p ppp 2.36
A 2.360.0
0.0-- .A1C 1.6
0.05CCOO1
0.05 .
0.00 1 .05
LU
0 0.95S0.00 -0.
L 0.0000.
Uo0.00- 0.3
AU
-0.0
0.0
0.001.
0.00- 1.3
0.00 - ~ 0 3 p~~~f0 - 1.05
-0.05, J L-8 -7 - 5 -4 -3 -2-1 0 1 2 3 4 5 6 7 8
ANGLE OF ATTACK (dog)
Figure 29. Variation of side force coefficient with angle
of attack, WAF, AR 1.33, CR/D 1.00, C /C~ 1.00,=0.
38
B1 F1
.0.2 BiiMACH NO.
o.0 pOOQ 2.88
0.0 2.36~C O iO() I
A 0.0 -A 1.9
0-.0.<>C 000O00.<>-<>.0. 1.6
-0.2 I II- 0.2
S0.0- 1.3) XXC%)O
U1.
o 0.0 1.20
C)c0.0 ppC-D OE p O O ,
w -0.2~3 0.2 -A
00-1.00
-00.1
-10 -.8 -8 -4 -2 0 2. 4 6
ANGLE OF ATTACK (dog)
Figure 30. Variation of side force coefficeint withaingle of- attack, WAF, A&. 0.75, /) ~O
C /D .75, tt 0.
39
B1F60.2 MAH NO.
0.0 2.86
0.0 *~2.36
.0.0 A1.9
0.0 CCO. 0 1.6
0.2
U. A A ~ ~ lL A~ 1.20.0)
0 '0 0-cOC-GocXJ- 0O)MDD0-O-O--O--O 1.1
0.0-O--O--p~li~O p 1.06
0.0 _ _ _ _ _ _ _ _ _ _ _ _ _ 0.950.0 -f~~ A A ~ ~ .
-0.020.
-10 -8 -6 -4 -2 0 2 4 6 8ANGLE OF ATTACK Ideg)
Figure 31. Vari~ation of side for'ce coefficient with angle ofattack, IMF, AR =0,75, C /D =1.0, C /CR 1.0, uuSyt6i-
maetrical leading edge, 0 =0.
40
0O 00
0cQ
444
Q 04
040
0
44
0I4
41
ale e _,6
.. R
.. ~,u geaaA'Au
'6q 1.6 AA
0n 0
422
-ta
P44
t 41
O ~r. .7 1' 0
It -A 's ;
43,
'U)
A 02
/. u
LU.
U .
0 0
4V
Iu
U4
44
000
04
Ajo4C
(AN)SUWA W3 "l NI
4_1I
M 0.88
-10 0 20 40 60 80 100 120 -10 0 20 40 50* I0 0
0.04 0.04 0.04
Mu2.0 W0 M Z60 M 3.0
-0.04 --- 0.041 -0-041-10 0 20 40 50 -10 0 20 40 50 -10 0 20 40 50
Figure 35, Effects of opening angle on WAF rolling momentzero angle of attack C RID 1.75, b/2D 0.665.
closing angle for Mach 0.8 to 3.0. No large influence was noted forsmall variations and, at any given angle, appear to follow the rollmoment variation with Mach number as the fully open case does. At anglesof attack above 6' some side force and yawing moment change was observedat opening angles other than zero.
VUil. WAF ROLL DYNAMICS
Tests were conducted where roll dumwping was measured for severalf ill configurations. Included in this was a comparison between a flat finlaud the stanidard WAV. These data are in a MICOM report (9). The tmodelwa-s spun up in the wind tunnel by an internal hydraulic motor. At aprescribed roll rate. the motor clutch was released and the model wasallowed to free spin until the steady state roll rate was reached.2 .Roll damping for ou,ý of the WAF's and one flat are shownt to vary little
theory aretifwtw to be good c~e~pt attransonic. spoeds. Figure 37 showsthe easred teay sate rol rate for the WAF with fill cant angles
of (V* and I a kt Mavih numbers f row 0. 3 to 1. 3. A comparison of the fla tfill and WAV is shouwn for Lthe I' cant. Tito roll rate for the flat fin
an 40~ -eins approximately the same through I~ael nlu ber 0.8. AboveHach 0.8 the 14AP deviated sharply away decreasing unitil at Mach 1. 3 theroll rato wag essenutially vero. Titus the free spinning results sub-atantiat.e the abrupt negative ultift in rolling moment shown by the static
4.5
twit
~~C14
I iT
I I
I gi
IL
zuul
Wu 0
* do
44
ý7'MA
200I FIN CANT= 0.0 dog
0
*~~c -~.I .200 -
-j WAF
*~A = 0R.75LUCR/Dl- .7 5
< -i-400.0
"-600-
FIN CANT 1. ldoo FLAT, 51F9
~400
4 * 0
0 .61.
fillWt il at
I4
I•I.
I, ' data (Figure 13). The effect of fin cant (incidence) on WAF static
rolling moment coefficient at zero angle of attack is shown through theV transonic Mach numbers on Figure 38. These data are for the fin with
geometry [9] shown in Figure 36, and the data implies that for moderatecant angles the self-induced WAF rolling moment simply produces a biasin total rolling moment. This is verified by the free spinning data
shown in Figure 37.
A three phase investigation was conducted by JPL. Several smallscale models were flown in the JPL 20-inch wind tunnel (Figure 4).
Al Some were flown solely for obtaining rolling moment and roll dampingcoefficients, others were flown for a bi-planar dynamic investigation.A sting-mounted free spinning test was conducted initially to observethe roll direction of models with WAF as a function of Mach number.Data for the standard WAF and equivalent flat fin from the AEDC spinningtest, theoretical estimate, and the JPL free-flight data for the flat
. and WAF are shown on Figure 39. The JPL data points (vertical linesindicate spread) have too much scatter for a thorough analysis. Eventhough some had initial roll rates with and against the fin fold direc-tion, the scatter prohibits definition of roll damping for spin in anygiven direction.
4
,I
I 48
U4
-00
ww
us w 0
49.
SLL
"" 40 O
41
0o 0
IL(IN
lo 0 L
. . . .. . . . (P t OwJx~lljjo3 OIMVO110
so_
IX. CONCLUSIONS
The general characteristics of a number of WAF's on a body ofrevolution at Mach numbers 0.3 to 3.0 have been presented. The effectsof geometric and flow parameters are summarized in the following
* statements:
a) The static stability derivatives at a 0 of missileswith WAF's are essentially the same as with equivalent planar fins andmay be estimated by using the flat fin techniques.
b) Drag of the WAF is larger than the flat fin with the sameprojected planform area. This increase is approximately a factor of1.1, for the fins tested, which corresponds to the increase in frontalarea of the WAF over the flat fin.
c) The WAF does induce roll moment to the missile at zeroangle of attack and zero fin cant. This self-induced roll moment canchange direction as a function of Mach number shown, from static data,to crossover near Mach 1.0 for smooth bodies. The parameter appearingto influence the subsonic roll moment most is the fin root chord length,indicating a fin-body juncture effect.
d) Step-downs on the afterbody, simulating a fin hinge recess,show additional crossover of the WAF-inducad roll moment. at supersonic.Mach numbers from 1.2 to 3.0.
e) The WAF rolling moment variation with total missile angleof attack is stmll for absolute angles of attack less than 2'. Above 2*the rolling moment may deviate significantly froem the zero angle of
Sattack caue depending upon fin geometry and Hach number.
f) (ross derivatives induced by the WAF do not appear to be'signifWcant at 'Mach numbers below 2.5. This may not be the case forMach numbers above 2.5, for three-fin configurations, WAF configurationswhere •fin opeoing directions are alternated, or ihigher angles of attack.
g) Aecurate weasurement of WAF rolling moment requires sonsi-Live roll motmnt measurentit strumeuntation and small tolerance oi theindividual fin geomotric incidence.
h) The IJAF moments do not appear to be intolerable, and"-is1 tt roll rates can be tailored by proper geeowtriie dusigu for manyapplieiatious.
Tito 4ummary v f WAF aerodynamieu presentted in thig report is bolievedto Ile ,Iideoqu•lte, iW my eases, as prclitminary estimates for aerodynamic&01des . n nditlon, tie moany paramneters pres.ted are for fa2iliariza-Lton ort as a guide for mitlal desigit ind testing witen WAFis are. aptliud
to spoecfie desigos. A corpletu sutrmiry of all statit, stability dwtaobtained during this study are cootained iui a. coupaion data report L 141.
.i3 %
, - , . an• .•, .:. ,. ,•: • ;:i ,..' ' ' " ," ...>' • " . . .' .b. . ... . . . .'
7ý7 r --
SYMBOLS2
A Reference area, 0 /4
2AR Fin aspect catio, (b/2) *S
b Fin total exposed span, 2 panels
C Drag coefficient less base-dragDF
C Rolling moment coefficient based on A*D
C Roll damping coefficient, d C /d(pD/2V)P
CN Normal force coefficient'
CN N
C Fin root chordR
CT Fin tip chord
C Side force coefficienty
D *Refert~nce length-body diameter, 4.0 in,
L Model total length, 40.0 in.
M Mach number
_P Wind tunnel stagnation pressure
Reyinpojdenumer lnr exposed area, b/4*(CR + CT)
t Fin thickness
WAF Wrap around fin
J~j X cp Center of pressure, longitudinal
Y Fin spanwise center of pressurecp Age
a -Angleof attack
Leading edge total included wedge angle (deg)
e Fin opening/closing angle (deg)
A Leading edge sweep angle (deg)
4) Roll attitude (deg)
TTCP' The Technical Cooperative P'rogram Exterior Ballastics Panel.-07
Kr3
I,06.
K *~VA
REFERENCES
1. Holmes,, John E., Wrap-Around Fin (WAF) Aerodynamics, Paper 9thNavy Symposium Aeroballistics, NavalOrdnance Laboratory, SilverSpring, Maryland.
V 2. 'Dahlke, C. Wayne and Craft, J. C., Aerodynamic Characteristics ofWrap-Around Fins Mounted on Bodies of Revolution and Their Influenceon the Missile Static Stability at Mach Numbers from 0.3 to 1.3,
tols and IIeUS Army Missile Command, Redstone Arsenal, Alabama,Mrh1972, Report No. RD-TM-72-l.
3. DalkeC. Wyeand Flowers, L. D., The Aerodynamic Characteristicsof rapArondFins, Including Fold Angle, at Mach Numbers From
0.5_to_1.3 US AryMissile Command, Redstone Arsenal, Alabama,*43December 1974, Report No. RD-75-19.
4. Dunkin, 0. L,, Influence of Curved-Fin Stabilizers on the RolingMoment Characteristics of 10-Cal Missiles at Mach Numbers from0.2 to 1.3, Propulsion Wind Tunnel Facility, Arnold EngineeringDevelopment Center, Air Force Systems Command, Arnold Air ForceStation, Tennessee, October 1971, Report No. AEJDC-TR-71-237.
;P5. Dahike, C. Wayne andOCraft, J. C., Static Aerodynamic StabilityCharacteristics of a Body of Revolution with Wrap-Around Fins atMach Numbers from 0.5 to 1.3, US Army Missile Command, RedstoneArsenal, Alabama, June 1972, Report No. RD-TM-72-6.
6. Craft, J. C. and Skorupski, Jeff, Static Aerodynamic StabilityCharacteristics of Munitions Designs at Transonic Mach Numbers,
r$ US Army Missile Command, Redstone Arsenal, Alabama, February 1973#Report No. RD-73-3.
7. Dahlke, C. Wayne and Craft, J. C., Static Aeroynmic $abilitCharacteristics of Bodies of Revolutiti withi Wrap-roud Fins atEachi Numbers from 1.6 to 2.86, US Army Missile Command, RedstoneArsenal, Alabama, September 1971. Report No. R0-TH-72-l4.
.8. Dahlke, C. Waynie and Flowers, L. D., The Aerodyaics Chracter-istics of Wra -Around Fins, Including Fold Angle at Mach Numbersfrom 0.5 to 3.0, US Army Mis~sile Command, Redstoue Arsenal, Alabama,.15 November 1974, Report No. RD-75"15.
9., Spring,, D. J., Static Stability and Roll Damdn iractrtsiettsfor Several Curved an Plianar Fin Coufigqratýnis at Transonic
< Speeds, US Army Misoile Co~and, Redstone Ars~enal# Alabama,24 September 1973o Report No. RD-73-32.
55
10. Featherstone, H. A., The Aerodynamic Characteristics of CurvedTail Fin, Convair/Pomona, Convair Division of General DynamicsCorporation, 26 September 1960, Report No. ERR-PO-019.
11. Dahlke, C. Wayne, Aerodynamics of Wrap-Around Fins, A Survey ofthe Literature, US Army Missile Command, Redstone Arsenal, Alabama,March 1971, Report No. RD-TR-71-7.
12, Stevens, F. L.; On, T. J.; and Clare, T. A., Wrap-Around VersusCruciform Fin: Effect on Rocket Flight Performances, Naval WeaponsLaboratory, Dahigren, Virginia, August 1974, ARAA Paper 74-777.
13. Shadow, T. 0., Transonic Static Stability and Roll-Damping Charac-teristics of a Directional Controlled Antitank Missile, PropulsionWind Tunnel Facility, Arnold Engineering Development Center, AirForce Systems Command, Arnold Air Force Station, Tennessee,August 1973, Report No. AEDC-TR-73-131.
14. llumphery, J. A. and Dahike, C. W. "A Summary of AerodynamicCharacteristics For Wrap Around Fins from Mach 0.-3 to 3.0"1,US Army Mlissil~e Command, Redstone Arsenal, Alabama (in Preparation.)
ni
* L x:*2
BIBLIOGRAPHY
MICOM Wrap-Around Studies
1. Dahike, C. Wayne, Aerodynamics of Wrap-Around Fins, A Survey ofthe Literature, US Army Missile Command, Redstone Arsenal, Alabama,March 1971, Report No. RD-TR-71-7.
2. Dahike, C. Wayne, "A Review and Status of Wrap-Around Fin Aero-dynamics," Volume 1, Proceedings, l0th Navy Symposium on Aero-ballistics, Naval Surface Weapons Center. Dahlgren Laboratory,Dahigren, Virginia, 15-17 July 1975, p. 279.
3. Dahike, C. Wayne, Experimental Investigation of Several Wrap-Around Fins on Bodies of Revolution From Mach 0.3 to 1.3, DataReport, US Army Missile Command, Redstone Arsenal, Alabama,September 1971, Report No. RD-TN-71-12.
4. Dahlke, C. Wayne and Craft, J. C., Aerodynamic Characteristics ofWrap-Around Fins Mounted on Bodies of Revolution and Their Influenceon the Missile Static Stability at Mach Numbers frm03 o13Vols. I and 11, US Army Missile Command, Redstone Arsenal,Alabama, March 1972, Report No. RD-TM-72-1.
5. Dahlke,-C. Wayne. and Craft, J. C., Static Aerodynamic StabilityCharacteristics of a Body of Revolution with Wrap-Around Fins atMach Nubr o 0 q1 US Army Missile Command, Redstone-Arsenal, Alabama, June 1972, Report No. RD-TM-72-6.
6. D-Ahlke, C., Wayne and Craft, J. C., Static Aerd namic Stability:Characteristic's of Bodies of ReolutionithWrap-Around FinisaMach Numbe's from' 1.6 to 2.86, US Army Missile Command, RedstoneArsenal., Alabama, 'Sept~ember 1972, Report No. RD-TH-72-14.'
7. Dahilke, C.: -Wayne anid Craft, J.1 C., Tito Effect fWrajp-Around FinsSt~d~iyand Rollin Moment Variations, US Araiy
Missile Command, Redstdon Arsonal,. Alabama, July 1973, Report
8. .Dahlkc, C. Wayne and Craft, J. C., "The Effect of Wrap-Around FilsOn Rolling. Moment atnd In''light Roll Rate Variations," Vol. 11,Proceei, Tcehnical Briefig (Presented under the AEGIS of
DA-G-160 at Eglin Air Foeco Base, Florida), US BallisticResearel. Labo atocies, Aberdeen. Proving Ground, Hairyland, 10-13Octatbor 1972.
-9. DahIke., C. Wayne and Elowers, L.. U)., Th erodynamic c~haracteristic's*~,.~4~4ngFold Ansoe at Mach~ Numbers FVrom
0" 05 to 1.3 US -Army Missile Command, Redstone, Arsenal, Alabama,December 1:974, Report No. RD-75-19.
57
1 Dahike, C. W. and Flowers, L. D., The Aerodynamics of Wrap-Around1 Fins, Including Fold Angle at Mach Numbers From 0.5 to 3.0, US
Army Missile Command, Redstone Arsenal, Alabama, 15 November 1974,Report No. RD-75-15.
MICOM Reports Projects and WAF Related
I 1. Craft, J. C., Summary of SMAWT Aerodynamics, US Army MissileCommand, Redstone Arsenal, Alabama, 5 September 1973, ReportNo. RD-73-13.
2. Craft, J. C., Wind Tunnel Tests of Curved and Tangential Fin forAdvanced LAW: Data Report, US Army Missile Command, RedstoneArsenal, Alabama, October 1969, Report No. RD-TM-69-12.
3. Craft, J. C. and Skorupski, J., Static Aerodynamic StabilityCharacteristics of Munitions Design at Transonic Mach Numbers,US Army Missile Command, Redstone Arsenal, Alabama, February 1973,Report No. RD-73-3.
4. Martin, T. A. and Spring, D. J., Wind Tunnel Results for the DCATMissile at Mach Numbers from 0.64 to 2.50, US Army Missile Command,Redstone Arsenal, Alabama, 12 October 1973, Report No. RD-73-27.
5. Mottinger, T. A. and Washington, W. D., An Experimental Investiga-tion of Low Aspect Ratio Fins Tested at Transonic Speeds on aReflection Plane, US Army Missile Command, Redstone Arsenal,Alabama, July 1971, Report No. RD-TM-71-15.
66. Spring, D. J., Static Stability and Roll Damping Characteristics''for Several Curved and Planar Fin Confi urations at Transonic
.. .. , :Speds, US Army Missile Command, Redstone Arsenal, Alabama,24 September 1.973, Report No. RD-73.23.
tIICOM Contract Reports
1. Dunkin, 0, L., Aerodynamic Characteristics of Curved Fins with§Swpt paind U L,2 eadýi l dmos rand Their Influence on Missile StaticStabilitya2t Mach Numbers from 0.5 to 1.3, Arnold EnigineeringDevelopment- Center, Arnold Air Force Station, Tennessee, May 1972,Reolort No. AEDC-Th-72-65 (ADg94217L).
2. Dunkin, 0. L. , Lfc of Fi olding andl LincI timdk Swcif-:" ' AJ•h•. n •heAe•'oF2•iý!.Lc G!taraetcristicq of Mtssilose, .EitjtqjL.,witli,
" nA •-~.hrod Fins at Mach Numbers from 0.5 to .3, A'nold Engineer-i.tg Development Center, Arnold Air F.orte SLation, Tennessee,November 1973, Repo~rt No. AElOC-TR-73-19l.
.......................... '.- .
3. Dunkin, O. L., Influence of Curved-Fin Stabilizers on the Rolling-Moment Characteristics of 10-Cal Missiles at Mach Numbers from0.2 to 1.3, Propulsion Wind Tunnel Facility, Arnold EngineeringDevelopment Center, Air Force Systems Command, Arnold Air ForceStation, Tennessee, October 1971, Report No. AEDC-TR-71-237.
4. Dunkin, 0. L. and German, R. C., Aerodynamic Characteristics ofCurved and Planar Fins and Their Influence on Missile Static Sta-bility at Mach Numbers from 0.3 to 1.3, Arnold EngineeringDevelopment Center, Air Force Systems Command, Arnold Air ForceStation, Tennessee, September 1971, Report No. AEDC-TR-71-201.
5. Hube, F. K., Aerodynamic Characteristics of a Fluidic-ControlledAntitank Missile at Mach Numbers From 2.0 to 3.0, Von KA'RXA'NGas Dynamics Facility, Arnold Engineering Development Center,Air Force Systems Command, Arnold Air Force Station, Tennessee,
4'. August 1971, Report No. AEDC-TR-71-158.
6. Shadow, T. 0., Transonic Static Stability and Roll-Damping Charac-teristics of a Directional Controlled Antitank Missile, PropulsionWind Tunnel Facility, Arnold Engineering Development Center, AirForce Systems Command, Arnold Air Force Station, Tennessee, August1973, Report No. AEDC-TR-73-131.
7. Whoric, J. M., Aerodynamic Characteristics of a Fluidic-ControlledAnt!tank Missile With Curved Fins at Mach Numbers From 0.2 to 1.3,Propulsion Wind Tunnel Facility, Arnold Engineering DevelopmentCen"ter, Air Force Systems Command, Arnold Air Force Station,Tennessee, July 1971, Report No. AEDC-TR-71-116.
8. Whoric, J. M., Aerodynamic Characteristics of Several Low AspectRatio Stabilizer Fins at Mach Numbers from 0.8 to 1.3, PropulsionWind Tunnel Facility, Arnold Engineering Development Center, AirForce Systems Command, Arnold Air Force Station, Tennessee,September 1972, Report No. AEDC-TR-72-143, AFATL-TR-72-189.
1 u, WAF Reports Government Other than MICON
1. Ailr, W.11. 1, Suersonie Aerodynamic Ciiara~teristics of a.. r-round. . 'ldin•Fin, Naval Ordnance Station, Indila lload,
S *,: 4Maryland, 10 June 1971, Report No. 337.
2. Blackaby, J. R., and Watson, E. C,, An Experimental Ilvestiapti-_1SatL d of Lthe Effects of n 4theDrag ad PressureRecUiL4 o of a Nose 1let im bSody of Revolution, April 1954,
i:.• :.NASA Teehimcal Note 3170.
S3. Butler , H. W. , Eal~ation of cite Pressure Distribution on tie Finsof A Wrap-Around Fin Model at Supersonic and Transonic Macht Numbers,.opusiun Wind Tunnel Faellity, Arnold Engineuing DeveloptentCenter, Air Foree Systems Cotnwand, Arnold Air Force Station,Teanesueo, December 1971, Report No. ALDC-TR-7.-273.
59
4. Daniels, P. and Hardy, S. R., Roll Rate Stabilization of a MissileConfiguration with Wrap-Around Fins in Incompressible Flow, Naval"Surface Weapons Center, Dahlgren, Virginia, December 1975,NSWC/DL TR-3346.
5. Featherstone, H. A., The Aerodynamic Characteristics of CurvedTail Fin, Convair/Pomona, Convair Division of General DynamicsCorporation, 26 September 1960, Report No. ERR-PO-019.
6. Gauzza, H. J., Static Stability Test of Tangent and Wrap-AroundFin Configuration at Supersonic Speeds, US Naval OrdnanceLaboratory, White Oak, Maryland, 17 January 1955, NAVORD ReportNo". 3743.
7. Holmes, John E., Wrap-Around Fin (WAF) Aerodynamics, Paper, 9thNavy Symposium Aeroballistics, Naval Ordnance Laboratory, SilverSpring, Maryland.
8. Holmes, John E., Wrap-Around Fin (WAF) Pressure Distribution, NavalOrdnance Laboratory, White Oak, Silver Spring, Maryland, 1 October1973, NOLTR Report No. 73-157.
9. Stevens, F. L., Analysis of the Linear Pitching and Yawin oion,of Curved-Finned Missiles, Naval Weapons Laboratory, Dahlgren,Virginia, October 1973, NWL Report No. TR-2989.
10. Stevens, F. L.; On, T. J.; and Clare, T. A., Wrap-Around VersusCruciform Fin: Effect on Rocket FlightPerformances, Naval WeaponsLaboratory, Dahlgren, Virginia, August 1974, ARAA Paper 74-777.
11. Weaver, R. W., The Aerodlnamic (haracteristics of WraV-Around Fins,for a RocketLyovem tProgra., Jet Propulsion Laboratory,30 Juno 1969, JPL Document 650-68.
Foreaign National WAF Reports
1. Carrington, B. L., Hurdle, C. V.; and Faneett, R. K., Wrp-AroundFitts -The Results of a Suversonic P~arainctric Study RoalArmme~t Research and Development Establishmeat, l"ort HtalsteadSeven Oaks Kent England, 9th Meeting of the-fl' EgLeriur BallisticsPanel 0-7, URILV, Quebec, September 1971.
2. Dixon, I. C. , Wind Tuhtn. Test oif a Hodel EI tioinB Waji'-ArouttdFins, National Aeronuautical Establishment, tHigh Speed AerodynamieSe'ctio., National Research Council of Canada, Ottawa, Harch 1972,.Report No. 5X5/0058.
60
3. Dixon, R. C,, Wind Tunnel Test of a Model Employing Wrap-AroundFins, National Aeronautical Establishment, High Speed AerodynamicSection, National Research Council of Canada, Ottawa, Addendumto Report 5X5/0058, October 1972.
4. Robinson, M. L. and Fenton, C. E., Static Aerodynamic Character-istics of a Wrap-Around Fin Configuration with Small RollingMoments at Low Incidence, Department of Supply, AustrailianDefense Scientific Service, Weapons Research Establishment (NoNumber), The Director, Weapons Research Establishment, Box1424H, G.P.O. Adelaide, South Australia, 5001.
5. Wingrove, J. S., Analysis of Errors and Zero Incidence RollingMoments, British Aircraft Corporation Limited, Guided WeaponsDivision: Bristol Works, Curved Aerodynamic Surfaces, StudyNote No. 1, June 1972, Report No. ST-7376.
6. Wingrove, J. S., Analysis of Zero Incidence Spin Rates and RollDamping Coefficients, British Aircraft Corporation Limited,Guided Weapons Division: Bristol Works, Curved AerodynamicSurfacesp Study Note No. 2, August 1972, Report No. 7645.
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