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UNCLASSIFIED
TR-3Q3e
* T'^^*-""> AERODYNAMICS OF GUIDED AND UNGUI DE) WEAPONS PART II COMPUTER PROGRAM AND USAGE
AUTMONC;
January 1974
IS T* MONITORING AGENCY NAME ADDRESV'f dlflmnni Item Ctmltolllnl Olllc) NUMBER OP PAGES IS. SECURITY CLASS, (ol tfil fport)
UNCLASSIFIED
ISa. DECLASSIPICATION/DOWNORADINO SCHEDULE I DISTRIBUTION STATEMENT (ol thli Raperf;
17.
DISTRIBUTION STATEMENT (et Ma abatract anfararf In Bloc* 20, II dlllmnl Iron Ktport)
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SUPPLEMENTARY NOTES
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20
This report describes a computer program for calculating static forces and moments on canard-body-tail configurations. The program is applicable in the Mach number range, O < M. < 3, and angle of attack range, o < a < 20. The theoretical development of the methods used in the program is given in Part I of the report; however, for reference purposes, the various theories used are listed hereii. DD 1 JAN 71 1473 EDITION OP I NOV It OBSOLETE
S/N 0103-014-01 ^___
UNCLASSIFIED
UNLLM^blHtU
.U*ITV LLASSiriClTION OF THIS PAOCrmxn Dal Enfni)
A detailed description of the program usage, including input and output quantities, is also given. Several example cases are considered and the calculated aerodynamics compared with experimental data. In general, accuracies of" +10" can be expected for normal force and drag and the center of pressure is expected to be accurate to within + 8% of the body length. It costs less than $8.00 per Mach number or angle of attack (on the CDC 6700 Computer) to calculate the static aerodynamics of a typical configuration.
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UNCLASSIFIED
SECURITY CLASSIFICATION OF THIS FAGCfWiwi OaM Mnfndf
AERODYNAMICS OF GUIDED AND UNCUIDED WEAPONS PART II - COMPUTER PROGRAM AND USAGE by Frank G. Moore C. William McKerley Surface Warfare Department
FOREWORD This work was performed to provide a design tool for use in estimating the aerodynamics of guided and unguided projectiles. Support for the work was provided by the Naval Ordnance Systems Command under ORDTASK 35A-501/090-1/UF 32-323-505. Thii report was reviewed and approved by Mr. D. A. Jones, III, Head of the Aeroballistics Group and by Mr. C. A. Cooper, Head of the Guided Projectile Division.
Released by:
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CONTENTS Page FOREWORD ABSTRACT LIST OF FIGURES I. INTRODUCTION II. PROGRAM DESCRIFTION A. Configuration Geometry B. Aerodynamics C. Subroutines III. INPUT IV. OUTPUT V. COMPARISON WITH EXPERIMENT RFFERENCES APPENDICES A. Glossary B. Computer Program Listing C. Distribution i ii iv i 4 4 7 7 14 24 27 34
iii
LIST OF FIGURES Figure 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. I la II b 12a 12b Methods Used to Compute Body Alone Aerodynamics Methods Used to Compute Wing Alone and Interference Aerodynamics Typical Examples of Input Options for Body Configurations Tail (or Canard) Input Geometry Nomenclature for a Modified Double Wedge Airfoil Sample Input Data for a Typical Body Alone Configuration Sample Input Data for a Typical Wing-Body Configuration Sample Input Data for a Typical Canard-Body-Tail Configuration Sample Input Data for a Typical Wing Alone Configuration (Biconvex Airfoil Design) Sample Output for Canard-Body-Tail Configuration of Figure 7 Comparison of Theory and Test Data for 5754 RAP Projectile Drag and Center of Pressure for a Typical Missile Configuration; AR = 4.5 Normal Force Coefficient Derivative for a Typical Missile Configuration; /R = 4.5 Normal Force and Center of Pressure of a Missile Configuration; >, = 4, >c = 2, M, = 1.6 Drag of a Missile Configuration and Its Components Page 2 3 S 6 20 21 22 23 25 28 29 30 32 33
IV
I.
INTRODUCTION
The goal of the present research is to develop the capability to compute static aerodynamics on configurations such as guided and unguided projectiles for the Mach number range zero to three and angle of attack range zero to about twenty degrees. The Mach number and angle of attack range cover present and probable future design requirements for gun-launched weapons. Included in the present report is a detailed description of the computer program, along with several example cases and a FORTRAN listing of the program. For the derivation and discussion of the various theoretical methods used in the development of the prediction program, the reader is referred to Part I of this report (Reference I). However, for information purposes, the methods used to compute the particular force or moment component in the given Mach number region are listed in Figures I and 2. Figure 1 gives the methods for the body alone and Figure 2 those for the tail (or canard) alone along with the interference effects. Most of the methods listed are standard in the .literature with the exception of the empirical methods and the combined Newtonian Perturbation theories. Detailed discussion of this new theoretical method for calculating body wave drag can be found in Reference 2 and for wing wave drag in Reference 1.
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The program is designed for four possible configurations: (I) wing alone, (2) body alone. (3) wing-body, and (4) canard-body-tail. Note that in present terminology, wing is interchangable with cither a canard or tail. There are several iliffcrcnt geometries which the wing or body may have as discussed below. 1. Body
The body may have a pointed or blunted nose. Blunt noses may have spherical caps or they may be truncated as shown in Figure 3. The program automatically accounts for this, however, if the correct inputs are given as decribed in the input section In addition to being pointed or blunt, the nose may have up to two different ogive segments present For example, on spin-stabilized projectiles there is norma'I', one ogive on the fuze and a different ogive between the fuze and shoulder. If the aerodynamics are desired in transonic flow, there is a minimum .illowable nose length of 1.5 calibers due to the tcMe look-up procedure used there. The total body alone may end with the nose or it may continue with an afterbody. If an afterbody is present it is assumed to be cylindrical. Again due to the empirical estimation of aerodynamics in transonic flow, the afterbody must be les than ten calibers because this is the upper limit of the tables. Following the afterbody, a conical or ogival boat tail may or may not be present Instead of a hoattail. a flare may be considered but the base drag must be disregarded because it is derived for a boattuil angle. Finally, the body alone may or may not have a rotating band present 2. Wing
The wing is assumed to have one of two airfoil sections: a biconvex or modified double wedge. Both airfoil sections may have sharp or blunt leading and trailing edges. Also, the wing thickness to chord ratio and the slope of the airfoil section may vary all along the span. It may appear at first sight that assuming the airfoil section to be one of the two shapes above severly limits the program. This is not the case for projectiles and missiles, however, since the fin geometry normally is of a simple planform with no camber. Also, referring to Figure 4, the modified double wedge
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NOSE SECTION IA) AFTERBODY
AFTERBODY
A) N SHAPE =3, Nl M AND N2 i 9 , N BLUNT !, NFL =2,NNIA2 B) N SHAPE'S; Nl a 5 AND N2 S9 ; N BLUNT 2, NFL * I, NNIA>2 C) N SHAPED; Nl Nt*8i N BLUNT = I D) N SHAPES! ; NI = N2 25; N BLUNT = I
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* DC/2 CANARD-BODY-TAIL CONFIGURATION
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CRW
Am
TAIL GEOMETRY
can cover all wedge airfoil shapes by adjusting the parameters CR1W and CR2W along with the angles GAW (1) through GAW (4). For example, if a double wedge airfoil is desired then it is sufficient to make the quantity (CRW-CR1W - CR2W] equal to zero and to make GAW (2) GAW (3). B. Aerodynamics
As mentioned previously, the various theoretical and empirical methods used to compute the static aerodynamics are listed in Figures ' and 2 and will not be discussed in this report as they are discussed fully in References I and 2. It is worthy of note that the overall guiding principle in the choice of methods listed in the above figures was to use techniques which could yield accuracies generally bi the range 10% and which were inexpensive on the computer. It is believed tha* this goal was accomplished in that drag and normal force for most configurations can be obtained within the above accuranes ana for a cost not exceeding $75.00 for ten Mach numbers or angles of attacx. The center of pressure is within a half caliber of experimental data for most configurations. C. Subroutines
A brief description of each subroutine will aid the user in understanding the methodology and logic of the program. These descriptions follow.
1.
MAIN
. This subroutine acts as a control for the entire program. It handles the calling of the various subroutine!: that calculate the different lift and drag components. The calling of the various subroutines depend on the different options present in the program. These options are given in the input section of this report. The MAIN also handles the summation of the different components to obtain the total lift, drag, and pitching moment coefficients.
2.
AINTER
A double interpolation routine used in the transonic Mach number
range.
hyperbolic
respectively. They are included because not all computers contain these particular functions in their library. 9. BASEP
Calculates the base drag for a body of revolution with or without a boattail throughout the Mach number range. It also includes an empirical estimate for the increase in base pressure drag due to the presence of fins. 10. BASEPW Computes the drag due to trailing edge separation of a blunt trailing edge fin. 11. BLUNT Derives the coordinates of a blunt nose tip on a body of revolution. 12. CP30W Determines the perturbation velocity at each point on a fin. These perturbation velocities are used by subroutine WING to compute pressures and forces on a fin. 13-16. DISCI, DISC2, DISCS, DISC4 These subroutine- put in appropriate perturbation solutions to simulate discontinuities in body shape and curvature. 17. DIST Computes flow. 18-19. ELIPT1, ELIPT2 These subroutines are used to evaluate the complete elliptic integrals of the first and second kind. the spanwise distribution of lifting pressure in subsonic
20. FBINT Calculates the fin body and body fin interference. The method used is that of Nielsen and Kaattari.(3) 21. POINT This is a simple linear interpolation routine. It is used in subroutines TRNCNA and SUBTRN. 22 21 FD5. FDP5 Theses subroutines are used to find the derivatives of a function at a given point. The five point Lagrange method is used. 24. GCALC Computes the spanwise interpolation lifting surface theory. 25. GEOM This subroutine reads input body coordinates and then computes the coordinates where the flow-field properties will be calculated. 26. GEOM1 Calculates the geometric properties of wings in subsonic flow. 27. GUIDED This subroutine is the controlling subroutine for subsonic wing lift. It establishes boundary conditions and applies the Prandtl dauert transformation. 28. HCALC Computes the chordwise interpolation function used in subsonic lifting surface theory. function for use in subsonic
29. HINT
Computes the chordwise integrals interpolation functions in subroutine HCALC to be used in the chordwisc
30. HYBRID
Determines the body pressure using the hybrid perturbation theory of Van Dyke. For a discussion of this theory, see Reference (2).
33. LIFT
Acts as an executive program responsible for the calculation of fin lift. It calls the interference subroutines and combines the lift of the isolated fins with the proper interference terms to obtain all fin lift components.
34. MINVR
Solves the matrix equation AX = B where A is a square coefficient matrix and B is a matrix of constant vectors. A-1 and |A| are also available. Solution is by the Gauss-Jordan elimination method.
36. NEWRAP
Uses the Newton-Raphson method to solve for the mean skin-friction coefficient for a given Reynolds number and Mach number.
36. NEWT
Computes the pressure and static aerodynamics on the blunt portion of the nose using modified Newtonian theory. It also calculates the match point to combine Newtonian theory with perturbation theory.
10
37. NORMFO Solves for the normal force coefficients on the various components of the body in transonic flow using mostly empirical methods. 38. FORINT Integrates the upwash effect of one wing panel on another 39. RBAND Estimates the increase in drag due to the presence of a rotating band. 40-41. REGONE, REGTWO These subroutines calculate the supersonic lift and center of pressure on a fin with a subsonic leading edge and a supersonic trailing edge by linear theory.
t
Intergrates wing pressure due to thickness to find w i .inp on .i wing by using Simpson's rule.
11
60. SING Applies Mangler's principle Value technique to obtain the solution to an improper intergral. 61. SKINF Calculates the axial force coefficient due to skin friction on the body. 52. SKINFW This subroutine computes the skin friction drag of a wing. The Reynold's number is based on the mean geometric chord. 63. SUBCNA Calculates the subsonic normal force coefficient and center of pressure for an isolated fin. It acts as a calling program for the subroutine that actually does the calculations. 64. SUBTRN This subroutine calculates the transonic normal force coefficient and center of pressure for an isolated fin. The method used can be found in the USAF Stability and Control DATCOM.(4) The method used in the program is a slight modification of that found in the DATCOM, but should be more accurate because the highest subsonic value of normal force derivative and lowest supersonic value are calculated by using lifting surface theory and linear theory, respectively. 66. SUBXCP Calculates the subsonic center of pressure for an isolated fin. The subroutine uses values of sectional center of pressure as calculated in subroutine DIST. 66. SUPCNA Computes the supersonic normal force coefficient for an isolated fir It acts as an executive program and it sets up fin geometry, determines what region a given point on the fin is in, and numerically adds all the lift increments in order to determine the normal force. The supersonic center of pressure for an isolated fin is also calculated in this subroutine.
12
57. TRANS Determines the wave drag of a boattail in transonic flow. It is also used to calculate the nose wave drag of tangent ogives in transonic flow. 58. TRAPE Trapezoidal rule of integration used to determine the surface area and volume of the body alone. 59. TRNCNA This subroutine is used, along with subroutine SUBTRN, to calculate the transonic normal force coefficient. It acts as an executive program a it calls the various subprograms necessary to determine a table of transonic normal forces for an isolated fin as a function of Mach number. 60. WAVE Integrates the body alone pressures in order to compute the static aerodynamics. 61. WING Calculates the pressures and forces on a fin due to thickness at supersonic .speeds. The airfoil thickness is assumed to be symmetrical about the x-axis. The method used is conical flow theory as modified in Reference 1. 62. WTINT Finds the decrement in normal force derivative of the tail of a configuration due to downwash from the canards. The method used is that of Nielsen and Kaattari<3) mentioned earlier.
13
III. INPUT The following is a list of the required inputs to the computer program described in this report.
CARD TYPE I FORMAT (13) Variable Name
Column
(1-3)
Variable Description Angle of attack (Degrees) Reference diameter of body (Ft) Mean height of the rotating band above the body surface (Calibers) Speed of sound (Ft/Sec) Density (Slugs/Ft3) Absolute viscosity (lb-Sec/Ft2) Equal 1 if pressure coefficients are to be printed Equal 2 no pressure coefficients printed Equal I body alone aerodynamics calculated Equal 2 body-wing aerodynamics calculated Equal 3 body-wing-canard aerodynamics calculated Equal 4 wing or canard alone aerodynamics calculated
CARD TYPE III FORMAT (6F5.3.I5) Variable Name XW DELTAW DW Column (1-5) (6-10) (11-15)
Variable Description Distance of wing leading edge from nose tip (Calibers) see Figure 4 Wing deflection angle (Degrees) Diameter of body at wing root chord. If the diameter varies, an average of the body diameters at the leading and trailing edge should be used (Ft). Distance of canard leading edge from nose tip (Calibers) 14
xc
(16-20)
Variable Description Canard deflection angle (Degrees) Diameter of body at canard root chord. If the diameter varies, an average of the body diameters at the leading and trailing edge should be used (Ft). Reference point for moments and center of pressure (measured in calibers from most forward point of nose). Number of Mach numbers to be computed
XCG
(31-35)
MN
(36-40)
Column (1-80)
Variable Description Tail leading edge sweep angle (Degrees) Angle at which first line of sinks is swept back from Y-axis of tail (Degrees), see Figure 4. Angle at which second line of sinks is swept back from Y-axis of tail (Degrees) Tail trailing edge sweep angle (Degrees) Tail root chord (Ft) Tail tip chord (Ft) Span of isolated tail panels (Ft) Distance from tail leading edge to first discontinuity measured from root of tail parallel to freestream (Ft) Distance from tail trailing edge to first discontinuity ui ream from root chord parallel to freestream (H) Leading edge radius of tail at root chord (Ft) Leading edge radius of tail at tip chord (Ft) Tail thickness at root (Ft) Tail thickness at tip (Ft)
CR2W
(41-45)
15
Column (66-70)
Variable Description Distance of wing trailing edge from base (positive upstream of base and measured in root chord lengths) Trailing edge radius of tail at root chord (Ft) Equal 1 double wedge or modified double wedge airfoil; Equal 2 biconvex airfoil
RTEW IW
(71-75) (76-80)
CARD TYPE VI FORMAT (16F5.3,I6) Variable Name GAC(l) GAC(2) GAC(3) GAC(4) CRC CTC BC CR1C Column (1-5) (6-10) (11-15) (16-20) (21-25) (26-30) (31-35) (36-40) Variable Description Canard Leading Edge Sweep Angle (Degrees) Angle at which first line of sinks is swept back from Y-axis of canard (Degrees), see Figure 1. Angle at which second line of sinks is swept back from y-axis of canard (Degrees) Canard trailing edge sweep angle (Degrees) Canard root chord (Ft) Canard tip chord (Ft) Span of isolated canard panels (Ft) Distance from canard leading edge to first discontinuity measured from root of "anard parallel to freestream (Ft) Distance from canard trailing edge to first discontinuity upstream from root chord parallel to freestream (Ft) Leading edge radius of canard at root chord (Ft) Leading edge radius of canard at tip chord (Ft) Canard thickness at root (Ft) Canard thickness at tip (Ft) Distance of canard trailing edge from base of projectile (positive upstream of base and measured in root chord lengths) Trailing edge radius of canard at root ch* d (Ft) Lqual 1 double wedge or modified double wedge airfoil Equal 2 biconvex airfoil
CR2C
(41-45)
RTEC IC
(71-75) (76-80)
16
Variable Name N
Column (1-5)
Variable Description Total number of points to be read in to describe the body alone geometry (limit of 30) Parameter used to describe the body geometry as defined below
Pointed bodies
NSHAPE
(6-10)
Nose only Nose plus afterbody Nose w ih a discontinuity (there may or may not be an afterbody present) Nose plus afterbody plus boattail Nose with discontinuity plus afterbody plus boattail
If NSHAPF=3 or 5 at least five points must be read in along each of the nose sections, even if the nose section is a straight line.
Blunted Bodies
NSHAPE must be 3 or 5 NSHAPE=3 NNIA=2 Blunted nose with a discontinuity so there are two nose sections present (no boattail present) NSHAPE=3 NNIA=I Blunted nose with no discontinuity (no boattail present) NSHAPE=5 NNIA=2 Blunted nose with a discontinuity so there are two nose sections present (boattail present) NSHAPE=5 NNIA=I Blunted nose with no discontinuity (boattail present) If NN1A=I. then Nl = l and N:^5 If NNIA=:. then Nl>5 and N:^ Nl N2 (11-15) (16-20) Number of points used to describe the first nose section Number o*" points used to describe the second nose section plus the number of points used to describe the first nose section.
17
Variable Name N3
Column (21-25)
Variable Description conical boattail Equal ogival boattail (if ogival boattail is Equal present at least fi>e points must be used to describe the boattail section) Equal 1 pointed body Equal 2 blunted body Equal I, spherical cap on nose equal 2, truncated nose Equal I, no discontinuities present in nose Equal 2, discontinuity present in nose so nose appears to be made of two distinct sections Parameter used to describe mesh spacing. For blunted or spherically capped nose, C2=.05 and for pointed nose C2=.9 are nominal values Another parameter used to describe mesh spacing. For blunted or spherically capped nose, C4=I; for pointed nose, C4=20 are nominal values Constant which determines limiting body slope for a given mach number (.95 recommended) Radius of spherical cap or truncated nose (Calibers)
C2
(41-50)
C4
(51-60)
F RR
(61-70) (71-80)
Column (1-15)
Variable Description Longitudinal body coordinate measured from nose (calibcrs). If nose is blunt, X(1H) is at the end of the spherical cap or at the truncated position. Body radius at given longitudinal station (calibers)
R(I)
(16-30)
There are as many Card Type VIII as arc needed to describe the body up to 30 points. It should also NTYPE! NTYPE2 NTYPE^ be pointed out that if: (Body alone) Card Types V and VI are omitted, (Wing-body) Card Type VI is left blank or contains all zeros, (Wing-body-canard) all Card Types contain data.
18
NTYPE-4 (Wing only) Type VI is left blank and Card Types VII and VIII are omitted. If several cases are to be computed. Card Type I is input one time only, but Card Types II - VIII are given for each case as needed. Figure 3 parameters. shows a few typical examples of body geometry and associated
At present, the maximum Mach number that can be input is three. This is due to limitations on tables present in the program. The upper limit on Mach number may be less than this if the local body slope becomes equal to 0.95 of the Mach angle based on the freestream Mach number. Mach numbers should be read in from highrsl to lowest. If a Mach number is .iesired between 1.05 and .95, then Mach 1.05 must be included. This is because values of wave drag on boatt; ils is assumed to vary linearly from 0 at M = .95 to an analytically calculated value at M = 1.05. Wave drag on fins is also assumed to vary linearly from 0 at M = 0.9 to an analytically calculated value at M = 1.05. The shortest nose length that can be considered in the transonic flow regime is 1.5 calibers. The longest afterbody length that can be considered in the transonic flow regime is 10 calibers. These limitations are due to limits in the tables that are internal to the program. Several sample accompanying sketch also given. Figure canard-body-tail, and input data sheets are shown in Figures 5 thru 8. An with the geometric parameters describing each configuration is 5 is a body alone. Figure 6 a wing-body. Figure 7 a Figure 8 a wing alone.
19
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23
IV. OUTTUT Before the aerodynamic forces and moments are given, the computer printout will list the freestream conditions and the wing-body geometries that were input. The force and moment output is then given in component form. Referring to the example computer output in Figure 9 (output corresponds to geometry input of Figure 7), the first table is the body alone drag which is broken down into skin-friction, base, wave, and protrusions (rotating band). The second and third tables are the tail and canard drags (if the canard is present), also broken down into the same drag components as above. The fourth table lists the normal force contributions from all geometry components: body alone, wing alone, wing-body, body-wing, canard alone, canard-body, body-canard, and canard-tail. The last table lists the total static aerodynamics of the entire configuration. These include drag, lift, pitching moment, and center of pressure. Also included are the secant slopes of normal force and pitching moment which for small angles of attack are the normal force and pitching moment coefficient derivatives.
24
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26
V.
Three cases are considered to show, first of all, the general accuracy of the method when compared with experiment and, second, how the program can be used to obtain engineering estimates of aerodynamics for configurations which do not exactly fit into one of the four categories listed previously. The three configurations are a body alone, a wing-body in which the wing is mounted on a strake, and a canard-body-tail in which the tail does not have streamwise tips. The first of these configurations is the 5"/54 Rocket Assisted Projectile (body alone) for which the configuration geomefty and input data are given in Figure 5 and the aerodynamics in Figure 10. This particular spin stabilised projectile has a nose length of about 2.5 calibers and a boattail length of 0.5 caliber. The theoretical drag coefficient is in very good agreement with experiment throughout the Mach number range. Fair agreement is obtained for normal force coefficient derivative and center of pressure. The normal force coefficient derivative is generally low in the lower supersonic speed range and approaches the experimental data at moderate supersonic Mach numbers. A wing-body configuration is shown in Figure 6 and the corresponding aerodynamics in 11A and 11B Note that in Figure 6. the tails are mounted on strakes which raises the question, "What does one use for the base diameter and wing planform?" The base diameter mainly determines the afterbody drag and the wing planform the wing lift Since both of these quantities are a direct function of the base area and wing area respectively, it seems reasonable to compute these areas and then define the base diameter and wing planform from them. Thus the base area is computed incl"'4'.ig the strakes and then an equivalent base diameter defined. Next, the total wing utca including the strake planform area, is computed and an equivalent wing obtained by adding this additional area to the chord and span. Although this does not change the configuration lift appreciably when based on wing area, it does change the lift considerably here because the wing lift is based on the body cross-sectional area. Using the above geometry modifications, the aerodynamics were computed and compared with experimental data in Figures 11A and 11B. The drag and center of pressure are shown in 11A and the normal force coefficient derivative in 11B. Excellent agreement with experiment is obtained for normal force and center of pressure. The theoretical drag is about ten percent high at transonic Mach numbers but according to Reference 5, the blockage of the test model in the wind tunnel was too high. Normally when the wind tunnel model is too large (too much blockage), drag values measured in the transonic Mach range fall off and it appears that this may have happened in this case to account for some of the above discrepency.
27
050
'0. 025
00 40
20
00 5 4
I
o o
3
c 9
0 -
0.5
LO
1.5
2.0
25
MACH NUMBER *~ MQO FIGURE 10 Comparison Thaory and Tatt Data for 6754 Rip Proitctile
28
0.6 r
/N
THEORY A EXPERIMENTAL
'
0.4 -
0.2 -
I ..
81-
2.3
4.3 0.5
8.5
0.5
1.0 M oo
1.5
20
FIGURE 11(A) Drag and Center of Prewure for a Typical Missile Configuration; /R 4.S 29
2 -
24 -
20
A
i 1.0
THEORY A EXPERIMENT
Ot
04 -
i O.S
1
1.6
1 2.0
1 2.5
Moo
FIGURE 1KB) Normal Fore Cotfficfont Darivativ for a Typical Miaail Configuration; >R-4.5 30
The third geometry considered is a very general canard-body-tail shown schematically in Figure I2A along with the normal force and center of pressure. Note that the tail does not have streamwise tips so the total wing area is again computed and an equivalent span calculated based on the chord and wing area. This gives reasonable values for normal force and center of pressure (Figure 12A). although it appears the tail alone lift is about ten percent too high causing a rearward shift in the center of pressure. The drag of the body alone, along with the canard and tail components, is shown in Figure 12B. The body alone drag agrees well with experiment in subsonic and supersonic flow but is unacceptable in transonic flow. This is because of the sixty percent blunt nose which the empirical transonic drag methodology does not account for. The wing drag is also high in transonic flow, but this is caused by the increase in body base pressure due to the presence of tail surfaces. This increase in drag is included in the curves at the bottom of Figure I2B. The empirical estimates of the body base pressure change due to fins is much higher for this case than the data suggest. However, the total configuration drag agrees with experiment within the accuracy bounds previously set forth, except in transonic flow.
31
THEORY
'N
FROM BASE)
FIGURE 12(A) Normal Force and Center of Pressure of A Missile Configuration; 4). -4, /R_ -2, M =1.6 32
0.8
.7A
06
SO;-
Co.
0.4
Q*/
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0.5 I
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2.5
0-21- TAIL
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O
+
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2.0
2.5
REFERENCES 1. Moore, F. G., Aerodynamics of Guided and Ungulded Weapons: Part I - Theory and Application. NWL Technical Report TR-3018, December 1973. Moore, F. G., Body Alone Aerodynamics of Guided and Ungulded Prvfectlles at Subsonic, Transonic, and Suppersonlc Mach Numbers. NWL Technical Report TR-2796, November 1972. Nielsen, J. N. and W. C. Pitts, Wing-Body Interference at Supersonic Spreds With an Application to Combinations With Retangular Wings. NACA Technical Note TN-2677, 1952. Douglass Aircraft Co., Inc., USAF Stability and Control DATCOM, Revisions by Wright Patterson Air Force Base, July 1963, 2 Vols. Touch, L. M., Transonic Wall Interference Effects on Bodies of Revolution. AIAA Paper No. 72-1008.
2.
3.
4.
5.
APPENDIX A Glossary
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41 /R, CD CL CM CM CN Cv,
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