AIAA-2002-3266

The Interaction Between Canards and Thick Bodies:

Implementation in the Missile Datcom Code

Eugene Shistik* and Asher Sigal**

Rafael, Haifa 31021, Israel

Abstract

A capability to include the effects of the vortex wake created by a canard unit on canard-thick-body-tail configurations was incorporated in the Missile Datcom code. A potential vortex tracker, that considers the mutual effects of up to four free vortices and their images and the effect of a variable body diameter, replaces the original tracker. A subroutine that evaluates the normal-force distribution, induced by the vortex wake on the body, was added. The estimation of wing-tail interference uses vortex location at the tail plane as obtained by the new tracker. Comparisons between predictions obtained by the modified code, the original code, and wind tunnel test data, for a variety of configurations, show that the new features considerably improve the agreement between predictions and test data.

Nomenclature

CL lift coefficient CN normal-force coefficient Cm pitching-moment coefficient f lateral position of a free vortex g lateral position of an image vortex L lift force M Mach number r body radius SR reference area v, w velocity components in the cross-flow

plan Vo free-stream velocity W complex potential, φ+iψ x longitudinal coordinate Greek α angle of attack Γ circulation δ canard deflection ζ complex coordinate in the cross-flow plan ρ air density φ, ψ potential, stream function Indices c canard C body cross-flow D body variable diameter FV, IV free, image vortex * Aerospace engineer. ** Fellow; Associate Fellow, AIAA. Copyright © 2002 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.

Introduction The first part of this study, Ref. 1, describes wind tunnel tests of a modular model consisting of a canard unit, that is mounted on a thin forebody, and five interchangeable main thick bodies. It analyses the characteristics of the canard unit and of the bodies alone. The following part, Ref. 2, identifies the interactions between the canard vortex wake and the thickenings and the boattails of the main bodies. An approximate analysis, that uses slender body theory to estimate the radial displacement of the free vortices as they trail along the body, was used. Then, the classic Pitts, Nielsen and Kaattari3 (P-N-K) methodology was used to evaluate the normal force distribution, induced by the canard vortices on body sections having a variable diameter. This analysis is valid for small angles of attack and weak vortices. It was verified by comparing predictions of these interactions with the test data of Ref. 1. Ref. 2 also applies the approximate analysis to four configurations that feature canards which are mounted upstream of body sections with variable diameter. The 1997 version of the Missile Datcom (M-Dat) code, Ref. 4, was used to obtain the longitudinal characteristics of the configurations and of their components. Then,

the effects of the trailing canard vortices on the bodies were manually added as corrections to the predictions by the code. It was found that the correction considerably improved agreement between estimated results and experimentally obtained data.

20th AIAA Applied Aerodynamics Conference24-26 June 2002, St. Louis, Missouri

AIAA 2002-3266

Copyright © 2002 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.

The objectives of this part of the study are: a) To expand the present method to medium angles of attack and strong vortices by using an accurate vortex tracker; b) To implement the vortex tracker and a subroutine that estimates the effects of canard vortices on bodies in the M-Dat code; and c) To compare predictions by the modified and original versions of the code with available test data in order to evaluate the capability of the methodology to improve the accuracy of the predictions.

Implementation Since the emphasis of this work is on configurations that have bodies with variable diameter, (i. e. thickenings, flares or boattails) two modifications of the M-Dat code are needed. First, a tracker that considers, among other influences, variable body thickness, should replace the existing vortex tracker, which assumes that all free vortices trail in the direction of the free stream. Second, the normal-force induced by the vortex wake should be added to the code. The addition of these features maintains the component buildup (CBU) concept of the code.

The Vortex Tracker

A two-dimensional potential vortex tracker was selected. It considers four factors that affect the trajectories of the vortices: a) mutual interference; b) body cross-flow; and c) contribution of variable body diameter. The analysis of the first two effects follows Rogers, 5 Spreiter and Sacks,6 and Nielsen,7 and that of the third effect is based on Portnoy8 and Sigal.2 The present tracker considers up to four free vortices and their images.

DIVnFVnnC WWWWiW )())(()(()()(4

1ζζζζϕφζ ++Σ+=+=

=

(1)

Where

)(sin)(2

0ζ

ζαζriVW C −−=

(2)

)log(2

)( nFVniW ζζπ

ζ −Γ

−= (3)

)log(2

)(2

nIVn

riWζ

ζπ

ζ −Γ

= (4)

ζαζ logcos)( 0VdxdrrW D = (5)

The velocity components in the cross-plan are derived from the complex potential by

( )FVnnn WWddiwv

n

)()(lim ζζζζζ

−=−

→

(6)

The trajectories of the vortices are obtained by integrating Eq. (6) from their origin, at the trailing edge of the canards, (or wings) to the center of pressure location of the tail.

Direct Added Normal-Force Acting on the Body

The P-N-K3 original CBU methodology analyzes the normal-force induced by the vortices originated by forward lifting surfaces on afterbodies. (This contribution is not considered by the M-Dat code.)

cgfVL )(2 0 −Γ= ρ (7)

In the present work, the analysis is performed individually for each panel of the canard unit. Thus the relationship between the circulation and the lift of a single panel is

c

Lc

gfSCV

)(20

−=Γ (8)

The additional lift induced on a body segment located downstream of the canards is

)(0 gfVL −Γ∆−=∆ ρ (9)

where ∆(f-g) is the change of (f-g) along this body section. The non dimensional form of Eq. (9) is

RL SV

gfC0

)(2 −Γ∆−=∆ (10)

The added lift induced by a single free vortex and its image, consisting of k segments, is

n

k

nR

L gfSV

C )(21

0

−∆ΣΓ−

==

(11)

The additional pitching-moment is calculated by multiplying ∆CL by the distance to the moment reference center, normalized by reference length.

Modification of the Missile Datcom Code

The features described above were implemented into the 1997 version of the M-Dat code, Ref. 4. The modifications were made in the SYNTHS routine, which performs CBU analysis, within the major AERO routine, that calculates the aerodynamic coefficients.

The SYNTHS routine of the M-Dat code includes a method for calculating the effects of downwash on aft lifting surfaces, due to vortices generated by forward fins. As previously mentioned, the code follows Ref. 3 and assumes that the free vortices trail in the free stream direction. The analysis is implemented in three subroutines: SFWRW that calculates the lateral position of vortex origin, SVTRAK that calculates the horizontal and vertical locations of vortices at the tail center of pressure,

and VRINTS that calculates the tail interference factor (following Appendix B of Ref. 3). These subroutines were modified to accommodate the new tracker. The following subroutines were added:

• VORPATH – This routine uses the normal force that acts on the individual panels of the canard unit and the points of vortex origins to calculate the strength and trajectories of the vortices. The lateral velocities of a vortex are calculated, at each iteration, by the subroutine VORVEL.

• VORBODINF – This routine calculates the added loads induced by the vortex wake on the afterbody. It uses the vortex trajectories computed by VORPATH as input. The results are added to the previously calculated body alone coefficients.

• SVTRAK_NEW – This subroutine (based on the original SVTRAK) computes the same parameters as the original subroutine, but uses the vortex trajectories computed by VORPATH as input, rather than those calculated by the original code.

Two new output units were added added to the code. The first contains the vortex trajectories, (For013) and the second contains the additional loads distributions on the afterbody. (For014) The modified code will be referred to as Mod. M-Dat.

Validation The modified code is validated using the Mod. M-Dat and M-Dat codes to analyze a variety of configurations that feature canards and variable body diameter, and comparing the results with experimentally obtained data.

Canard-Thick-Body Configurations

Two of the configurations that were tested by Sigal and Victor1 at a Mach number of 0.8 were analyzed first. Their schematic is depicted in Fig. 1. The diameter of their main bodies is double that of the forebody, on which the canards are mounted. This diameter is the mid value, among those tested in Ref. 1. Canard inclusive span to body diameter is 4.0. Configuration b-C-B20 has a plain afterbody, while b-C-B20bt features a 5 deg. boattail. Reference length and area are forebody diameter and cross-sectional area, respectively. The reference point for the pitching moment is the interface plane between the forebody and the main body. It should be noted that Ref. 1 compared the dependence of the normal-force coefficient of the canard unit (forebody and canards) on angle of attack and canard deflection with estimates by the M-Dat code. It was observed that the code over-

predicted the normal-force curve slope and the values of the normal-force at high angles of attack.

Option 2 for body geometry input of the M-Dat code was selected for most of the present study. This option inputs body contour line by coordinates, thus enabling accurate presentation of the thickening of the main bodies. The three parts of Fig. 2 show the vortex wake for configurations b-C+-B20bt, at an angle of attack of 8 deg. (The lines emerging from the vertical canards are streamlines rather than vortex lines.) The outward shift of the free vortices around the thickening of the main body is apparent. The effect of body cross flow is seen along the aft part of the forebody and the cylindrical part of the main body. There is an inward shift of the trajectories along the boattail. This effect is strongest for the lower vortices with the canards in the x position, as they are closest to the boattail. The matching additional normal-force and pitching-moment distributions are presented in Fig. 3. The loads on the thickenings of the main body are negative, (downwash.) those acting on the main body are slightly positive, and the boattails produce positive normal-force. These findings reflect the horizontal shift of the trajectories along the bodies.

For the plain (no boattail) configuration, at both roll orientations, the Mod. M-Dat estimate of CN due to canard deflection is lower that that of the original code, and in better agreement with test data. The Mod. M-Dat code predicts a slightly smaller CNα than that of the M-Dat, in agreement with the trend of the data. At large angles of attack, a gap develops, which reflects the gap associated with the prediction of the characteristics of the canard unit by the M-Dat code. The predictions of the pitching-moment coefficients, due to canard deflection, by the Mod. M-Dat code is larger than those obtained from the M-Dat code, and are in very good agreement with test data. As angle of attack increases, the modified code follows the trends of the data, but in a few cases a gap remains.

Comparisons between predictions and test data for configuration b-C-B20bt, at the + and x canard positions are presented in Figs. 4 and 5, respectively. The modified code predicts smaller CN due to canard deflections, relative to the original code, what improves agreement with test data. As the angle of attack increases, results of the two codes become closer, and deviate from the data, as mentioned before. The Mod. M-Dat estimate of Cm due to canard deflection is smaller than that of the original code and is in very good agreement with the test data. This result reflects the

positive load, predicted only by the Mod. M-Dat, acting on the boattail. Generally, the modified code improves Cm agreement with test data at high angles of attack. One exception is configuration b-Cx-B20bt, with 12 deg. canard deflection. The normal-force and pitching-moment coefficients, due to canard deflection, for the two configurations at the two roll orientations are presented in Appendix A. The average gaps obtained by the M-Dat and the Mod. M-Dat codes are 18.4% and 9.4% for CN, and 13.7 and 3.3 for Cm, respectively.

Configurations b-C+-B20 and b-Cx-B20 were also analyzed using Option 1 for body geometry. An equivalent ogive, that maintains forebody diameter at the plane of the middle of the root chord represented the actual front end of the bodies. The findings from these runs are very similar to those obtained by Option 2.

Canard-Body-Flare Configurations

Spearman and Robinson9 tested several canard-body-flare configurations at a Mach number of 2.01. The family of configurations, having a 10 deg. flare as stabilizer, was selected for the present study. It consists of three body noses: sharp tangent ogive; partially blunted; and hemispherical. The geometry and designation of the noses are shown in Fig. 6. The canards were mounted at the + position and the horizontal ones were deflected at 0.0, 10.0, and 20.0 deg. The reference length and area for the aerodynamic coefficients are center-body diameter and cross sectional area, respectively. The reference point for moments is the middle of each body.

The canard vortex trajectories for configuration BN1-C1-FL10 at an angle of attack of 8 deg. are shown in Fig. 7. A spread of the trailing vortices around the flare is apparent. Fig. 8 presents the distributions of the added normal-force and pitching-moment coefficients. As expected, the flare produces a down load. (down-wash) Comparisons between predicted longitudinal characteristics, obtained by both codes, and test data are shown in Fig. 9. Similar findings were observed with the two other body shapes. The Mod. M-Dat predictions of the normal-force coefficients due to canard deflection are lower than those predicted by the original code and are in better agreement with the test data. Predictions of the pitching-moment coefficient due to canard deflection are much larger (configuration N1-B-C-FL10) to larger (configurations N2-B-C-FL10 and N3-B-C-FL10) than those obtained by the basic code, and are in very good agreement with the data. As angles of attack increase, the differences

between the two predictions of CN decrease, and both codes overestimate the test data. The pitching-moment curve slopes as estimated by the Mod. M-Dat are larger than those obtained from the M-Dat code, and are in better agreement with the experimentally obtained slopes. Predictions by the Mod. M-Dat are in better agreement with the test data than those by the M-Dat, at large angles of attack. Appendix B summarizes the normal-force and pitching-moment coefficients, due to canard deflection, at zero angle of attack. The average errors obtained by the M-Dat and the Mod. M-Dat codes are 37.4% and 24.0% for CN, and 48.2 and 21.5 for Cm, respectively. As in the previous case, the advantage of the added features is apparent.

Canard Controlled Missile

Kassner and Wettlaufer10 investigated the aerodynamic characteristics of a modular canard-body-tail model, with emphasis on the effects of canard location on these characteristics. The configuration that features a small forward canard (B-C3-T1) was selected for this study. A schematic of this configuration ais depicted in Fig. 10.

Trajectories of the vortices are presented in Fig. 11 for M=1.5 and angle of attack of 8 deg. The free vortices are shifted outward, along the aft section of the ogive, due the thickening of the nose. Along the cylindrical main body the cross flow dominates and inward shift can be seen.

Analysis of canard-body combination showed little difference between the two codes, and good agreement with the data. This finding reflects the fact that the canard is small, and so is its contribution to the characteristics of the whole (tailless) configuration.

Comparison between predicted longitudinal characteristics and test data for configuration B-C3-T1 is shown in Fig. 13. The difference between the two predictions of the normal-force coefficients is small, as argued above. The pitching-moment coefficient vs. angle of attack curves, as obtained by the M-Dat show a local hump at a small negative angle of attack. There, the canard vortices are closest to the tail and their influence is strongest. The Mod. M-Dat improves the agreement of the pitching-moment caused by canard deflection, at zero angle of attack. The local hump is shifted slightly to small positive angles of attack. These reflect the improvement in the

prediction of the location of the vortices in the vicinity of the tail.

Concluding Remarks The Missile Datcom code was modified in order to include features that can analyze canard-body-tail configurations, having bodies with a variable diameter.

Results of analysis using the modified and the original codes were compared with available test data, for configurations that feature variable diameter main body. It was found that the new capabilities improve the accuracy of predicting the longitudinal and the control characteristics of variety of configurations.

References

1. Sigal, A., and Victor, M., “The Interactions Between a Canard and Thick Bodies: Characteristics of the Components,” Journal of Spacecraft and Rockets, Vol. 38, No. 6, Nov.-Dec. 2001, pp. 882-887.

2. Sigal, A., “The Interactions Between a Canard and Thick Bodies: Analysis and Applications,” Journal of Spacecraft and Rockets, Vol. 38, No. 6, Nov.-Dec. 2001, pp. 888-896.

3. Pitts, W. C., Nielsen, J. N., and Kaattari, G. E., “Lift and Center of Pressure of Wing-Body-Tail Combinations at Subsonic, Transonic and Supersonic Speeds,” NACA Report 1307, 1957.

4. Blake, W. B., “Missile Datcom: User’s Manual – 1997 Fortran 90 revision,” USAF Research Laboratory, Report AFRL-VA-WP-TR-1988-3009, Wright-Patterson AFB, OH, Feb. 1998.

5. Rogers, A. W., “Application of Two-Dimensional Vortex Theory to the Predication of Flow Behind Wings of Wing-Body Combinations at Subsonic and Supersonic Speeds”, NACA TN 3227, 1954.

6. Spreiter, J. R., and Sacks, A. H., A Theoretical Study of the Aerodynamics of Slender Cruciform-Wing Arrangements and their Wakes”, NACA Rept. 1296, 1957.

7. Nielsen, J. N., “Missile Aerodynamics,” NEAR Inc., Mountain View, CA, 1988.

8. Portnoy, H., “Calculation of the Aerodynamic Forces and Moments on Complex Cruciformed-Winged Missile Configurations up to Intermediate Angles of Attack”, Israel Journal of Technology, Vol. 23, Nos. 1-2, 1986, pp.33-46.

9. Spearman, M. L., and Robinson, R. B., “Longitudinal Stability and Control Characteristics of a Winged and Flared Hypersonic Missile Configuration at a Mach Numbers 2.01,” NASA TM X-693, 1962.

10. Kassner, D. L., and Wettlaufer, B, ”Effects of Canard Location on the Aerodynamic Characteristics of a Sharp-Nosed Missile at Mach Numbers of 1.5 and 2.0,” NASA TM 73,221, Sep. 1977.

Appendix A: The normal-force and pitching-moment coefficients due to canard deflection, canard-body configurations,1 α=0.

Table A.1 Canards at the + position

δ → 6 deg. 12 deg. Source CN (% error) Cm (% error) CN (% error) Cm (% error)

WT Data 1.75 5.8 3.15 12.5 M-Dat 2.05 (17.4%) 5.09 (12.2%) 4.32 (37.0%) 10.70 (14.4%)

bC+B

20

Mod. M-Dat 1.84 (5.3%) 5.52 (4.8%) 3.76 (19.5%) 12.74 (1.95%)

WT Data 1.9 4.4 3.35 10

M-Dat 2.05 (8.1%) 5.09 (15.8%) 4.32 (28.8%) 10.70 (7.0%)

bC+B

20bt

Mod. M-Dat 1.94 (2.2%) 4.36 (0.9%) 3.94 (17.5%) 10.45 (4.5%)

Table A.2 Canards at the x position

δ → 6 deg. 12 deg. Source CN (% error) Cm (% error) CN (% error) Cm (% error)

WT Data 2.7 7.8 4.9 15.6 M-Dat 2.91 (7.6%) 7.20 (7.7%) 6.10 (24.6%) 15.13 (3.0%)

bCxB

20

Mod. M-Dat 2.66 (1.6%) 7.49 (4.0%) 5.60 (14.3%) 15.71 (0.7%)

WT Data 2.8 6 5.1 11.7

M-Dat 2.91 (3.8%) 7.20 (20.1%) 6.10 (19.7%) 15.13 (29.4%)

bCxB

20bt

Mod. M-Dat 2.79 (0.5%) 5.84 (2.6%) 5.84 (14.6%) 12.47 (6.6%)

Appendix B: The normal-force and pitching-moment coefficients due to canard deflection, canard-body-flare configurations,6 α=0.

Table B.1 Configuration BN1-C-FL10

δ → 10 deg. 20 deg. CN (%error) Cm (%error) CN (%err.) Cm (%error)

WT Data 0.5 0.7 1.3 1.1

M-Dat 0.794 (58.8%) 0.15 (79.1%) 1.626 (25.1%) 0.30(72.9%)

BN1-

C-F10

Mod. M-Dat 0.701 (40.2%) 0.51 (27.0%) 1.424 (9.5%) 1.06 (3.5%)

Table B.2 Configuration BN2-C-FL10

δ → 10 deg. 20 deg. CN (% error) Cm (% error) CN (% error) Cm (% error)

WT Data 0.75 0.5 1 2

M-Dat 0.796 (6.1%) 0.49 (1.4%) 1.630 (63.0%) 1.01 (49.5%)

BN

2-C

-F10

Mod. M-Dat 0.703 (6.3%) 0.82 (63.2%) 1.428 (42.8%) 1.68 (15.9%)

Table B.3 Configuration BN3-C-FL10

δ → 10 deg. 20 deg. CN (% error) Cm (% error) CN (% error) Cm (% error)

WT Data 0.55 1.35 1 2.55

M-Dat 0.796 (44.7%) 1.01 (25.3%) 1.630 (63.0%) 2.06 (19.1%)

BN

3-C

-F10

Mod. M-Dat 0.703 (27.8%) 1.27 (5.9%) 1.428 (42.8%) 2.61 (2.2%)

Table B.4 Configuration BN1-C-FL5

δ → 10 deg. 20 deg. CN (% error) Cm (% error) CN (% error) Cm (% error)

WT Data 0.7 0.6 1.3 0.8

M-Dat 0.794 (13.4%) 0.15 (75.7%) 1.626 (25.1%) 0.30 (62.8%)

BN1-

C-F

5

Mod. M-Dat 0.746 (6.6%) 0.33 (44.5%) 1.509 (16.1%) 0.72 (9.9%)

Fig. 1 Schematic of canard-thick-body configuration.1

a)

b)

c)

Fig. 2 Vortex trajectories for configurationbC+B20bt at M=0.8, α=8o, δ=0o: a) Sideview; b) Top view; and c) Back View.

-0.03

-0.02

-0.01

0

0.01

0.02

11 16 21 26 31 36 41 46

CL

Dis

trib

utio

n

CL DistributionBody contour

a)

-0.16

-0.12

-0.08

-0.04

0

0.04

0.08

11 16 21 26 31 36 41 46

Cm

Dis

trib

utio

n

CM DistributionBody contourXref

b)

Fig. 3 Distribution of the additional normal-force and pitching-moment coefficients

acting on the main body, configutation bC+B20bt at M=0.8, α=8o, δ=0o: a) Additional lift force; and b) Additional pitching moment.

a) b)

Fig. 4 Comparison of longitudinal aerodynamic coefficients of configuration bC+C20bt at M=0.8: a) Normal force; and b) Pitching moment.

0

2

4

6

8

10

12

0 3 6 9 12αααα [deg]

CN

M-Dat.

Mod. M-Dat.

WT Data, del.=0 [deg]

WT Data, del.=6 [deg]

WT Data, del.=12 [deg]

0

3

6

9

12

15

18

21

24

0 3 6 9 12αααα [deg]

Cm

a) b)

Fig. 5 Comparison of longitudinal aerodynamic coefficients of configuration bCxC20bt at M=0.8: a) Normal force; and b) Pitching moment.

Fig. 6 Schematic of canard-body-flare configurations.9

0

2

4

6

8

10

12

14

16

0 3 6 9 12αααα [deg]

CN

M-Dat.

Mod. M-Dat.

WT Data, del.=0 [deg]

WT Data, del.=6 [deg]

WT Data, del.=12 [deg]

0

5

10

15

20

25

30

35

40

0 3 6 9 12αααα [deg]

Cm

a)

b)

c)

-0.004

-0.002

0

0.002

15 17 19 21 23 25 27 29 31

CL D

istr

ibut

ion

CL DistributionBody contour

a)

-0.03

-0.02

-0.01

0

0.01

0.02

15 17 19 21 23 25 27 29 31

Cm

Dis

trib

utio

n

CM DistributionBody contourXref

b)

Fig. 8 Distribution of the additional normal-force and pitching-moment coefficients acting on the main body, configuration N1-B-C-F10 at M=2.01, α=8o,

δ=0o: a) Additional lift force; and b) Additional pitching moment.

Fig. 7 Vortex trajectories for configuration N1-B-C-F10 at M=2.01, α=8o, δ=0o: a) Side view;b) Top view; and c) Back view.

a) b)

Fig. 9 Comparison of the longitudinal aerodynamic coefficients of configuration N1-B-C-F10 at M=2.01: a) Normal force; and b) Pitching moment.

Fig. 10 Schematic of canard controlled missile.10

0

1

2

3

4

5

6

7

8

9

-4 0 4 8 12 16 20 24αααα [deg]

CN

M-Dat.

Mod. M-Dat.

WT Data, del.=0 [deg]

WT Data, del.=10 [deg]

WT Data, del.=20 [deg]

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

-4 0 4 8 12 16 20 24

αααα [deg]

Cm

a)

b)

c)

a) b) (a) (b)

Fig. 13 Comparison of the longitudinal aerodynamic coefficients of configuration

BN1-C3-T1 at M=1.5: a) Normal force; and b) Pitching moment.

Fig. 11 Vortex trajectories for configurationBN1-C3-T1 at M=2.01, α=8o, δ=0o: a) Sideview; b) Top view; and c) Back view.

-3

-2.5

-2

-1.5

-1

-0.5

0

0.5

1

1.5

-2 0 2 4 6 8 10

αααα [deg]

Cm

-0.5

0

0.5

1

1.5

2

2.5

-2 0 2 4 6 8 10 12

αααα [deg]

CN

M-Dat.

Mod. M-Dat.

WT Data, del.=0 [deg]

WT Data, del.=6 [deg]

WT Data, del.=12 [deg]