artillery precision guided munition airframe definitionwhere guidance and control elements will be...

Artillery precision guided munition

airframe definitionBallistic performance

N. HamelF. C. WongDRDC Valcartier

Defence R&D Canada – ValcartierTechnical Report

DRDC Valcartier TR 2008-287April 2009

Artillery precision guided munition airframe definition Ballistic performance

N. Hamel F. C. Wong DRDC Valcartier

Defence R&D Canada Valcartier Technical Report DRDC Valcartier TR 2008-287 April 2009

Author

Nicolas Hamel, Franklin Wong

Approved by

Alexandre Jouan

Section Head, Precision Weapons

Approved for release by

Christian Carrier

Chief Scientist

This work was performed at DRDC Valcartier between April 2006 and February 2007, under WBE 12qj04, “Artillery Precision Guided Munitions External Aerodynamics”.

Terms of release: The information contained herein is proprietary to Her Majesty and is provided to the recipient on the understanding that it will be used for information and evaluation purposes only. Any commercial use including use for manufacture is prohibited. Release to third parties of this publication or information contained herein is prohibited without the prior written consent of Defence R&D Canada.

© Her Majesty the Queen as represented by the Minister of National Defence, 2009

© Sa majesté la reine, représentée par le ministre de la Défense nationale, 2009

DRDC Valcartier TR 2008-287 i

Abstract As stated in the Defence Policy, Canada must have a full spectrum of capabilities to make meaningful contributions in multilateral overseas operations that are aimed at stabilizing failed or failing states. The Canadian Forces is gradually acquiring precision strike capabilities in its gun-launched indirect fire weapon systems, since transformation documents support the acquisition of this kind of capability. DRDC initiated the project entitled “Concept Development of Artillery Precision Guided Munitions” to respond to and support the CF in making difficult performance-based choices and decisions on sub-155 mm artillery precision guided munitions. The objective of this study was to identify promising airframe geometries that could contribute to extending the range of an APGM through reduced drag and increased lift. A parametric analysis of the six candidate projectile configurations and their variants was carried out. It was found that none of the six candidate projectile configurations exhibited any obvious undesirable ballistic characteristics, so all six configurations should be carried forward to a follow-on study where guidance and control elements will be added before re-evaluation.

Résumé Comme énoncé dans la politique de défense, le Canada doit avoir une gamme complète de capacités afin d’apporter une contribution significative aux opérations multilatérales à l'étranger qui visent à stabiliser les États défaillants ou en déroute. Les Forces canadiennes acquièrent petit à petit des capacités d’attaque de précision à partir de systèmes d’armes à tir indirect depuis que les documents sur la transformation soutiennent l'acquisition de ce type de capacité. RDDC a entrepris le projet intitulé "Développement de concepts de munitions guidées de précision tirées par canon " ayant pour but d’assister et de soutenir les FC lors de prises de décisions basées sur les performances des munitions guidées de précision tirées par canon de calibre inférieur à 155 mm. L'objectif de cette étude était d'identifier les géométries prometteuses de projectiles qui pourraient contribuer à augmenter la portée d’une MGPC grâce à la réduction de la traînée et à l'augmentation de la portance. Une analyse paramétrique de six configurations de projectiles candidats et leurs variantes a été effectuée. On a constaté qu'aucune des six configurations de projectiles n’a affiché de caractéristiques balistiques fortement indésirables de sorte que toutes les configurations devraient être référées à une étude suivante où des éléments de guidage et de contrôle seront ajoutés avant d'être réévalués.

ii DRDC Valcartier TR 2008-287

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DRDC Valcartier TR 2008-287 iii

Executive summary

As stated in the Defence Policy, Canada must have a full spectrum of capabilities to make meaningful contributions in multilateral overseas operations that are aimed at stabilizing failed or failing states. In this context, Defence Strategy 2020 identified modernization as a key attribute to preparing the Canadian Forces (CF) for the 21st century. The CF is gradually acquiring precision strike capabilities in its gun-launched indirect fire weapon systems, since transformation documents support the acquisition of this kind of capability. As well, development of advanced warheads could significantly improve the performance of smaller calibre munitions in the near future. These facts have motivated the CF to sponsor a study to examine the options and requirements for smaller calibre APGM packages. DRDC initiated the project entitled “Concept Development of Artillery Precision Guided Munitions” to respond to and support the CF in making difficult performance-based choices and decisions on sub-155 mm APGM. The research effort examines the effects of guidance and control hardware such as inertial measurement units (IMU), Global Positioning System (GPS), electromechanical actuation systems, and conventional and novel airframes on the precision and range of guided munition concepts. The objective of this study was to identify promising airframe geometries that could contribute to extending the range of an APGM through reduced drag and increased lift. The DRDC Munition Model Component Library was used in conjunction with DATCOM to carry out a parametric analysis of the six projectile configurations and their variants. The parameters were muzzle velocity, gun elevation, projectile mass and projectile stability margin. Range, for ballistic flight, was used as the metric for performance. The ranking, from longest to shortest range, based on configuration type was: 1) Type B - high L/D, 2) Type D - robust, 3) Type A - low drag, 4) Type C - maneuverable, 5) Reference B - LCCCF, and 6) Reference A - pseudo-Excalibur. Since none of the six candidate projectile configurations exhibited any obvious undesirable ballistic characteristics, all six configurations should be carried forward to the follow-on study where guidance and control elements will be added before re-evaluation.

Artillery precision guided munition airframe definition – Ballistic performance Hamel, N., Wong, F.; DRDC Valcartier TR 2008-287, Defence R&D Canada –Valcartier; April 2009

iv DRDC Valcartier TR 2008-287

Sommaire

Comme énoncé dans la politique de défense, le Canada doit avoir une gamme complète de capacités afin d’apporter une contribution significative aux opérations multilatérales à l'étranger qui visent à stabiliser les États défaillants ou en déroute. Dans ce contexte, la stratégie de Défense 2020 a défini la modernisation comme un attribut essentiel afin de préparer les Forces canadiennes (FC) au 21e siècle. Les Forces canadiennes acquièrent petit à petit des capacités d’attaque de précision à partir de systèmes d’armes à tir indirect depuis que les documents sur la transformation soutiennent l'acquisition de ce type de capacité. De plus, le développement d’ogives avancées permettra, dans un proche avenir, d’améliorer les performances des munitions de petit calibre de manière significative. Ces faits ont incité les FC à parrainer une étude visant à examiner les options et les exigences des munitions guidées de précision tirées par canon (MGPC) de plus petit calibre. RDDC a entrepris le projet intitulé "Développement de concepts de munitions guidées de précision tirées par canon" ayant pour but d’assister et de soutenir les FC lors de prises de décisions basées sur les performances des munitions guidées de précision tirées par canon de calibre inférieur à 155 mm. L'effort de recherche examine l’influence qu’ont sur la précision et la portée des concepts munitions guidées le matériel de guidage et de contrôle comme les Unités de mesure inertielle (IMU), Global Positioning System (GPS), les systèmes d’actionnement électromécanique, ainsi que les formes de projectiles conventionnelles et novatrices. L'objectif de cette étude était d'identifier les géométries prometteuses de projectiles qui pourraient contribuer à augmenter la portée d’une MGPC grâce à la réduction de la traînée et à l'augmentation de la portance. Le «DRDC Munition Model Component Library» a été utilisé conjointement avec DATCOM pour procéder à une analyse paramétrique des six configurations de projectiles et leurs variantes. Les paramètres étaient la vitesse à la bouche du canon, l'élévation du canon, la masse du projectile et la marge de stabilité du projectile. La portée du vol balistique a été utilisée comme paramètre de performance. Le classement, de la plus longue à la plus courte portée, selon la configuration type, était: 1) Type B - L/D élevé, 2) Type D - robuste, 3) Type A - faible traînée, 4) Type C - manœuvrable, 5) Référence B - LCCCF, et 6) Référence A - pseudo-Excalibur. Étant donné qu'aucune des six configurations de projectiles n’a affiché de caractéristiques balistiques fortement indésirables, toutes les configurations devraient être référées à une étude suivante où les cas des éléments de guidage et de contrôle seront ajoutés avant d'être réévalués.

Artillery precision guided munition airframe definition – Ballistic performance Hamel, N., Wong, F.; DRDC Valcartier TR 2008-287, R&D pour la Défense Canada –Valcartier; Avril 2009

DRDC Valcartier TR 2008-287 v

Table of contents

Abstract........................................................................................................................................ i

Executive summary ................................................................................................................... iii

Sommaire................................................................................................................................... iv

Table of contents ........................................................................................................................ v

List of figures ........................................................................................................................... vii

List of tables ............................................................................................................................... x

Acknowledgements ................................................................................................................... xi

1. Introduction ................................................................................................................... 1

2. Aerodynamic Projectile Components ............................................................................ 2 2.1 Problem Definition ........................................................................................... 2 2.2 Fore-Body Geometries ..................................................................................... 5 2.3 Nose Geometries .............................................................................................. 6 2.4 Mid-body Geometries....................................................................................... 9 2.5 Aft-body Geometries ...................................................................................... 10 2.6 Aerodynamic Surface Geometries.................................................................. 16 2.7 Summary ........................................................................................................ 20

3. Projectile Configuration Definition ............................................................................. 22 3.1 Introduction .................................................................................................... 22 3.2 Reference-A.................................................................................................... 22 3.3 Reference-B.................................................................................................... 22 3.4 Type-A............................................................................................................ 23 3.5 Type-B............................................................................................................ 24 3.6 Type-C............................................................................................................ 24 3.7 Type-D............................................................................................................ 25 3.8 Summary ........................................................................................................ 26

vi DRDC Valcartier TR 2008-287

4. Parametric Ballistic Performance Study...................................................................... 27 4.1 Simulation Environment................................................................................. 27 4.2 Projectile Geometries ..................................................................................... 27 4.3 Initial Conditions ............................................................................................ 28 4.4 Typical Ballistic Results................................................................................. 29

5. Conclusions ................................................................................................................. 35

6. Recommendations ....................................................................................................... 36

7. References ................................................................................................................... 37

Annex A.................................................................................................................................... 39

List of symbols/abbreviations/acronyms/initialisms ................................................................ 53

Distribution list ......................................................................................................................... 55

DRDC Valcartier TR 2008-287 vii

List of figures

Figure 1. Typical projectile trajectory with significant aerodynamic coefficients identified for each phase. See Table 1 for definitions of the coefficients. ................................................ 2

Figure 2. Ogive reference projectile with a) hemispheric nose cap and b) meplat..................... 5

Figure 3. Drag coefficient at zero angle of attack compared to the mach number for the fore body geometries. ................................................................................................................. 6

Figure 4. Simplified nose cone ................................................................................................... 7

Figure 5. Nose shapes with a hemispherical cap. a) ogive, b) von Karman, c) Haack and d) ½ power law nose geometries. ................................................................................................ 8

Figure 6. Drag coefficient at zero angle of attack compare to the mach number for the nose geometries. .......................................................................................................................... 9

Figure 7. Mid-body cross sections a) circular, b) square and c) diamond. ............................... 10

Figure 8. Aft-body type from top to bottom super calibre flare, boattail, mid-body length flare and sting length flare; straight aft body is not shown........................................................ 11

Figure 9. Drag generated by the flare aft body compared to the straight base projectile. ........ 12

Figure 10. Center of pressure measured from the nose tip generated by the flare aft body compared to the straight base projectile. ........................................................................... 12

Figure 11. Drag generated by the boattail aft body compared to the straight base projectile... 13

Figure 12. Center of pressure measured from the nose tip generated by the boattail aft body compared to the straight base projectile. ........................................................................... 14

Figure 13. Drag generated by the sting length flare (SLF) and mid body length flare (MLF) aft body compared to the straight base projectile. .................................................................. 15

Figure 14. Center of pressure measured from the nose tip as generated by the sting length flare (SLF) and mid-body length flare (MLF) aft body compared to the straight base projectile.16

Figure 15. Canard mounted on the reference frame. ................................................................ 17

Figure 16. Wing mounted on the reference frame at the center of gravity............................... 17

Figure 17. Strake mounted on the reference frame at the center of gravity.............................. 18

Figure 18. Tail mounted on the reference frame. ..................................................................... 18

viii DRDC Valcartier TR 2008-287

Figure 19. Drag generated by the different aerodynamic surfaces compared to a clean projectile............................................................................................................................ 19

Figure 20. Center of pressure measured from the nose tip generated by the different aerodynamic surfaces compared to a clean projectile. ...................................................... 19

Figure 21. Lift to drag ratio at Mach 0.75 generated by the different aerodynamic surfaces compared to the clean projectile........................................................................................ 20

Figure 22. Reference-A, Pseudo-Excalibur projectile. ............................................................. 22

Figure 23. Reference-B, LCCCF projectile. ............................................................................. 23

Figure 24. Type-A, Low Drag projectile. ................................................................................. 23

Figure 25. Type-B, Subsonic Glider projectile......................................................................... 24

Figure 26. Type-C, Highly Maneuverable projectile................................................................ 25

Figure 27. Type-D, Robust projectile. ...................................................................................... 26

Figure 28. LG-1 Mk II muzzle velocity.................................................................................... 29

Figure 29. Reference-A ballistic trajectory, CPCG 0.1, Mass 14.7 kg..................................... 30

Figure 30. Kinetic energy, Ek, and momentum, p, as a function of LG-1 interior ballistic curve. ................................................................................................................................. 31

Figure 31. Influence of mass on the maximum range for the Reference-A CPCG 0.1. ........... 32

Figure 32. Ballistic trajectory results for Reference-A CPCG 1.0 calibre ............................... 39



Figure 35. Ballistic trajectory results for Reference-B............................................................. 42

Figure 36. Ballistic trajectory results for Type-A..................................................................... 43

Figure 37. Ballistic trajectory results for Type-B CPCG 1.0 calibre........................................ 44



Figure 40. Ballistic trajectory results for Type-C CPCG 1.0 calibre........................................ 47


DRDC Valcartier TR 2008-287 ix


Figure 43. Ballistic trajectory results for Type-D CPCG 1.0 calibre ....................................... 50



x DRDC Valcartier TR 2008-287

List of tables

Table 1. Definition of aerodynamic coefficients ....................................................................... 3

Table 2. Aerodynamic projectile components examined........................................................... 4

Table 3. Aerodynamic components selected for defining candidate projectile configurations 21

Table 4. Summary of the ballistic projectile configurations studied ........................................ 28

Table 5. Parametric ballistic performance results showing range (m) as a function of elevation angle (deg), muzzle velocity (m/s) and stability margin (calibre) for an elevation of 15 deg. .................................................................................................................................... 32



DRDC Valcartier TR 2008-287 xi

Acknowledgements The authors would like to thank Mr. Vincent Trudel, LTI Inc., for the invaluable help in the production of Munition Model Component Library (MMCL) results and to Mr. Marc Lauzon for discussions and troubleshooting of the MMCL code.

xii DRDC Valcartier TR 2008-287


DRDC Valcartier TR 2008-287 1

1. Introduction The current battlefield deployment depends on a mix of mobile armour and towed artillery. In all cases, with the exception of the 155 mm Excalibur system, the munitions are unguided. In large-scale long-term combat situations, a large quantity of fire, often referred to as a “mountain of metal”, can be directed onto chosen targets. The target will eventually be overwhelmed by the quantity of munitions delivered. There are, however, timeliness and effectiveness issues that make higher precision munition delivery an essential need in combat, peacekeeping and police actions. Precision delivery reduces collateral damage both in terms of structures and loss of life, providing timely and efficient debilitation of the intended target by the use of a small number of accurate rounds, quickly placed on target. In particular, this type of precision capability would enable the Canadian Forces to defend themselves and others effectively against nearby hostile forces during their various missions. As stated in the Defence Policy, Canada must have a full spectrum of capabilities to make meaningful contributions in multilateral overseas operations that are aimed at stabilizing failed or failing states. In this context, Defence Strategy 2020 identified modernization as a key attribute to preparing the Canadian Forces (CF) for the 21st century. The CF is gradually acquiring precision strike capabilities in its gun-launched indirect fire weapon systems, since transformation documents support the acquisition of this kind of capability [1]. As well, development of advanced warheads could significantly improve the performance of smaller calibre munitions in the near future. These facts have motivated the CF to carry out options and requirements analyses for smaller calibre Artillery Precision Guided Munitions (APGM) packages. DRDC initiated the project entitled “Concept Development of Artillery Precision Guided Munitions” to respond to and support the CF in making difficult performance-based choices and decisions on sub-155 mm APGM. The research effort examines the effects of guidance and control hardware such as inertial measurement units (IMU), Global Positioning System (GPS), electromechanical actuation systems, and conventional and novel airframes on the precision and range of guided munition concepts. The objective of this study is to identify promising airframe geometries that could contribute to extending the range of an APGM through reduced drag and increased lift. Section 2 presents the candidate geometries and the aerodynamic performances calculated for the various components that comprise a complete projectile. Section 3 presents the family of projectiles that were conceived based on the results of Section 2. Section 4 discusses the modeling and simulation method used to predict the unguided ballistic trajectory results for the family of projectiles. The study concludes with a selection of the promising airframe geometries for further modeling under guided non-ballistic conditions.

2 DRDC Valcartier TR 2008-287

2. Aerodynamic Projectile Components

2.1 Problem Definition Figure 1 shows the four phases of a typical projectile flight [1]. The most significant aerodynamic coefficients of each phase were identified for use as performance metrics in the parametric study. Ideally, candidate projectile configurations would be composed of component geometries that possessed aerodynamic coefficients that were most appropriate for extended range and maneuverability. The definition of the coefficients are given in Table 1.

Figure 1. Typical projectile trajectory with significant aerodynamic coefficients identified for each phase.

See Table 1 for definitions of the coefficients.


Table 1. Definition of aerodynamic coefficients

Parameter Definition

CD0 Drag Coefficient at CL=0

CLLP Rolling moment coefficient due to roll rate

CNA Normal force coefficient derivative with angle of attack

CMA Pitching moment coefficient derivative with angle of attack

CL Lift Coefficient

CL/CDmax Maximum Lift to drag ratio

CA Axial force coefficient

XCP Center of pressure position, measured from the nose tip, divided by the projectile calibre

CN Normal force coefficient

CM Pitching moment coefficient

The selection of aerodynamic components for defining candidate projectile configurations in Sec. 3 was organized around five components: 1) fore body, 2) nose, 3) body, 4) aft body, and 5) aerodynamic surfaces. Missile Datcom [2] was used in conjunction with Aeroprediction 05 (AP05) [3] to determine the aerodynamic characteristics of each component shape as a function of Mach number. Table 2 summarizes the combinations of component geometries examined in the parametric study. Descriptions of the component geometries and their aerodynamic performance are provided in Section 2.2 to Section 2.6. Section 2.7 summarizes the components selected for defining candidate projectile configurations.


Table 2. Aerodynamic projectile components examined


2.2 Fore-Body Geometries The fore-body of the projectile is defined as the nose tip. Figure 2 shows the two nose shape variations called the hemispherical cap and the meplat. The pointed nose has not been included because of its manufacturing complexity and its fragility when being handled. The reference fore body is the hemispherical cap. The diameter of the meplat or hemispherical cap was kept constant for all configurations at 0.14 calibres.

Figure 2. Ogive reference projectile with a) hemispheric nose cap and b) meplat.

When comparing the meplat results with the reference hemispherical cap results, the meplat can be seen to have little influence for the drag coefficient. In Figure 3, a slight decrease in drag at high supersonic speed is evident. However, an increase in drag in the subsonic and transonic region is also present. Since gun-launched projectiles typically fly a majority of their trajectory in the Mach 0.5 to 1.5 range, the meplat geometry is at disadvantage because its drag is generally higher in this region. Therefore, the hemispheric nose cap was retained for defining candidate projectile configurations.


Figure 3. Drag coefficient at zero angle of attack compared to the mach number for the fore

body geometries.

2.3 Nose Geometries Four nose geometries were considered (see Figure 5). The tangent ogive was used as a reference and compared to the von Karman, Haack and ½ power law geometries. The length of the nose from the nose tip to the base of the nose was 2.94 calibres for all configurations. All noses could be described in terms of an equation. The tangent ogive is the simplest nose cone geometry. It is described by the segment of a circle tangent to the body that is rotated about the body’s longitudinal axis. As sowed in Figure 4, for a given nose length, Lnose, and radius, Rbase, at the base of the nose, the radius that describes the tangent ogive, ρ, is specified by eq. 1. The radius of the nose, r, for any point position along the nose length, x, while x varies from 0 to Lnose, can be calculated from eq. 2. The shortest tangent ogive occurs when Lnose is equal to Rbase which gives the degenerate case of the hemispherical cap.

base

basenose

RRL

2

22 +=ρ (1)

)()( 22 ρρ −+−−= basenose RLxr (2) The shapes of the von Karman and Haack nose shapes are mathematically optimized. The von Karman nose shape is designed to produce the minimum drag for a given length and diameter while the Haack nose shape is designed to produce maximum volume. The nose shapes are described by eqs. 3 and 4.


Figure 4. Simplified nose cone

⎟⎟⎠

⎞⎜⎜⎝

⎛−=

noseLx21arccosθ (3)

π

θθθ 3sin2

)2sin( CRr

base +−= (4)

where C = 1/3 for a Haack nose shape and C = 0 for a von Karman nose shape. The power series nose is created by rotating a parabola (eq. 5) about its axis.

n

nosebase L

xRr ⎟⎟⎠

⎞⎜⎜⎝

⎛= (5)

where n can vary from 0 to 1.


Two interesting cases of this family are worth mentioning. First, if n = 0, the nose would be a flat faced cylinder. Second, if n = 1, the shape of the nose would be conical. In this study, the factor, n, was selected to be 0.5. The nose shape essentially influences the drag coefficient of the projectile. Figure 6 shows the drag coefficient for the nose shapes studied. The ½ power law possesses the lowest drag in the supersonic regime due to its narrower profile. It is also true in the subsonic regime but the differences between geometries are marginal. The two main drawbacks of the ½ power law nose are the increase in drag in the transonic regime and the lower available volume.

Figure 5. Nose shapes with a hemispherical cap. a) ogive, b) von Karman, c) Haack and d) ½ power law

nose geometries.


The three other noses produce almost the same amount of drag. The von Karman geometry is more efficient in the high supersonic range. However, the projectile will not be flying in that regime for a long time. The Haack nose is much like the von Karman nose except that it has more useable space. Therefore, the low drag ½ power law geometry and the spacious Haack geometry were retained for defining candidate projectile configurations.

2.4 Mid-body Geometries The mid-body follows immediately after the nose geometry. Three different types of mid-bodies have been considered (see Figure 7). The circular body shape has been selected as the reference configuration. More unusual shapes include the square cross section and the diamond cross section. The square and diamond diagonals have been size to equal 1 calibre. The mid-body length was constant at 2.44 calibres. Changing the body shape for an artillery projectile is not a trivial matter. If the shape is anything other than a cylinder, new fabrication techniques for the mid-body must be developed. Launching a non-circular mid-body would require a sabot to support the projectile in the gun barrel. Square and diamond shapes have a slight increase in the lift to drag ratio at high Mach number. Due to the lack of the advantages related to the square and diamond shapes, only the cylindrical mid-body was retained for defining candidate projectile configurations.

Figure 6. Drag coefficient at zero angle of attack compare to the mach number for the nose

geometries.


Figure 7. Mid-body cross sections a) circular, b) square and c) diamond.

2.5 Aft-body Geometries The aft body is situated at the back of the projectile. The function of the aft-body is to stabilize the projectile in flight or to reduce the drag. In addition to the straight base projectile, four other types of after bodies were investigated (Figure 7). The total length of the projectile was kept constant with variation of the mid-body length allowed. The length of the aft-body varied from 0 to 2.44 calibres. A straight base was selected as a reference case. Three super calibre flares, three boattails, three mid-body length flares and three sting length flares were evaluated. The length of super calibre flare was held constant to 1.5 calibres for all three cases. In the boattail evaluation, the angle of the boattail was held constant to 8 degrees. The two mid-body and sting aft geometries were a combination of an 8 degree boattail followed by a 45 degree flare. For the mid-body length flare, the boattail and the flare are joined together leaving a mid-body of 1.74 to 0.11 calibres in length. For the sting length flare, the boattail was directly attached to the base of the nose with the flare joined by a sting of 1.74 to 0.11 calibres in length.


Figure 8. Aft-body type from top to bottom super calibre flare, boattail, mid-body length flare and sting

length flare; straight aft body is not shown.

The first aft-body studied is the flare. Flares are typically used to stabilize a projectile. However, flares add some drag to the projectile. Figure 8 shows the drag as a function of Mach number for different flares calibres. Flares are increasing calibre for a 1.0 calibre straight body to 2.0 calibres. The drag increases nonlinearly with flare calibre in the subsonic, transonic, and low supersonic regimes. Figure 9 shows the position of the pressure center relative to the nose tip. The further the center of pressure is from the nose tip, the more stable is the projectile. The figure shows that the flare with the 2.0 calibre base diameter gave the highest stability. Also, fluctuations in the position of pressure center diminished with increasing flare diameter.


Figure 9. Drag generated by the flare aft body compared to the straight base projectile.

Figure 10. Center of pressure measured from the nose tip generated by the flare aft body compared to

the straight base projectile.

Boattails are commonly used on spin stabilized rounds to reduce drag and increase range. Figure 10 shows the drag reduction for various boattail configurations. Since the projectile, described in Sec. 2.1, would fly below Mach 3, the boattail would help in the reduction of the


drag. However, contrary to the flare geometry, the boattail destabilizes the projectile by pushing forward the center of pressure. Figure 11 shows that the boattail affected only the behavior in the transonic and subsonic regimes. So for a non spinning projectile the use of a stabilizing devise would be mandatory to keep the projectile stable in the end of flight phase.

Figure 11. Drag generated by the boattail aft body compared to the straight base projectile.


Figure 12. Center of pressure measured from the nose tip generated by the boattail aft body compared

to the straight base projectile.

To avoid the Xcp shift caused by the use of a boattail, two engraved flares are introduced, the sting length flare (SLF) and mid-body length flare (MLF). Figure 12 shows the drag coefficient at zero degree angle-of-attack (AoA) with respect to Mach number. Each of those configurations increase the drag in the supersonic regime when compared to the reference configuration. The drag generated for a sting length flare or mid-body length flare was the same for a given sting diameter.


Figure 13. Drag generated by the sting length flare (SLF) and mid body length flare (MLF) aft body

compared to the straight base projectile.

The position of the center of pressure is shown in Figure 13. The engraved flares stabilized the projectile over the entire flight. A more engraved flare would give better stability. However, the sting length flare has better stability in the subsonic regime than the mid-body length flare. In the supersonic regime, the mid-body length flare is slightly more stable. Since the boattail destabilized the projectile in the subsonic and transonic regimes, the sting length flare is more suitable since it produces better stability for the same amount of drag.


Figure 14. Center of pressure measured from the nose tip as generated by the sting length flare (SLF)

and mid-body length flare (MLF) aft body compared to the straight base projectile.

To summarize, four types of aft body were presented and studied. The flare produced a good increase in stability but with a huge drag augmentation in the subsonic regime. The boattail reduced the drag but destabilized the projectile in the subsonic and transonic regimes. The engraved flare gave good stability with an acceptable increase in drag. Therefore, boattail and the sting length flare were retained for defining candidate projectile configurations because of their lower drag characteristics.

2.6 Aerodynamic Surface Geometries Three types of aerodynamic surface geometries were examined. They were: 1) canards, 2) wings, and 3) tail fins. Canards are defined as a small set of fins in front of the main lifting surface. They are usually placed near the nose tip to control or assist in the control of the projectile. The canard can be fixed, actuated or passive. This parametric study covers only the fixed canard configuration; a guided projectile study will cover the actuated canard. Two sizes of canards at the same location were studied. The smallest protruded 0.25 calibre out of the body while the larger protruded out by 0.5 calibre. Both had a 0.5 calibre length.


Figure 15. Canard mounted on the reference frame.

Wings are described as a main lifting surface. The wing could be installed anywhere on the body. For this study, the wings were placed on the center of gravity. A detailed design of a functional wing went beyond the scope of this study. Two different types of straight wings were chosen. A standard straight wing (Fig. 15) of 0.25 calibre chord and 5 calibres span was compared to an equivalent strake type wing (Fig. 16) with a chord of 2 calibres and a total span of 1.5 calibres. A wing typically has a longer chord for a given length, but the intention here was to compare the wing orientation.

Figure 16. Wing mounted on the reference frame at the center of gravity.


Figure 17. Strake mounted on the reference frame at the center of gravity.

The tail fins are the fins at the back of the projectile. The main goal of the fins is to stabilize the projectile. They could also act as control surfaces if actuated. Three sizes of tail fins were studied. The chord of all fins were 1 calibre long with only variation in span of 1.5 calibres, 2.0 calibres and 4 calibres.

Figure 18. Tail mounted on the reference frame.

Figure 18 shows the drag coefficient for all the configurations. As expected the largest aerodynamic surfaces produced the highest drag augmentation. The reference clean body produced the lowest drag. In terms of change in the stability of the projectile, all the aerodynamic surfaces except the canard increased the stability of the projectile. In Figure 19, the stability obtained by the addition of the aerodynamic surfaces is plotted. When compared to the flare, the tail fins gave the same stability with a fraction of the drag augmentation. However, the tail fins lost efficiency at the higher Mach numbers. The principal use of the wing is to help the projectile glide. A useful coefficient ratio to determine the efficiency of a gliding configuration is the lift over drag ratio (L/D) known also as the finesse. The best arrangement will be a good L/D at low AoA, since an increase in the AoA generates more drag. Figure 20 shows a general view of the configurations studied.


Data was plotted at a Mach of 0.75 since it gives a representative view of the aerodynamic behavior in a regime where the projectile would most likely glide (Figure 21).

Figure 19. Drag generated by the different aerodynamic surfaces compared to a clean projectile.

Figure 20. Center of pressure measured from the nose tip generated by the different aerodynamic

surfaces compared to a clean projectile.


Figure 21. Lift to drag ratio at Mach 0.75 generated by the different aerodynamic surfaces compared to

the clean projectile.

All three aerodynamic surfaces were retained for defining candidate projectile configurations.

2.7 Summary A series of aerodynamic components were studied to determine their suitability for use in candidate projectile configurations. Five component types were defined: 1) fore body, 2) nose, 3) body, 4) aft body, and 5) aerodynamic surfaces. Drag and center of pressure were used as the metrics for the selection process. Table 3 summarizes the components that will be used in Sec. 3 to define candidate configurations.


Table 3. Aerodynamic components selected for defining candidate projectile configurations

COMPONENTS GEOMETRY

Fore body Hemispheric nose cap

½ power law Nose

Haack

Body Cylindrical

Straight

Boattail

Aft body

Sting length flare

Canard

Wing or Strake

Aerodynamic surface

Tail


3. Projectile Configuration Definition

3.1 Introduction Six candidate projectiles were created using the selected aerodynamic components from Sec. 2. Two configurations were designed as reference configurations because they were inspired by 155 mm rounds currently under development. Four other configurations were defined by combining aerodynamic components to examine their ability to achieve specific performance behaviors. For each configuration, a description of the performance goal and how it would be fulfilled will be given in the following sub-sections. All projectiles have a hemispheric nose cap and a cylindrical mid body since only those choices were selected in Sec. 2.

3.2 Reference-A The goal of this projectile configuration is to evaluate the performance of the current Excalibur guided munition.

Figure 22. Reference-A, Pseudo-Excalibur projectile.

3.3 Reference-B The goal of this configuration is to evaluate the performance of Low Cost Course Correction Fuzes (LCCCF) in development in various countries.


Figure 23. Reference-B, LCCCF projectile.

3.4 Type-A The goal of the Type-A projectile is to achieve the lowest drag possible. Less drag will extend the range of the projectile. To do so, the component that create the lowest drag in each component category was chosen. Also, since canards, wings and tail fins create drag, it was assumed that the Type-A projectile would be guided by diverter system like impulse jets.

Figure 24. Type-A, Low Drag projectile.


3.5 Type-B A different way to increase the range of a projectile is to provide lift. The Type-B projectile is conceived to achieve high lift to drag ratios by the use of large wings. The projectile must minimize the drag for a given lift so only tail fins are used for flight control.

Figure 25. Type-B, Subsonic Glider projectile.

3.6 Type-C The goal is to achieve the highest control authority possible. To realize this objective, many aerodynamic surfaces are used with less importance placed on the drag penalty. To increase the turning force, a strake is added to the projectile since strakes do not increase significantly the inertia of the projectile.


Figure 26. Type-C, Highly Maneuverable projectile.

3.7 Type-D The Type-D projectile has the lowest number of moving parts where deployed tail fins are used for stability and control. The tail fins have a maximum span of the projectile calibre. Since the tail fins and the sting flare stabilize the projectile, a new aft-body was created called the sting-length-fins. This configuration should increase reliability due to the elimination of aerodynamic components that must be deployed during flight.


Figure 27. Type-D, Robust projectile.

3.8 Summary Six projectile configurations were created from the aerodynamic components from Sec. 2. Two configurations were inspired from current projectiles in development and were used as reference configurations. Four other projectiles were designed to achieve specific characteristics: low drag, high lift over drag ratio, high maneuverability and robustness. .


4. Parametric Ballistic Performance Study A parametric ballistic trajectory of the six projectile configurations designed in Sec. 3 was undertaken. The purpose was to determine the configurations that showed desirable flight characteristics in terms of range in an unguided mode before undertaking a more detailed analysis that includes guided flight.

4.1 Simulation Environment Missile Datcom [3] and the DRDC Valcartier Munition Model Component Library (MMCL) [4] were used to simulate the ballistic trajectory. The MMCL is part of DRDC Valcartier’s simulation tool set used to calculate guided weapon performance. It is based on the in-house USAF project MSTARS (Munition Simulation Tools and Resources) at the Air Force Research Lab/Munitions Directorate, the DSTO Weapon System Division port of the MSTARS Public Release to MATLAB/ Simulink, and the DRDC Munition Toolbox Library.

4.2 Projectile Geometries For all projectiles that were stabilized with the tail fins, three different stability margins were selected. The stability margin, CPCG, is the distance in calibres between the center of gravity (C.G.) and the center of pressure (Xcp) of the projectile. The C.G. is measured from projectile nose and it was fixed at 56% of projectile total length [5]. Table 4 summarizes the configurations tested in the parametric ballistic performance study.


Table 4. Summary of the ballistic projectile configurations studied

4.3 Initial Conditions The physical proprieties of the projectile were derived from the 105 mm C132 HE ER round which has a mass of 12.2 kg [6]. Since the total mass of the projectile is not yet defined, 90%, 110%, 120% of the C132 mass was used in the simulations. The CF LG-1 Mark II 105mm howitzer was selected as the reference delivery system to study the ballistic performance of the concepts. Muzzle velocity was calculated using the projectile weight and the data shown in Figure 28 [7]. A variation of ±5% in the muzzle velocity and three gun elevations of 15°, 30° and 45°, were included in the parametric analysis. Therefore, with 14 individual projectile configurations, 3 projectile masses, 3 muzzle velocities, and 3 gun elevation angles, a total 378 test cases were produced for the parametric analysis.


Figure 28. LG-1 Mk II muzzle velocity

4.4 Typical Ballistic Results Figure 29 shows typical ballistic results obtained during the study. The figure plots the altitude of the projectile compared to the slant range for the given elevation and muzzle velocity for the Ref. A, CPCG 0.1, 14.7 kg configuration. As expected, the higher elevation angles and higher muzzle velocities gave the longer ranges. Graphical results for all configurations are presented in Annex A. Table 5 to Table 7 summarize the numerical results for all test cases. For this study, the actual magnitude of the range was not important because none of the projectile configurations were optimal. It was more important to compare the range between competing configurations to determine if there were any that were obviously inferior. The maximum range was obtained by the Type-B configuration, CPCG 0.1, for an elevation of 45 degree, muzzle velocity of 727.1 m/s and a mass of 14.7 kg. The rankings of the configurations based on range were the similar whether elevation angle, muzzle velocity or mass was used as a criterion. All configurations had increased range with an increase in elevation angle, an increase in muzzle velocity, or an increase of mass. The ranking, from longest to shortest range, based on configuration type was: 1) Type B - high L/D, 2) Type D - robust, 3) Type A - low drag, 4) Type C - maneuverable, 5) Reference B - LCCCF, and 6) Reference A - pseudo-Excalibur. Given the kinetic energy equation (eq. 6), the momentum equation (eq. 7) and the LG-1 interior ballistic results (Figure 28), a plot of kinetic energy and momentum versus mass was


created. From Figure 30, it can be seen that the momentum is rising while the kinetic energy is at a maximum for a projectile mass of about 18.5 kg. 2

21 mvEk = (6)

mvp = (7)

Figure 29. Reference-A ballistic trajectory, CPCG 0.1, Mass 14.7 kg.


Projectile Mass (kg)

Kin

etic

Ene

rgy

(J)

Mom

entu

mN

·s

0 5 10 15 20 25 300

1E+06

2E+06

3E+06

4E+06

0

2000

4000

6000

8000

10000

12000

14000

16000

Kinetic Energy (J)Momentum N·s

Figure 30. Kinetic energy, Ek, and momentum, p, as a function of LG-1 interior ballistic curve.

To verify that longer trajectories could be realized with masses higher than 14.7 kg, additional analyses were carried out for the Ref. A, CPCG 0.1 configuration. Figure 31 shows that the range increased as expected. The figure also shows that elevation angle played a secondary role in the determination of an optimal projectile mass.


Figure 31. Influence of mass on the maximum range for the Reference-A CPCG 0.1.

Table 5. Parametric ballistic performance results showing range (m) as a function of elevation angle

(deg), muzzle velocity (m/s) and stability margin (calibre) for an elevation of 15 deg.


Table 6. Parametric ballistic performance results showing range (m) as a function of elevation angle (deg), muzzle velocity (m/s) and stability margin (calibre) for an elevation of 30 deg.


Table 7. Parametric ballistic performance results showing range (m) as a function of elevation angle (deg), muzzle velocity (m/s) and stability margin (calibre) for an elevation of 45 deg.

The results from the parametric analysis did not reveal any serious flaws in performance of the six baseline projectile configurations. Therefore, the follow-on study, where guidance and control factors are considered, should include all configurations identified in Table 4.


5. Conclusions A parametric study was performed to examine the ballistic performance of six candidate projectile configurations that could be considered for future artillery precision guided munitions. The configurations were developed through an aerodynamic study of components that comprise the projectile, namely, the fore-body, nose, mid-body, aft-body, and aerodynamic surface. Components were accepted based on their ability to exhibit desired aerodynamic characteristics during each phase of a ballistic-like trajectory. Following the selection of the candidate components, six projectile configurations were created by assembling the components to achieve specific objectives. Two reference projectile configurations were inspired by commercial systems in development. Four projectile configurations were designed to attain lowest drag, high lift to drag ratio, high maneuverability and robustness. The DRDC Munition Model Component Library was used in conjunction with DATCOM to carry out a parametric analysis of the six projectile configurations and their variants. The parameters were muzzle velocity, gun elevation, projectile mass and projectile stability margin. Range was used as the metric for performance. A total of 378 trajectories were produced. Stable trajectories were obtained for all the configurations. The ranking, from longest to shortest range, based on configuration type was: 1) Type B - high L/D, 2) Type D - robust, 3) Type A - low drag, 4) Type C - maneuverable, 5) Reference B - LCCCF, and 6) Reference A - pseudo-Excalibur.


6. Recommendations Since none of the six candidate projectile configurations exhibited any obvious undesirable ballistic characteristics, all six configurations should be carried forward to the follow-on study where guidance and control elements will be added before being re-evaluated. Furthermore, the mass of the projectile should be optimized because it was shown that the mass had a significant influence on the projectile range.


7. References

1. “The Army of Tomorrow - Assessing Concepts and Capabilities for Land Operations Evolution”, Director General Land Capability Development, Directorate of Land Strategic Concepts, Kingston, ON, 2006.

2. McCoy, R.L., “Modern Exterior Ballistics - The Launch and Flight Dynamics of Symmetric Projectiles”, Schiffer Publishing, Ltd., Atglen, PA, 1999.

3. Blake, William B., “Missile DATCOM user’s manual - 1997 Fortran 90 revision”, AFRL-VA-WP-TR-1998-3009, Air Force Research Laboratory Wright-Patterson Air Force Base, USA, February 1998.

4. Moore, Frank G., and al. “The 2005 Version of the Aeroprediction code: Part II – user guide”, API report no.2, Aeroprediction Inc., USA, June 2004.

5. “Munition Model Component Library (MMCL), Library Version 1.4”, DRDC Valcartier, June 2007.

6. Fleeman, Eugene L. “Professional Development Short Course on Tactical Missile Design”, Georgia Institute of Technology, USA, 2004.

7. Tanguay, V., “Parametric study on the interior ballistics of 105 mm and 155 mm artillery guns”, DRDC TM 2007-350, March 2008.


Annex A

Figure 32. Ballistic trajectory results for Reference-A CPCG 1.0 calibre


Figure 35. Ballistic trajectory results for Reference-B


Figure 36. Ballistic trajectory results for Type-A


Figure 37. Ballistic trajectory results for Type-B CPCG 1.0 calibre


Figure 40. Ballistic trajectory results for Type-C CPCG 1.0 calibre


Figure 43. Ballistic trajectory results for Type-D CPCG 1.0 calibre


List of symbols/abbreviations/acronyms/initialisms

AoA Angle-of-attack [deg] AP05 Aeroprediction code vertion 2005 APGM Artilery precision guided munition C Haack constant C=1/3 for a Haack nose shape and C=0 for a VonKarman nose

shape. C.G. Center of gravity [calibre] Ca Axial force coefficient CD0 Minimum drag coefficient CF Canadian Forces CL/CD Lift to Drag coefficient ratio CLLP Roling Damping coefficient CM pitching moment coeficient Cma pitching-moment derivatives CN Normal force coefficient CNa Normal force coefficient slope CPCG Distance between the center of gravity and the center of pressure [calibre] d, D diameter [m] DND Department of National Defence DRDC Defence resherche and developpement Canada DSTO Defence Science and Technology Organisation Ek Kinetic energy [joule] LCCCF Low cost course correction fuse L Length [m] M Mach number m mass [kg] MLF mid body length flare MMCL Munition Model Component Library Mstars Munition Simulation Tools and Resources p Momentum [N-s] r Tip of the nose radius [m] Rbase Radius at the base of the nose [m] RDDC Recherche et development pour la defence Canada SLF sting length flare USAF US Air Force v velocity [m/s] Vissim Visual Solutions x position along the projectile axys [m] Xcp Center of pressure [calibre] Z Altitude [m] θ Haack variable ρ radius of the tangent ogive [m]


Distribution list Internal 1 – Director General 3 – Document Library 1 – Hamel, N. (author) 1 – Wong, F.C. (author) 1 – Corriveau, D. 1 – Pimentel, R. 1 – Lesage, F. 1 – C/AP External 1 – Director Research and Development Knowledge and Information Management (pdf file) 1 – Library and Archives Canada 1 – Director Science and Technology Land 1 – Director Science and Technology Land 5 1 – Director Science and Technology Air 1 – Director Science and Technology Maritime 1 – Director Science and Technology Maritime 3 Defence R&D Canada 305 Rideau St. Ottawa, ON, K1A 0K2 1 – Director of Land Requirements 1 – Director of Land Requirements 2-3 National Defence Headquarters Louis St-Laurent Building 555 boul. de la Carrière Gatineau, QC, K1A 0K2

dcd03e rev.(10-1999)

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1. ORIGINATOR (name and address) Recherche et Développement pour la Défence Canada - Valcartier 2459 Pie-XI Nord Quebec, Quebec G3J-1X5

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3. TITLE (Its classification should be indicated by the appropriate abbreviation (S, C, R or U) Artillery precision guided munition airframe definition (U) Ballistic performance (U)

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5. DATE OF PUBLICATION (month and year) April 2009

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UNCLASSIFIED SECURITY CLASSIFICATION OF FORM

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13. ABSTRACT (a brief and factual summary of the document. It may also appear elsewhere in the body of the document itself. It is highly desirable that the abstract of classified documents be unclassified. Each paragraph of the abstract shall begin with an indication of the security classification of the information in the paragraph (unless the document itself is unclassified) represented as (S), (C), (R), or (U). It is not necessary to include here abstracts in both official languages unless the text is bilingual).

As stated in the Defence Policy, Canada must have a full spectrum of capabilities to make meaningful contributions in multilateral overseas operations that are aimed at stabilizing failed or failing states. The Canadian Forces is gradually acquiring precision strike capabilities in its gun-launched indirect fire weapon systems, since transformation documents support the acquisition of this kind of capability. DRDC initiated the project entitled “Concept Development of Artillery Precision Guided Munitions” to respond to and support the CF in making difficult performance-based choices and decisions on sub-155 mm artillery precision guided munitions. The objective of this study was to identify promising airframe geometries that could contribute to extending the range of an APGM through reduced drag and increased lift. A parametric analysis of the six candidate projectile configurations and their variants was carried out. It was found that none of the six candidate projectile configurations exhibited any obvious undesirable ballistic characteristics, so all six configurations should be carried forward to a follow-on study where guidance and control elements will be added before re-evaluation.

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DATCOM Artillery Guided Munition Balistic airframe extended range Model Munition Component Library

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