A Parameter Study and Comparison of Projectiles with Fins and Flares at Hypervelocities

Sidra I. Silton* U.S. Army Research Laboratory, Aberdeen Proving Ground, MD, 21005-5066

A parameter study of kinetic energy long rod projectiles was conducted using an analytical model. Specifically, fin and flare afterbody configurations were investigated to determine the effects on deceleration, stability, and aerodynamic jump sensitivity. Within the constraints of the problem, the fin afterbody configuration was found to be more suitable. The introduction of sabot grooves on two reasonable fin afterbody configurations was found to significantly increase deceleration while having little effect on either stability or aerodynamic jump sensitivity.

Nomenclature A = reference area d = reference diameter D = penetrator diameter Decel = deceleration L = penetrator length L/D = length-to-diameter ratio Cmα = pitching moment coefficient derivative CNα = normal force coefficient derivative CX = axial force coefficient Ix = axial moment of inertia Iy = transverse moment of inertia m = projectile mass SAJ = aerodynamic jump sensitivity SM = static margin V0 = initial projectile velocity Xcg = center of gravity location XCP = center of pressure location ρ = air density

I. Introduction HE continued development of the electromagnetic gun is increasing the probability that projectile launch at hypervelocity will occur. If one assumes that a projectile can be built to withstand launch, it then becomes

necessary to determine the best configuration for the projectile’s aerodynamic flight to its target. This includes, but is not necessarily limited to, the projectile’s deceleration, stability, and accuracy.

Previous work has been completed looking at both fin-stabilized and flare-stabilized projectiles, but mostly at subscale and individually rather than comparatively. Additionally, emphasis has tended to be on the aeroballistics of the projectile and not the trajectory parameters. Plostins et al.1 looked at the effects of different afterbody configurations on the aeroballistics for a given Mach number. The effects of changing the parameters of a given configuration were not investigated. The launch dynamics and the effect on the trajectory of both a fin-stabilized and a flare-stabilized projectile were considered by Schmidt et al.2, but again were limited to a single configuration of each at a single Mach number. A more recent study looked at the effect of materials on the aerodynamic behavior of theses same projectiles through changes in static margin and moments of inertia. This limited the extent to which the data could be interpreted. A study conducted in the late 1980’s3 compares an existing fin-stabilized round and

T

* Aerospace Engineer, Aerodynamics Branch, AMSRD-ARL-WM-BC, Member AIAA.

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23rd AIAA Applied Aerodynamics Conference6 - 9 June 2005, Toronto, Ontario Canada

AIAA 2005-4969

This material is declared a work of the U.S. Government and is not subject to copyright protection in the United States.

two flare-stabilized configurations at supersonic velocities (up to Mach 5). A follow-on parameter study considered quite a few flare-stabilized projectiles both experimentally4 and numerically.5 These two studies give a good idea of what to expect from a flare-stabilized projectile at supersonic speeds and suggested possible avenues of exploration.

The present study was undertaken in order to better quantify the effect of both a fin- and flare-stabilized kinetic energy (KE) long rod projectile on the trajectory parameters. It is the objective to minimize the aerodynamic jump sensitivity with a maximum deceleration of 200 m/s in 2 km while maintaining projectile stability. A range of velocities from 1500 m/s to 2500 m/s was investigated for projectiles with fin and flare afterbodies. Many of the parameters of both the fin and the flare afterbody were investigated. The study was completed using semi-empirical analysis software in order to maximize the number of configurations investigated in a limited amount of time.

II. Geometry Each projectile consisted of a tungsten forebody and a steel afterbody. The forebody consisted of the nose and

penetrator. The nose was a hemisphere-cone, 52.5 mm in length. The hemisphere was 5 mm in diameter and the cone had an 8° half angle. The penetrator was 15 mm in diameter (D) and had a length-to-diameter ratio (L/D) of 23. The initial modeling was completed without sabot grooves. When sabot grooves were introduced, there were 5 grooves with the first groove located 118.125 mm from the nose. The grooves were 3.175 mm long and had a 12.7 mm pitch. Both sub-caliber and super-caliber grooves were introduced and were 0.762 mm deep or high, respectively.

The parameter study was completed on the projectile afterbody. Both a fin afterbody (Fig. 1) and a flare afterbody (Fig. 2) were considered. The fin afterbody was modeled as a clipped delta fin. Within the parameter study the root chord, the tip chord, the fin span, the fin thickness, and the number of fins were all varied.

D

L/Dchord

angle

Figure 2: Flare afterbody configuration with parameters indicated.

span

Root chord

Tip chord

Figure 1: Fin afterbody configuration with parameters indicated.

III. Solution Technique The PRODAS (Projectile Design and Analysis System) software6 was used to complete the study presented

herein. PRODAS is an analytic tool that allows for rapid and complete design of projectiles. Using proven methodologies and techniques, performance of “designed” projectiles is estimated bsaed, in part, on prior experimental testing. PRODAS is made up of multiple modules. Only the modules used in this study are discussed.

A. Model Generation and Mass Properties Upon starting PRODAS, either a pre-existing model can be read in or a new model can be generated. A new

model is generated through specification of assemblies, components and elements in the model editor. For each element, the aerodynamic function (ogive, fin, flare, etc.), element type (solid or void), and geometric type (axisymmetric or fin) are specified along with the left and right diameter, the length and reference relative to the

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component. A component is a collection of elements that have the same material properties and physical function. Thus, the material properties are defined at the component level and can be retrieved from the Materials Reference database within PRODAS. Assemblies are a collection of components and are used to establish the zero datum.

For the current study, each model was comprised of a single assembly. The assembly consisted of three components: nose-tip, penetrator, and afterbody. The nose-tip component has a structural physical function and the material properties of tungsten and consists of two elements: the nose-tip and the cone. The nose-tip is modeled as a solid, axisymmetric, wetted element and the cone as a solid, axisymmetric, ogive element. The penetrator component also has the material properties of tungsten, but the physical function of a penetrator. The element defined under the penetrator component is a solid, axisymmetric, wetted element. The afterbody component has the material properties of steel and the physical function of “drag stabilized” specified. The remainder of the specifications depends on whether a projectile with fins or flares is being created. For the projectile with fins, a stabilizer type of fin is specified and a fin type of clipped delta. At the component level, the fin parameters of root chord, tip chord, span, thickness and number are also specified. The fin geometry and hub (through the use of voids) are created at the element level. For the flared projectiles, a stabilizer type of flare is specified. The flare span and root chord are also specified at the component level. The flare geometry and hollowing (through voids) is completed on the element level.

Once the assembly was completed, the mass properties module is used to calculate the weight, axial and transverse moments of inertia, and center of gravity location of each component as well as the total assembly. Standard analytical methods are used to calculate the mass properties and can be found in PRODAS Technical Manual.6

B. Aerodynamic Coefficients and Stability Evaluation Once the physical properties are known, the FINNER module is used to determine the aerodynamic coefficients

for drag-stabilized projectiles. The FINNER module augments the body alone aerodynamic coefficients obtained from the SPINNER module using empirical equations in order to obtain the fin/flare aerodynamic coefficients. The coefficients obtained from this module include axial force, normal force, normal force center of pressure, pitching moment, and damping moment. Using these coefficients, one can then complete the stability analysis.

The stability analysis is completed using Linear Theory at a given velocity. The closed form solutions used in PRODAS are derived from References 7 and 8. While many outputs are available from the stability analysis, those of concern here were aerodynamic jump sensitivity (SAJ), deceleration (Decel), and static margin (SM). Each of these is obtained analytically from the aerodynamic coefficients and is given by equations (1) – (3), respectively.

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( )( ) y xN XAJ

m

I IC C dSC Vmdα

α

−−= (1)

where CNα is the normal force coefficient derivative, CX is the axial force coefficient, Cmα is the pitching moment coefficient derivative, Iy is the transverse moment of inertia, Ix is the axial moment of inertia, d is the reference diameter, m is the mass, and V0 is the initial velocity.

010002

xV ACDecel

mρ

= (2)

where ρ is the air density and A is the reference area.

cg CPX XSM

D D= − (3)

where Xcg is the center of gravity location and XCP is the center of pressure location.

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IV. Results

A. PRODAS Validation Prior to beginning the hypervelocity study on projectiles with fin and flare afterbodies, it was desired to validate

PRODAS against a experimental hypervelocity data set as well as another semi-empirical code, AP02.9 An experimental data set for both fin-stabilized and flared-stabilized hypervelocity projectiles shot at Mach 6 was available.10 The models were created in PRODAS (and AP02) from the drawings used to machine the experimental projectiles. Each projectile was machined from a single piece of 17-4 stainless steel. The forebody of each projectile consisted of a nose with an 8° half angle cone and a cylindrical penetrator. The afterbody of the projectile with fins had a square cross section 20 mm long and consisted of four delta fins 1 mm thick with a sweep angle of 77° and a span of 15 mm. The flared projectile had an afterbody length of 15.25 mm, a half angle of 12.5° and a span of 11.5 mm. The results of the validation study were originally presented in Plostins et al.11 and are briefly summarized here for completeness

PRODAS accurately predicts CX, and CNα, found in the range for the finned projectile. The pitching moment coefficient and the pitch-damping moment coefficient, Cmq, are quite poorly predicted by both PRODAS and AP02 due to a small static margin is so small (i.e.XCP, is very close to Xcg). Hence, small discrepancies in center of pressure location (approximately 9%) cause extremely large discrepancies in moment coefficients. For finned projectiles, PRODAS should predict the aerodynamic coefficients fairly well as long as the projectile is stable.

PRODAS also predicts CX and XCP fairly well for the flare stabilized projectile. CNα and Cmα are not as well predicted, but are still reasonable (within 10-15%). The are some serious discrepancies between the predicted values of Cmq and those found in the experimental range test. However, since the predicted values are somewhat consistent, it is possible that it may be experimental error. Although the predictions may be a bit high for CNα and Cmα, PRODAS results should still be reliable for a parameter study.

B. Parameter Study A parameter study was conducted for the flare afterbody configuration and the fin afterbody configuration for

five launch velocities between 1500 m/s and 2500 m/s. Once completed the effect of sabot grooves was investigated. For each parameter investigated, plots of deceleration, static margin, and aerodynamic jump sensitivity are presented. There are three constraints to the problem. First, minimize aerodynamic jump sensitivity. The goal was to have a maximum SAJ of 0.154 mils/rad/sec. Second, the maximum desired deceleration is 200 m/s in 2 km. For example, if a projectile were launched at 2300 m/s, it must impact no slower than 2100 m/s after having traveled 2 km. Finally, the projectile must remain stable (i.e. the static margin must be greater than 0.5 cal.). 1. Flare

The parameter study for the flare afterbody configuration was completed first. Nine flare configurations were investigated (Table 1) to include variation in flare angle and chord, and hence span. The effects of small flare angles and chords were determined first in order to keep deceleration below the desired level. The results of configurations flare2, flare3, flare4, and flare5 are compared in Fig. 3. The results of flare1 are not shown as the projectile was not stable so the values are not reliable. The deceleration for the remainder of these configurations is acceptable, though not always below 100 m/s per 1000 m (Fig. 3a). Unfortunately, one immediately notices that for these small flare angles and short chord lengths, these projectiles are barely statically stable as indicated by their small static margin (Fig. 3b). As such, the aerodynamic jump sensitivity is quite large (Fig. 3c) and, therefore, unacceptable.

Table 1. Mass and physical properties of flare afterbody configurations.

Config# Angle (deg)

Span (mm)

Chord (mm)

Mass (kg)

Ix (kg-m2)

Iy(kg-m2)

Xcg(mm from nose)

Flare1 4 22 50 1.25 4e-5 1.56e-2 219.543 Flare2 4 25.5 75 1.27 4e-5 1.71e-2 224.23 Flare3 5 23.7 50 1.25 4e-5 1.58e-2 220.14 Flare4 5 22.87 45 1.24 4e-5 1.55e-2 219.22 Flare5 4 22.69 55 1.25 4e-5 1.59e-2 220.39 Flare6 4 26.89 85 1.27 4e-5 1.74e-2 225.18 Flare7 4 30.50 110.817 1.31 5e-5 1.96e-2 231.76 Flare8 6 30.29 110.817 1.36 6e-5 2.29e-2 241.84 Flare9 8 46.15 110.817 1.37 8e-5 2.32e-2 242.93

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Figure 3: Plots of (a) deceleration, (b) static margin, and (c) aerodynamic jump coefficient for flare configurations flare2 – flare5.

The effect of changing the length of the chord while keeping the flare angle constant was investigated next. From the previous portion of the parameter study, it was known that a minimum chord length was needed. For a flare angle of 4°, chord lengths of 75 mm, 85 mm, and 110.817 mm (corresponding to configurations flare2, flare6, and flare7, respectively) were chosen. As was expected, increasing the chord length increased deceleration (Fig 4a). Deceleration increases because, for a given flare angle, increasing chord length increases span. As such, the axial force (i.e. drag) increases which directly increases deceleration (equation 2). With the increase in chord length, the static margin also increases (Fig. 4b), indicating an increase in projectile stability. The aerodynamic jump sensitivity decreases with the increase in chord length (Fig. 4c). For the longest flare, the sensitivity is below that of the desired maximum at all velocities. This would make flare7 a reasonable configuration except that the deceleration is 50% greater than the maximum desired deceleration.

The last flare parameter to be investigated was flare angle. For a given chord of 110.817 mm, flare angles of 4°, 6°, and 8° were set. This corresponds to configurations flare7, flare8, and flare9. Configuration flare7 is carried over from the chord length parameter study. It is known to have good static margin and low aerodynamic jump sensitivity, but high deceleration. Increasing the flare angle, while keeping the chord constant, further increases the span. This, of course, causes an increase in projectile drag and a corresponding increase in deceleration (Fig. 5a). For the 8° flare half angle, deceleration is more than double the desired maximum value. It is unlikely that this would be an acceptable configuration for a fielded round. If one were to assume for the moment that the deceleration could be acceptable if the aerodynamic jump sensitivity was of a minimal level, it becomes interesting to observe the trends in static margin and aerodynamic jump sensitivity. The trends from the chord parameter study hold. Static margin continues to increase as the flare angle (and span) increases (Fig. 5b) and the aerodynamic jump sensitivity decreases (Fig. 5c). The aerodynamic jump sensitivity is in fact of extremely small levels with the larger flare angle. It then becomes a question of trade-offs. Is a greater amount of deceleration acceptable in order to obtain these low aerodynamic jump sensitivities? It is also possible that a fin afterbody configuration may have acceptable deceleration levels while only slightly increasing aerodynamic jump sensitivity. Thus, a fin afterbody was the next portion of the parameter study.

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Figure 4: Plots of (a) deceleration, (b) static margin, and (c) aerodynamic jump sensitivity for flare configurations with 4° flare angle and varying chord.

Figure 5: Plots of (a) deceleration, (b) static margin, and (c) aerodynamic jump sensitivity for flare configurations with a 110.817 mm chord and varying flare angle.

2. Fins The basic fin afterbody, configuration fin1, was based on a currently fielded fin afterbody. Variations were then

made to individual fin parameters to determine the effect on deceleration, static margin, and aerodynamic jump sensitivity. The parameters investigated include fin thickness, the number of fins, fin root chord, fin tip chord, and fin span. Thirteen configurations were investigated at five velocities between 1500 m/s and 2500 m/s. The mass properties and physical characteristics of these 13 configurations are listed in Table 2.

The effect of fin thickness was investigated first. A nominal fin thickness of 2.5 mm was chosen. Fin thickness was varied between 1.25 mm and 5 mm. As increasing fin thickness increases flat plate area, axial force, and hence, deceleration was also expected to increase. Figure 6(a) shows that this is indeed the case and that all but the thickest fins (5 mm) satisfy the deceleration requirements. While static margin decreases slightly with increasing Mach number, the 1.25 mm thick fins consistently have the greatest static margin (Fig. 6b). It is unclear why a thicker fin would be less stable than a thinner fin even at hypersonic velocities. It would be interesting to look at this with

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Table 2. Mass and physical properties of fin afterbody configurations.

Sweep (deg)

Span (mm)

Root Chord (mm)

Tip chord (mm)

Thickness (mm) # fins Mass Config

# (kg) Ix

(kg-m2) Iy

(kg-m2)

Xcg(mm from

nose) Fin1 74 65.2 110.817 23.275 2.5 6 1.65 1.1e-3 3.43e-2 279.15 Fin2 74 65.2 110.817 23.275 1.25 6 1.55 7e-5 3.04e-2 267.04 Fin3 74 65.2 110.817 23.275 3.75 6 1.74 1.4e-4 3.77e-2 289.90 Fin4 74 65.2 110.817 23.275 5 6 1.84 1.7e-4 4.08e-2 299.50 Fin5 74 65.2 110.817 23.275 2.5 4 1.58 8.0e-5 3.17e-2 271.25 Fin6 74 65.2 110.817 23.275 2.5 8 1.71 1.3e-4 3.66e-2 286.45 Fin7 67.87 65.2 85 23.275 2.5 6 1.60 1.1e-4 3.06e-2 278.84 Fin8 56.03 65.2 50 12.75 2.5 6 1.44 8.0e-5 2.28e-2 246.99 Fin9 70.84 65.2 85 12.75 2.5 6 1.58 1.0e-4 3.00e-2 268.61 Fin10 75.65 65.2 110.817 12.75 2.5 6 1.63 1.0e-4 3.37e-2 277.47 Fin11 68.67 65.2 110.817 46.55 2.5 6 1.68 1.3e-4 3.52e-2 282.58 Fin12 69.63 80 110.817 23.275 2.5 6 1.70 1.6e-4 3.64e-2 285.64 Fin13 78.70 40 110.817 23.275 2.5 6 1.55 6.0e-5 3.03e-2 266.99

Figure 6: Plots of (a) deceleration, (b) static margin, and (c) aerodynamic jump sensitivity for fin afterbody configurations with varying fin thickness.

computational fluid dynamics (CFD) in the future to see how the flow field was changing. Configuration Fin2 (1.25 mm fin thickness) also has the smallest aerodynamic jump sensitivity (Fig. 6c), which is expected based on the large static margin. As the ability of a 1.25 mm fin to survive a 2500 m/s flight is questionable due to launch survivability as well as thermodynamic heating during flight, the 2.5 mm thick fin is chosen as appropriate to carry forward in the parameter study.

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Therefore, using a fin thickness of 2.5 mm, the number of fins on the projectile afterbody was varied. In addition to the 6 fin configuration already investigated, a 4 fin configuration (fin5) and an 8 fin configuration (fin6) were also considered. It was thought that increasing the number of fins would increase the deceleration because of the increase in flat plate area due to the increased number of fins of the same thickness. Figure 7a confirms that this is indeed the case and that for the 2.5 mm fin thickness, any of these three configurations would meet the deceleration requirement. What was not clear prior to modeling these configurations was how static margin (i.e. stability), and hence, aerodynamic jump sensitivity would be affected. Figure 7b shows that increasing the number of fins from 6 to 8 on the afterbody has virtually no effect on the static margin. The difference is likely within the accuracy of PRODAS. However, decreasing to 4 fins on the afterbody decreases the static margin. Figure 7c shows that changing the number of fins on the afterbody has some influence on the aerodynamic jump sensitivity at the lower Mach numbers, but almost none at the higher velocities of interest. Based on these results, fin count does not seem to play a major role in aerodynamic jump sensitivity. In order to maximize stability and minimize deceleration, without possibly compromising structural integrity, the 6 fin, 2.5 mm thick configuration (fin1) is chosen as the baseline configuration for the next part of the parameter study.

The effect of changing the tip chord is investigated next. In addition to the nominal tip chord of 23.275 mm (fin1), tip chords of 12.75 mm (fin10) and 46.55 mm (fin11) are modeled. Figures 8(a)-(c) reveal that changing the tip chord has little effect on deceleration, static margin or aerodynamic jump sensitivity. All three configurations meet our constraints.

Investigation of the effect of fin span with all other values nominal (fin1), showed that decreasing the span 40 mm (fin13) and increasing the span to 80 mm (fin12) had a bit more effect on our three constraint values than did changing the tip chord. Deceleration increased with increasing fin span (Fig. 9a), which was again expected as the flat plate area has increased. What was unexpected, however, was that any variation the span from its nominal value decreased the static margin (Fig. 9b) and increased the aerodynamic jump sensitivity (Fig. 9c). Without a closer look at the flow field (perhaps with CFD) it is impossible to tell if this is an artifact within PRODAS or a real flow phenomenon.

Figure 7: Plots of (a) deceleration, (b) static margin, and (c) aerodynamic jump sensitivity for fin afterbody configurations with a varying number of fins.

Finally, the investigation into the effect of changing the root chord was completed. In all cases, the investigated configurations utilized 6 fins having a thickness of 2.5 mm and a fin span of 65.2 mm. A tip chord of 12.75 mm with root chords of 50 mm (fin8), 85 mm (fin9), and 110.817 mm (fin10) were modeled as were a tip chord of 23.275 mm with root chords of 110.817 mm (fin1) and 85 mm (fin7). Deceleration decreased with increasing root chord and varied little with tip chord (Fig. 10a). This is not surprising since the sweep angle increased as the root chord increased and a more swept wing is going to have less drag regardless of tip chord. This also confirms the tip chord parameter study that showed tip chord had little effect on deceleration. Configuration fin8 does not meet the deceleration constraints at the highest velocities indicating that there is a minimum acceptable root chord length. Static margin increased with increasing root chord (little change with tip chord) (Fig. 10b). Again, this is not

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Figure 8: Plots of (a) deceleration, (b) static margin, and (c) aerodynamic jump sensitivity for fin afterbody configurations with varying fin tip chord.

Figure 9: Plots of (a) deceleration, (b) static margin, and (c) aerodynamic jump sensitivity for fin afterbody configurations with varying fin span.

unexpected as an increase root chord means increased fin area and increased fin area, of course, means greater stability. The results of aerodynamic jump sensitivity are not quite as straight forward. At the higher velocities, aerodynamic jump sensitivity decreases with increasing root chord (and static margin), as expected (Fig. 10c). However, at the lower velocities (2000 m/s and below), the slope of the aerodynamic jump sensitivity changes significantly for each root chord length, regardless of tip chord length, such that the values seem to converge at 1500 m/s. This may just be a coincidence or it may indicate that there may be a limit to how large the aerodynamic jump sensitivity can become. A more in depth investigation into the cause of this phenomenon at the lower Mach numbers could be investigated using CFD if further clarification were desired. The fin parameter study shows that many of the fin afterbody configurations meet all of the study constraints. Hence, a flare-stabilized projectile would not be considered feasible at this time for these velocities.

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Figure 10: Plots of (a) deceleration, (b) static margin, and (c) aerodynamic jump sensitivity for fin afterbody configurations with varying fin root chord.

3. Sabot Grooves Any hypervelocity projectile would be launched in a sabot and therefore expected to have sabot grooves on the

penetrator. Thus, the effect of these sabot grooves was investigated. At this time it is not known whether super caliber or sub caliber sabot grooves would be utilized, so both were investigated.

Two of the fin afterbody configurations, fin1 and fin8, were chosen for the investigation of the effect of the addition of sabot grooves. The characteristics of the grooves are as follows:

• 5 grooves • begin 118.125 mm from nose • 3.175 mm long • 12.7 mm pitch • 0.762 mm deep/high

The baseline configuration model was altered within PRODAS and the sabot groove option utilized for both the sub caliber and the super caliber grooves. The results are shown in Fig. 11. As expected the addition of the sabot grooves had little effect on either the static margin or the aerodynamic jump sensitivity (Fig. 11(b) and 11(c), respectively). Sabot grooves are known to have little effect on any aerodynamic coefficient other than increasing the axial force. Thus, the increased deceleration (Fig. 11a) is expected as well. What is unfortunate is that the increase in deceleration is so great that it takes a penetrator that may have adequate deceleration with no sabot introduction of the grooves increase the deceleration beyond the acceptable level. This indicates how important the inclusion of the sabot grooves in the aerodynamic analysis are if deceleration is considered a major constraint. Alternatively, one could make sure to augment the deceleration by a given amount to account for the grooves if it is significantly easier to model the projectile without them.

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Figure 11: Plots of (a) deceleration, (b) static margin, and (c) aerodynamic jump sensitivity for fin afterbody

V. Conclusion A parameter study of flare- and fin- stabilized projectiles for a hypervelocity KE penetrator has been completed.

A hemisphere-cone nose with 8° half angle and a penetrator with L/D=23 was used for all configurations. Only afterbody parameters were varied. For the flare afterbody configuration, the parameters of flare half angle and chord were investigated. For the fin afterbody configuration, the number of fins, and fin thickness, root chord, tip chord, and span were all considered. Constraints on deceleration (200 m/s per 2 km), static margin (greater than 0.5) and aerodynamic jump sensitivity (no more than 0.154 mils/rad/s) were used to determine acceptable configurations.

Based on these constraints, the flare afterbody configuration does not appear to be practical. In order to meet the deceleration constraint, stability becomes marginal and aerodynamic jump sensitivity relatively large. Many of the fin afterbody configurations meet the constraint requirements. Thinner fins are better. However, the minimum thickness that can be used will depend on the materials used as heating and warping could become an issue for an extremely thin fin set. It is also possible that one could reduce the fin count on the afterbody which reduces deceleration, but has very little effect on either stability or aerodynamic jump sensitivity.

Finally the effect of sabot grooves was investigated on two promising fin afterbody configurations. This showed that sub-caliber and super-caliber sabot grooves had minimal effect on stability and aerodynamic jump sensitivity, and need not be considered for these constraint requirements. The introduction of the sabot grooves, however, did substantially increase deceleration and, therefore, must be considered in the design process.

Acknowledgments The author would like to thank Dr. Edward Schmidt, ARL, for providing the funding and impetus for this

parameter study.

References 1Plostins, P., Soencksen, K. P., Zielinski, A., and Hayden, T., “Aeroballistic Evaluation of Kinetic Energy Penetrators for

Electromagnetic Gun Applications,” AIAA 96-0454, January 1996. 2Schmidt, E. M., Held, B. J., and Savick, D. S., “Hypervelocity Launch Dynamics,” AIAA 93-0502, January 1993.

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3Celmins, I., “Aerodynamic Characteristics of Fin- and flare-stabilized 25 mm XM910 Prototypes,” BRL-TR-2882, U.S. Army Ballistic Research Laboratory, Aberdeen Proving Ground, MD, December 1997.

4Danberg, J.E., Sigal, A. and Celmins, I., “Aerodynamic Characteristics of a Family of Cone-Cylinder-Flare Projectiles,” J. of Spacecraft and Rockets,” Vol. 27, No. 4, July – August 1990, pp 335-360.

5Weinacht, P., “Navier-Stokes Predictions of Pitch Damping for a Family of Flared Projectiles,” ARL-TR-591, U.S. Army Research Laboratory, Aberdeen Proving Ground, MD, October 1994.

6ArrowTech Associates, “PRODAS Technical Manual,” Burlington, VT, 2002. 7Murphy, C.M., “Free Flight Motion of Symmetric Missiles,” BRL Report 1216, July 1963. 8Nicolaides, J.D., “Free Flight Dynamics,” University of Notre Dame, 1968. 9Moore, F.G. and Hymer, T.C., “The 2002 Version of the Aeroprediction Code: Part I – Summary of New Theoretical

Methodology,” NSWCDD/TR-01/108, Dahlgren, VA, March 2002. 10Hathaway, W., “BFUS Spark Range Flight Tests, ” Letter Report, ArrowTech Associate, Burlington, VT, May 2004. 11Plostins, P., Silton, S. and Schmidt, E., “Aerodynamic Jump at Hypervelocity,” AIAA-2005-438, January 2005.

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