Dispersion sensitivity analysis&consistency improvement of APFSDS

Sangeeta Sharma Panda,L.K.Gite,A.Anandaraj,R.S.Deodhar,D.K.Joshi,K.M.Rajan

Armament Research Development Establishment(ARDE),Defence Research Development Organization,Ministry of Defence,Government of India,Pashan, Pune,Maharashtra,411 021,India

Dispersion sensitivity analysis&consistency improvement of APFSDS

Sangeeta Sharma Panda*,L.K.Gite,A.Anandaraj,R.S.Deodhar,D.K.Joshi,K.M.Rajan

Armament Research Development Establishment(ARDE),Defence Research Development Organization,Ministry of Defence,Government of India,Pashan, Pune,Maharashtra,411 021,India

A R T I C L E I N F O

Article history:

8 May 2017

Accepted 17 May 2017

Available online 20 May 2017

APFSDS

Dispersion

Consistency

Accuracy

Yaw rate

Spin

Muzzle jump factor

In-bore dynamics

Monte Carlo simulation

The purpose of this study is to investigate and quantify some possible sources of dispersion of 120 mm APFSDS tank ammunition both experimentally and numerically.This paper aims to point out the most in fluential source during In-Bore Balloting Motion phase as well as in External Ballistics phase of the ammunition and quanti fies its effect on dispersion.Data obtained from flight trials is critically analysed and parameters affecting dispersion such as initial yaw/pitch rates,yaw/pitch dampening,plane start angle,launch spin,clearance,centre of gravity shift,dynamic imbalance angle,cross wind,etc.are observed and,later on,studied in detail by extensive External Ballistics Monte Carlo(EBMC)simulation and Six Degree of Freedom(6-DOF)trajectory analysis.

In Bore Balloting Motion simulation shows that reduction in residual spin by about 5%results in drastic 56%reduction in first maximum yaw.A correlation between first maximum yaw and residual spin is observed.Results of data analysis are used in design modi fication for existing ammunition.Number of designs are evaluated numerically before freezing five designs for further soundings.These designs are critically assessed in terms of their comparative performance during In-bore travel&external ballistics phase.Results are validated by free flight trials for the finalised design.

©2017 The Authors.Published by Elsevier Ltd.This is an open access article under the CC BY-NC-ND license(http://creativecommons.org/licenses/by-nc-nd/4.0/).

1.Introduction

Armour Piercing Fin Stabilized Discarding Sabot(APFSDS) ammunition is primarily a direct fire,hypersonic,kinetic energy (KE),anti-armour projectile.In last decade or two,there has been a constant strive amongst ballisticians to improve the penetration performance of existing APFSDS projectiles in their inventories. Mono block KE projectiles,which emerged after World War-II had L/D ratio between 10 and 15.Present developments in armour strength demands this ratio to be around 30-40 in order to attain higher impact kinetic energy.These high L/D ratio projectiles carry larger kinetic energy with them,which enhances penetration performance.But at the same time the design is susceptible to poor dispersion due to lateral vibrations during in-bore travel and poor dampening of initial flight disturbances in free flight due to insufficient stiffness[5].

During in-bore travel,a long kinetic energy(KE)projectiles is, not only subjected to transverse loads due to tube flexure but also this balloting motion is supplemented by longitudinal flexure of sabot&projectile relative to the sabot[1].Statistical In-Bore Balloting Motion analysis adopted in present work,can provide a realistic set of data regarding first maximum yaw&yaw rates of a projectile at muzzle exit,since the effects of variations in initial projectile orientation,manufacturing tolerances,perturbed internal ballistics parameters,launch spin,etc.are dealt in detail.Data analysis showed that the first maximum yaw is closely associated with in-bore spin pro file[4]and plane start angle of projectile inside barrel[3].Both of these factors were quanti fied numerically and effect of initial residual spin was validated by flight trial for the base design.

During free flight phase,a well-designed projectile quickly damps out initial perturbations.Dampening response of long KE projectile is modi fied by appropriate inertia distribution along its length.Flight trials results of base design showed poor dispersion. Based on results of flight trial data and EBMC simulation,parameters affecting minimise muzzle jump factor&in turn dispersion were quanti fied.Simultaneously,outcomes of this study were implementedformodi ficationofbasedesign forimproved consistency.

2.Ammunition design

As mentioned earlier,the base design or Design 1 is a hypersonic kinetic energy projectile fired from a ri fled bore gun.Ri fled bore provides initial spin to the ammunition.However,the spin rate of an APFSDS round must lie within limits set by the requirement to keep the spin low enough to avoid Magnus problems and high enough to keep inaccuracy due to fin unit asymmetries down to a low level[2].By providing a slipping driving band, fitted to the sabot when firing APFSDS from a normally ri fled gun,the spin rate of the projectile can be controlled.This small residual spin imparted by the use of slipping driving bands along with fin leading-edge chamfer gives some advantages in avoiding any initial effects due to inaccurately aligned fins,slightly reducing drag,improving sabot discard and avoiding any possibility of spin yaw lock-in.All designs mentioned below,are provided with a slipping driving band to regulate the percentage of initial spin imparted to the projectile.

Design 1 is essentially consists a cylindrical heavy metal rod with a tapered nose(taper angle～8°)with a steel tip insert and threaded rear end for attaching the stabilising fin.It is a sub calibre projectile and hence the acceleration loads are transferred by the sabot(3 petals)via a long threaded portion of rod.The geometry of base design of APFSDS ammunition is given in Fig.1.

Design 2 to Design 5 are modi fications over base design.

-Design 2 has L/D ratio of 18 as compared to all other designs having L/D ratio of 26.Static margin of Design 2 is also low as compared to other design,since the AR of fins used for Design 2 is 32%less than other designs.

-Design 3 has a segmented penetrator design.Up to 85%length of rod from nose tip,heavier material is used and last 15%was made with lighter material.Here also,stabilising fins are made up of lighter material as compared with the base design.

-Design 4 consists of a penetrator in a shape of tapered rod from both the sides so as t

-o get the appropriate inertia distribution along the length of the projectile.

-Design 5,has a cut of 30 mm in length from rear end.Lesser density material was used for fins.Thickness of the fins was increased by 2 mm.Entire fin cylinder and fin assembly was fitted as a cap over heavy penetrator body.

Dimensional details of each of these designs is given in Figs.1-5.

3.Flight trial setup and measurements

Fig.1.Design 1 or base design(All dimensions in calibre).

Fig.2.Design 2(All dimensions in calibre).

Fig.3.Design 3(All dimensions in calibre).

Fig.4.Design 4(All dimensions in calibre).

Fig.5.Design 5(All dimensions in calibre).

Five series,each of eight rounds were fired for the base design in free flight range at sea level conditions.A total of ninety rounds were fired.In each series one warmer round is also included.Internal ballistics measurements were done to determine Muzzle Velocity and Chamber Pressure for each trial.In first trial itself, ammunition exhibited yaw of 2-3 deg.Subsequent trial consisted of placing yaw frames at known distance from muzzle.For measuring yaw pro file, first yaw card was placed at 25 m and last was placed at 100 m distance from muzzle.In between first and last yaw cards 10 yaw cards were placed at equal distance.High speed video camera were deployed to capture the orientation/movement of ammunition during its flight between first and last yaw cards. Distance of around 40 m is covered by single camera.MET data is recorded for sea level firing and used for the prediction of six DOF trajectory and EBMC simulation.Cross wind variation for Monte Carlo simulation were taken from day to day MET data variation of five series of flight trial.

In the same way,nominal values#and variation*(σ),in yaw angle,yaw rates,MV,chamber pressure,cross wind,CG shift,etc. Observed during flight trials were used in numerical analysis (Table 1).

Consistency firing was carried out on Rolled HomogeneousArmour(RHA)target erected at a range of 1100 m.

Table 1 Dispersion contribution of individual variable.

A comparative yaw dampening response of all five designs is presented in Fig.6.Yaw measured viayaw mapping trials for Design 1 and Design 2 was back calculated to get the initial maximum yaw of two degree near muzzle exit.A closed matched with the flight trial data was found with the numerical prediction of yaw/pitch angle and calculated yaw rates.This first maximum yaw measured during flight trial was used as initial condition for EBMC simulation and 6 DOF trajectory model.

4.Numerical analysis

4.1.In-bore dynamics analysis

A detailed in-bore dynamics analysis is carried out to find out the in-bore parameters inducing the initial yaw/pitch rates at muzzle exit.

To simulate In-Bore Balloting Motion of projectile,the BALANS module of PRODAS is used.BALANS is a finite element lumped parameter code that has the provision to model a flexible projectile's travel inside a flexible gun tube.Two-dimensional detailed geometry of the projectile and the barrel are modelled in PRODAS and exported to BALANS wherein the geometrical model of the projectile and the barrel are converted into lumped parameter model made up of nodes and two-noded beam elements.The internal ballistics Baer Frankle analysis is used to produce Pressuretime curve of the ammunition.Recoil stiffness and stiffness of the projectile/bore interface,Modulus of elasticity,Poisson ratio are taken based on the materials properties of projectile and the barrel. Bore centreline pro file is assumed straight and no diameter variationwith length is assumed.Projectile and boreinterface tolerances are de fined as per manufacturing limits.

Fig.6.Comparative yaw dampening response all designs for initial yaw angle of 2 deg.

4.2.External ballistics Monte Carlo simulation

A rigid body six degree of freedom(6-DOF)trajectory model is used to simulate the free- flight nominal trajectory.The geometry of the projectile was modelled in PRODAS software and the aerodynamics coef ficient were generated.

Monte Carlo Simulation Studies were then carried out by perturbing the nominal values of each input parameter within its limit of±3σ.The sample size is chosen to be 1000,so as to keep the sample to sample variation insigni ficant(Fig.7).The complete set of initial values are then passed to 6-DOF trajectory model and impact points are observed at a range of 1100 m.

A sample of Muzzle Velocity and Initial yaw rates following normal distribution is shown in Fig.8.This ensures that the random number generated for MV,Yaw rates and likewise for other variables also follow Normal distribution,which is primary requirement for Monte Carlo simulation.

Table 1 shows nominal values of External ballistics parameters and their variation,which were estimated during flight trials. Contribution due variation to each parameter to the dispersion is also listed in last column.

Fig.7.Plot of Dispersion vs.no.Of samples(Results of numerical analysis).

Fig.8.Yaw rate spread&Muzzle velocity spread following normal distribution used for Monte Carlo Simulation.

5.Results and discussion

5.1.Dispersion observed for different designs configuration

External Ballistic Monte-Carlo simulations shows that,dispersion is a function of Muzzle Jump Factor(MJF)and initial yaw/ pitch angle and its rates.Muzzle jump factor of projectile is a multiplication factor to the initial yaw and pitch rates which ampli fies the initial disturbances.Hence,it is always required to design a projectile with a lower MJF.Muzzle jump is directly proportional to normal force coef ficient gradient,the transverse moment of inertia,spin rate and the initial yaw angle at the muzzle and inversely proportional to projectile mass,diameter and its velocity.The expression for muzzle jump factor is given below,

5.2.Effect of yaw/pitch rate on dispersion

Initial angular motion of a projectile directly impacts on the fall of shot pattern[4].Dispersion pattern of Base Design was evaluated for varying initial pitch/yaw rates(Table 3).Yaw dampening history obtained via 6DOF trajectory model and validated by yaw mapping trial for the Base Design can be seen in Fig.6.It was observed that the projectile set to initial oscillations due to higher initial rates takes more time to damp these oscillations.Hence,for a given weapon system,a projectile with better yaw/pitch rate dampening characteristics has lesser dispersion and vice-versa.

5.3.Effect of cant angle offin on dispersion

Stabilising fins for APFSDS are given a cant angle of 0.5 deg.

Data analysis of results of flight trial&simulation showed that the ammunition with higher L/D ratio requires appropriate moment of inertia(MOI)distribution along the length of the projectile for adequate dampening of flight disturbances.

Design 2 with lowest L/D ratio has Inertia ratio(Iyy/Ixx)of 128. This design has higher accuracy&consistency as compared with all designs.Design 1,with L/D ratio of 26 and MJF of 1.14 was observed to have poor dispersion.Design 3 and Design 5,with the same L/D ratio but with lower MJF exhibited better dispersion of its round around Mean Point of impact(MPI)(Table 2)(see Figs.9 and 10). Since the projectile is fired from ri fled barrel,it is fired with some residual spin.The cant angle provided maintain the spin during free flight phase to nullify the effect of aerodynamic&mass asymmetry, if any.Table 4,shows contribution of fin cant angle on dispersion. Optimal value of Cant angle so as to maintain a minimal spin for nullifying asymmetry effects is required for improving dispersion.

5.4.Effect of clearance on dispersion

Design 2 was provided a clearance of about 0.4 mm betweendriving band outer diameter and inner diameter of barrel,whereas Design1 or base design was tested with clearance of 0.2 mm and 0.6 mm.It was observed that increase in-bore clearance resulted in improved dispersion of ammunition(Table 5).Judicial selection of optimum clearance is required since it affects both in-bore spin as well as obturation for hot combustion gases during launch phase.

Table 2 Comparison between computed and measured dispersion at target end for different design con figurations.

Fig.9.Dispersion plot of various con figurations obtained by numerical simulation.

Fig.10.Flight Trials based dispersion plots of Base Design&Design 5.

Table 3 Comparison between computed and measured dispersion at target end for yaw/pitch rates for Base Design.

Table 4 Computed dispersion at target end for varying cant angle for Base Design.

Table 5 Comparison between computed and measured dispersion at target end for varying in-bore clearance for Base Design and Design 2.

5.5.Effect of dynamic imbalance(DI)angle on dispersion

Small mass asymmetries(principal axis misalignment and lateral CG offset)inherent in ammunitions can have large effects on the magnitude of the projectiles'initial angular motion.The first maximum yaw levels produced by these asymmetries can cause unacceptable changes in range.

EBMCS was carried out for Dynamic Imbalance angle of 0.1 deg. to0.5 deg(Table 6).Even tough,it is infeasible foran ammunition to pass quality criterion with such an exaggerated figure of DI angle, still it was needed to quantify the effect of mass asymmetry on dispersion for this class of ammunition.

5.6.Effect of wheelbase length on dispersion

It is needed to design adequate'wheelbase'for projectile to prevent excessive balloting inside the barrel during launch.Here, the term wheelbase refers to the distance between the front and rear bore-riding surfaces of the sabot[3].It was seen that larger the ratio of length of penetrator to wheel base length,the better dispersion(Table 7).

5.7.Effect of in-bore plane start angle on dispersion

If variation in plane start angle increases,then yaw rate at muzzle exit increases.It was observed repeatedly that the effect of yaw on dispersion can be minimized by controlling the plane of initial maximum yaw of the projectile.In-Bore balloting motion simulation showed that a projectile when rammed into the barrel for firing,the initial position it takes inside barrel,affects its initial maximum yaw,which in turn control the dispersion.In simulation, nominal value of projectile seating angle or plane start angle was taken as 180 deg inside the barrel,i.e.bottom most part of the barrel where projectile will rest due to effect of gravity.But if the projectile is rammed in slightly angular direction,plane start angle will vary.These variation in plane start angle for series of 450rounds and corresponding average yaw rates at muzzle exit are plotted in Fig.11.

Fig.11.Effect of Projectile orientation variation on yaw rate as obtained via Statistical In Bore Balloting Motion analysis.

Table 6 Computed dispersion at target end for varying Dynamic imbalance angle for base design.

Table 7 Computed&measured dispersion at target end for varying‘Length of penetrator/Wheel base Length ratio’for Base Design$and Design 2+.

Table 8 Residual spin at muzzle and corresponding initial yaw rate for Base Design.

5.8.Effect of residual spin on dispersion

Even though,APFSDS ammunition is fired from a ri fled barrel, provision of sabot with Slipping Driving Band(DB)controls the percentage of spin imparted to the round.This percentage depends upon the ef ficacy of the DB in providing required obturation during in-bore travel.It was observed that the spin generated in-bore serves to be the most important parameter in yaw/pitch rate analysis.The yaw rate depends almost linearly on in-bore spin imparted by Slipping DB as presented in Table 8.To have minimum yaw/pitch rate at muzzle it is essential that,the projectile has near zero spin at the muzzle by judicious optimization of clearance between DB and in-bore diameters.

6.Conclusions

In general,for a direct fire ammunition,sources of dispersion, can be segregated in three ballistics phases:In-bore balloting Motion Phase,Muzzle disengagement phase including effect of muzzle blast&sabot discard and finally the External Ballistics phase.

In this paper,parameters causing dispersion of APFSDS tank ammunition during in bore and external ballistics phases are studied.The sensitivity of each parameter and its contribution in dispersion is quanti fied.Existing design is evaluated and modi fied in term of geometrical and mass/inertial properties to improve the consistency of the ammunition after extensive Monte Carlo and Six Degree of Freedom(6 DOF)trajectory simulations.A detailed Inbore dynamics simulation is also performed to assess the effect of initial conditions at launch,on consistency.In general, flight trial results agree well with the simulation results,further validation via planned experimental trial is needed for the barrel and projectile balloting motion during in-bore travel.Effect of sabot discard and muzzle blast on dispersion is planned in future for further soundings.

In this work,In-bore balloting studies suggested that

-Plane start angle of projectile affects first maximum yaw and projectile should be rammed in-line with the barrel centre line.

-Clearance between DB and In-bore is a parameter which not only affects obturation for combustion gases but also has a controlling effect on residual spin and hence on dispersion.

-It is observed that variation due to stiffness of the barrel and projectile front&rear bore riders,wheel base,Muzzle Velocity, pressure pro file and location of obturator have less effect on yaw rate and dispersion.

External ballistic phase studies suggested that

-Muzzle jump factor needs due attention even for the draft design of ammunition.Yaw/pitch rate and their dampening are directly dependent upon designed value of MJF.

-MJF can be reduced by modifying the mass properties of the projectile.

-Ammunition design in which mono-block of single high density material is replaced with two sections of different densities showed huge improvement in consistency.

Acknowledgement

The authors wish to express their sincere gratitude to Shri RS Deodhar&entire Ballistics team of ARDE for their valuable guidance and support&Shri R.Bhandari&Shri S.Patil for providing crucial data for this study.

[1]Analysis of sources of firing Errors Schmidt Edward.9th International symposium on ballistics.Royal Military College of Science;May 1986.Shrivenham,29 April-01.

[2]Text Book of Ballistics&Gunnery Vol.1,Her Majesty’s Stationery Of fice 1987.

[3]The effect of sabot wheelbase and position on the launch dynamics of finstabilized kinetic energy ammunition Plostins Peter,Celmins Ilmars, Bornstein Jonathan.San Antonio,Texas.In:12th International symposium on ballisticsvol.30;October-1 November,1990.

[4]The impactoflnteriorballisticson kineticenergy projectile accuracy Wilkerson Dr Stephen.Jerusalem,Israel.In:15th International symposium on ballisticsvol.2;May 1995.p.21-4.

[5]Kinetic Energy Projectiles:Development History,State of the Art,Trends Lanz W,Odermatt W,Weihrauch Dr G.In:19th International symposium of ballistics,Interlaken,Switzerland;May 2001.p.7-11.

List of symbols

MJF:Muzzle Jump factor,mil/radians/sec

D:Diameter of the projectile in m

M:Mass of the projectile in kg

Vm:Muzzle Velocity of the projectile in m/s

pm:Muzzle Exit Spin of the projectile in rad/s

Ixx:Axial Moment of Inertia of the projectile in kg.m2

Iyy:Transverse Moment of Inertia of the projectile in kg.m2

HSD:Horizontal Standard Deviation,mils

VSD:Vertical Standard Deviation,mils

ASD:Average Standard Deviation,mils

Σ:Standard Deviation

αg:Yaw Angle at Muzzle Exit,radians

ΔCG:CG Offset of the projectile in the gun tube

CD:Axial Force(Drag)Coef ficient

CNα:Normal Force Coef ficient gradient of the projectile,in rad-1

Cmα:Pitching Moment Coef ficient gradient of the projectile,in rad-1

19 January 2017

*Corresponding author.

E-mail addresses:sangeeta_eca@yahoo.co.in(S.Sharma Panda),lkgite@arde. drdo.in(L.K.Gite),aranadraj@arde.drdo.in(A.Anandaraj),rsdeodhar@arde.drdo.in (R.S. Deodhar), dkjoshi@arde.drdo.in (D.K. Joshi), kmrajan@arde.drdo.in (K.M.Rajan).

Peer review under responsibility of China Ordnance Society.

http://dx.doi.org/10.1016/j.dt.2017.05.005

2214-9147/©2017 The Authors.Published by Elsevier Ltd.This is an open access article under the CC BY-NC-ND license(http://creativecommons.org/licenses/by-nc-nd/4.0/).

in revised form