Complex experimental analysis of rifle-shooter interaction

Micha? Taraszewski,M.ScEng,PhD.candidate,Janusz Ewertowski,PhD.,D.ScEng

Warsaw University of Technology,Faculty of Production Engineering,Department of Mechanics and Armament Technology,ul.Narbutta 85,02-524 Warszawa,Poland

Complex experimental analysis of rifle-shooter interaction

Micha? Taraszewski,M.ScEng,PhD.candidate*,Janusz Ewertowski,PhD.,D.ScEng

Warsaw University of Technology,Faculty of Production Engineering,Department of Mechanics and Armament Technology,ul.Narbutta 85,02-524 Warszawa,Poland

1.Introduction

Working on a new weapon model it is necessary to solve many technical problems,for instance interior ballistic,endurance,variety of mechanisms etc.One of the most important aspect is to design a gunwith as high as possible accuracy.Analyzing a problem of rifle movement during a discharge requires free body diagram determination,especially forces between shooter and given weapon model.Up to date man-weapon interaction efforts,including experiments,focus on measurement and assessment of rifle influence on shooter's shoulder.Force and energy of recoil were measured at contact point between rifle's butt and a shoulder.Results were analyzed with respect to shooter subjective feeling under applied recoil energy.Ranges of recommended recoil energy vs.weapon model were introduced.Designers focused on shooter and neglected mutual interaction between shooter and rifle.Particularly,weapon accuracy phenomenon was not considered.To date,no published effort has been made to indicate correlation between rifle-shooter interaction and weapon accuracy.Rifle's impact on a shooter was solely highlighted.

This paper is focused on the kbk AKM(AKM rifle)-shooter interaction.It is proposed to disjoin nodes of rifle-shooter system,which may be treated as a new approach of the analysis.Moreover,a following hypothesis is stated:human reactions on rifle are crucial to weapon accuracy.Those forces will be introduced to the nodes(points of rifle-shooter contact)together with forces generated due to propellant burn.Above approach will let to determine and solve system of motion equations(Fig.1).

Mathematical model of the analyzing system is derived by utilizing the formalism of Lagrange equations of the second kind[9]

Trying to obtain an analytical description of shoulder-fired rifle motion during both the shot and interaction with the user,it is necessary to determine wide spectrum of input data.One of them are reactions between rifle and shooter in the mutual contact points,namely:rifle butt and user shoulder,hand and pistol grip,hand and hand grip/forend.

Thinking of complex analysis,it was decided to measure reactions in all three directions of orthonormal basis in Euclidean vector space[7],where coordinate system(CSYS)is attached to contact point between rifle butt and shooter shoulder(Fig.2).

Introduced approach rids entirely of human modeling and focuses how forces of mutual reaction impact on gun motion.Shooter is represented as reactions of specified characteristics.Such approach allows to new weapon design optimization or already existed ones by variations of individual parameters.

Fig.1.Effect of shooter-rifle interaction.

Fig.2.Definition of vector space and coordinate system.

Experimental results of reaction forces in defined contact points(nodes)and theirs initial analysis are subject of this paper.Analysis of kinematic and dynamic of motion(both linear and angular)will be topics of subsequent papers.

2.To date methods of rifle-shooter interaction analysisoverview

Considering existing methods of rifle-shooter interaction analysis is worth to mention Piotr Wilniewczyc,an ingenious polish weapon designer who one of the first begun working of this phenomenon.In monograph[8]he has formulated requirements for allowable level of recoil energy based on weapon model and subjective shooter feeling.

Another polish scientist who worked on that subject was S.Kochanski,who in monograph[5]shown the kbk AKM rifle reactions on shooter and named existing impact as pushing/breech force.Unfortunately,entire analysis was restricted only to a period where gases from propellant burn were active in the barrel.That is essential disadvantage of the approach.

More accurate analysis was conducted by J.Ewertowski in Ref.[2].He managed a complex analysis of the kbk AKM rifle's impact on shooter and proved that this interaction has two related stages.First one named-impulsive weapon effect,second(which starts right after 1st ends)-elongated weapon effect.Simultaneously claimed that recoil energy is higher in the 2nd period than in the 1st.

Lately,J.Ewertowskii R.Piekarski published a paper[3],where they did a comparative analysis of reaction forces at weapon butt using a various types of gun with different level of recoil energy.The kbks(sport rifle),the kbk AKM and shot-gun were tested.At each model two related stages of interaction were observed,moreover,recoil energy was always higher in the 2nd period.

Considering already known,it may be anticipated that new weapon model will behave in similar manner with similar reactions characteristic according to its caliber and construction(e.g.type of bolt carrier with piston).Of course magnitudes will differ,however they may by estimated based on incorporated design changes.Essential fact is that reaction characteristic is known,magnitude level can be estimated based on changes in design,e.g.mass distribution,center of gravity of each components separately or in total or barrel-ammunition ballistic interaction.

Another topic related papers are[4]and[1].The former is focused on possibility of modeling a human as a set of conjugated together the Kelvin-Voigt rheological elements.Objective was to develop a mathematical model which may help to design a universal mounting fixture that would be capable of testing a variety of new models,similar in size to the M16A1 rifle,the M79 and M203 grenade launchers.In the latter paper problem of developing computer program able to evaluate efficiency of the recoil energy absorbers is considered.Weapon used for verification:the 40 mm M203 grenade launcher and a 12 Ga Remington.Likewise,the Kelvin-Voigt rheological elements were utilized for mathematical model development.

Difference in the shooter-rifle interaction approach has to be underlined.To date papers were focused on modeling a human as a various set(s)of springs and dampers.Authors of this paper think that it is oversimplified.Each person has a unique body,skeleton,musculature etc.,therefore a universal shooter cannot be determined by set(s)of a viscoelastic elements.

Another simplification in preceding papers was a reference coordinate system and tests related with it.The attention was focused only on motion in vertical/midsagittal plane(Side view),neglecting entirely motion in lateral/transverse plane(Top view)-see Fig.3.

3.Experiment methodology

Thinking of developing in the near future a mathematical model which describes a complex weapon motion in three-dimensional space,it was decided to conduct detailed testing of the kbk AKM rifle during the shot.Results will be utilized both to analyze phenomenon of rifle-shooter interaction and to verify accuracy of the proposed mathematical model.Assuming such approach the following research program is recommended:

1.Measurement of angular displacements,in vertical and lateral planes,of the kbk AKM rifle during the discharge.To ensure that,each shot will be recorded by Photron FASTCAM-a video camera for ultra-fast images taking.Displacements measurement will be conducted in specific manner.Namely,two sources of laser light mounted to the rifle.First,parallel to rifle's barrel and second,perpendicularly to rifle's barrel(in lateral plane).Both laser lights will be transposed to the aiming shield,where the 2nd by mirror.Laser spots motion at the aiming shield will be recorded by Photron FASTCAM.Knowing geometry of the laboratory it is possible to transpose"spots motion"to equivalent rifle displacements.See Fig.4 for details.

2.Measurements will be carried out in three nodes of shooter-rifle system.First one is the rifle's butt-location of interest in foregoing papers.Additional ones are naturally chosen rifle's supports:pistol grip and hand grip/forend(Fig.4).

In order to complete research plan,it was necessary to design new pistol grip and hand grip able to contain piezoelectric force sensors within them.Those sensors measure reactions with respect to specified direction of reference CSYS.Example design of modified grips shown in Fig.5.

Test stand equipment:

.modified the kbk AKM rifle;

.3 sets of modified grips(6 in total),for each direction of CSYS;

Fig.3.Motion in:a)Side view,b)Top view.

Fig.4.Experiment methodology-overview.

Fig.5.Example,modified:a)pistol grip,b)hand grip.

.piezoelectric force sensors,type:9311,9312 and 2x 9313AA1(a Kistler company);

.charge amplifier x4(a Kistler company);

.digital recorder-custom made recorder dedicated for WUT ballistic lab;

.Photron FASTCAM-ultra-fast video camera.

At initial phase of the new approach for rifle-shooter interaction it was decided to conduct firing for one shooter with one positionkneeling.Table 1 presents shooter's parameters.

Shooter will fire 10 times for each modified grip,using 7,62 mm caliber ammo,to record reactions at each direction of CSYS.Reaction at rifle butt will be recorded simultaneously and at each shot,regardless of mounted sets of grips.Shots will be performer as single ones.

4.Results discussion

Choosing shooting position,which were used during experiment,authors did a comparative analysis of kneeling and standing positions,based on papers[2]and[3].Fig.6 reveals example characteristic of sum of two rifle butt sensors,standing position(shooter A Table 3),published in above papers.Data without filtering.

Table 1 Shooter's body details.

Fig.6.Sum of reactions for upper and lower rifle butt sensors along X direction,standing position.

Following Fig.7 exhibits results of present experiment for kneeling position and different shooter than were used during past analysis.Data without filtering.

Table 2 presents comparison of impulses of force in both impulsive weapon effect and elongated weapon effect stages for standing and kneeling positions.

Presented benchmarking of characteristics of reaction forces and values of force impulses in specific stages lets to conclude that standing and kneeling positions are comparable.

J.Ewertowski in paper[2]examined influence of shooter(body weight,height)and position(standing and lying)diversity on characteristics registered on rifle butt sensors.It turned out that characteristics remain two-stage,comparable in nature.Table 3 indicates differences between shooters who participated in experiment.

Table 4 presents comparison of impulses of force in both impulsive weapon effect and elongated weapon effect stages for standing and lying positions and for different shooters.

Based on presented information,kneeling position can be assumed as representative in rifle-shooter interaction.Following analysis will discuss on results which are topic of this paper.

Example results of reactions for modified pistol and hand grips for X direction(along rifle barrel axis),Y direction(vertical axis,perpendicular to X axis)and Z direction(lateral axis,perpendicular to X axis)of chosen coordinate system are shown in Figs.8-10.

Fig.7.Sum of reactions for upper and lower rifle butt sensors along X direction,kneeling position.

Table 3 Shooters diversity.

Registered results were evaluated in termsof spectral analysis of signal to exclude noise.iSignal and iPeak-open software available on website[6]-were utilized to perform that effort.Those are source codes of Matlab language,which allow to perform spectral analysis of signal using Fast Fourier Trans form(FFT).Frequencies and amplitudes were studied,next Lowpass,Infinite Impulse Response(IIR)Butterworth filter was designed using Matlab Toolbox and then applied on input raw signals.Choosing criteria of slope increase speed for theoretically calculated mechanical characteristics,it was decided to use 2[kHz]filter for cutoff.Results of filtered signals are presented simultaneously with raw data on Figs.8-10.

Received results from experiment are repetitive in terms of characteristic and magnitude and similar to shown examples,therefore we can use them as a representation.At each CSYS direction three unique periods are visible.Moreover,beginning and ending for those periods are the same for each CSYS direction and for both supports as well.Following hypothesis is proposed:three visible unique periods represent three main impacts on weapon:

.1st range is an effect of force generated due to propellant burning-blue color rectangle(Figs.8-10);

.2nd range is an effect of bolt carrier with piston system impact at aft position in the rifle-orange color rectangle(Figs.8-10);definition of this period was never seen in literature by authors of this paper;

.3rd range is an effect of bolt carrier with piston system impact at forward position in the rifle-green color rectangle(Figs.8-10);neither definition of this period was seen in literature by authors of this paper.

Analysis of filtered experiment results leads to information:

.rifle-shooter interaction for single shot lasts~90[ms];

.period where forces act due to gases from propellant burn lasts~24[ms];

.period of an effect of bolt carrier with piston system impact at aft position in the rifle lasts from 24 to 72[ms];

.period of an effect of bolt carrier with piston system impact at forward position in the rifle lasts from 72 to 90[ms];

.each of the three ranges has two stages:first-impulsive weapon effect,second-elongated weapon effect,according to J.Ewertowski's nomenclature[2];

.absolute reactions for all directions,for both pistol and hand grips,are higher in the 2nd range except hand grip in X direction-such result is caused by higher bolt carrier with piston system impact energy than energy generated by the propellant burn(see results for sum of reactions for two rifle butt sensors,Fig.9);hypothesis:lower hand grip reaction in the second range may result from both distance from impact area and system stiffness-other elements absorb energy first;

Table 2 Values of force impulses of AKM rifle acting on the shooter's arm,based on position type.

Table 4 Values of force impulses of AKM rifle acting on the shooter's arm,based on shooter type and position.

Fig.8.Pistol and hand grips reactions,X direction:before and after filtering.

Fig.9.Pistol and hand grips reactions,Y direction:before and after filtering.

Fig.10.Pistol and hand grips reactions,Z direction:before and after filtering.

.max value for X direction for hand grip~260[N],for pistol grip~190[N];max value for pistol grip is within 2nd rangeprobably due to rifle's design,namely pistol grip is closer,than hand grip,to aft position where bolt carrier with piston system impacts with rifle's receiver;

.max absolute value for Y direction for hand grip~40[N],for pistol grip~185[N];

.max absolute value for Z direction for hand grip~40[N],for pistol grip~35[N];

.positive magnitudes in reaction graphs indicate tension of piezoelectric force sensors(rifle's resistance/reaction with shooter body)whereas negative denote no contact between rifle and shooter,apart from Z direction(see explanation below);

.positive Z direction value designates rifle motion according to Z versor of left-handed CSYS whereas negative denotes rifle motion according to Z versor of right-handed CSYS;usage of signum function is applicable.

5.Conclusion

It may be stated that this paper and proposed approach introduce new look into rifle-shooter interaction phenomenon.To date,no published effort has been made to analyze and describe comprehensively and integrally mutual interaction between shooter and rifle.So far contact between shooter's shoulder and rifle's butt was under consideration only while hand-pistol grip and hand-hand grip were neglected.Research experiments were conducted to evaluate energy level which has to be absorbed by a human depending onweapon caliber and what subjective feeling is caused by this energy.This paper presents different approach for rifle-shooter interaction,trying to assess what conclusions and advantages are gathered and how they can be useful in the future.Attached experimental results explicitly show that reactions in examined nodes(pistol and hand grips)and in all CSYS directions have essential influence on rifle motion in three-dimensional space.That observation substantiates correlation between proposed approach and weapon accuracy.It is worth to underline that such approach lets to optimize new weapons and already existed ones.

Presented in this paper results show crucial effect onto rifle motion by reactions incorporated by shooter,which justifies hypothesis of this correlation stated at the beginning.Reactions level in all CSYS directions in both pistol and hand grips are considerable and,which is very important,those reactions have global effect.Theirs characteristics and values are not local,therefore they cannot be omitted in complex analysis of shot phenomenon.Without measured reactions in grip nodes there is no possibility to develop an effective analytical description of rifle motion during the shot.Additionally,significant effect of bolt carrier with piston system impact with rifle's construction is worth to underline.

Fig.11.Sum of reactions for upper and lower rifle butt sensors along X direction,before and after filtering.

In this paper it is proposed to introduce common terminology of ranges:

.effect of force generated due to propellant burning;

.effect of bolt carrier with piston system impact at aft position in the rifle;

.effect of bolt carrier with piston system impact at forward position in the rifle;

Which are observed in each CSYS direction.

Using J.Ewertowski approach[2]fora period of gases acting due to propellant burning,a nomenclature regarding quantifying forces of rifle's impact on shooter can be extended for two remaining periods(Fig.11):

-in terms of forces:

.max force value of impact at aft position in the rifle in the first stage,PutI;

.max force value of impact at aft position in the rifle in the second stage,PutII;

.max force value of impact at forward position in the rifle in the first stage,PupI;

.max force value of impact at forward position in the rifle in the second stage,PupII;

-in terms of impulses of force:

.level of impulse of force of impact at aft position in the rifle in the first stage,IutI;

.level of impulse of force of impact at aft position in the rifle in the second stage,IutII;

.level of impulse of force of impact at forward position in the rifle in the first stage,IupI;

.level of impulse of force of impact at forward position in the rifle in the second stage,IupII;

-in terms of time:

.duration of first stage of impact at aft position in the rifle,tutI;

.duration of second stage of impact at aft position in the rifle,tutII;

.duration of first stage of impact at forward position in the rifle,tupI;

.duration of second stage of impact at forward position in the rifle,tupII.

Presented herein approach lets to build an atlas of shooter-rifle interaction characteristics for wider number of weapon models,differentiated each other in terms of construction or ammunition,including caliber.Such atlas would accelerate entire design process and limit possible mistakes during evaluation.Concurrently it would make possible to re-design already existed weapons to improve functionality,particularly in accuracy.

It may be concluded that presented approach will also find an application in multi-shot mode.Ending and boundary conditions of first/current shot are initial and boundary conditions for next one.It is very important,because weapons with multi-shot are commonly used in present battle field and accuracy is the most desired feature.Further steps of shooter-ri fle interaction analysis should also include a new field of research:theory of the multi-shots.

Acknowledgments

This research did not receive any specific grant from funding agencies in the public,commercial,or not-for-profit sectors.

[1]Benzkofer PD.Dynamic analysis of shoulder-fired weapons.In:Proceedings of the U.S.Army symposium on gun dynamics(7th).Newport:Rhode Island;1993.

[2]Ewertowski J.The analysis of humeral weapons interaction strength on the shooter during the shot(in Polish)vol.LVI.Bulletin of the Military University of Technology;2007.nr 1.

[3]Ewertowski J,Piekarski R.The impact of selected sorts of rifles on shootercomparative analysis,vol.138.Issues of Armament Technology,Scientific Bulletin of Military Institute of Armament Technology;2016.p.73-86.No 2/2016.

[4]Hutchings TD,Rahe AE.Study of man-weapon reaction forces applicable to the fabrication of a standard rifle firing fixture.Rock Island Arsenal,Rock Island:General T.J.Rodman Laboratory;1975.ADA 034523.

[6]O'HaverT.Interactive signal processing tools.Website.2017.https://terpconnect.umd.edu/~toh/spectrum/SignalProcessingTools.

[7]Ostrowska-Maciejewska J,Kowalczyk-Gajweska K.Tensor calculus in the continuum mechanics(in Polish).Warsaw:Library of the Applied Mechanics,The Institute of Fundamental Technological Research of the Polish Academy of Sciences Publishing House;2013.

[8]Wilniewczyc P.Automatic weapons(in Polish).Ministry of National Defence Publishing House;1958.

A R T I C L E I N F O

Article history:

29 December 2016

in revised form

18 April 2017

Accepted 26 May 2017

Available online 28 May 2017

Rifle-shooter interaction

Man-weapon forces

Muzzle climb

Firearm

Recoil

Accuracy

In this study,a complex analysis of a man-weapon interaction based on experimental effort is presented.The attention is focused on how a shooter can influence on a rifle,opposite to generally considered in literature rifle's impact on a shooter.It is shown,based on the kbk AKM weapon,that each support point of the rifle has an substantial impact on the system.It is said that identifying human reactions on weapon may let to describe gun movement and thus may be applied to weapon accuracy determination.

?2017 The Authors.Production and hosting by Elsevier B.V.on behalf of China Ordnance Society.This is an open access article under the CC BY-NC-ND license(http://creativecommons.org/licenses/by-nc-nd/4.0/).

*Corresponding author.ul.Cyprysowa 36/9,05-650,Su?kowice,Poland.

E-mail addresses:michal.taraszewski@gmail.com(M.Taraszewski),jewert@imik.wip.pw.edu.pl(J.Ewertowski).

Peer review under responsibility of China Ordnance Society.