The Firing Dispersion of Bullet Test Sample Analysis

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1 Iteratioal Joural of Materials, Mechaics ad Maufacturig, Vol., No., Ma 5 The Firig Dispersio of Bullet Test Sample Aalsis Youliag Xu, Jubi Zhag, Li Ma, ad Yoghai Sha Udisputed, this approach does reduce the ifluece of radom factors i a certai extet, but ol decreases ad has ot bee completel elimiated, effect still exists, but iversel with the amout of sample selectio, the larger the sample sie, the less effect, shootig rage test data is more close to the true value, but the actual situatio is ot possible samples rage test the extracted amout is large eough, so the estimate value does ot exist ca be compared with the true value. I this paper, statistical aalsis, ad strive to draw the permissible level of sigificace, ad kept withi the limits of pseudo-probabilit optimum firig. Abstract For the past, bullet dispersio test firig bullets more tha the umber of groups, the cosumptio of large bombs ad other issues, This article adopts a ew method, usig the previous tests produce a lot of dispersio test data, basig o statistical theor of bullets dispersio test sample sie i-depth aalsis ad research to determie the test firig is reasoabl ecessar umber of groups ad sigle group umber issued, which will help bullet-dispersio test methods to improve ad perfect. Usig this method, we ca use the previous bullet shootig precisio data, scietificall determie the bullet itesive experimetal group umber ad the umbers each group. Save ammuitio test fud ad time. Idex Terms Bullet, dispersio, test, the umber of bullets. II. SCATTERED ROJECTILES RELATIONSHI WITH I Chia, the projectile dispersio models alwas use []: I. INTRODUCTION Weapos sstems productio ad processig is a complex process, despite the strict cotrol of the productio coditios, there are idividual differeces, but also i the shootig, also caot cotrol the shootig coditio ad weather coditio completel, so the ammuitio i the placemet appears scatter is ievitable. Because of effect of iitial velocit, agle ad the ballistic coefficiet ad the resultig dispersal distace; directio spread because of aimuth agle, iitial disturbace ad the bias curret (drift) effect. So, the itesit of weapo sstem is affected b ma ucertai factors, therefore, the itesit of result evaluatio should ot ol rel o the small sample test data were radoml selected to, but should use the method of mathematical statistics to carr o the sstem aalsis. The curret domestic dispersio test [], mail has the followig two kids of test ad evaluatio methods: A. A Series of Test Method Tested uder the coditio of ormal temperature is shootig 6 groups, i each group, the mea value of the test results are compared with the tactical ad techical idex, ad get the coclusio of the sample dispersio whether meet the requiremets. a a f (, ) e () The formula: f (, ) : Height, directio of coordiate (, ) probabilit dispersio fuctio;, : The probabilit dispersio fuctio of the variables, amel the impact poit coordiate; a, a : The level ad directio of the coordiates of the ceter poit of impact spread;, : The level ad directio of the impact poit spread stadard deviatio. R, o the basis of the defiitio of The fire itesit of R, the: f, ddx.5 () R (, ) of the probabilit dispersio fuctio ut the B. The Method of Hpothesis Testig Statistical aalsis of experimetal data, usig K test o the tested cocetratio whether meet the requiremets give the exact coclusio. At preset, the rage of dispersio test is take b the first method, this method is based o the test data are averaged to elimiate the ucertait of shootig ad meteorological coditios of the resultig effects o the dispersio, the estimated value is closer to the true itesit of the test values. of f (, ) ito tpe. There are: R e a Let r cos, Mauscript received October 9, 4; revised December 5, 4. The authors are with the Baicheg Ordace Test Ceter, Chia ( hemmler@6.com). DOI:.776/IJMMM.5.V.8 R 4 R d e a ddx.5 () r si ;,the: r cos a r si a rdr.5 (4)

2 Iteratioal Joural of Materials, Mechaics ad Maufacturig, Vol., No., Ma 5 Assumptio coicides of projectiles dispersio ceter ad the ceter of the target or target poit [], there are a a, formula (4) ca be trasformed ito: R de r cos si rdr.5 Hpothesis a projectile overall as two-dimesioal ormal radom variable,, the stadard deviatio is: (5) i ˆ i (6) i ˆ i (7) where ˆ is the estimated value of stadard deviatio. III. THE SAMLE SIZE ESTIMATION OF SHOOTING A. Give Sigificace Level ad Kept Shootig seudo-robabilit Sample of the Total Amout To determie the sample sie, is oe of the most importat problems i the dispersio test. I the parameter estimatio, there are two methods for determiig sample sie: ) The accurac of the estimates requested this requiremet to determie the sample sie ) permissible deviatio is give as well as the cofidece level, accordig to the give ad, determie the sample sie. Give the probabilit of makig the first mistake ad allowed deviatio, overall distributio i the ˆR case it is ukow S whether the comparative sample R ad ˆR required overall, the cofidece level for a give, the average meas icluded i the iterval ( X, X )[4]. I the curret bullets itesit test, a desig-dispersio requiremet is (R ) ad R accordig to the give test whe a sigificat level decided to test the boudaries. Whe the itesit idex exceeds the specified value to a certai extet ( R R ), the probabilit of its existece o more tha pseudo- [5]. Do statistic : R R Whe the R R uder the coditios established, the statistic degrees of freedom of the variable, for a give level of sigificace, ca determie boudaries. So that ( ). Whe the R R uder the coditios established b the probabilit of ( )., ma decide to, so that This has, where R r. r R The upper side is give probabilit, satisf the threshold value as:, e It follows that the overall sample: v u x- v- - ru r, draw: dx The overall sample sie ca be expressed as u ru r B. The Total Sample Sie ad Error Aalsis For R, with formula (8), sample sie ca be calculated (R ) R R ( R) u u r The is the relative test error. (R ) From the above formula ca be see, with the icrease of overall sample sie, the relative errors are graduall reduced, whe the sample sie teds to ifiit, the relative test error teds to ero. The total sample above formula from ero to ifiit [6], the calculated relative test error tred with the chage of sample sie as show i Fig.. As ca be see, the relative test error decreases as the sample sie icreased overall, but the sample sie after more tha oe hudred rouds of ammuitio, the relative test error decrease slowl. Ca be selected i the test error coditios are relativel acceptable uder ecoomic sample volume. I order to further stud of the relative error chages with the sample sie, the Fig. amplificatio (see Fig. ), it ca be see from Fig., the test sample sie of more tha 4 rouds of ammuitio, the relative error is less tha.. (reducig test applicatio percetage or scores of thousads). So, eed (8) 5

3 Iteratioal Joural of Materials, Mechaics ad Maufacturig, Vol., No., Ma 5 Assumig dispersio test, optimum sample sie for N=4, i.e.: m N, It ca cosider two cases. Fixed, make m chage; or fixed m, chages. to test meet the itesit overall sample volume dispersio check 4 bullets ca be better. That is: m 4 4, m Will it ito (9) formula, there is: R 8( ) Rˆ Rˆ.77 () R 4 m () The formula (), (), the umber of groups ad the umber of bullets m from ero to ifiit, the chage tred of Fig.. Relative to examie the relatioship betwee error ad the overall sample sie. ito three-dimesioal images: Fig.. artial elargemet of Fig. That is: whe the =%, =%, the total sample Fig.. ad the group ad group M relative umber. shootig is =4. See from Fig., uder certai shootig sample coditio, C. Shootig Group Number ad the Number of Its Estimatio Accurac Geerall speakig, i the firig dispersio test, ofte some sstem errors, ad iterfere with test results. I order to reduce the iterferece, we ofte use multiple shootig methods. Accordig to the limit law, sstem error radom obe ormal distributio, the distributio ceter for the O, variace of the bullet firig dispersio estimatio accurac of decided b the group umber ad bullet umber m, the firig precisio of the For the m ˆ Ri m i D. Shootig Groups ad Bullets to Determie the Number This paper will aalsis ad deductio o the basis of the above theor, the test data for the support, to cofirm the bullet dispersio test sample. Check our troops i recet ears a small-bore rifle bullet dispersio test results, the umerical values are listed i the followig table: R : For a small-bore rifle bullet. R i oe hudred (9) meters is.cm, i three hudred meters is 6.6cm. TABLE I: A SMALL-BORE RIFLE BULLET DISERSION TEST FOR M the estimatio accurac is: R m ( ) R m( ) coditios, the optimal umber must have a group of ad the bullets of m i pairs. R, ca be approximated as ubiased estimatio, Rˆ I the shootig test group ad each shot umber the same, Rˆ was half will hit the radius estimatio formula for () i 6

4 Iteratioal Joural of Materials, Mechaics ad Maufacturig, Vol., No., Ma 5 Check for ears archive i our troops, durig the period 999 ~5,some small-bore rifle bullets i the dispersio test R for m, m results are show i Table I ad Table II. TABLE II: A SMALL-BORE RIFLE BULLET DISERSION TEST FOR M Fig. 7. Fig. 6 amplificatio. Accordig to the above formula ()-(), ad the total sample sie of 4 bullets, trasform test group umber ad bullet umber m, obtais the m dispersio test i the estimatio accurac ad the group umber, the bullet umber of the relatioship betwee D graph ( Fig. 4-Fig. 7). From Fig. 5 ad Fig. 7 ca be see, the estimatio accurac sigificatl chage state (i.e. color chages rage) correspodig to 4 groups, each group i group te bullets. Fig. 4. The relatioal graph betwee estimated accurac ad group umber the bullet umber i a small-bore rifle bullet dispersio test for m. IV. CONCLUSION From the above aalsis results show that, for small-bore rifle bullet, the best umber of bullet samples ad packet for dispersio test should be: overall sample sie of 4 bullets, 4 groups, each group of rouds.: total umber of samples take 4 bullets, divided ito 4 groups, each group has bullet. Usig the method described i this article, ca be based o extesive experimetal dispersio data, scietific ad itesive sample take the bullet test. REFERENCES [] [] Fig. 5. Fig. 4 amplificatio. [] [4] [5] [6] X. Tag et al., Test Aalsis ad Evaluatio of Weapo Equipmet i Small Samples, Natioal Defese Idustr ress, Chia,, pp Z. Ya et al., Statistical Aalsis of Test Data, Natioal Defese Idustr ress, Chia,, pp C. eg, Error ad Retur, Weapo Idustr ress, Chia, 989, pp. -. Z. He ad G. Li, robabilit Theor ad Mathematical Statistics, Weapo Idustr ress, Chia, 99, pp C. a ad Z. Ha, Weapos ad Ammuitio Test ad Ispectio robabilit, Weapo Idustr ress, Chia, 98, pp G. Wag et al., Dispersio of multiple weapo sstem simulatio techolog, Joural of Sstem Simulatio, vol. 6, pp , Ma, 4. Xu Youliag was bor i 978, Sichua provice, Chia, who received his master degree from Uiversit of Sciece ad Techolog of Chia. He is a mechaical ad electroic professioal, ad a seior egieer of Baicheg Ordace Test Ceter. His preset professioal occupatio is focused o mechaical performace test. He has ma ears of experiece i simulatio testig ad data processig, His curret research iterests are i the comprehesive evaluatio of mechaical properties. Fig. 6. The relatioal graph betwee estimated accurac ad group umber the bullet umber i a small-bore rifle bullet dispersio test for m. 7

5 Iteratioal Joural of Materials, Mechaics ad Maufacturig, Vol., No., Ma 5 Zhag Jubi was bor i 97, Sichua provice, Chia. He received his bachelor degree from North Chia Istitute of Techolog. He is a mechaical ad electroic professioal, ad a seior egieer of Baicheg Ordace Test Ceter. He preset professioal occupatio is focused o mechaical desig ad aalsis of optimiatio. At preset, his research iterest is data optimiatio aalsis. Sha Yoghai was bor i 964, Jili provice, Chia. He is a researcher of Baicheg Ordace Test Ceter, a hd of Xia Jiao Tog Uiversit, ad a sstems egieerig professioal. His preset professioal occupatio is focused o mechaical desig ad test appraisal work. His curret research iterests is i the mechaical sstem overall plaig. Ma Li was bor i 96, Jili provice, Chia. He received his master degree from Uiversit of Sciece ad Techolog of Chia. He is a mechaical ad electroic professioal, a researcher of Baicheg Ordace Test Ceter ad a chief egieer. His preset professioal occupatio is focused o large overall data aalsis work. His curret research iterest is i the mechaical sstem overall plaig. 8

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