15th International Syposiu on Ballistics Jerusale, Israel, 21-24 May, 1995 OS-ERFORAION LENGH AND VELOCIY OF KE ROJECILES WIH SINGLE OBLIQUE ARGES R. Jeanquartier, W. Oderatt Defence echnology and rocureent Agency Ballistics and Weapons Systes Branch CH-3602 hun, Switzerland In the context of vulnerability studies there is a strong need for siple ethods for predicting the perforation liit and - in case of perforation - the reaining length and velocity. An epirical forula for the perforation liit of long rod penetrators with single oblique targets has been deduced fro a non-diensional ansatz with analytical constraints. he following agnitudes enter the forula: aterial properties (tensile strength and density), length to diaeter ratio of penetrator, obliquity and thickness of target and ipact velocity. If the ipact velocity is greater then the one required for the perforation liit, the reaining length and velocity of the penetrator can be deterined with a siple calculation on the base of the penetration forula. INRODUCION At the 13th International Syposiu on Ballistics an ansatz has been presented for calculating the perforation liit of ADSFS aunition in the caliber range of 105 to 140 hitting an oblique single target [1]. In the eantie this ansatz could be refined by including results about the influence of tensile strength of the target aterial. he necessary experients were carried out in our indoors firing facility. he set of experients now available covers the following range of values: - 74 test results with 19 different penetrators - Calibers 25, 30, 35, 105, 120, 140 15th International Syposiu on Ballistics - 1 -
- enetrators properties Lengths L 90-825 Diaeters D 8 32 Length to diaeter ratios L/D 11-31 Rod densties 17000 17750 kg/ 3 Rod asses 0.1 0 kg Ipact velocities v 1100 1900 /s - arget properties late thickness d 40 400 ensile strength R 800 1600 Ma Obliquities (NAO) θ 0 74 Density 7850 kg/ 3 Fig 1: Definitions he effective penetrator length L is defined in the following way: starting fro the actual penetrator the tip is replaced by a cylinder of equal ass and diaeter D and the reaining length reduced by D (see Fig 1). ERFORAION LIMI he perforation forula is coposed of four diensionless ters with separate representation of the influences of length to diaeter ratio 1, target obliquity 2, density ratio of penetrator to target 3 as well as aterial properties and incident velocity 4. he forula is valid for L/D greater than 10 and within the range of experiental values as listed above. 15th International Syposiu on Ballistics - 2 -
General penetration forula d D = a L D ( cos θ) e c R 2 v (1) 1 2 3 4 L 10 L L where: a = + 3.94 1 tanh D (2) D D 11.2 c = 22.1 + 1.274e -8 R 9.47e -18 R 2 = 0.775 R easured in [a] (3) Influence of length to diaeter ratio he ter 1 tends to L/D as L/D gets large (L/D greater than 20). he plate thickness for liiting perforation is given by d = L ( cos θ) e c R 2 v Considerations for the transition region For perpendicular ipact (obliquity = 0 ) and very high velocities, the ters 2 and S tend to 1. For L/D greater than 20 the penetration forula now becoes identical to the one for hydro-dynaic penetration: (4) d = L (5) Influence of tensile strength of the tar get plate he product c-r is increasing with increasing tensile strength up to 1300 Ma and then reains practically constant up to the the investigated tensile strength of slightly ore than 1600 Ma. hus an increase of target tensile strength beyond 1300 Ma did not result in a decrease of the liiting perforation length in our experients. If this behaviour is valid in general cannot deterined, because in this range of tensile strength, to date we have only few results available as can be seen fro Fig 2. We intend to carry out additional experients. However with the penetration forula presented here the range of 700 to 1300 Ma is covered reliably. 15th International Syposiu on Ballistics - 3 -
Fig 2: Values for c-r fro experiental results Accuracy of the forula In Fig 3 the results of 74 perforation liits are presented in a diensionless for. he axes have been chosen as follows:fig 3: Accuracy of the forula x-axis: c R v y-axis: d a D L D 1 ( cosθ) Fig 3: Accuracy of the forula he correspondance between experient and the forula is good. he axiu differences are only 6% and the standard deviation is 2.6%. 15th International Syposiu on Ballistics - 4 -
OSERFORAION LENGH AND VELOCIY erinal ballistc test procedure A sooth bore 38 experiental gun is used to launch test rods at velocities V = 1200-1600 /s. We use rods with length to diaeter ratios of 14 and 20 which are supported by an aluiniu sabot. argets are set at obliquities of either 0 or inbetween 42 and 52 degrees NAO. At short distance before the target a sheet of paper is placed in order to deterine the yaw of the projectile (the yaw angle ust not exceed 1 ). he postperforation paraeters (residual length and velocity) are deterined with two flash X-rays. he trigger for the first X-ray is placed on the target itself, the trigger for the second at 0.67 behind. he whole test arrangeent is depicted in Fig 4. Fig 4: est arrangeent 15th International Syposiu on Ballistics - 5 -
Fig 5 shows the picture of a residual projectile 0.2 s after hitting the target, as recorded by the first X-ray. Fig 6 shows the sae projectile after another 0.476 s, recorded by the second X-ray. he effective flight distance in between the two pictures is 0.54 which gives a residual velocity of 1134 /s. Fig 5: 1 st X-ray picture Fig 6: 2 n d X-ray picture Definition of the effective residual length Residual length LR e ff is deterined with the help of X-ray pictures right behind the target. he total length of the residual projectile is coposed of the length of the practically non-defored part of the projectile and the average length of the head fragents (see Fig 7) Fig 7: Definition of residual length ostperforation penetrator velocity ostperforation velocity could be calculated in a siple anner. Fig 8 presents our experiental results and shows the dependence of scaled residual velocity on the ratio of actual perforation to perforation liit according to forula (1). 15th International Syposiu on Ballistics - 6 -
Fig 8: est results together with approxiation function. he penetrator tail is gradually slowed down by the elastic shock waves which are induced by reflection off the penetrator tip. In a tension-free rod the velocity difference can be deduced with considerations fro continuu echanics: σ tensile strength 2 σ Δ v = (6) E Young's odulus penetrator E density For the present case a Δv of 45 /s yielded the best agreeent with test results, deonstrated by the stair line which has been calculated on this base. If the tensile strength is deterined fro Δv, the Young's odulus and the density, a value of 1800 Ma is obtained. In static pull experients, a tensile strength of 1400 Ma has been easured. he difference can be explained by dynaic effects. Very good fitting results are obtained with the following ansatz: v R v 1 + a ln 1 d d = li (7) he coefficient a depends indirectly proportional on ipact velocity and less strongly on aterial properties und geoetry of the penetrator. Fitting of our test results gave a value of 0.14. With consideration of the velocity level alone this value is already well suited for arbitrary estiates. 15th International Syposiu on Ballistics - 7 -
ostperforation penetrator length Fig 9 presents our test results of scaled residual length as a function of the ratio of actual perforation to perforation liit according to forula (1). Fig. 9: est results together with approxiation function he length L is defined according to Fig 1. he residual length LR corresponds to the effective residual length LR e ff according to Fig 7, reduced by one-and-a-half ties the diaeter D. With these definitions the following siple relation in between scaled residual length and scaled perforation is obtained: L R /L=l-(l-b)-d/d ]i -b-(d/d ]i ) 2 (8) In the considered range of velocities of 1400-1500 /s the coefficient b takes the value of 0.2. With higher velocities b tends to zero i.e. the parabola is reduced to a straight line through points (0/1) and (1/0). With saller velocities b becoes larger than 0.2, the parabola has a slightly bigger curvature. CONCLUSIONS Instead of coplicated coputing codes, the siple forulae presented here can be used effectively for paraeter and perforance studies and in vulnerability odels. REFERENCES [1] W. Lanz, W. Oderatt, "enetration Liits of Conventional Large Caliber Anti ank Guns / Kinetic Energy rojectiles", roceedings of the 13th International Syposiu on Ballistics (1992), Vol. 3, pp. 225-233. 15th International Syposiu on Ballistics - 8 -