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    • In order to obtain the analytic expression

    2018-11-03

    In order to obtain the analytic nuclear receptors of , we assume that the is a constant. Thus, Eq. (9) can be integrated from t0 to t.note that, from Eq. (10) that, in order for to be convergent, should be greater than 2. Integrating Eq. (10) at the interval from t0 to t,when t = tf, λf is the final LOS angleThus, the rate bias is obtained from Eq. (12),in Eq. (13), the rate of offset angle is a constant. In order that a more accurate rate of offset angle is achieved by using BRPN guidance law, Eq. (13) can be rewritten aswhere tgo is time-to-go. And time-to-go is defined as . λf can be obtained from Ref. [9] as Thus, the final path angle γf is the impact angle as mentioned above. Therefore, we can determine the impact angle to identify the value of λf by Eq. (15). The BPN lateral commanded acceleration is defined as [9] In the above derivation, Eqs. (14) and (16) are used for TV-BPN guidance. Note that, in the classical BPN guidance law, the navigation ratio N is larger than 0. The interception path is shown in Fig. 1 (path DC). On the other hand, the BRPN guidance law is to compute the interceptor lateral acceleration using Eq. (16) but use a negative value for navigation ratio N; that is N < 0. The interception path is shown in Fig. 1 (path DA). In BRPN guidance, the current time can be considered as the initial time to get better accuracy. And time-to-go is defined as .
    Simulation results Simulations were run in a MATLAB environment where they were terminated when Vc < 0. The range value Rf at this final instant happens to be the miss distance. The target speed Vt is 1500 m/s with (Xt,Yt) = (10,000 m, 10,000 m).The interceptor speed Vm is 600 m/s; and the initial range Ri is 10,000 m. The initial position of interceptor can be calculated by using R and initial LOS angle λi. The seeker model is of a perfect seeker (without noise) with a sufficient large field of view, but it is assumed to be unable to track the target when the range is shorter than 30 m [1], after which the guidance command maintains its last value. The simulations are carried out in a planar engagement scenario.
    Conclusions
    Acknowledgments
    Introduction Explosive reactive armors (ERA) have been widely used as add-on-armors against shaped charge jets and long rod armor piercing projectiles. The disturbance of explosive reactive armors on jet penetration was studied in this paper. Most ERA has a sandwich configuration consisting of a front plate, an interlayer explosive, and a rear plate. When the interlayer explosive is penetrated by a shaped-charge jet, it explodes, accelerating the front and rear plates to move outwards in their normal directions. The moving plates and detonation products interact continuously with the jet, significantly disturbing its motion. The jet may bend, break and scatter around its original axis, resulting in a significant reduction in the penetration into the primary target behind the reactive armor [1]. To increase its disturbance on the jet, which frequently strikes the target at various impact angles, V-shaped sandwich reactive armors were introduced. In a V-shaped configuration, two sets of flat ERAs, consisting of its own front plate, high interlayer explosive and rear plate, are placed at a specific angle [2]. A number of experimental and analytical studies have been made to investigate the disturbance mechanism of reactive armors on jet penetration. With the aid of X-ray photography, Wu and Huang measured the plate velocity of ERA detonated by a jet [3,4]. Mayseless, Rototaev and Liu established the theoretical models which could predict the disturbance effect of ERA [5–8], respectively. Murr and Held have studied the effects of the thicknesses of sandwich plate and interlayer explosive on the efficiency of ERA [9,10]. Held also investigated the influences of the boundary effect of an ERA [11] and the distance between ERA and the main target on the efficiency of ERA [12]. Held found out that the reduction effect in penetration remains also more or less constant in the case of hitting the top or the bottom, where only the front and rear plates interact with the jets, in vertical directions.