The Capability of Destroying a Maneuvering Target Prof. Yacov Bar-Shlomo ORT Braude College UNCLASSIFIED

ORT Braude College UNCLASSIFIED The Capability of Destroying a Maneuvering Target 2 Introduction In the present work a system analysis of the capability of destroying a maneuvering target is performed. The probability of killing a target is dependent on: The pursuer warhead size; The miss distance size; The geometry of warhead fragments and their energy; Each of the factors of a successful pursuit, is influenced and contributes to all other. In that presentation we will discuss the interaction between the main factors to a successful encounter. The presentation is based on independent research done by the author.

ORT Braude College UNCLASSIFIED The Capability of Destroying a Maneuvering Target 3 Warhead Assumptions Spherical Warhead radius Discrete spherical fragments Condensed envelope of fragments. Spherical explosive with specific velocity Sealed envelope. Warhead total weight: Detonation according to Gurney assumption

ORT Braude College UNCLASSIFIED The Capability of Destroying a Maneuvering Target 4 Gurney Assumption The product gasses of the detonation are at rest in the center of the sphere, and their velocity increases linearly with the distance from the center. In that case it can be shown that the energy is divided between the gasses and the metal enclosure according to: We assume that the fragments energy does not diminish during their flight to the target. It can be shown that fragments velocity at the target is: where:

ORT Braude College UNCLASSIFIED The Capability of Destroying a Maneuvering Target 5 Fragments Quantity and Energy In case that we maintain the warhead geometry, the weight relation between the metal envelop and if the explosive fills all the allowed spherical volume, we can reach the following conclusion about the lower bound of fragments quantity: where: In that case, it is possible to estimate that the single fragment energy is: where:

ORT Braude College UNCLASSIFIED The Capability of Destroying a Maneuvering Target 6 Pursuing Missile Assumption We assume that the pursuing missile characteristics are: Length: Diameter big enough to hold the warhead: The ratio between the length and the diameter is: Aerodynamic steering with lateral forces proportional to the angle of attack: The conclusion is that the pursuer aerodynamic time constant is: where:

ORT Braude College UNCLASSIFIED The Capability of Destroying a Maneuvering Target 7 The Miss Distance and The Vulnerable Cross Section To estimate the miss distance, a simplified model is used. We assume that the miss distance is proportional to pursuing missile maneuver: It can be estimated that: For that miss distance, the footprint of a single fragment is: Assume that the total needed energy for the target kill is: Then the total needed footprint at the target is: Therefore it is requested that the target vulnerable cross section is bigger then :

ORT Braude College UNCLASSIFIED The Capability of Destroying a Maneuvering Target 8 Conclusions from the Last Equation The research main problem is the minimization of the total needed footprint. is not an explicit function of the miss distance. is proportional to the total needed damage energy, and to the square of the maneuvers. is inverse proportional to the explosive energy, fragments specific weight, and the warhead size. There is an optimal value for which the needed fragments footprint is minimal:

ORT Braude College UNCLASSIFIED The Capability of Destroying a Maneuvering Target 9 Numerical Example We choose a warhead radius of 0.1m, steel fragments (specific weight 7.9), explosive Comp. B (s.w. 1.71) angle of attack of and maneuver of ; It is calculated that: (that is about 10% of the expected missile weight) and fragment energy. On the assumption that the kill energy is 1MJ, then:

ORT Braude College UNCLASSIFIED The Capability of Destroying a Maneuvering Target 10 Parametric Analysis In that figure we analyze the total needed footprint as function of metal proportion in the total warhead weight, in a case of 0.4m diameter warhead, steel fragments and Comp. B explosive:

ORT Braude College UNCLASSIFIED The Capability of Destroying a Maneuvering Target 11 Minimal Damaged Cross Section Next, in the attached figure we analyze the total needed footprint as function of the warhead size and diverse fragment metals.

ORT Braude College UNCLASSIFIED The Capability of Destroying a Maneuvering Target 12 Summary and Conclusions In that work, based on some simple assumptions, we estimate the damaged cross section of maneuvering target, and the capability of its destruction. The warhead weight and size determine the pursuer size and its aerodynamic time constant and therefore influence the encounter miss distance. It is feasible to use diverse models for the warhead or miss distance that differ from those used here, but the end results are expected to be essentially similar. The main conclusion is that in a certain envelope, the bigger the warhead the smaller is the necessary damaged cross section.