Prediction Model for the Dispersion Pattern of Pre-Controlled Fragments from a Multi- Layer Ring Casing

When a cylindrical shell filled with high explosives is detonated from one end, the metal casing does not simply blow apart into a random cloud of debris. Instead, the force of the explosion drives the metal outward, breaking it into distinct pieces that fly away at specific angles. This behavior is critical for modern weapons known as pre-controlled fragmentation warheads, where engineers deliberately shape the casing to break into uniform, predictable pieces. The goal is to control exactly where these pieces go and how fast they travel, ensuring the weapon hits its target with maximum effectiveness. However, predicting the exact path of these flying fragments is a difficult problem. The explosion creates complex waves of pressure that travel through the metal, and these waves do not act the same way at every point along the cylinder. The pressure is strongest near the point where the explosion starts and weaker at the far end, creating a gradient that pushes the fragments in slightly different directions depending on their position. For decades, scientists have used mathematical rules to guess these angles, but those rules often fail to account for the subtle ways the metal bends and turns as it flies, leading to significant errors in prediction.

A team of researchers at Nanjing University of Science and Technology and North Huaan Industry Group set out to solve this specific puzzle for a type of warhead made of stacked metal rings. These multi-layer ring casings are popular because they are cheap to make and produce fragments of very consistent size. The researchers wanted to understand why the fragments from these rings fly at the angles they do, and to build a new way to predict that behavior accurately. They began by creating detailed computer simulations of the explosion. Using powerful software, they modeled the warhead as a quarter of a cylinder, filling it with explosive material and surrounding it with air. They tested twenty-one different versions of the warhead, changing the length of the cylinder, the height of the individual rings, the depth of the grooves cut into the metal, and even the type of explosive used. By watching these virtual explosions unfold, they could track the speed and direction of every single fragment as it was born and flew outward.

The simulations revealed a clear pattern that existing theories had missed. The fragments do not fly in a straight line away from the center; they tilt. Near the end where the explosion starts, the fragments tip backward, pointing toward the rear of the warhead. Near the opposite end, they tip forward. In the middle section, they fly almost straight out. This tilting happens because the explosion creates a difference in speed along the length of the cylinder. The metal in the middle is pushed harder and moves faster than the metal at the ends. As a fragment flies away, this difference in speed between its top edge and its bottom edge causes it to rotate, much like a spinning top that leans as it moves. The researchers found that the size of this tilt depends heavily on how tall the individual metal rings are and how fast the explosion wave travels through the specific type of explosive used. Surprisingly, they discovered that the material of the metal casing, the overall diameter of the warhead, and the depth of the grooves cut into the metal had almost no effect on the angle at which the fragments flew. The tilt was driven almost entirely by the speed difference created by the explosion itself.

To turn this observation into a useful tool, the team developed a new prediction model. They realized that the angle of the fragment is the result of two separate forces acting together. The first is the direct push from the explosion, which sends the fragment outward. The second is the tilt caused by the speed difference along the ring. By measuring how long it takes for a fragment to stop changing its direction after the explosion, they could calculate the exact amount of tilt. They introduced a concept they called "stabilization time," which is the moment when the fragment's flight path becomes steady. They found that this time is directly related to the height of the ring and the speed of the detonation wave. Using this relationship, they created a formula that combines the outward push and the tilt to predict the final angle. When they tested this new formula against their computer simulations, it matched the results almost perfectly, capturing the complex curve where the angle is negative at one end, positive at the other, and flat in the middle.

To be sure their computer models were correct, the researchers built real warheads and tested them in a controlled environment. They constructed two different versions of the ring-casing warhead and detonated them in front of a steel plate. Using high-speed cameras and sensors, they recorded exactly where the fragments hit the plate and how fast they were traveling. The real-world results matched their computer simulations closely, confirming that the fragments did indeed tilt backward at the start and forward at the end. When they applied their new formula to these real-world measurements, the predictions were accurate within a margin of error of less than fifteen percent. This was a vast improvement over older methods, which could be off by as much as seventy percent at the ends of the warhead. The researchers then tested their formula against data from other scientists who had studied different types of pre-formed fragments, including square and spherical shapes. The formula worked well for those as well, suggesting that the physics of the tilt applies to many different kinds of cylindrical warheads, not just the ring-casing type they studied.

The work provides a reliable way for engineers to design warheads with precise control over where their fragments will fly. By understanding that the tilt is caused by the speed difference along the cylinder and that this tilt can be predicted based on the ring height and explosive speed, designers can now calculate the lethal range of a weapon with much greater confidence. The study confirms that the material of the casing and the diameter of the warhead are not the primary factors in determining the flight angle, allowing engineers to focus on the dimensions of the rings and the type of explosive to achieve the desired effect. This new model offers a clear, practical path for improving the design of modern munitions, ensuring that the energy of the explosion is directed exactly where it is needed.