Method for calculating safe distance and vertical height of static explosion test
Calculate the safety distance and vertical height of the static explosion test through the ballistic differential equation model and the fourth-order Runge-Kutta numerical integration method, which solves the problem of inaccurate safety distance in the existing technology, and achieves more accurate safety assessment and test safety improvement.
Patent Information
- Application Number
- CN202410153361.3
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2024-02-04
- Publication Date
- 2025-08-05
AI Technical Summary
When calculating the safe distance of the static explosion test, the prior art ignores the velocity changes and gravity of the vertical direction of the fragment in the air, resulting in inaccurate safety distance and inability to provide information in the height direction, affecting the safety and reliability of the test.
The ballistic differential equation model is used to combine the fourth-order Runge-Kutta numerical integration method, considering the influence of air resistance and gravity, traversing different elevation angles, and calculating the motion trajectory and velocity of the prefabricated fragments, and determining the safe distance and vertical height by comparing the end velocity with the threshold.
It improves the accuracy and reliability of the safety distance of the static explosion test, can provide three-dimensional safety assessment, and ensures the safety and reliability of the test.
Smart Images
Figure CN120429531A_ABST
Abstract
Description
Technical Field
[0001] The present invention relates to the technical field of warhead testing, and in particular to a method for calculating a safety distance and a vertical height of a static explosion test. Background Art
[0002] A high-kill explosive warhead is a warhead that uses the explosion of explosives to drive prefabricated fragments or natural fragments to fly in all directions, and uses kinetic energy to penetrate the target. A high-kill explosive warhead is generally composed of explosives, prefabricated fragments, a liner, a shell, a cover plate, and a fuse. A static explosion test is a common range test in which the warhead is detonated under static conditions to examine its various powers. For a high-kill explosive warhead, the main focus is on its shock wave and fragment penetration power. A static explosion test is a highly dangerous test that requires identifying the source of danger based on the specific details of the test, determining countermeasures one by one, formulating detailed test safety protection plans and implementation details, and implementing strict safety protection for test personnel and equipment. Safety distance is the primary indicator for evaluating the safety of static explosion tests and implementing further safety protection measures. It determines the feasibility of implementing a specific static explosion test at a specific test site.
[0003] At present, the safety distance assessment for static explosion tests of anti-explosive warheads usually adopts the engineering calculation method, which uses empirical or semi-empirical formulas to calculate the velocity attenuation of fragments to determine the safety distance. However, this method ignores the actual movement trajectory of fragments in the air and only considers the velocity attenuation in the horizontal direction. It does not consider the velocity change and gravity effect in the vertical direction. As a result, the obtained safety distance is inaccurate and cannot accurately reflect the movement pattern and distribution of prefabricated fragments in the air. It also cannot provide information in the height direction, resulting in poor safety and reliability of static explosion tests. Summary of the Invention
[0004] The purpose of the present invention is to solve the problem that the safety distance of the static explosion test obtained by the existing technology is inaccurate and cannot provide information in the height direction, which leads to poor safety and reliability of the static explosion test, and proposes a method for calculating the safety distance and vertical height of the static explosion test.
[0005] A method for calculating the safety distance and vertical height of a static explosion test is as follows:
[0006] Step 1: Obtain prefabricated fragment information and environmental parameters at each elevation angle of the static explosion test, and input the prefabricated fragment information and environmental parameters at each elevation angle into the ballistic differential equation model. Traverse different elevation angles and solve the ballistic differential equation model using fourth-order Runge-Kutta numerical integration to obtain the lateral position, vertical position, and velocity of the prefabricated fragment at different times at each elevation angle. The lateral position, vertical position, and velocity are stored in the lateral position array X, vertical position array Y, and velocity array V at each elevation angle, respectively.
[0007] Step 2: Obtain the terminal velocity of the prefabricated fragment in the velocity array V at each elevation angle, and compare the terminal velocity of the prefabricated fragment with the preset velocity threshold v L For comparison, if the terminal velocity of the prefabricated fragment is less than or equal to v L , then the lateral position corresponding to the terminal velocity of the prefabricated fragment is the safety distance, and all safety distances are stored in a new array to obtain a safety distance array;
[0008] The terminal velocity of the prefabricated fragment is the last element in the velocity array V;
[0009] Step 3: Get the maximum value R in the safe distance array. The distance greater than R is the safe distance range, and obtain the trajectory height in the vertical position array Y based on the safe distance array.
[0010] Furthermore, the prefabricated fragment information includes: the initial velocity v0 of the prefabricated fragment, the mass m of the prefabricated fragment, the cross-sectional area A of the prefabricated fragment, the drag coefficient C of the prefabricated fragment, and the initial velocity v0 of the prefabricated fragment. d ;
[0011] The environmental parameters include: air density ρ and gravitational acceleration g.
[0012] Furthermore, the ballistic differential equation model is as follows:
[0013]
[0014]
[0015]
[0016]
[0017] Where x is the horizontal position of the prefabricated fragment, y is the vertical position of the prefabricated fragment, and v x is the horizontal velocity of the prefabricated fragment, v y is the vertical velocity of the prefabricated fragment, t is the time, and ρ is the air density.
[0018] Furthermore, the fourth-order Runge-Kutta numerical integration is used to solve the ballistic differential equation model, specifically:
[0019] First, the preset elevation angle θ is traversed every 1°. For each elevation angle within the range, the following parameters are initialized: initial horizontal position x = 0, vertical position y = 1.5 meters, time t = 0, horizontal speed v x =v0cosθ, vertical velocity v y =v0sinθ;
[0020] Then, the fourth-order Runge-Kutta method is used to solve the differential equation model as follows:
[0021]
[0022]
[0023]
[0024]
[0025] Where n∈[0,+∞], n is the number of time steps, x n is the horizontal position of the prefabricated fragment at the nth time step, x n+1 is the horizontal position of the prefabricated fragment at the n+1th time step, y n is the vertical position of the prefabricated fragment at the nth time step, y n+1 is the vertical position of the prefabricated fragment at the n+1th time step, v x,n+1 is the lateral velocity of the prefabricated fragment at the n+1th time step, v x,n is the lateral velocity of the prefabricated fragment at the nth time step, v y,n+1 is the vertical velocity of the prefabricated fragment at the n+1th time step, v y,n is the vertical velocity of the prefabricated fragment at the nth time step, k 1x 、k 2x 、k 3x 、k 4x 、k 1y 、k 2y 、k 3y 、k 4y 、k 1vx 、k 2vx 、k 3vx 、k 4vx 、k 1vy 、k 2vy 、k 3vy 、k 4vy is an intermediate variable.
[0026] Furthermore, k 1x 、k 1y 、k 1vx 、k 1vy Obtained by the following formula:
[0027]
[0028]
[0029]
[0030]
[0031] Where Δt is the time step, t n is the time of the nth time step.
[0032] Furthermore, k 2x 、k 2y 、k 2vx 、k 2vy Obtained by the following formula:
[0033]
[0034]
[0035]
[0036]
[0037] Furthermore, k 3x 、k 3y 、k 3vx 、k 3vy Obtained by the following formula:
[0038]
[0039]
[0040]
[0041]
[0042] Furthermore, k 4x 、k 4y 、k 4vx 、k 4vy Obtained by the following formula:
[0043]
[0044]
[0045]
[0046]
[0047] The beneficial effects of the present invention are:
[0048] The present invention considers the effects of air resistance, gravity, and the shape, mass, and material of prefabricated fragments on their motion and proposes a ballistic differential equation model. The ballistic differential equation model proposed by the present invention more accurately captures the trajectory and velocity attenuation of prefabricated fragments in the air, improving the accuracy of obtaining safe distances for static explosion tests. The present invention can determine the horizontal distribution of safe and dangerous distances and provide information in the height direction to facilitate subsequent three-dimensional safety assessments, thereby improving the safety and reliability of static explosion tests. The present invention employs a fourth-order Runge-Kutta numerical integration method to solve the precise ballistic differential equation model, which exhibits high stability and convergence, is easy to implement and program, and saves computational time and resources. BRIEF DESCRIPTION OF THE DRAWINGS
[0049] Figure 1 Flowchart of the present invention;
[0050] Figure 2 This is an example diagram of the results of the present invention. DETAILED DESCRIPTION
[0051] Specific implementation method 1: Figure 1 As shown, the specific process of the calculation method of the static explosion test safety distance and vertical height in this embodiment is as follows:
[0052] Step 1: Obtain prefabricated fragment information and environmental parameters at each elevation angle of the static explosion test, and input the prefabricated fragment information and environmental parameters at each elevation angle into an accurate ballistic differential equation model that considers resistance. Traverse different elevation angles and solve the accurate ballistic differential equation model that considers resistance using fourth-order Runge-Kutta numerical integration to obtain the lateral position, vertical position, and velocity of the prefabricated fragment at different times at each elevation angle, and store them in the lateral position array X, vertical position array Y, and velocity array V at each elevation angle, respectively.
[0053] The prefabricated fragment information includes: the initial velocity v0 of the prefabricated fragment, the mass m of the prefabricated fragment, the cross-sectional area A of the prefabricated fragment, the resistance coefficient C of the prefabricated fragment d ;
[0054] The environmental parameters include: air density ρ, gravity acceleration g;
[0055] An accurate ballistic differential equation model that takes resistance into account is established. This model describes the motion of prefabricated fragments in the air, taking into account the effects of air resistance, gravity, etc. on the motion of prefabricated fragments, as well as factors such as the shape, mass, and material of the prefabricated fragments. The ballistic differential equation model is as follows:
[0056]
[0057]
[0058]
[0059]
[0060] Where x is the horizontal position of the prefabricated fragment, y is the vertical position of the prefabricated fragment, and v x is the horizontal velocity of the prefabricated fragment, v y is the vertical velocity of the prefabricated fragment, t is the time, C d is the drag coefficient, A is the cross-sectional area of the prefabricated fragment, ρ is the air density, m is the mass of the prefabricated fragment, and g is the acceleration due to gravity.
[0061] The fourth-order Runge-Kutta numerical integration solves the accurate ballistic differential equation model considering resistance. When the vertical position y of the prefabricated fragment is less than or equal to 0, the integration stops and the ballistic data of the prefabricated fragment at this elevation angle is stored in the corresponding array. Specifically:
[0062] First, the preset elevation angle θ is traversed every 1°. For each elevation angle within the range, the state is initialized, including: initial horizontal position x = 0, vertical position y = 1.5 meters, time t = 0, horizontal speed v x =v0cosθ, vertical velocity v y =v0sinθ;
[0063] Then the fourth-order Runge-Kutta method is used to solve the differential equation model, namely:
[0064]
[0065]
[0066]
[0067]
[0068]
[0069]
[0070]
[0071]
[0072]
[0073]
[0074]
[0075]
[0076]
[0077]
[0078]
[0079]
[0080]
[0081]
[0082]
[0083]
[0084] Where n = 0, 1, 2, ..., n is the number of time steps, x n is the horizontal position of the prefabricated fragment at the nth time step, x n+1 is the horizontal position of the prefabricated fragment at the n+1th time step, k 1x 、k 2x 、k 3x 、k 4x 、k 1y 、k 2y 、k 3y 、k 4y 、k 1vx 、k 2vx 、k 3vx 、k 4vx 、k 1vy 、k 2vy 、k 3vy 、k 4vy is the intermediate variable, y n is the vertical position of the prefabricated fragment at the nth time step, y n+1 is the vertical position of the prefabricated fragment at the n+1th time step, v x,n+1 is the lateral velocity of the prefabricated fragment at the n+1th time step, v x,n is the lateral velocity of the prefabricated fragment at the nth time step, v y,n+1 is the vertical velocity of the prefabricated fragment at the n+1th time step, v y,n is the vertical velocity of the prefabricated fragment at the nth time step, Δt is the time step, t n is the time of the nth time step,
[0085] Step 2: Obtain the terminal velocity of the prefabricated fragment in the velocity array V at each elevation angle, and compare the terminal velocity of the prefabricated fragment with the preset velocity threshold v L For comparison, if the terminal velocity of the prefabricated fragment is greater than v L , then skip the current elevation angle, obtain the terminal velocity of the prefabricated fragment from the velocity array V at an elevation angle, and re-execute step 2; if the terminal velocity of the prefabricated fragment is less than or equal to v L , then the lateral position corresponding to the terminal velocity of the prefabricated fragment is the safety distance. All safety distances are stored in a new array as the safety distance array:
[0086] The last element in the velocity array V is the terminal velocity of the prefabricated fragment;
[0087] In this step, specifically, the speed threshold is set to v L , that is, when the speed of the prefabricated fragment is lower than v L , it is considered to have lost its lethality and can be used as a reference for safe distance. For each elevation angle, the last element from the velocity array V is taken, i.e., the terminal velocity of the prefabricated fragment, and compared with the velocity threshold. If the terminal velocity is less than or equal to the velocity threshold, the range at that elevation angle, i.e., the last element in the horizontal position array X, is used as the safe distance and stored in a new array, thus obtaining the safe distance array. If the terminal velocity is greater than the velocity threshold, the prefabricated fragment at that elevation angle still has lethality and cannot be used as a reference for safe distance. Therefore, that elevation angle is skipped and the traversal continues to the next elevation angle.
[0088] Step 3. Get the maximum value R in the safe distance array. The distance greater than R is the safe distance range. At the same time, get the trajectory height in the vertical position array Y. At the same time, evaluate whether the current position is safe based on the safe distance and obtain the evaluation result.
[0089] Example:
[0090] The simulation test was carried out according to the method described in the specific embodiment as follows:
[0091] An accurate ballistic differential equation model considering drag is established, which consists of the following four differential equations:
[0092]
[0093]
[0094]
[0095]
[0096] Where x and y are the horizontal and vertical positions of the prefabricated fragments, and v x and v y are the horizontal and vertical velocities of the prefabricated fragments, t is the time, C d is the drag coefficient, A is the cross-sectional area of the prefabricated fragment, ρ is the air density, m is the mass of the prefabricated fragment, and g is the acceleration due to gravity.
[0097] Set the integration parameters, initialize the storage array, and input the prefabricated fragment's initial velocity, mass, shape, material, and environmental parameters (such as air density and gravity) into the ballistic differential equation model. The integration parameters include the time step Δt, which is set to 0.01 seconds.
[0098] The storage array includes a horizontal position array X, a vertical position array Y, and a velocity array V, which are used to store the trajectory data of the prefabricated fragments at each elevation angle;
[0099] The input parameters include the initial velocity v0 of the prefabricated fragment, which is 1500 m / s; the mass m of the prefabricated fragment, which is 0.002 kg; the cross-sectional area A of the prefabricated fragment, which is 0.00002827 m2; the drag coefficient C of the prefabricated fragment. d , takes the value of 0.47; the air density ρ, takes the value of 1.225 kg / cubic meter.
[0100] Traversing different elevation angles, the fourth-order Runge-Kutta numerical integration is performed to solve the model, and the ballistic data of the prefabricated fragments at each elevation angle, including position and velocity, are obtained and stored in the corresponding array.
[0101] Specifically, the elevation angle θ is traversed from 0° to 90° at intervals of 1°; for each elevation angle, the initial state is set as follows: time t = 0 seconds; horizontal position x = 0 meters; vertical position y = 1.5 meters; horizontal speed v x =v0cosθ; vertical velocity v y =v0sinθ; then the fourth-order Runge-Kutta method is used to solve the differential equation model, namely:
[0102]
[0103]
[0104]
[0105]
[0106] in,
[0107]
[0108]
[0109]
[0110]
[0111]
[0112]
[0113]
[0114]
[0115]
[0116]
[0117]
[0118]
[0119]
[0120]
[0121]
[0122]
[0123] Where n is the number of time steps, n = 0, 1, 2, ...; when the vertical position y of the prefabricated fragment is less than or equal to 0, the integration is stopped, and the trajectory data of the prefabricated fragment at this elevation angle is stored in the corresponding array.
[0124] Analyze the trajectory characteristics at each elevation angle and determine whether the prefabricated fragments have reached a safe state based on a predetermined speed threshold, i.e., the speed is lower than the threshold. If yes, record the range at that elevation angle as a candidate safe distance; if not, continue to traverse the next elevation angle. Specifically:
[0125] For each elevation angle, take the last element from the velocity array V, which is the terminal velocity of the prefabricated fragment, and compare it with the preset velocity threshold. If the terminal velocity is less than or equal to the preset velocity threshold, then the range at this elevation angle, that is, the last element in the horizontal position array X, is used as a candidate safe distance and stored in a new array; if the terminal velocity is greater than the velocity threshold, it means that the prefabricated fragment at this elevation angle still has lethality and cannot be used as a reference for safe distance, so skip this elevation angle and continue to traverse the next elevation angle. Traverse the result arrays X, Y, and V of each angle, calculate the ballistic range of the current angle: range = the last element of the X array, find the maximum value of the height Y array: maximum height = max(Y array), find the maximum value at the end of the speed V array: maximum terminal velocity = the last element of the V array, and preset speed threshold v L It is set to 100 m / s, that is, when the speed of the prefabricated fragments is lower than 100 m / s, it is considered to have lost its killing ability and can be used as a reference for safe distance.
[0126] After calculation, the fragment trajectory distribution is as follows Figure 2 As shown, the maximum range is 998.8225 meters, the corresponding height is 232.4955 meters, the corresponding angle is 20 degrees, and the corresponding terminal velocity is 45.3912 meters per second. The ballistic range that meets the terminal velocity requirements is 405.7074 meters to 652.7241 meters, and the safe distance range is greater than 652.7241 meters.
Claims
1. A method for calculating the safety distance and vertical height of a static explosion test, characterized in that The specific process of the method is: Step 1: Obtain prefabricated fragment information and environmental parameters at each elevation angle of the static explosion test, and input the prefabricated fragment information and environmental parameters at each elevation angle into the ballistic differential equation model. Traverse different elevation angles and solve the ballistic differential equation model using fourth-order Runge-Kutta numerical integration to obtain the lateral position, vertical position, and velocity of the prefabricated fragment at different times at each elevation angle. The lateral position, vertical position, and velocity are stored in the lateral position array X, vertical position array Y, and velocity array V at each elevation angle, respectively. Step 2: Obtain the terminal velocity of the prefabricated fragment in the velocity array V at each elevation angle, and compare the terminal velocity of the prefabricated fragment with the preset velocity threshold v L For comparison, if the terminal velocity of the prefabricated fragment is greater than v L , then skip the current elevation angle, obtain the terminal velocity of the prefabricated fragment from the velocity array V at an elevation angle, and re-execute step 2; if the terminal velocity of the prefabricated fragment is less than or equal to v L , then the lateral position corresponding to the terminal velocity of the prefabricated fragment is the safety distance, and all safety distances are stored in a new array to obtain a safety distance array; The terminal velocity of the prefabricated fragment is the last element in the velocity array V; Step 3: Get the maximum value R in the safe distance array. The distance greater than R is the safe distance range, and get the trajectory height in the vertical position array Y.
2. The method for calculating the safety distance and vertical height of a static explosion test according to claim 1, characterized in that: The prefabricated fragment information includes: the initial velocity v0 of the prefabricated fragment, the mass m of the prefabricated fragment, the cross-sectional area A of the prefabricated fragment, the resistance coefficient C of the prefabricated fragment d ; The environmental parameters include: air density ρ and gravitational acceleration g.
3. The method for calculating the safety distance and vertical height of a static explosion test according to claim 2, characterized in that: The ballistic differential equation model is as follows: Where x is the horizontal position of the prefabricated fragment, y is the vertical position of the prefabricated fragment, and v x is the horizontal velocity of the prefabricated fragment, v y is the vertical velocity of the prefabricated fragment, t is the time, and ρ is the air density.
4. The method for calculating the safety distance and vertical height of a static explosion test according to claim 3, characterized in that: The fourth-order Runge-Kutta numerical integration is used to solve the ballistic differential equation model, specifically: First, the preset elevation angle θ is traversed every 1°. For each elevation angle within the range, the following parameters are initialized: initial horizontal position x = 0, vertical position y = 1.5 meters, time t = 0, horizontal speed v x =v0cosθ, vertical velocity v y =v0sinθ; Then, the fourth-order Runge-Kutta method is used to solve the differential equation model as follows: Where n∈[0,+∞], n is the number of time steps, x n is the horizontal position of the prefabricated fragment at the nth time step, x n+1 is the horizontal position of the prefabricated fragment at the n+1th time step, y n is the vertical position of the prefabricated fragment at the nth time step, y n+1 is the vertical position of the prefabricated fragment at the n+1th time step, v x，n+1 is the lateral velocity of the prefabricated fragment at the n+1th time step, v x，n is the lateral velocity of the prefabricated fragment at the nth time step, v y，n+1 is the vertical velocity of the prefabricated fragment at the n+1th time step, v y，n is the vertical velocity of the prefabricated fragment at the nth time step, k 1x 、k 2x 、k 3x 、k 4x 、k 1y 、k 2y 、k 3y 、k 4y 、k 1vx 、k 2vx 、k 3vx 、k 4vx 、k 1vy 、k 2vy 、k 3vy 、k 4vy is an intermediate variable.
5. The method for calculating the safety distance and vertical height of a static explosion test according to claim 4, characterized in that: k 1x 、k 1y 、k 1vx 、k 1vy Obtained by the following formula: Where Δt is the time step, t n is the time of the nth time step.
6. The method for calculating the safety distance and vertical height of a static explosion test according to claim 5, characterized in that: k 2x 、k 2y 、k 2vx 、k 2vy Obtained by the following formula:
7. The method for calculating the safety distance and vertical height of a static explosion test according to claim 6, characterized in that: k 3x 、k 3y 、k 3vx 、k 3vy Obtained by the following formula:
8. The method for calculating the safety distance and vertical height of a static explosion test according to claim 7, characterized in that: k 4x 、k 4y 、k 4vx 、k 4vy Obtained by the following formula: