What Is the Ballistic Coefficient?

Ballistic Coefficient (BC) is a mathematical model used to measure the warhead's ability to overcome air resistance and maintain flight speed. There are two main factors that determine the ballistic coefficient: the section density and the shape of the warhead.

The ballistic extrapolation algorithm is one of the key technologies of the artillery reconnaissance and calibration radar software system.

The development of the ballistic coefficient dates back to 1881, and the German Kluber company conducted a detailed test of a blunt-head flat-bottomed warhead. Russian Army Colonel Mayevski used Kluber's data to develop a mathematical model to predict the warhead trajectory. US Army Colonel James B. James Ingalls then printed a ballistic data sheet based on the information from the former two. The definition of the ballistic coefficient was invented by the British Structural Division. Many modern ballistic data sheets have been revised, and new data sheets have appeared. However, the most commonly used G1 mode is basically based on the original mode, and the characteristics of most warheads on the market within 500 meters are still very close, so it is still used. ^[2]

Ballistic data is the basis for ballistic extrapolation calculations. Due to the noise of the radar measurement system, the ballistic data denoising process must be performed first when performing the ballistic extrapolation calculation. Currently, ballistic data noise reduction methods mainly include Kalman filtering, polynomial fitting methods, and other methods. The former has higher filtering accuracy under known trajectory parameters, while the trajectory parameters are difficult to obtain accurately during actual extrapolation, so the use of this method is greatly limited; the latter does not rely on trajectory parameters, but the accuracy is not high.

Wavelet transform is a time-frequency analysis method, which can better characterize the local characteristics of the signal in the time and frequency domains. It is very suitable for detecting transient anomalies in normal data. It is known as the "microscope for signal analysis" It has been widely used in the fields of automatic control, data processing, signal analysis and so on.

The real data and the time-frequency characteristics of noise in the ballistic measurement data sequence have different characteristics. The real data appears as low-frequency characteristics or relatively stable signals. Noise signals exist everywhere in the time domain and appear as high-frequency signals in the frequency domain. This characteristic of ballistic measurement data allows the data to be filtered using wavelet transforms.

Ballistic coefficient is an important parameter to characterize the characteristics of the projectile and its interaction with the air. Different types of missiles have different ballistic coefficients. The ballistic coefficients of the same projectile are slightly different at different firing angles and ranges. How to accurately calculate The trajectory coefficient is very important for the trajectory calculation.

This algorithm can reduce the detection error of various shooting conditions into the trajectory coefficient. Therefore, if the analysis is only based on the impact on the trajectory calculation, the trajectory coefficient is optimal under the least squares criterion for the detection arc of the trajectory.

In the process of ballistic fitting, there are two key issues: the determination of the initial ballistic coefficient and the solution of the ballistic equation. The initial value of the ballistic coefficient in the ballistic fitting algorithm can be set to zero, but at this time, the algorithm takes too much time, which affects the real-time performance of the algorithm. For this reason, a reasonable initial ballistic coefficient should be determined to reduce the running time of the algorithm.

The six-degree-of-freedom rigid body trajectory equation and the four-degree-of-freedom centroid motion equation can more accurately simulate the projectile flight process. Considering that the six-degree-of-freedom rigid body trajectory equation is very complicated, the calculation amount is intolerable, and many parameters are difficult to obtain, the conventional ammunition is rarely used. Therefore, the four-degree-of-freedom equation is used for analysis ^[3]

The basic principle of extrapolation calculation is: take a point on the detection ballistic segment as the starting point to perform ballistic integration towards the ballistic starting point (or landing point), and stop when the integration reaches the ballistic height to a given value, thereby obtaining the extrapolation .

The values of the integration starting point can be calculated based on the filtered measurement data. The shooting conditions during the integration calculation take the values when the ballistic coefficient is fitted. When integrating toward the starting point, the integration step is negative. When integrating toward the falling point, the integration step is integrated. Take positive.

The factors that affect ballistic extrapolation include ballistic data processing, ballistic equation solution, and estimation of firing conditions. Among them, the estimation of ballistic coefficient is particularly important in ballistic equation solution. The wavelet transform is used to filter the ballistic data, the fitted ballistic coefficient is calculated under the least squares criterion, and the extrapolation is performed using the ballistic integral method. This method can overcome the impact of the extrapolation of the detection error of the shooting conditions, thereby improving the extrapolation. Precision. Simulation experiments show that in the presence of large random noise in the radar detection data, the probability of extrapolation errors between 0 and 0.3% D reaches more than 99.5% ^[1] .