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Based on the analysis equation for real -time update of the artillery ballistic synthetic function array and its applica

2024-12-10 17:52:43|Myriagame |source：minecraft skins

This tutorial is set by the author to use the CC By-NC-SA protocol.

introduction

In the application of artillery, the frequency and timeliness of ballistic computing can affect the hit effect and experience.In the high -precision model of the tutorial shell ballistic and its simple applications (that is, a tutorial next door), the author (ZX1316) has given the analysis equation of the ballistic data.Since there is no analytical solution in this equation, the use of Newtonian or two -point method is needed to obtain value solution.In real -time and new fire control, each cycle needs to be iterated, greatly reducing the calculation efficiency and update frequency.At the same time, the initial value of the iterative method will also generate offset according to the number of medicines, and there will be magical points in the large interval. The range of artillery will be limited in the community. Therefore, the ballistic function can be used to combine the above problems.

1. Confirm the mathematical model

For the artillery system, the following factors are related to their expectations:

Horizontal distance W

Shooting angle α

Vertical height difference H

Generally speaking, the shooting angle and height difference can be calculated. However, in order to facilitate the application, this article sets the shooting angle as an unknown amount, that is,

α = f (w, h)

However, within the effective range, the function is not unique.Based on experience and preliminary analysis methods, different artillery of different medicines is generally obtained to maximize the maximum effective range below 30 degrees.

Figure 1: Artillery Analysis Method (N = 4)

The picture above shows that the resolution curve of the decorated medicine artillery at different height differences is mixed with a fitting curve. The height from top to bottom is+15m,+10m,+5m, the benchmark, -5m, -10m.Get the maximum position at 30 degrees (exceeding the obvious split).Therefore, the ballistic can be divided into different intervals at a limit of 30 degrees.Thirty degrees can be called a flat -firing interval, and the span of this interval ranges from the maximum torn angle to the maximum range.More than 30 degrees can become a suspension range. The range is across the maximum range from a maximum range of more than 30 degrees to the maximum elevation angle of the artillery (the default is 60 degrees, maybe some methods can be scaled to 90 degrees or even in turn).

At the same time, according to image research, within a certain height difference (where can you go?), For a fixed shooting angle, the angle is proportional to the height difference (is it also the small value characteristics of the SIN?????) Therefore, the shooting angle difference caused by the height difference can be based on a height difference to combine an error equation, and then a proportional correction.

Figure 2: Height relative benchmark difference curve (the benchmark is 0, not drawn)

After getting the basic nature, you can use the fourth -order fitting distance function to correct the third -order fitting height difference.At this point, the mathematical model of ballistic computing has been established.

2. Function fit

This chapter tests your numerical analysis kung fu. You are sitting in the center of the computer, and you have thrown 2*8 artillery shells. You can give the artillery shells to give a numerical painting diagram and mark the effective interval. Do you understand!Calculation King (

2.1 Flat -fire trajectory

According to the images of numerical solutions, the preliminary range interval is established. If the boundary boundary is encountered, the interval is reduced, so the following range table is obtained:

Table 1: The range interval under different medicines

The above table is the range interval, where the min is the minimum range of the fitting, the min (R) is the minimum range in actual use, and MAX is the maximum range.Mathematical fitting is that the correct result cannot be reached when the minimum value cannot be too low. Therefore, the minimum range can be appropriately reduced, so that the angle of the artillery angle when the minimum value is less than 5 degrees of physics commonly used in the small angle constant.The first version of the tutorial is increased by 40m/s at an initial speed of 40m/s.

Based on the Polyfit function of MATLAB, the distance function and height difference can be fixed.The following table is the coefficient of the distance function C0:

Table 2: Flat -shooting distance function coefficient

In this table, the C0 refers to the coefficient of the flat shooting function.

F 1 (w) = c0 1 *w 4 +c0 2 *w 3 +C0 3 *w 2 +c0 4 *w+c0 5

n is the number of medicines, W is the target distance, and the output value is angle (DEG).Among them, when n = 1, because the range interval is too abstract, it is more useful to throw stones in the range, so it is zero.

The following table is the height difference correction coincide coefficient during the flat shot:

Table 3: The correction coefficient of flat shot high difference difference

This coefficient table is orderly, symbol C1, how to use:

F 2 (w) = c1 1 *w 3 +c1 *w 2 +C1 3 *w+c1 4

Similarly, n = 1 was zero because of being too abstract.

The synthesis function comes from the difference function when the height difference is+5m. The complete function use method is:

F (w) = f 1 (w)+(h/5)*f 2 (w)

Among them, H is a relatively high difference, and its formula is:

h = h t -hg

Among them, H T is the target height, and H G is not mercury in the height of the artillery.

In this way, the fitting function is in line with mathematical modeling α = f (w, h). At the same time, n = 4 and n = 8 as an example, you can get a complete fitting curve:

Figure 3: The fitting curve set of at N = 4

Figure 4: The fitting curve set of at n = 8

In this way, from the figure, the fixing curve set with basically similar shapes is obtained, and the shooting angle when the minimum value is less than 5 degrees, which is convenient for actual use.

2.2 Hanging ballistic

Hanging is a monotonous reduction range from the angle of the artillery higher than the maximum range angle.Look at that cannonball, round like eggs, flying towards your head ~ The advantage of cracking is the obstacle leap and efficient strike on certain targets (just you tilted armor)A alternative shooting method can be used when the armor is strong.The disadvantages of the crane are also obvious. Because the maximum elevation angle is often limited, the shooting mode is a bit confusing to the excessive target.In addition, the characteristics of long flight time, small ring ring, and other characteristics should not be completely disadvantaged.This mode will have an applicable environment in some occasions, so it is fixed with the flat shooting.

The effective range of the crane is shown in the table below.

Table 4: Effective range of shooting fire

Among them, n is a medicine, min is the minimum fit, and the minimum MAX is the maximum value.Because there is a gap between the minimum value and the minimum fitting value, when choosing the minimum value, the artillery angle may be higher than 60 degrees.The reason why this parameter is retained is because the existence of some mysterious technology swing turrets can make the angle breakthrough limit.It can be seen from the above table that the minimum effective range of the crack is much higher than the flat firing, so this mode is mostly suitable for alternative shooting on specific occasions, as a rib for conventional shooting mode.

The following table is the distance function coefficient of the suspension:

Table 5: Fighting distance function coefficient

The following table is the function coefficient of the height difference correction of the suspension:

Table 6: Fitting height correction function coefficient

The altitude correction function of the suspension is very small on the distance function, and it can even be selected (zero).In addition, the usage method is exactly the same as Pingjie, and I won't go into details here.

The total ballistic diagram of the suspension function is as follows:

Figure 5: The suspension function at N = 4

Figure 6: The suspension function of the n = 8 o'clock

The above is the characteristics and overall viewing of the ballistic function.

3. Application of ballistic function

After getting the ballistic function, you will find that the fitting function is relatively accurate within the effective range interval. It will start to turn around after this interval, so the function needs to be applied to apply it.

For flat shooting, according to the table in the effective range interval, the ballistic calculation will be directly calculated according to the function within the interval.When the target exceeds the range, it can be directly fixed as the maximum range angle to prevent random movement.When the target distance is smaller than the minimum effective range of the ballistic, the angle of the artillery at this time is generally less than 5 degrees, so the distance is no longer an important factor affecting the angle of the artillery.In this case, the angle of the artillery is mainly affected by the geometric angle of the target point and the firing point, namely.

α = TAN -1 (h/w)

Among them, α is the angle of the artillery, H is the height difference, and W is the distance.In this formula, the ballistic is considered a straight line. At this time, the distance factor becomes an optional factors.One of the corrections is to use a linear fit (a positive proportional function) to receive the minimum value point of the effective range to the origin to correct.

For suspension, its application is slightly more complicated than flat shooting.In the lifting mode, the effective range interval is short and lower than the effective range of the range. It is obviously not directly linear to fit. Therefore, it can increase a flat shooting interval to transition to avoid the embarrassing situation that cannot be completely unable to beat.Generally speaking, the range of the suspension can be divided into three parts: linear fitting, flat shooting fitting, and hanging shooting.With the compensation of flat shooting, except for the strange points between the flat shot and the suspension, most of the remaining problems such as shooting blind spots can be solved.

4. Data analysis and outlook

After obtaining the fitting data, you can further analyze the conclusions that try to obtain more universality.The first is the maximum distance, the picture below is the relationship between the maximum distance and the medicine installation.I always feel that this paragraph is nonsense

Figure 7: distance-pretending

The relationship between the distance with the medicine can be regarded as linear. From the data, it can be seen that the increased linear impact range of the pill can be used, which can be used to calculate the maximum range expectation of any initial speed.

The following figure shows the relationship between the fourth -order coefficient and secondary coefficient of the flat shooting distance function (can be understood as the initial speed):

Figure 8: Fourth-order coefficient-Putting medicine

Figure 9: Second-order coefficient-Putting medicine

The above two figures use a dual -paired coordinate system.From the results of the trend line, the coefficient of the fitting function and the number of drug installations have become a power function relationship, so that the coefficient suitable for any initial velocity point can be obtained.

The following figure is the relationship between the number of power and coefficient sequence of the fitting function trend line:

Judging from this seemingly meaningless picture, when the sequence reaches 5, that is, the constant coefficient is 0.But why did I fit a different constant?IntersectionIntersection

In short, this is here. If there is an error, please comment to remind me to modify it.I have a limited time and energy. As for the expansion and application of these data and the analysis of universalization, I will also give it to future generations.) References

[1] ZX1316, high -precision model and simple application of artillery bullet ballistic, https://www.mcmod.cn/post/2983.html

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