CN115146468A - Air defense missile shooting accuracy assessment model - Google Patents
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Abstract
The invention discloses an air-defense missile shooting accuracy evaluation model, which comprises the following steps: firstly, according to guidance precision and trajectory parameters, determining a blast point of a warhead relative to a target through fuze characteristic simulation; secondly, determining a target explosion point by combining the fuze matching efficiency simulation according to a fuze starting rule of fuze characteristic simulation; thirdly, simulating and calculating the damage probability of the missile to the target according to the characteristics of the warhead to determine the shooting precision of the missile and evaluate the fighting performance; the anti-aircraft missile shooting precision evaluation model selects corresponding trajectory parameters according to specific target types, and calculates the damage probability of the missile on the target through the simulation of the warhead characteristic simulation, the fuze characteristic simulation and the missile and battle matching efficiency simulation model so as to determine the shooting precision of the missile and evaluate the fighting performance.
Description
Technical Field
The invention relates to an air-defense missile shooting precision evaluation model, and belongs to the technical field of system performance evaluation.
Background
The hit precision of the air-defense missile system directly reflects the statistic characteristics of the impact point and the target aiming point of the air-defense missile. Common weapon Precision indicators are Accuracy (Accuracy), concentration (Precision), and circle Probability Error (CEP). Wherein the accuracy refers to the deviation degree of the scattering center of the impact point relative to the target aiming point; the density refers to the discrete degree of the impact points relative to the scattering center; the CEP is a circle which is made by taking the scattering center of the impact point as the center of the circle, and the radius of the circle is the value of the CEP when the probability that the impact point falls into the circle is 50%.
In shooting accuracy evaluation, the traditional statistical method can process the accuracy evaluation problem; however, since the missile system belongs to an expensive weapon system, the actual test sample is very limited, and the traditional statistical method can hardly deal with the evaluation problem.
Disclosure of Invention
In order to solve the problems, the invention provides an air-defense missile shooting precision evaluation model, which effectively determines key measurement index values of the air-defense missile shooting precision and solves the problem that the evaluation result in the existing air-defense missile shooting precision evaluation is inaccurate.
The invention discloses an air defense missile shooting accuracy evaluation model, which comprises the following steps:
firstly, according to guidance precision and ballistic parameters, determining a blasting point of a warhead relative to a target through fuze characteristic simulation;
secondly, determining a target explosion point by combining the fuze matching efficiency simulation according to a fuze starting rule of fuze characteristic simulation;
and thirdly, simulating and calculating the damage probability of the missile to the target according to the characteristics of the warhead to determine the shooting precision of the missile and evaluate the fighting performance.
Further, the specific steps of the warhead characteristic simulation are as follows:
analyzing the dynamic flying characteristic of the fragments of the warhead according to the static flying characteristic of the fragments of the warhead;
firstly, setting a target to be immobile, enabling a warhead fragment to approach the target at a bullet relative speed, adopting a coordinate system which is superposed with a longitudinal axis of the target, wherein the head of the pointed target is positive, and the origin of the coordinate system is the tail of the target;
then, the following assumptions are made according to the actual situation when the bullets meet: 1) When the missile encounters a target, the velocity vectors of the missile and the target are in the same plane; 2) The influence of the rotation of the missile and the target around the respective mass centers on the speed vectors of the warhead and the target is not considered; 3) The target velocity vector coincides with its longitudinal axis; 4) The target speed change in the bullet-and-target intersection stage can be ignored relative to the high-speed fragment flow;
the included angle between the velocity vector of the missile and the longitudinal axis thereof satisfies the following relationship:
cosθ＝cosα×cosβ， (1)
in the formula, alpha is a missile attack angle, beta is a sideslip angle, and theta is a longitudinal axis included angle;
the velocity of the missile is decomposed into a component along the longitudinal axis of the missile body and a component along the central line of the static dispersion angle of the fragment flow by using the sine theorem, and then
V m1 ＝V m ×sinθ/sinφ， (2)
V m2 ＝V m ×sin(φ-θ)/sinφ， (3)
In the formula (I), the compound is shown in the specification,
in order to determine the velocity of the missile,
along the longitudinal axis of the projectile for the velocity of the projectileThe direction component of the light beam is,
the velocity of the missile is the component of the missile along the central line of the static dispersion angle of the fragment flow;
and decomposing the target speed along the longitudinal axis direction of the missile and the direction vertical to the longitudinal axis to obtain the included angle between the central line of the dynamic dispersion angle of the fragment flow and the longitudinal axis of the missile:
in the formula (I), the compound is shown in the specification,
to be the average velocity of the dynamic fragment stream,
is the target speed, phi I The included angle between the central line of the dynamic scattering angle of the fragment flow and the longitudinal axis of the missile is shown;
two symbol portions in equation (4): the upper side symbol is taken when the head-on chases, and the lower side symbol is taken when the head-on hits.
Furthermore, the relative indexes of the static flying characteristic of the fragments of the warhead comprise initial fragment speed, fragment quality, fragment flying angle, total fragment number, a fragment and hit target mathematical detection model and fragment hit point parameters.
Further, the specific steps of the fuze characteristic simulation are as follows, according to the characteristics of the air-defense missile and the requirement of shooting effect, setting the optimal initiation point to meet the condition that the relative distance between the missile and the target is smaller than the dynamic killing radius of the warhead, and if the warhead is initiated at the point, positioning a certain point on the target critical part right on the central line of the dynamic dispersion angle of the fragments of the warhead; the optimal delay time of the fuze delays a period of time after the fuze is started to detonate the warhead, so that the intersection point of the center of the fragment flow and the target is just coincided with or is closest to a certain point on the key part of the target; the optimal delay time of the fuze is expressed as:
F(τ)＝min(R p )s.tR＜R o ， (5)
wherein tau is the optimum delay time of the fuze, R p The distance R between the intersection point of the center of the fragment flow and the target and a certain point on the critical part of the target o The dynamic killing radius of the warhead is defined, and R is the distance from the center of mass of the warhead to the intersection point.
Furthermore, the specific steps of the guidance engagement efficiency simulation are as follows,
if the coordinates of the geometric center of the target in the ground launching coordinate system and the coordinates of the mass center of the warhead of the missile in the ground launching coordinate system are known, the vector of the longitudinal axis of the target is +/-x (x-x) 1 ，y-y 1 ，z-z 1 )＝(a x ，a y ，a z ) Due to vector (x) o -x，y o -y，z o -z)＝(b x ，b y ，b z ) Is at an angle phi with respect to the longitudinal axis vector of the target I + ξ, i.e.:
wherein x, y and z are coordinate points of the ground emission coordinate system of the dynamic divergence angle central line and the target intersection point respectively, and x 1 、y 1 、z 1 Respectively as a coordinate point, x, of the geometric center of the target in a ground emission coordinate system o 、y o 、z o Respectively are coordinate points of the mass center of the warhead of the missile in a ground launching coordinate system;
the formula (6) is combined with the constraint conditions such as target characteristic dimension parameters, attitude angles and the like to obtain the coordinates of the intersection point of the central line of the dynamic fly-away angle and the target; especially when the target moves horizontally, the longitudinal axis vector of the target is (+/-a) x 0, 0) when the intersection point of the central line of the dynamic dispersion angle and the longitudinal axis of the missile is set as (x, y) in the ground launching coordinate system 1 ，z 1 ) Equation (6) can be simplified as:
let m = (y) 0 -y 1 ) 2 +(z 0 -z 1 ) 2 ，n＝[1/cos 2 (φ I +ξ)]-1, then:
and the coordinates of the intersection point in the impact process can be obtained in the same way:
the distance from the center of mass of the warhead to the intersection point can be obtained by a distance formula between the two points as follows:
the coordinate X of the intersection point on the coordinate system is:
(x) in the formula (11) to ，y to ，z to ) The coordinates of the tail part of the target in a ground launching coordinate system can be obtained from the coordinates of the center of the target according to the characteristic dimension parameters and the related attitude angle of the specific target; when x > x to Taking a positive sign; otherwise, taking the negative sign; specifically, the coordinates of the intersection point on the coordinate system when the target moves horizontally are:
X＝x-x to ， (12)
x in formula (12) to ＝x 1 + L, L is the length between the center and the tail of the target and is determined by the size parameter of the specific target;
the optimal detonation position meets the following conditions:
wherein (x) p ，y p ，z p ) The coordinates of the key part P in a ground emission coordinate system are related to a specific target; if the missile moves horizontally, then:
R p ＝|x p -x|， (14)
in the above formula x p ＝x to S, S is the distance between point P and the tail, and can be given by specific target size parameters.
Compared with the prior art, the anti-air missile shooting precision evaluation model selects corresponding trajectory parameters according to specific target types, calculates the damage probability of the missile on the target through the simulation of the warhead characteristic simulation, the fuze characteristic simulation and the missile cooperation efficiency simulation model to determine the shooting precision of the missile, evaluates the battle performance, effectively determines the key measurement index value of the anti-air missile shooting precision, and solves the problem that the evaluation result in the existing anti-air missile shooting precision evaluation is inaccurate.
Drawings
Fig. 1 is a schematic diagram of the framework of the shooting accuracy evaluation method of the present invention.
Fig. 2 is an operational flow diagram of the shooting accuracy evaluation method of the present invention.
FIG. 3 is a schematic view of the static fly-off angle density distribution of warhead fragments in accordance with the present invention.
Fig. 4 is a geometric relationship diagram of the present invention at the time of bullet meeting.
Detailed Description
The air defense missile shooting accuracy evaluation model shown in fig. 1 and 2 comprises the following steps:
firstly, according to guidance precision and trajectory parameters, determining a blast point of a warhead relative to a target through fuze characteristic simulation;
secondly, according to a fuse starting rule of the fuse characteristic simulation, combining the fuse fighting matching efficiency simulation to determine a target explosion point;
and thirdly, simulating and calculating the damage probability of the missile to the target according to the characteristics of the warhead to determine the shooting precision of the missile and evaluate the fighting performance.
The specific operation steps of the shooting precision evaluation method are as follows, firstly, the type of a target is determined; then selecting ballistic parameters according to the target type; then, carrying out simulation calculation on the relative motion parameters of the bullet eyes; then, calculating a dynamic flying area of the fragments of the warhead and the starting delay time of the fuze according to the characteristics simulation of the warhead, the fuze characteristics simulation and the fuze matching efficiency simulation model, thereby obtaining fragment distribution; and finally, calculating the single-shot killing probability.
The specific steps of the warhead characteristic simulation are as follows:
analyzing the dynamic flying characteristic of the fragments of the warhead according to the static flying characteristic of the fragments of the warhead;
1. the static flying characteristic of the fragments of the warhead,
research on the relative indexes (initial fragment speed, fragment quality, fragment flight angle, total fragment number, fragment and hit target mathematical detection model and fragment hit point parameters) of static fragment flying of the fighting part is the basis for analyzing dynamic fragment flying; the static flyaway zone of the warhead refers to a flyaway area of fragments when the warhead explodes in a static state, and generally the static flyaway zone of the warhead has axial symmetry, namely the static flyaway of the fragments is symmetrical around the longitudinal axis of the projectile along with the density distribution of flyaway angles; the distribution of static fly-off angle density of the warhead fragments is shown in FIG. 2, which is a graph of FIG. 2
The angle of the scattering center of the static fragments, i.e. the included angle between the average scattering direction of the fragments and the bomb axis,
the static scattering angle of a fragment is generally the width of the scattering angle occupied by 90% of the fragment; initial velocity v of static scattering of fragments 0 Has a certain transformation range and following the flight angle
And the initial speed of the fragment is generally determined by a static experiment; the initial velocity is usually averaged without taking into account the change in angleValue, but if v 0 If the change is large, the influence of the change on the dynamic dispersion angle must be considered;
2. the dynamic flying characteristic of the fragments of the warhead,
after the warhead explodes dynamically, the motion parameters of each fragment change to form a dynamic flying area of a fragment group, which is also called as a dynamic killing area, and the dynamic fragment flying cone formed after the fragment type warhead explodes can be obtained by superposing the missile speed with a static fragment cone;
first, assuming the target is stationary, the warhead fragment approaches the target at the projectile relative velocity, using a coordinate system OX coinciding with the target longitudinal axis, pointing to the target head as positive, the origin O of the coordinate system being the target tail, as shown in figure 3,
is the speed of the missile,
is the target speed of the vehicle,
is the speed of the missile relative to the target, xi is the included angle between the longitudinal axis of the missile and the longitudinal axis of the target, theta is the included angle between the velocity vector of the missile and the longitudinal axis of the missile body (the upper part of the longitudinal axis of the missile body is positive, and the reverse is negative), phi is the static flying direction angle of fragments (the direction of a central line), and phi is the direction of the fragments I Is the fragment dynamic scattering direction angle (centerline direction);
then, the following assumptions are made according to the actual situation when the bullets meet: 1) When the missile encounters a target, the velocity vectors of the missile and the target are in the same plane; 2) The influence of the rotation of the missile and the target around the respective mass centers on the speed vectors of the warhead and the target is not considered; 3) The target velocity vector coincides with its longitudinal axis; 4) The target speed change in the bullet-and-target intersection stage can be ignored relative to the high-speed fragment flow;
if the missile attack angle and the sideslip angle are respectively alpha and beta, the included angle theta between the speed vector of the missile and the longitudinal axis thereof satisfies the following relation:
cosθ＝cosα×cosβ， (1)
speed of missile by sine theorem
Resolved into components along the longitudinal axis of the projectile
And the central line direction component of the static dispersion angle of the debris flow
As can be derived from the geometrical relationship shown in figure 3,
V m1 ＝V m ×sinθ/sinφ， (2)
V m2 ＝V m ×sin(φ-θ)/sinφ， (3)
setting the average velocity of the dynamic fragment flow to
The target speed is
Decomposing along the longitudinal axis direction of the missile and the direction vertical to the longitudinal axis to obtain the included angle phi between the central line of the dynamic dispersion angle of the fragment flow and the longitudinal axis of the missile I Satisfies the following conditions:
two symbol portions in equation (4): the upper side symbol is taken when the vehicle overtakes the vehicle, and the lower side symbol is taken when the vehicle is hit.
The specific steps of the fuze characteristic simulation are as follows, according to the characteristics of the air-defense missile and the requirement of shooting effect, the optimal initiation point is set to meet the condition that the relative distance between the missile and the target is smaller than the dynamic killing radius of the warhead, if the warhead is detonated at the point, as shown in figure 3, a certain point P on a target vital part (such as a tail engine) is just positioned on the central line of the dynamic dispersion angle of a warhead fragment; the optimal delay time of the fuze delays a period of time after the fuze is started to detonate the warhead, so that the intersection point A of the fragment flow center and the target is just coincided with the point P or is closest to the point P; the optimal delay time of the fuze is expressed as:
F(τ)＝min(R p )s.tR＜R o ， (5)
wherein tau is the optimum delay time of the fuze, R p Is the distance, R, between the intersection point A of the center of the debris flow and the target and the point P o The dynamic killing radius of the warhead is shown, and R is the distance from the center of mass of the warhead to the intersection point A.
The specific steps of the war induction matching efficiency simulation are as follows,
and (3) setting the coordinates of the intersection point A of the dynamic divergence angle central line and the target in the ground emission coordinate system as (x, y, z), and if the geometric center of the target is known, setting the coordinates in the ground emission coordinate system as (x) 1 ，y 1 ，z 1 ) And the coordinates of the mass center of the missile warhead on the ground launching coordinate system are (x) o ，y o ，z o ) Then the target longitudinal axis vector is ± (x-x) 1 ，y-y 1 ，z-z 1 )＝(a x ，a y ，a z ) The vector (x) is known from the geometric relationship o -x，y o -y，z o -z)＝(b x ，b y ，b z ) Is at an angle phi with respect to the longitudinal axis vector of the target I + ξ, i.e.:
the coordinate of the intersection point A can be obtained by combining the formula (6) with constraint conditions such as target characteristic dimension parameters, attitude angles and the like; especially when the target moves horizontally, the longitudinal axis vector of the target is (+ -a) x 0, 0) when the intersection A of the central line of the dynamic dispersion angle and the longitudinal axis of the missile is set as (x, y) in the ground launching coordinate system 1 ，z 1 ) Equation (6) can be simplified as:
let m = (y) 0 -y 1 ) 2 +(z 0 -z 1 ) 2 ，n＝[1/cos 2 (φ I +ξ)]-1, then:
and the coordinates of the intersection point in the impact process can be obtained in the same way:
the distance from the center of mass of the warhead to the intersection point A can be obtained by a distance formula between the two points as follows:
the coordinate X of intersection a on coordinate system 0X is:
(x) in the formula (11) to ，y to ，z to ) The target tail part is subjected to coordinate launching in a ground coordinate system, and the target central coordinate can be obtained according to the characteristic dimension parameters and the related attitude angle of a specific target; when x > x to Taking a plus sign; otherwise, taking the negative sign; specifically, the coordinate of the intersection point a on the coordinate system 0X when the object moves horizontally is:
X＝x-x to ， (12)
x in formula (12) to ＝x 1 + L, L is the length between the center and the tail of the target and is determined by the size parameter of the specific target;
the optimal detonation position should satisfy the following conditions:
wherein (x) p ，y p ，z p ) Is the critical part PThe ground emission coordinate system coordinates are related to a specific target; if the missile moves horizontally, then:
R p ＝|x p -x|， (14)
in the above formula x p ＝x to S, S is the distance between the point P and the tail, and can be given by specific target size parameters.
The above-described embodiments are merely preferred embodiments of the present invention, and all equivalent changes or modifications of the structures, features and principles described in the claims of the present invention are included in the scope of the present invention.
Claims (5)
1. An air defense missile shooting accuracy evaluation model is characterized by comprising the following steps:
firstly, according to guidance precision and trajectory parameters, determining a blast point of a warhead relative to a target through fuze characteristic simulation;
secondly, according to a fuse starting rule of the fuse characteristic simulation, combining the fuse fighting matching efficiency simulation to determine a target explosion point;
and thirdly, simulating and calculating the damage probability of the missile to the target according to the characteristics of the warhead to determine the shooting precision of the missile and evaluate the fighting performance.
2. The airdefense missile shooting accuracy evaluation model of claim 1, wherein the specific steps of the warhead characteristic simulation are as follows:
analyzing the dynamic flying characteristic of the fragments of the warhead according to the static flying characteristic of the fragments of the warhead;
firstly, setting a target to be immobile, enabling a warhead fragment to approach the target at a bullet relative speed, adopting a coordinate system which is superposed with a longitudinal axis of the target, wherein the head of the pointed target is positive, and the origin of the coordinate system is the tail of the target;
then, the following assumptions are made according to the actual situation when the bullets meet: 1) When the missile encounters a target, the velocity vectors of the missile and the target are in the same plane; 2) The influence of the rotation of the missile and the target around the respective mass centers on the speed vectors of the fighting part and the target is not considered; 3) The target velocity vector coincides with its longitudinal axis; 4) The target speed change in the bullet-and-target intersection stage can be ignored relative to the high-speed fragment flow;
the included angle between the velocity vector of the missile and the longitudinal axis thereof satisfies the following relationship:
cosθ＝cosα×cosβ， (1)
in the formula, alpha is a missile attack angle, beta is a sideslip angle, and theta is a longitudinal axis included angle;
the velocity of the missile is decomposed into a component along the longitudinal axis direction of the missile body and a component along the central line direction of the static dispersion angle of the fragment flow by utilizing the sine theorem, and then
V m1 ＝V m ×sinθ/sinφ， (2)
V m2 ＝V m ×sin(φ-θ)/sinφ， (3)
In the formula (I), the compound is shown in the specification,
is the speed of the missile (the speed of the missile),
is the component of the missile speed along the longitudinal axis direction of the missile body,
the component of the missile speed along the central line direction of the static dispersion angle of the fragment flow;
and decomposing the target speed along the longitudinal axis direction of the missile and the direction vertical to the longitudinal axis to obtain the included angle between the central line of the dynamic dispersion angle of the fragment flow and the longitudinal axis of the missile:
in the formula (I), the compound is shown in the specification,
to be the average velocity of the dynamic fragment stream,
is the target speed, phi I The included angle between the central line of the dynamic scattering angle of the fragment flow and the longitudinal axis of the missile is shown;
two symbol portions in equation (4): the upper side symbol is taken when the head-on chases, and the lower side symbol is taken when the head-on hits.
3. The air-defense missile shooting accuracy assessment model of claim 2, wherein the relative indicators of the static fly-away characteristics of the warhead fragments comprise fragment initial velocity, fragment mass, fragment fly angle, total number of fragments, fragment and hit target mathematical detection model and fragment hit point parameters.
4. The model of claim 1, wherein the fuze characteristic simulation comprises the steps of setting the optimal initiation point to meet the requirement that the relative distance between the missile and the target is smaller than the dynamic killing radius of the warhead, and if the warhead is detonated at the optimal initiation point, locating a certain point on the critical part of the target right on the central line of the dynamic dispersion angle of the warhead fragments; the optimal delay time of the fuze delays a period of time after the fuze is started to detonate the warhead, so that the intersection point of the center of the fragment flow and the target is just coincided with or is closest to a certain point on the key part of the target; the optimal delay time of the fuze is expressed as:
F(τ)＝min(R p )s.tR＜R o ， (5)
wherein tau is the optimum delay time of the fuze, R p The distance R between the intersection point of the center of the fragment flow and the target and a certain point on the key part of the target o The dynamic killing radius of the warhead is defined, and R is the distance from the center of mass of the warhead to the intersection point.
5. The air-defense missile shooting accuracy evaluation model according to claim 1, wherein the specific steps of the missile engagement efficiency simulation are as follows,
if the coordinates of the geometric center of the target in the ground launching coordinate system and the coordinates of the mass center of the warhead of the missile in the ground launching coordinate system are known, the vector of the longitudinal axis of the target is±(x-x 1 ，y-y 1 ，z-z 1 )＝(a x ，a y ，a z ) Due to vector (x) o -x，y o -y，z o -z)＝(b x ，b y ，b z ) Is at an angle phi with respect to the longitudinal axis vector of the target I + ξ, i.e.:
wherein x, y and z are coordinate points of the ground emission coordinate system of the dynamic divergence angle central line and the target intersection point respectively, and x 1 、y 1 、z 1 Respectively as a coordinate point, x, of the geometric center of the target in a ground emission coordinate system o 、y o 、z o Respectively is a coordinate point of the missile warhead mass center in the ground launching coordinate system;
the formula (6) is combined with the constraint conditions such as target characteristic dimension parameters, attitude angles and the like to obtain the coordinates of the intersection point of the central line of the dynamic fly-away angle and the target; especially when the target moves horizontally, the longitudinal axis vector of the target is (+/-a) x 0, 0), the coordinates of the intersection point of the central line of the dynamic dispersion angle and the longitudinal axis of the missile in the ground launching coordinate system can be set as (x, y) 1 ，z 1 ) Equation (6) can be simplified as:
let m = (y) 0 -y 1 ) 2 +(z 0 -z 1 ) 2 ，n＝[1/cos 2 (φ I +ξ)]-1, then:
in the same way, the coordinates of the meeting time intersection point can be obtained:
the distance from the center of mass of the warhead to the intersection point can be obtained by a distance formula between two points as follows:
the coordinate X of the intersection point on the coordinate system is:
(x) in the formula (11) to ，y to ，z to ) The coordinates of the tail part of the target in a ground launching coordinate system can be obtained from the coordinates of the center of the target according to the characteristic dimension parameters and the related attitude angle of the specific target; when x > x to Taking a positive sign; otherwise, taking the negative sign; specifically, the coordinates of the intersection point on the coordinate system when the target moves horizontally are:
X＝x-x to ， (12)
x in formula (12) to ＝x 1 + L, L is the length between the center and the tail of the target and is determined by the size parameter of the specific target;
the optimal detonation position meets the following conditions:
wherein (x) p ，y p ，z p ) The coordinates of the key part P in a ground emission coordinate system are related to a specific target; if the missile moves horizontally, then:
R p ＝|x p -x|， (14)
in the above formula x p ＝x to S, S is the distance between point P and the tail, and can be given by specific target size parameters.
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