CN113821996A - Novel method for quickly calculating high-speed water-entering trajectory of projectile - Google Patents
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Abstract
本发明公里了一种新型的射弹高速入水弹道快速计算模型，基于空泡独立扩张原理，考虑了空泡的记忆效应，通过建立新的空泡形态算法和沾湿特征算法来实现射弹高速入水过程中空泡形态和流体动力准确计算，实现高速入水过程中回转体运动姿态和轨迹的快速计算。该方法能够有效的计算射弹高速入水过程中空泡形态的生成、发展和闭合等过程，准确的计算射弹运行过程中的流体动力和运动姿态。本项发明可以为研究射弹高速入水弹道和射弹稳定性设计提供一种快速和有效的计算方法。
The present invention has developed a new fast calculation model of projectile high-speed water entry trajectory, based on the principle of independent expansion of cavitation, taking into account the memory effect of cavitation, and establishing a new cavitation shape algorithm and wetting feature algorithm to achieve high-speed projectile Accurate calculation of cavitation shape and hydrodynamics in the process of water entry, and rapid calculation of the motion attitude and trajectory of the revolving body during high-speed water entry. The method can effectively calculate the formation, development and closure of cavitation in the process of high-speed projectile entering water, and accurately calculate the hydrodynamics and motion attitude of the projectile during its operation. The invention can provide a fast and effective calculation method for studying the projectile high-speed water entry ballistic and the projectile stability design.
Description
Technical Field
The invention relates to a novel method for quickly calculating a high-speed water-entering trajectory of a projectile, and belongs to the technical field of cross-medium weapon launching.
Background
The problem of water entry is an important field of fluid mechanics research, and has wide application prospects in natural disciplines and engineering technologies, wherein high-speed water entry is a focusing hot spot in recent years. The projectile is involved in complex physical processes such as water-entering impact, liquid level breaking and fluid-solid coupling in the high-speed water-entering process, and has strong nonlinearity and transient property. When the projectile enters water at high speed, water entering vacuoles are generated by the head part, the projectile is wrapped in the cavity, and the resistance is reduced. Because the projectile is disturbed when entering water generally, the projectile can swing in the cavity, and the tail beat phenomenon occurs, so that the trajectory is changed. Furthermore, the difference of the head type, the water inlet angle, the speed and the like of the high-speed water-entering projectile makes the trajectory have great difference. Therefore, the key of the projectile high-speed water entering technology is to find the influence factors of the structural characteristics of the projectile on the high-speed water entering cavitation bubble characteristics and the ballistic characteristics, and further quantify the structure of the projectile.
In the initial stage of the projectile entering water, the projectile is influenced by disturbance and water surface impact force, so that the projectile has a certain longitudinal plane rotation angular speed. When an included angle exists between the water surface and the projectile direction, the water surface at the lower side of the projectile expands along a radial cavity, liquid level splashing can be formed at the upper side due to no lateral water pressure restriction, surface closure cannot be formed, and curvatures of the upper surface and the lower surface of the cavity are not consistent. After entering water, the projectile can swing in the cavity, and the attitude angle of the projectile can be changed. When the tail of the projectile intrudes into the cavity wall, the tail of the projectile generates a gliding lift force that retards the rotation of the projectile. As the depth of penetration of the projectile tail into the cavity wall increases, the kinetic energy of the projectile rotation is dissipated and the projectile pitch will reach a critical point when the projectile reaches maximum penetration depth. The wetted portion of the projectile tail is then subjected to a radially high velocity fluid to rapidly push the projectile in the opposite direction of rotation out of the cavity wall. During this process, the projectile attitude angle will change significantly, peaking. And the stability of the projectile is reduced and the trajectory is bent due to the fact that the attitude angle of the projectile is too large. Therefore, the cavity shape, the hydrodynamic force and the trajectory of the projectile after entering water at high speed need to be accurately calculated, the influence of the structural change of the projectile on the trajectory characteristic is found, a theoretical basis is further provided for optimizing the shape of the projectile, and the projectile structure with good stability is designed.
At present, the research method of high-speed water entry is mainly through experimental observation and numerical simulation, and the document of Shanlow angle water entry of balistic projects researches the cavitation form, the motion attitude and the displacement of a projectile after entering water at high speed through a high-speed camera shooting technology, and finds that the long diameter ratio of the projectile has influence on the stability of the trajectory. The document "Experimental in-vestation on trajectory stability of high-speed water entry projects" studies the ballistic characteristics of different high-speed projectiles after entering water by high-speed photography, and determines the influence of the projectile head shape and the water entering speed on the stability of the high-speed water entering ballistic. The document, "research on small water entry angle and high-speed inclined water entry of supercavity projectile" researches the trajectory stability of high-speed projectiles at small angles by high-speed photography technology, and finds that the stability of the high-speed water entry projectiles is influenced by the sideslip angle. The literature, "study on cavitation and hydrodynamic characteristics of vertical entry into water of high-speed projectile" studies the cavitation morphology and hydrodynamic characteristics of vertical entry into water of supersonic projectile by numerical simulation. Numerical simulation of the projectile high-speed inclined water entering process researches the influence of the initial attack angle of the projectile entering water on the water entering trajectory through numerical simulation.
In the above-mentioned documents, the high-speed water entry trajectory is studied experimentally by observing the process of the projectile entering water at a high speed at a fixed position above the water surface at a certain angle by means of a high-speed photography technique, and analyzing the trajectory characteristics by means of experimentally recorded images and experimental results. The numerical simulation aspect is mainly to iteratively research the cavitation property and the ballistic property of the water-entering ballistic by a differential equation. However, due to the limitation of the test technology, the experimental observation can only observe a limited field of view, and the changes of the attitude angle of the projectile, the hydrodynamic force, the tail-shooting effect and the like can not be observed. The numerical simulation needs to select a proper physical model and large-scale grid calculation to obtain effective precision, each calculation is under a single working condition, a large amount of calculation force and time are consumed, and the cavitation characteristic, the ballistic characteristic and the like of the high-speed water entering process cannot be efficiently and quickly calculated.
Disclosure of Invention
The invention solves the problems that: the method overcomes the limitations of the existing high-speed water-entering trajectory experimental observation technology and the low efficiency of numerical simulation calculation, and provides a rapid calculation method for the high-speed water-entering trajectory of the projectile. The invention provides a novel method for rapidly calculating the high-speed water-entering trajectory of a projectile based on the cavitation independent expansion principle and by considering the cavitation memory effect. The calculation method can effectively calculate the cavitation property, the hydrodynamic force, the ballistic trajectory and the like of the projectile in the high-speed water entering process, and provides an efficient and accurate technical method for researching the cavitation property and the ballistic trajectory of the projectile in the high-speed water entering process.
The technical solution of the invention is as follows:
(1) set up as shown in FIG. 1, a fixed coordinate system (o) is set upExEzE) And a projectile coordinate system (o)BxBzB). Fixed coordinate system origin oEPlaced at the water entry point, x, of a horizontal planeEThe axis being parallel to the horizontal plane, zEThe positive direction of the axis is vertically upward and horizontally upward. Projectile coordinate system origin oBAt the center of gravity of the body of revolution, xBIn the positive axial direction, z is directed to the head of the rotor along the axis of the rotorBPositive axial direction perpendicular to xBAxially. x is the number ofBAxis and xEThe included angle of the shaft is the pitch angle theta of the revolving body and is positioned at xEThe upper side of the shaft is positive.
(2) Establishing a 3DOF motion equation of the projectile in a projectile coordinate system, and solving the velocity component, attitude angle and displacement of the projectile by combining initial conditions:
wherein m is the mass of the rotating body, IyIs the moment of inertia of the revolving body, u and w are the components of the revolving body mass center speed in the elastic body coordinate system, q is the revolving body in xEoEzEAngular velocity of rotation of plane, GxAnd GzIs the gravity of a revolving bodyComponent in the projectile coordinate system, FDAnd FLFor the component of the hydrodynamic force of the head of the body of revolution in the elastic coordinate system, FfAnd FpThe friction force and the sliding lift force of the fluid of the wetted part at the tail part of the revolving body McIs the resultant moment of the hydrodynamic force of the head of the revolving body to the center of mass of the revolving body, MpThe resultant moment of the hydrodynamic force at the tail part of the revolving body to the center of mass of the revolving body.
(3) The section of the 1 st cavity generated when the projectile enters water is numbered, and the like. According to the mass center speed of the projectile solved in the step (2), the radius of the section of the newly generated cavity of the projectile head and the radius of the section of the generated cavity can be solved:
in the formula, τiThe moment when the ith cavitation section is formed, and t is the navigation time after the revolving body enters water. Rc(t,τi) Is the cavitation radius of the ith cavitation section at the time t, RnIs the radius of the circular section of the head part of the revolving body. N is an empirical coefficient and is taken to be 1.4. Cd0The resistance coefficient when the cavitation number of the disc cavitator is 0 is taken as 0.83. V (tau)i) And σ (τ)i) Is a body of revolution tauiCentroid velocity and cavitation number at time.
(4) The whole movement process of the water-entering vacuole can be regarded as an independent expansion process of each section of the vacuole according to a certain rule. In the longitudinal plane, the profile of the cavitation bubbles may be defined by the upper and lower apices of the respective cavitation bubble cross-section. Under a fixed coordinate system, the vertex coordinates of each cavitation section in the longitudinal plane can be calculated as follows:
and (4) upper vertex:
lower vertex:
in the formula, xEiAnd zEiIs the coordinate of the vacuole vertex in a fixed coordinate system, xEoiAnd zEoiIs the coordinate of the revolving body particle in the fixed coordinate system, theta (tau)i) Is a body of revolution tauiAngle of pitch, x, of the body of revolution at the momentcThe distance from the head of the revolution body to the position of the center of gravity.
(5) The head of the revolving body can be regarded as a disc cavitator after entering water at a high speed, and the hydrodynamic force can be calculated as follows:
FL＝0
Mc＝0
in the form of characteristic area of cavitator
Angle of attack of cavitator
(6) Converting the vacuole coordinates under the fixed coordinate system in the step (4) into coordinates under a projectile coordinate system, converting the vacuole coordinates under the fixed coordinate system into coordinates under the projectile coordinate system, equally slicing the revolving body into a limited number of sections under the projectile coordinate system, sequentially calculating the wetting depth of each revolving body section invading the vacuole wall surface from the tail part, wherein the first section at the tail part is taken as the wetting depth h of the revolving body, and when the wetting depth is 0, calculating the distance between the revolving body section and the revolving body tail section as the wetting length l and the wetting area S of the revolving bodywThe fan shape is approximate and can be calculated by a fan shape area formula.
(7) Sliding lift force F at tail part of revolving bodypCan be calculated as follows:
wherein R is the radius of the tail part of the revolving body, Delta R-R, R is the tail part of the revolving bodyRadius of partial cavity, V1＝-w+q(L-xc)+VwcL is the length of the body of revolution, VwcFor cavitation transverse velocity, V2The tail cavitation shrinkage rate is shown, and the shrinkage is positive.
The resultant moment at the tail part of the revolving body is as follows:
(8) friction force F at tail of revolving bodyfCan be calculated as follows:
in the formula, Reynolds number Reμ is the dynamic viscosity of water, and at 20 ° the dynamic viscosity of water is 1.01 × 10- 3Pa.s, wetted area SwCan be calculated as follows:
(9) component G of projectile centroid gravity in projectile coordinate systemxAnd GzComprises the following steps:
Gx＝-mgsinθ
Gz＝-mgcosθ
(10) substituting the projectile external force calculated in the steps (5), (6), (7), (8) and (9) into the motion equation in the step (2), setting the time step, and performing time propulsion solution through an Euler method.
(11) Visualizing the result of the step (4) to obtain a high-speed water entry vacuole form, initializing the results calculated in the steps (5), (6), (7) and (8) to obtain a hydrodynamic force change curve in the high-speed water entry process, and visualizing the result solved in the step (2) to obtain a mass center speed, an angular speed, displacement and motion attitude change curve in the high-speed water entry process of the projectile.
Compared with the prior art, the invention has the advantages that:
(1) compared with the limitation brought by experimental observation, the technical method provided by the invention can more comprehensively obtain some details of the projectile entering water at high speed.
(2) The calculation period of the relative numerical simulation is long, and the technical method provided by the invention can be used for quickly calculating under the condition of ensuring the effectiveness and the precision.
Drawings
FIG. 1 shows a fixed coordinate system and a projectile coordinate system established by the present invention.
Figure 2 shows the section of each cavity during the high speed entry of the projectile into the water.
Figure 3 shows the hydrodynamic force of the head during high velocity entry of the projectile into the water.
Figure 4 shows the hydrodynamic force of the tail of the projectile during high velocity entry into the water.
Detailed Description
The invention is described in further detail below with reference to the accompanying drawings, comprising the following steps:
(1) as shown in fig. 1, a fixed coordinate system (o) is established as shown in fig. 1ExEzE) And a projectile coordinate system (o)BxBzB). Fixed coordinate system origin oEPlaced at the water entry point, x, of a horizontal planeEThe axis being parallel to the horizontal plane, zEThe positive direction of the axis is vertically upward and horizontally upward. Projectile coordinate system origin oBAt the center of gravity of the body of revolution, xBIn the positive axial direction, z is directed to the head of the rotor along the axis of the rotorBPositive axial direction perpendicular to xBAxially. x is the number ofBAxis and xEThe included angle of the shaft is the pitch angle theta of the revolving body and is positioned at xEThe upper side of the shaft is positive.
(2) Establishing a 3DOF motion equation of the projectile in a projectile coordinate system, and solving the velocity component, attitude angle and displacement of the projectile by combining initial conditions:
wherein m is the mass of the rotating body, IyIs the moment of inertia of the revolving body, u and w are the components of the revolving body mass center speed in the elastic body coordinate system, q is the revolving body in xEoEzEAngular velocity of rotation of plane, GxAnd GzIs the component of the gravity of the revolution body in the projectile coordinate system, FDAnd FLFor the component of the hydrodynamic force of the head of the body of revolution in the elastic coordinate system, FfAnd FpThe friction force and the sliding lift force of the fluid of the wetted part at the tail part of the revolving body McIs the resultant moment of the hydrodynamic force of the head of the revolving body to the center of mass of the revolving body, MpThe resultant moment of the hydrodynamic force at the tail part of the revolving body to the center of mass of the revolving body.
(3) As shown in FIG. 2, the section of the 1 st cavitation bubble generated at the time of the projectile entering the water is numbered, and so on. According to the mass center speed of the projectile solved in the step (2), the radius of the section of the newly generated cavity of the projectile head and the radius of the section of the generated cavity can be solved:
in the formula, τiThe moment when the ith cavitation section is formed, and t is the navigation time after the revolving body enters water. Rc(t,τi) Is the cavitation radius of the ith cavitation section at the time t, RnIs the radius of the circular section of the head part of the revolving body. N is an empirical coefficient and is taken to be 1.4. Cd0The resistance coefficient when the cavitation number of the disc cavitator is 0 is taken as 0.83. V (tau)i) And σ (τ)i) Is a body of revolution tauiCentroid velocity and cavitation number at time.
(4) As shown in FIG. 2, the whole movement process of the water-entering vacuole can be regarded as the independent expansion process of each section of the vacuole according to a certain rule. In the longitudinal plane, the profile of the cavitation bubbles may be defined by the upper and lower apices of the respective cavitation bubble cross-section. Under a fixed coordinate system, the vertex coordinates of each cavitation section in the longitudinal plane can be calculated as follows:
and (4) upper vertex:
lower vertex:
in the formula, xEiAnd zEiIs the coordinate of the vacuole vertex in a fixed coordinate system, xEoiAnd zEoiIs the coordinate of the revolving body particle in the fixed coordinate system, theta (tau)i) Is a body of revolution tauiAngle of pitch, x, of the body of revolution at the momentcThe distance from the head of the revolution body to the position of the center of gravity.
(5) Referring to fig. 3, the head of the rotator after entering water at high speed can be regarded as a disk cavitator, and the hydrodynamic force can be calculated as follows:
FL＝0
Mc＝0
in the form of characteristic area of cavitator
Angle of attack of cavitator
(6) As shown in fig. 4, the cavity coordinates in the fixed coordinate system in step (4) are converted into coordinates in the projectile coordinate system, the cavity coordinates in the fixed coordinate system are converted into coordinates in the projectile coordinate system, the revolving body is equally sliced into a finite number of cross sections in the projectile coordinate system, and the cross sections are compiled from the tail partAnd sequentially calculating the wetting depth of each section of the revolving body invading the wall surface of the cavity, wherein the first section at the tail part is taken as the wetting depth h of the revolving body, when the wetting depth is 0, the distance between the section of the revolving body and the section at the tail part of the revolving body is calculated as the wetting length l of the revolving body, and the wetting area S of the revolving bodywThe fan shape is approximate and can be calculated by a fan shape area formula.
(7) Sliding lift force F at tail part of revolving bodypCan be calculated as follows:
wherein R is the tail radius of the rotator, Δ R-R, R is the tail cavity radius of the rotator, and V1＝-w+q(L-xc)+VwcL is the length of the body of revolution, VwcFor cavitation transverse velocity, V2The tail cavitation shrinkage rate is shown, and the shrinkage is positive.
The resultant moment at the tail part of the revolving body is as follows:
(8) friction force F at tail of revolving bodyfCan be calculated as follows:
in the formula, Reynolds number Reμ is the dynamic viscosity of water, and at 20 ° the dynamic viscosity of water is 1.01 × 10- 3Pa.s, wetted area SwCan be calculated as follows:
(9) component G of projectile centroid gravity in projectile coordinate systemxAnd GzComprises the following steps:
Gx＝-mg sinθ
Gz＝-mg cosθ
(10) substituting the projectile external force calculated in the steps (5), (6), (7), (8) and (9) into the motion equation in the step (2), setting the time step, and performing time propulsion solution through an Euler method.
(11) Visualizing the result of the step (4) to obtain a high-speed water entry vacuole form, initializing the results calculated in the steps (5), (6), (7) and (8) to obtain a hydrodynamic force change curve in the high-speed water entry process, and visualizing the result solved in the step (2) to obtain a mass center speed, an angular speed, displacement and motion attitude change curve in the high-speed water entry process of the projectile.
The above description is included within the scope of the present invention, and the detailed description of the present invention is not given in detail in the prior art.
Claims (5)
1. A novel method for quickly calculating the high-speed water-entering trajectory of a projectile is characterized by comprising the following steps: comprises that
Step one, establishing a fixed coordinate system (o)ExEzE) And a projectile coordinate system (o)BxBzB)；
Step two, establishing a projectile coordinate system (o)BxBzB) Solving the velocity component, attitude angle and displacement of the projectile by combining the initial conditions according to the following three-degree-of-freedom motion equation:
wherein m is the mass of the rotating body, IyIs the moment of inertia of the revolving body, u and w are the components of the revolving body mass center speed in the elastic body coordinate system, q is the revolving body in xEoEzEAngular velocity of rotation of plane, GxAnd GzIs the component of the gravity of the revolution body in the projectile coordinate system, FDAnd FLFor the component of the hydrodynamic force of the head of the body of revolution in the elastic coordinate system, FfAnd FpThe friction force and the sliding lift force of the fluid of the wetted part at the tail part of the revolving body McIs the resultant moment of the hydrodynamic force of the head of the revolving body to the center of mass of the revolving body, MpThe resultant moment of the hydrodynamic force at the tail part of the revolving body to the center of mass of the revolving body;
thirdly, numbering the 1 st cavitation interface generated at the moment that the projectile enters water, and analogizing in sequence to solve the radius of a new cavitation section and a generated cavitation section at the head of the projectile;
step four, regarding the whole movement process of the vacuole entering the water as a process of independently expanding each section of the vacuole according to a rule, wherein the process is realized by defining the vertex coordinates of each vacuole section in a longitudinal plane;
step five, calculating the external force of the projectile and substituting the external force into the motion equation in the step two, and setting a time step to carry out time propulsion solution through an Eulerian method;
and sixthly, obtaining a visual result, wherein the visual result comprises a high-speed water entering vacuole form, a hydrodynamic force change curve, and a centroid speed, angular speed, displacement and motion attitude change curve.
2. The novel method for rapidly calculating the high-speed water-entering trajectory of a projectile according to claim 1, wherein the method comprises the following steps: in the first step, the fixed coordinate system origin oEPlaced at the water entry point, x, of a horizontal planeEThe axis being parallel to the horizontal plane, zEThe positive direction of the axis is vertical and horizontal upwards;
the projectile coordinate system origin oBAt the center of gravity of the body of revolution, xBThe positive direction of the axis points back along the axis of the rotorHead of swivel, zBPositive axial direction perpendicular to xBIn the axial direction; x is the number ofBAxis and xEThe included angle of the shaft is the pitch angle theta of the revolving body and is positioned at xEThe upper side of the shaft is positive.
3. The novel method for rapidly calculating the high-speed water-entering trajectory of a projectile according to claim 1, wherein the method comprises the following steps: in the third step, according to the mass center speed of the projectile solved in the step (2), the radius of the section of the newly generated cavity and the radius of the section of the generated cavity at the head part of the projectile can be solved:
in the formula, τiThe moment when the ith cavitation section is formed is t, and the navigation time after the revolving body enters water is t; rc(t，τi) Is the cavitation radius of the ith cavitation section at the time t, RnIs the radius of the circular section of the head part of the revolving body; n is an empirical coefficient and is taken as 1.4; cd0The resistance coefficient when the cavitation number of the disc cavitator is 0 is taken as 0.83; v (tau)i) And σ (τ)i) Is a body of revolution tauiCentroid velocity and cavitation number at time.
4. The novel method for rapidly calculating the high-speed water-entering trajectory of a projectile according to claim 1, wherein the method comprises the following steps: in the fourth step, in the longitudinal plane, the shape of the vacuole can be determined by the upper and lower vertexes of each vacuole section; under a fixed coordinate system, the vertex coordinates of each cavitation section in the longitudinal plane can be calculated as follows:
and (4) upper vertex:
lower vertex:
in the formula, xEiAnd zEiIs the coordinate of the vacuole vertex in a fixed coordinate system, xEoiAnd zEoiIs the coordinate of the revolving body particle in the fixed coordinate system, theta (tau)i) Is a body of revolution tauiAngle of pitch, x, of the body of revolution at the momentcThe distance from the head of the revolution body to the position of the center of gravity.
5. The novel method for rapidly calculating the high-speed water-entering trajectory of a projectile according to claim 4, wherein the method comprises the following steps: the projectile external force comprises FD，FL，Mc，Fp，Mp，GxAnd GzThe respective solving processes are as follows:
the head of the revolving body can be regarded as a disc cavitator after entering water at a high speed, and the hydrodynamic force can be calculated as follows:
FL＝0
Mc＝0
in the form of characteristic area of cavitator
Angle of attack of cavitator
Converting vacuole coordinates under a fixed coordinate system into coordinates under a bomb coordinate system, converting the vacuole coordinates under the fixed coordinate system into coordinates under the bomb coordinate system, equally slicing the revolving body into a limited number of sections under the bomb coordinate system, sequentially calculating the wetting depth of each revolving body section invading a vacuole wall surface from the tail part, wherein the first section at the tail part is taken as the wetting depth h of the revolving body, when the wetting depth is 0, calculating the distance between the revolving body section and the revolving body tail section as the wetting length l of the revolving body, and the wetting area S of the revolving bodywThe fan-shaped area is approximate to a fan shape and can be calculated through a fan-shaped area formula;
sliding lift force F at tail part of revolving bodypCan be calculated as follows:
wherein R is the tail radius of the rotator, Δ R-R, R is the tail cavity radius of the rotator, and V1＝-w+q(L-xc)+VwcL is the length of the body of revolution, VwcFor cavitation transverse velocity, V2The tail cavitation shrinkage speed is shown, and the shrinkage is positive;
the resultant moment at the tail part of the revolving body is as follows:
friction force F at tail of revolving bodyfCan be calculated as follows:
in the formula, Reynolds number Reμ is the dynamic viscosity of water, at 20 ° 1.01 × 10-3Pa.s, wetted area SwCan be calculated as follows:
component G of projectile centroid gravity in projectile coordinate systemxAnd GzComprises the following steps:
Gx＝-mg sinθ
Gz＝-mg cosθ。
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| CN114547989A (en) * | 2021-12-30 | 2022-05-27 | 南京理工大学 | A fast calculation method and system for the ballistic trajectory of truncated oval projectile into water |
| CN114818540A (en) * | 2022-04-28 | 2022-07-29 | 哈尔滨工业大学 | Construction method of non-torpedo-shaped navigation body high-speed water-entering trajectory prediction model |
| CN114839988A (en) * | 2022-04-28 | 2022-08-02 | 哈尔滨工业大学 | Protective tail cover separation time sequence control method during high-speed water entry of navigation body |
| CN114840999A (en) * | 2022-04-28 | 2022-08-02 | 哈尔滨工业大学 | Method for constructing large slenderness ratio revolving body water-entering vacuole evolution model |
| CN115562271A (en) * | 2022-10-10 | 2023-01-03 | 哈尔滨工业大学 | An open-loop control method suitable for high-speed water entry |
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| CN114547989A (en) * | 2021-12-30 | 2022-05-27 | 南京理工大学 | A fast calculation method and system for the ballistic trajectory of truncated oval projectile into water |
| CN114818540A (en) * | 2022-04-28 | 2022-07-29 | 哈尔滨工业大学 | Construction method of non-torpedo-shaped navigation body high-speed water-entering trajectory prediction model |
| CN114839988A (en) * | 2022-04-28 | 2022-08-02 | 哈尔滨工业大学 | Protective tail cover separation time sequence control method during high-speed water entry of navigation body |
| CN114840999A (en) * | 2022-04-28 | 2022-08-02 | 哈尔滨工业大学 | Method for constructing large slenderness ratio revolving body water-entering vacuole evolution model |
| CN115562271A (en) * | 2022-10-10 | 2023-01-03 | 哈尔滨工业大学 | An open-loop control method suitable for high-speed water entry |
| CN115562271B (en) * | 2022-10-10 | 2023-09-15 | 哈尔滨工业大学 | An open-loop control method suitable for high-speed water entry |
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