WO2021098886A1 - 箭弹俯仰力矩系数和压力中心系数修正方法及存储介质 - Google Patents

箭弹俯仰力矩系数和压力中心系数修正方法及存储介质 Download PDF

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WO2021098886A1
WO2021098886A1 PCT/CN2020/132800 CN2020132800W WO2021098886A1 WO 2021098886 A1 WO2021098886 A1 WO 2021098886A1 CN 2020132800 W CN2020132800 W CN 2020132800W WO 2021098886 A1 WO2021098886 A1 WO 2021098886A1
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projectile
coefficient
rocket
configuration
pitching moment
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PCT/CN2020/132800
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English (en)
French (fr)
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郝赓
刘子腾
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蓝箭航天空间科技股份有限公司
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Priority to GB2207206.0A priority Critical patent/GB2604077B/en
Publication of WO2021098886A1 publication Critical patent/WO2021098886A1/zh

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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01M—TESTING STATIC OR DYNAMIC BALANCE OF MACHINES OR STRUCTURES; TESTING OF STRUCTURES OR APPARATUS, NOT OTHERWISE PROVIDED FOR
    • G01M9/00—Aerodynamic testing; Arrangements in or on wind tunnels
    • G01M9/08—Aerodynamic models
    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F42—AMMUNITION; BLASTING
    • F42B—EXPLOSIVE CHARGES, e.g. FOR BLASTING, FIREWORKS, AMMUNITION
    • F42B10/00—Means for influencing, e.g. improving, the aerodynamic properties of projectiles or missiles; Arrangements on projectiles or missiles for stabilising, steering, range-reducing, range-increasing or fall-retarding
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01M—TESTING STATIC OR DYNAMIC BALANCE OF MACHINES OR STRUCTURES; TESTING OF STRUCTURES OR APPARATUS, NOT OTHERWISE PROVIDED FOR
    • G01M9/00—Aerodynamic testing; Arrangements in or on wind tunnels
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02T—CLIMATE CHANGE MITIGATION TECHNOLOGIES RELATED TO TRANSPORTATION
    • Y02T90/00—Enabling technologies or technologies with a potential or indirect contribution to GHG emissions mitigation

Definitions

  • the application belongs to the technical field of missile-type aircraft coefficient correction, and specifically relates to a method for correcting the pitching moment coefficient and the pressure center coefficient of the projectile and a storage medium.
  • aerodynamic forces received by the aircraft in the atmosphere are usually normalized and written in the form of aerodynamic coefficients, which are collectively referred to as aerodynamic characteristics.
  • the pitch moment coefficient and the pressure center coefficient in the aerodynamic characteristics of the aircraft affect the stability and maneuverability of the aircraft, and occupy an important position in the design of the aircraft.
  • the aerodynamic characteristics of the aircraft also change accordingly, which affects the flight performance of the aircraft.
  • the wind tunnel test technology requires the design and processing of the scaled model of the aircraft, and the installation of the scaled model of the aircraft in the wind tunnel test equipment, conduct a blowing test, measure the aerodynamic characteristics of the aircraft, and obtain the pitching moment coefficient and the pressure center coefficient of the aircraft.
  • the configuration of the aircraft changes, if the wind tunnel test is used to obtain the aerodynamic characteristics of the aircraft, it is necessary to redesign and process the test model of the aircraft, and perform the wind tunnel test again; however, this will inevitably lead to cost Increase and lengthen the calculation period.
  • Numerical calculation technology needs to establish a mathematical model based on the shape of the aircraft.
  • Calculation methods usually include engineering experience calculation methods and CFD calculation methods based on solving the N-S equation.
  • the engineering experience calculation method is generally used for the calculation of the initial stage of the scheme, which is fast but has low accuracy.
  • the calculation progress of the CFD calculation method can meet the engineering requirements, but the calculation pre-processing and calculation time are longer than the engineering experience calculation method; in addition, if the configuration of the aircraft changes, the pre-processing needs to be re-processed and the new configuration is recalculated
  • the flow field, cost and calculation cycle will inevitably increase.
  • the present application provides a method and storage medium for correcting the pitching moment coefficient and the pressure center coefficient of the projectile.
  • the present application provides a method for modifying the pitching moment coefficient and the center of pressure coefficient of the projectile, which is suitable for an axisymmetric rotary body shape, a tailless layout or a + or x tail layout. , which includes the following steps:
  • the acquired aerodynamic characteristic parameters of the projectile of the original configuration include the pitching moment coefficient and the pressure center coefficient of the projectile of the original configuration.
  • the acquired shape change data of the projectile aircraft includes the reference length change of the projectile of the original configuration and the projectile of the improved configuration.
  • the pressure center coefficient model of the improved rocket projectile constructed is:
  • C mz,old represents the pitching moment coefficient of the projectile in the original configuration
  • C mz,old,tail represents the pitching moment coefficient of the tail wing of the projectile in the original configuration
  • l ref,old represents the pitching moment coefficient of the projectile in the original configuration.
  • Reference length, l ref, new represents the reference length of the rocket with the improved configuration
  • l ref, new l ref, old + ⁇ l ref
  • ⁇ l ref represents the reference length of the rocket with the original configuration and the rocket with the improved configuration
  • the amount of change, X cp,old represents the pressure center coefficient of the projectile in the original configuration
  • CN represents the normal force coefficient of the projectile. Among them, the normal force coefficient of the projectile in the original configuration and the projectile in the improved configuration The normal force coefficients are equal.
  • M z represents the pitching moment of the projectile
  • q ⁇ represents the dynamic pressure of the projectile in flight
  • S ref represents the reference area
  • l ref represents the reference length
  • the pitching moment coefficient C mz,new of the rocket with the improved configuration is:
  • M Z,new represents the pitch moment of the improved configuration of the projectile
  • M Z,new,nose represents the head pitch moment of the improved configuration of the projectile
  • M Z,new,tail represents the improved configuration of the projectile
  • the tail wing pitching moment of, M Z,new,p represents the pitching moment produced by the protrusions on the surface of the rocket body of the improved configuration rocket;
  • the pitching moment of the tail wing of the modified rocket projectile is:
  • N new,tail represents the normal force of the tail wing of the rocket with the improved configuration
  • M Z,new,tail represents the pitch moment of the tail wing of the rocket with the improved configuration
  • l cp,new,tail represents the arrow with the improved configuration
  • N old,tail represents the normal force of the tail of the projectile in the original configuration
  • M Z,old,tail represents the pitch moment of the tail of the projectile in the original configuration
  • l ref, old,tail represents the reference length of the tail wing of the rocket in the original configuration
  • the pitching moment coefficient model of the projectile with the improved configuration is:
  • the present application also provides a computer storage medium on which a computer program is stored, and when the computer program is executed by a processor, the pitch moment coefficient of any one of the above-mentioned projectiles and The steps of the method of correcting the center of pressure coefficient.
  • the present application also provides a server, which includes a memory and a processor, the memory stores an executable program, and the processor implements any of the foregoing when calling the executable program.
  • a server which includes a memory and a processor, the memory stores an executable program, and the processor implements any of the foregoing when calling the executable program.
  • the application aims at the change of the length of the rocket-like aircraft with the shape of an axisymmetric spiral body, the tailless layout or the + and x-tail layout, and the arrow based on the original configuration
  • the aerodynamic characteristic parameters of the missile-like aircraft are obtained by obtaining the pressure center coefficient and pitching moment coefficient of the improved configuration of the rocket; this application can solve the high cost and long period of the aerodynamic characteristic parameters of the improved configuration based on wind tunnel tests and numerical calculations.
  • the problem is to quickly and accurately obtain the pressure center coefficient and pitching moment coefficient of the improved configuration rocket after the length of the projectile changes; so that the calculation of the distributed aerodynamic characteristics of the projectile can get rid of the dependence on the wind tunnel test and the complicated calculation process. Greatly shorten the design cycle, reduce design costs, and improve design efficiency.
  • FIG. 1 is a flowchart of a method for correcting the pitch moment coefficient and the pressure center coefficient of a projectile provided by an embodiment of the application.
  • Fig. 2 is a schematic diagram of the change of the configuration of the projectile in a method for correcting the pitching moment coefficient and the pressure center coefficient of the projectile provided by an embodiment of the application.
  • FIG. 3 is a comparison result diagram of the pitch moment coefficient obtained by testing the rocket with the improved 3-stage configuration and the pitch moment coefficient modified based on the original 4-stage configuration provided by an embodiment of the application; in which, Represents the pitch moment coefficient curve diagram obtained based on the original 4-level configuration modification, Shows the curve graph of the pitch moment coefficient obtained from the test of the rocket with the improved three-stage configuration.
  • Fig. 4 is a comparison result diagram of the center of pressure coefficient obtained by testing the rocket with the improved 3-stage configuration and the center-of-pressure coefficient corrected based on the original 4-stage configuration provided by an embodiment of the application; where, Represents the pitch moment coefficient curve diagram obtained based on the original 4-level configuration modification, Shows the curve graph of the pitch moment coefficient obtained from the test of the rocket with the improved three-stage configuration.
  • the missile bodies of launch vehicles and missile-type aircraft are mostly in the shape of axisymmetric spiral body, with no tail layout or empennage layout.
  • the tails of carrier rockets or missile-type aircraft with tail wing are mostly in the form of + or x layout, which have such characteristics.
  • the main configuration changes faced are the changes in the length of the arrow body or the projectile body, the changes in the shape of the warhead, and the geometric changes in the tail wing surface.
  • the configuration changes will affect the aerodynamic characteristics of the aircraft.
  • the method for correcting the pitching moment coefficient and the center of pressure coefficient of the projectile provided by the embodiment of the application is based on the aerodynamic characteristic data of the original configuration of the projectile, and obtaining the pitching moment of the improved configuration of the projectile after the change in length
  • the coefficient and the center of pressure coefficient, as shown in Figure 1 include the following steps:
  • the method for modifying the pitching moment coefficient and pressure center coefficient of the projectile provided in the embodiments of this application is not limited to the longitudinal pressure center coefficient and The correction calculation of the longitudinal pitching moment coefficient can also correct the lateral pressure center coefficient and the lateral yaw moment.
  • the acquired aerodynamic characteristic parameters of the projectile of the original configuration include: the pitch moment coefficient and the pressure center coefficient of the projectile of the original configuration.
  • the acquired shape change data of the rocket aircraft includes the reference length change ⁇ l ref of the rocket projectile of the original configuration and the projectile of the improved configuration.
  • step S3 when the shape change data of the rocket aircraft includes the reference length changes of the rocket with the original configuration and the rocket with the improved configuration, the constructed model for the pitching moment coefficient of the rocket with the improved configuration is:
  • the pressure center coefficient model of the improved rocket projectile constructed is:
  • C mz,old represents the pitching moment coefficient of the rocket in the original configuration
  • C mz,old,tail represents the pitching moment coefficient of the tail of the rocket in the original configuration
  • l ref,old Indicates the reference length of the rocket in the original configuration
  • l ref,new means the reference length of the rocket in the improved configuration
  • l ref,new l ref,old + ⁇ l ref
  • ⁇ l ref means the rocket in the original configuration and the improvement
  • X cp,old represents the pressure center coefficient of the projectile of the original configuration
  • C N represents the normal force coefficient of the projectile
  • the normal force of the projectile of the original configuration The coefficient is equal to the normal force coefficient of the improved configuration of the projectile.
  • the normal force and pitching moment are mainly composed of the head, column, and surface protrusions of the rocket.
  • the rear wing is produced.
  • the column section has a small contribution to the normal force, which is negligible compared to the head and tail.
  • the normal force generated by the protrusions on the surface of the arrow body is not affected by the length of the arrow body. influences. Therefore, it can be considered that the normal force is all provided by the head of the projectile, the projections on the surface of the projectile and the tail wing.
  • each parameter is distinguished by the subscripts old and new, respectively.
  • C mz represents the pitching moment coefficient of the projectile
  • CN represents the normal force coefficient of the projectile
  • N old,nose represents the head normal force of the original configuration of the projectile
  • N new,nose represents the head normal force of the improved configuration of the projectile
  • N old,tail represents the original configuration
  • N new,tail represents the normal force of the tail wing of the improved configuration of the projectile
  • N old,p represents the normal force generated by the projection on the surface of the projectile of the original configuration
  • N new,p represents the normal force generated by the protrusions on the surface of the rocket body of the improved configuration
  • N old,b represents the normal force of the column section of the original configuration of the rocket, N new,b of the improved configuration The normal force of the column of the bullet.
  • N old N old, nose + N old, tail + N old, p (5)
  • N new N new, nose + N new, tail + N new, p (7)
  • the normal force and the normal force coefficient of the projectile have the following relationship:
  • M Z,old represents the pitching moment of the projectile in the original configuration
  • M Z,old,nose represents the pitching moment of the head of the projectile in the original configuration
  • M Z,old,tail represents the pitching moment of the tail wing of the rocket of the original configuration
  • M Z,old,p represents the pitching moment of the projectile on the surface of the rocket of the original configuration
  • C mz,old represents the pitch moment coefficient of the projectile in the original configuration
  • C mz,old,nose represents the head pitch moment coefficient of the projectile in the original configuration
  • C mz,old,tail represents the pitch moment coefficient of the projectile in the original configuration
  • the pitching moment coefficient of the tail wing, C mz,old,p represents the pitching moment coefficient produced by the projections on the surface of the rocket body of the original configuration
  • l cp,old represents the pressure center of the original configuration of the rocket to the moment reference point Distance
  • l ref,old represents the reference length of the rocket in the original configuration
  • q ⁇ represents the dynamic pressure of the projectile in flight
  • S ref represents the reference area
  • M Z,new represents the pitch moment of the improved configuration of the projectile
  • M Z,new,nose represents the head pitch moment of the improved configuration of the projectile
  • M Z,new,tail represents the pitching moment of the tail wing of the rocket with the improved configuration
  • M Z,new,p represents the pitching moment produced by the protrusion on the surface of the rocket with the improved configuration
  • C mz,new represents the pitching moment coefficient of the improved configuration of the projectile
  • C mz,new,nose represents the head pitching moment coefficient of the improved configuration of the projectile
  • C mz,new,tail represents the improved configuration of the projectile
  • the pitching moment coefficient of the tail wing, C mz,new,p represents the pitching moment coefficient produced by the projections on the surface of the rocket body of the improved configuration
  • l cp,new represents the pressure center of the improved configuration of the rocket to the moment reference point Distance, l ref, new represents the reference length of the rocket with improved configuration.
  • N new, tail represents the normal force of the tail wing of the improved configuration of the rocket
  • M Z, new, tail represents the tail pitching moment of the improved configuration of the projectile
  • l cp, new, tail represents the improved configuration.
  • the distance from the center of pressure of the tail wing of the missile to the reference point of torque; N old,tail represents the normal force of the tail of the rocket of the original configuration, M Z,old,tail represents the pitch moment of the tail of the rocket of the original configuration, l ref, old, tail represent the reference length of the tail wing of the rocket in the original configuration.
  • the pitching moment coefficient model of the improved rocket projectile is further organized as:
  • the pitching moment coefficient and pressure center coefficient of the improved configuration of the missile can be used with the original configuration of the rocket’s pitching moment coefficient, pressure center coefficient, reference length and length Incremental expression, that is, the pitch moment coefficient and pressure center coefficient of the modified rocket projectile can be obtained through the correction of the pitch moment coefficient and pressure center coefficient of the projectile of the original configuration.
  • the method for modifying the pitching moment coefficient and the pressure center coefficient of the projectile provided by the embodiment of the application can be based on the aerodynamic characteristic parameters of the projectile of the original configuration, and obtain the projectile pitching moment coefficient and the pressure center coefficient of the improved configuration after the length of the projectile is changed. , Can make the calculation of the aerodynamic characteristic parameters of the rocket get rid of the dependence on the wind tunnel test and numerical calculation, greatly shorten the design cycle, reduce the design cost, and improve the design efficiency.
  • the following describes the method for correcting the pitching moment coefficient and the pressure center coefficient of the projectile provided by the embodiments of the present application in conjunction with the actual development process of a certain type of launch vehicle.
  • the existing full-arrow normal force coefficient C N and pitching moment coefficient C based on the original configuration mz , pressure center coefficient X cp , tail pitching moment coefficient C mz,tail , reference length l ref , reference length of the rocket with improved configuration And the length increment ⁇ l ref , the pitch moment coefficient of the improved configuration rocket is obtained by the correction method of this application
  • the pitching moment coefficient C mz and pressure center coefficient X cp of the original 4-stage configuration rocket are shown in Table 1.
  • Table 2 shows the reference lengths and correction factors of the rockets in the 4-stage configuration and the 3-stage configuration.
  • the angle of attack When the angle of attack is greater than 6°, the separation zone of the leeward surface of the rocket body expands, and the nonlinear lift produced by the viscous separation causes the change of the rocket's normal force and pitching moment to be non-negligible.
  • the accuracy of the aerodynamic characteristic data is generally 10% to 15%.
  • the angle of attack is less than or equal to 6°, the correction method of this application can be used to obtain better calculation results; when the angle of attack is greater than 6°, although the accuracy of the data obtained by the correction calculation decreases, there is still a strong point in engineering applications. Reference value and guiding significance.
  • the embodiment of the present application also provides a computer storage medium, which is a computer-readable storage medium, for example, a memory including a computer program, which can be executed by a processor to complete the aforementioned projectile pitch moment.
  • a computer storage medium which is a computer-readable storage medium, for example, a memory including a computer program, which can be executed by a processor to complete the aforementioned projectile pitch moment. The steps in the correction method of coefficient and pressure center coefficient.
  • the embodiment of the present application further provides a server, which includes a memory and a processor, the memory stores an executable program, and the processor implements the aforementioned projectile pitch moment coefficient and The steps in the method of correcting the coefficient of pressure center.
  • the embodiment of the present application may also represent the program code for executing the above method in a digital signal processor (DSP).
  • DSP digital signal processor
  • This application may also involve multiple functions performed by a computer processor, a digital signal processor, a microprocessor, or a field programmable gate array (Field Programmable Gate Array, FPGA).
  • the above-mentioned processor can be configured to perform a specific task according to the present application, which is completed by executing machine-readable software code or firmware code that defines the specific method disclosed in the present application.
  • the software code or firmware code can be developed to express different programming languages and different formats or forms. It can also mean that the software code is compiled for different target platforms. However, the different code styles, types and languages of the software code for performing tasks according to this application and other types of configuration codes do not depart from the spirit and scope of this application.

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Abstract

一种箭弹俯仰力矩系数和压力中心系数修正方法及存储介质，修正方法适用于轴对称旋成体外形，无尾布局或+、x尾翼布局的箭弹类飞行器，包括以下步骤：获取原始构型的箭弹的气动特性参数（S1）；获取箭弹飞行器的外形变化数据（S2）；构建改进构型的箭弹的俯仰力矩系数模型和压力中心系数模型（S3）；将原始构型的箭弹的气动特性参数和箭弹飞行器的外形变化数据输入到改进构型的箭弹的俯仰力矩系数模型和压力中心系数模型中，得到改进构型的箭弹的俯仰力矩系数和压力中心系数，以缩短设计周期，降低设计成本（S4）。修正方法能够摆脱对风洞试验、复杂的计算过程的依赖，大大缩短设计周期，降低设计成本，提高设计效率。

Description

箭弹俯仰力矩系数和压力中心系数修正方法及存储介质 技术领域
本申请属于箭弹类飞行器系数修正技术领域，具体涉及一种箭弹俯仰力矩系数和压力中心系数修正方法及存储介质。
背景技术
大气层中运动的飞行器在空气的作用下，会产生包括升力、阻力的气动力。工程上通常将大气层中的飞行器受到的气动力进行归一化，写成气动力系数的形式，并统称为气动特性。飞行器的气动特性中的俯仰力矩系数和压力中心系数影响飞行器的稳定性和操纵性，在飞行器设计中占有重要地位。当飞行器的构型发生变化时，飞行器的气动特性也相应变化，从而影响飞行器的飞行性能。
随着计算机技术和试验技术的进步，飞行器气动特性的获得方式和手段不断丰富和进步。工程上通常使用风洞试验技术和数值计算技术来获得飞行器的气动特性。
风洞试验技术需要设计、加工飞行器的缩比模型，并将飞行器的缩比模型安装在风洞试验设备中，进行吹风试验，测量飞行器的气动特性，获得飞行器的俯仰力矩系数和压力中心系数。而当飞行器的构型发生变化时，如果采用风洞试验的方式获得飞行器的气动特性，就需要重新设计、加工飞行器的试验模型，并重新进行风洞试验；然而，这不可避免会导致成本的增加和计算周期的加长。
数值计算技术需要根据飞行器的外形建立数学模型。计算方法通常包括工程经验计算方法和基于求解N-S方程的CFD计算方法。工程经验计算方法一般用于方案初期阶段的计算，速度快，但是精度较低。CFD计算方法的计算进度能够满足工程需求，但是计算前处理和计算时间相对工程经验计算方法较长；另外，如果飞行器的构型发生变化，则需要重新进行前处理，并重 新计算新构型的流场，成本和计算周期亦不可避免的增加。
发明内容
为至少在一定程度上克服相关技术中存在的问题，本申请提供了一种箭弹俯仰力矩系数和压力中心系数修正方法及存储介质。
根据本申请实施例的第一方面，本申请提供了一种箭弹俯仰力矩系数和压力中心系数修正方法，适用于轴对称旋成体外形，无尾布局或+、x尾翼布局的箭弹类飞行器，其包括以下步骤：
获取原始构型的箭弹的气动特性参数；
获取箭弹飞行器的外形变化数据；
构建改进构型的箭弹的俯仰力矩系数模型和压力中心系数模型；
将原始构型的箭弹的气动特性参数和箭弹飞行器的外形变化数据输入到改进构型的箭弹的俯仰力矩系数模型和压力中心系数模型中，得到改进构型的箭弹的俯仰力矩系数和压力中心系数，以缩短设计周期，降低设计成本。
上述箭弹俯仰力矩系数和压力中心系数修正方法中，获取的所述原始构型的箭弹的气动特性参数包括原始构型的箭弹的俯仰力矩系数和压力中心系数。
上述箭弹俯仰力矩系数和压力中心系数修正方法中，获取的所述箭弹飞行器的外形变化数据包括原始构型的箭弹与改进构型的箭弹的参考长度变化量。
进一步地，构建的改进构型的箭弹的俯仰力矩系数模型为：
Figure PCTCN2020132800-appb-000001
构建的改进构型的箭弹的压力中心系数模型为：
Figure PCTCN2020132800-appb-000002
式中，C mz,old表示原始构型的箭弹的俯仰力矩系数，C mz,old,tail表示原始构型的箭弹的尾翼俯仰力矩系数，l ref,old表示原始构型的箭弹的参考长度，l ref,new 表示改进构型的箭弹的参考长度，l ref,new＝l ref,old+Δl ref，Δl ref表示原始构型的箭弹与改进构型的箭弹的参考长度变化量，X cp,old表示原始构型的箭弹的压力中心系数，C N表示箭弹的法向力系数，其中，原始构型的箭弹的法向力系数和改进构型的箭弹的法向力系数相等。
更进一步地，所述改进构型的箭弹的俯仰力矩系数模型的具体构建过程为：
根据箭弹的俯仰力矩系数C mz的表达式：
Figure PCTCN2020132800-appb-000003
式中，M z表示箭弹的俯仰力矩，q ∞表示箭弹飞行动压，S ref表示参考面积，l ref表示参考长度；
得到改进构型的箭弹的俯仰力矩系数C mz,new为：
Figure PCTCN2020132800-appb-000004
式中，M Z,new表示改进构型的箭弹的俯仰力矩，M Z,new,nose表示改进构型的箭弹的头部俯仰力矩，M Z,new,tail表示改进构型的箭弹的尾翼俯仰力矩，M Z,new,p表示改进构型的箭弹的箭体表面凸起物产生的俯仰力矩；
原始构型的箭弹的头部俯仰力矩和箭体表面凸起物产生的俯仰力矩均不受长度调整的影响，得到：
Figure PCTCN2020132800-appb-000005
则进一步得到改进构型的箭弹的俯仰力矩系数C mz,new为：
Figure PCTCN2020132800-appb-000006
根据压力中心到力矩参考点的距离l cp与箭弹受到的法向力N和俯仰力矩M z的关系式：
Figure PCTCN2020132800-appb-000007
得到改进构型的箭弹的尾翼的俯仰力矩为：
M Z,new,tail＝N new,taill cp,new,tail，
箭弹的长度变化前后，尾翼产生的法向力系数保持不变，有：
Figure PCTCN2020132800-appb-000008
式中，N new,tail表示改进构型的箭弹的尾翼法向力，M Z,new,tail表示改进构型的箭弹的尾翼俯仰力矩，l cp,new,tail表示改进构型的箭弹的尾翼压力中心到力矩参考点的距离；N old,tail表示原始构型的箭弹的尾翼法向力，M Z,old,tail表示原始构型的箭弹的尾翼俯仰力矩，l ref,old,tail表示原始构型的箭弹的尾翼参考长度；
则进一步得到改进构型的箭弹的尾翼的俯仰力矩为：
Figure PCTCN2020132800-appb-000009
进一步得到改进构型的箭弹的俯仰力矩系数模型为：
Figure PCTCN2020132800-appb-000010
更进一步地，所述改进构型的箭弹的压力中心系数模型的具体构建过程为：
根据压力中心系数X cp与箭弹的俯仰力矩系数C mz和箭弹的法向力系数 C N之间的关系式
Figure PCTCN2020132800-appb-000011
以及改进构型的箭弹的俯仰力矩系数模型，得到改进构型的箭弹的压力中心系数模型为：
Figure PCTCN2020132800-appb-000012
根据本申请实施例的第二方面，本申请还提供了一种计算机存储介质，其上存储有计算机程序，所述计算机程序被处理器执行时实现上述任一项所述箭弹俯仰力矩系数和压力中心系数修正方法的步骤。
根据本申请实施例的第三方面，本申请还提供了一种服务器，其包括存储器和处理器，所述存储器存储可执行程序，所述处理器在调用所述可执行程序时，实现上述任一项所述箭弹俯仰力矩系数和压力中心系数修正方法的步骤。
根据本申请的上述具体实施方式可知，至少具有以下有益效果：本申请针对轴对称旋成体外形，无尾布局或+、x尾翼布局的箭弹类飞行器的长度变化，基于原有构型的箭弹类飞行器的气动特性参数，得到改进构型的箭弹的压力中心系数和俯仰力矩系数；本申请能够解决基于风洞试验和数值计算得到改进构型的气动特性参数的成本高、周期长的问题，能够快速、准确的得到箭弹长度变化后改进构型箭弹的压力中心系数和俯仰力矩系数；使得箭弹的分布气动特性的计算能够摆脱对风洞试验、复杂的计算过程的依赖，大大缩短设计周期，降低设计成本，提高设计效率。
应了解的是，上述一般描述及以下具体实施方式仅为示例性及阐释性的，其并不能限制本申请所欲主张的范围。
附图说明
下面的所附附图是本申请的说明书的一部分，其示出了本申请的实施例，所附附图与说明书的描述一起用来说明本申请的原理。
图1为本申请实施例提供的一种箭弹俯仰力矩系数和压力中心系数修正方法的流程图。
图2为本申请实施例提供的一种箭弹俯仰力矩系数和压力中心系数修正方法中箭弹构型的变化示意图。
图3为本申请实施例提供的对改进3级构型的火箭进行试验得到的俯仰力矩系数与基于原始4级构型修正得到的俯仰力矩系数的对比结果图；其中，
Figure PCTCN2020132800-appb-000013
表示基于原始4级构型修正得到的俯仰力矩系数曲线图，
Figure PCTCN2020132800-appb-000014
表示对改进3级构型的火箭进行试验得到的俯仰力矩系数曲线图。
图4为本申请实施例提供的对改进3级构型的火箭进行试验得到的压力中心系数与基于原始4级构型修正得到的压力中心系数的对比结果图；其中，
Figure PCTCN2020132800-appb-000015
表示基于原始4级构型修正得到的俯仰力矩系数曲线图，
Figure PCTCN2020132800-appb-000016
表示对改进3级构型的火箭进行试验得到的俯仰力矩系数曲线图。
具体实施方式
为使本申请实施例的目的、技术方案和优点更加清楚明白，下面将以附图及详细叙述清楚说明本申请所揭示内容的精神，任何所属技术领域技术人员在了解本申请内容的实施例后，当可由本申请内容所教示的技术，加以改变及修饰，其并不脱离本申请内容的精神与范围。
本申请的示意性实施例及其说明用于解释本申请，但并不作为对本申请的限定。另外，在附图及实施方式中所使用相同或类似标号的元件/构件是用来代表相同或类似部分。
关于本文中所使用的“第一”、“第二”、…等，并非特别指称次序或顺位的意思，也非用以限定本申请，其仅为了区别以相同技术用语描述的元件或操作。
关于本文中所使用的方向用语，例如：上、下、左、右、前或后等，仅是参考附图的方向。因此，使用的方向用语是用来说明并非用来限制本创作。
关于本文中所使用的“包含”、“包括”、“具有”、“含有”等等，均为开放性的用语，即意指包含但不限于。
关于本文中所使用的“及/或”，包括所述事物的任一或全部组合。
关于本文中的“多个”包括“两个”及“两个以上”；关于本文中的“多组”包括“两组”及“两组以上”。
关于本文中所使用的用语“大致”、“约”等，用以修饰任何可以细微变化的数量或误差，但这些微变化或误差并不会改变其本质。一般而言，此类用语所修饰的细微变化或误差的范围在部分实施例中可为20％，在部分实施例中可为10％，在部分实施例中可为5％或是其他数值。本领域技术人员应当了解，前述提及的数值可依实际需求而调整，并不以此为限。
某些用以描述本申请的用词将于下或在此说明书的别处讨论，以提供本领域技术人员在有关本申请的描述上额外的引导。
运载火箭的箭体和导弹类飞行器的弹体大多呈轴对称旋成体外形，无尾翼布局或有尾翼布局，有尾翼的运载火箭或导弹类飞行器尾翼多为+或x布局形式，具有此类特点的飞行器在设计过程中，主要面对的构型变化为箭体或弹体长度的变化、弹头外形变化，尾翼翼面几何变化等，构型变化会对飞行器的气动特性产生影响。
针对上述箭弹飞行器的长度变化，本申请实施例提供的箭弹俯仰力矩系数和压力中心系数修正方法基于箭弹原始构型的气动特性数据，得到长度变化后的箭弹改进构型的俯仰力矩系数和压力中心系数，如图1所示，其包括以下步骤：
S1、获取原始构型的箭弹的气动特性参数。
S2、获取箭弹飞行器的外形变化数据。
S3、构建改进构型的箭弹的俯仰力矩系数模型和压力中心系数模型。
S4、将原始构型的箭弹的气动特性参数和箭弹飞行器的外形变化数据输入到改进构型的箭弹的俯仰力矩系数和压力中心系数模型中，得到改进构型的箭弹的俯仰力矩系数和压力中心系数，以缩短设计周期，降低设计成本。
对于轴对称旋成体外形，无尾布局或“+”、“x”尾翼布局的箭弹类飞行器，本申请实施例提供的箭弹俯仰力矩系数和压力中心系数修正方法不限于 纵向压力中心系数和纵向俯仰力矩系数的修正计算，还可以对横向压力中心系数和横向偏航力矩进行修正计算。
上述步骤S1中，获取的原始构型的箭弹的气动特性参数包括：原始构型的箭弹的俯仰力矩系数和压力中心系数。
上述步骤S2中，获取的箭弹飞行器的外形变化数据包括原始构型的箭弹与改进构型的箭弹的参考长度变化量Δl ref。
上述步骤S3中，当箭弹飞行器的外形变化数据包括原始构型的箭弹与改进构型的箭弹的参考长度变化量时，构建的改进构型的箭弹的俯仰力矩系数模型为：
Figure PCTCN2020132800-appb-000017
构建的改进构型的箭弹的压力中心系数模型为：
Figure PCTCN2020132800-appb-000018
式(1)和式(2)中，C mz,old表示原始构型的箭弹的俯仰力矩系数，C mz,old,tail表示原始构型的箭弹的尾翼俯仰力矩系数，l ref,old表示原始构型的箭弹的参考长度，l ref,new表示改进构型的箭弹的参考长度，l ref,new＝l ref,old+Δl ref，Δl ref表示原始构型的箭弹与改进构型的箭弹的参考长度变化量，X cp,old表示原始构型的箭弹的压力中心系数，C N表示箭弹的法向力系数，其中，原始构型的箭弹的法向力系数和改进构型的箭弹的法向力系数相等。
对于轴对称旋成体外形，无尾布局或“+”、“X”尾翼布局的箭弹类飞行器，法向力和俯仰力矩主要由箭弹的头部、柱段、箭体表面凸起物和尾翼产生。尤其在小攻角飞行时，其中柱段对法向力的贡献较小，相对于头部和尾翼而言可以忽略，而箭体表面凸起物产生的法向力不受箭体长度变化的影响。因此，可以认为法向力全部由箭弹头部、箭体表面凸起物和尾翼提供。
下面以纵向压力中心系数和纵向俯仰力矩系数的修正为例，具体说明本申请实施例提供的箭弹俯仰力矩系数和压力中心系数修正方法中改进构型 的箭弹的俯仰力矩系数模型和压力中心系数模型的构建过程。
如图2所示，对应箭弹的原始构型和长度变化后的改进构型，各参数分别使用下标old和new进行区分。
取箭弹的理论尖点作为力矩参考点，箭弹受到的法向力为N，俯仰力矩为M z，压力中心到力矩参考点的距离为l cp，压力中心系数为X cp，箭弹飞行动压为q ∞，参考面积为S ref，参考长度为l ref，各参数之间存在以下关系式：
Figure PCTCN2020132800-appb-000019
式(3)中，C mz表示箭弹的俯仰力矩系数；C N表示箭弹的法向力系数。
对于原始构型和改进构型的箭弹，可以得到如下法向力及法向力系数关系：
Figure PCTCN2020132800-appb-000020
式(4)中，N old,nose表示原始构型的箭弹的头部法向力，N new,nose表示改进构型的箭弹的头部法向力；N old,tail表示原始构型的箭弹的尾翼法向力，N new,tail表示改进构型的箭弹的尾翼法向力；N old,p表示原始构型的箭弹的箭体表面凸起物产生的法向力，N new,p表示改进构型的箭弹的箭体表面凸起物产生的法向力；N old,b表示原始构型的箭弹的柱段法向力，N new,b改进构型的箭弹的柱段法向力。
原始构型的箭弹的法向力N old为：
N old＝N old，nose+N old,tail+N old,p           (5)
原始构型的箭弹的法向力系数C N,old为：
C N,old＝C N,old，nose+C N,old,tail+C N,old,p      (6)
改进构型的箭弹的法向力N new为：
N new＝N new，nose+N new,tail+N new,p           (7)
改进构型的箭弹的法向力系数C N,new为：
C N,new＝C N,new，nose+C N,new,tail+C N,new,p      (8)
箭弹的构型调整前后，箭弹的法向力及法向力系数存在如下关系：
Figure PCTCN2020132800-appb-000021
根据式(3)，原始构型的箭弹的压力中心到力矩参考点的距离l cp,old、压力中心系数X cp,old和俯仰力矩系数C mz,old的展开式分别为：
Figure PCTCN2020132800-appb-000022
Figure PCTCN2020132800-appb-000023
Figure PCTCN2020132800-appb-000024
式(10)、式(11)和式(12)中，M Z,old表示原始构型的箭弹的俯仰力矩，M Z,old,nose表示原始构型的箭弹的头部俯仰力矩，M Z,old,tail表示原始构型的箭弹的尾翼俯仰力矩，M Z,old,p表示原始构型的箭弹的箭体表面凸起物产生的俯仰力矩；
C mz,old表示原始构型的箭弹的俯仰力矩系数，C mz,old,nose表示原始构型的箭弹的头部俯仰力矩系数，C mz,old,tail表示原始构型的箭弹的尾翼俯仰力矩系数，C mz,old,p表示原始构型的箭弹的箭体表面凸起物产生的俯仰力矩系数；l cp,old表示原始构型的箭弹的压力中心到力矩参考点的距离，l ref,old表示原始构型的箭 弹的参考长度；
q ∞表示箭弹飞行动压，S ref表示参考面积。
根据式(3)，改进构型的箭弹的压力中心到力矩参考点的距离l cp,new、压力中心系数X cp,new和俯仰力矩系数C mz,new的展开式分别为：
Figure PCTCN2020132800-appb-000025
Figure PCTCN2020132800-appb-000026
Figure PCTCN2020132800-appb-000027
式(13)、式(14)和式(15)中，M Z,new表示改进构型的箭弹的俯仰力矩，M Z,new,nose表示改进构型的箭弹的头部俯仰力矩，M Z,new,tail表示改进构型的箭弹的尾翼俯仰力矩，M Z,new,p表示改进构型的箭弹的箭体表面凸起物产生的俯仰力矩；
C mz,new表示改进构型的箭弹的俯仰力矩系数，C mz,new,nose表示改进构型的箭弹的头部俯仰力矩系数，C mz,new,tail表示改进构型的箭弹的尾翼俯仰力矩系数，C mz,new,p表示改进构型的箭弹的箭体表面凸起物产生的俯仰力矩系数；l cp,new表示改进构型的箭弹的压力中心到力矩参考点的距离，l ref,new表示改进构型的箭弹的参考长度。
由于原始构型的箭弹的头部俯仰力矩和箭体表面凸起物产生的俯仰力矩均不受长度调整的影响，因此有：
Figure PCTCN2020132800-appb-000028
则由式(15)和式(16)得到改进构型的箭弹的俯仰力矩系数C mz,new可以表示为：
Figure PCTCN2020132800-appb-000029
由于箭弹的长度变化对尾翼周围空气流动状态影响较小，根据式(3)， 尾翼产生的法向力系数保持不变，因此有：
Figure PCTCN2020132800-appb-000030
式(18)中，N new,tail表示改进构型的箭弹的尾翼法向力，M Z,new,tail表示改进构型的箭弹的尾翼俯仰力矩，l cp,new,tail表示改进构型的箭弹的尾翼压力中心到力矩参考点的距离；N old,tail表示原始构型的箭弹的尾翼法向力，M Z,old,tail表示原始构型的箭弹的尾翼俯仰力矩，l ref,old,tail表示原始构型的箭弹的尾翼参考长度。
由式(18)得到改进构型的箭弹的尾翼的俯仰力矩为：
Figure PCTCN2020132800-appb-000031
由式(19)可以看出，改进构型的箭弹的尾翼的俯仰力矩可以用原始构型的箭弹的尾翼的俯仰力矩表示。
因此，由式(17)和式(19)得到改进构型的箭弹的俯仰力矩系数为：
Figure PCTCN2020132800-appb-000032
从式(20)可以看出，改进构型的箭弹的俯仰力矩系数可以采用原始构型的箭弹的俯仰力矩系数表示。
由式(20)进一步整理得到改进构型的箭弹的俯仰力矩系数模型为：
Figure PCTCN2020132800-appb-000033
由式(21)得到改进构型的箭弹的压力中心系数模型为：
Figure PCTCN2020132800-appb-000034
从式(21)和式(22)可以看出，改进构型的箭弹的俯仰力矩系数和压力中心系数均可以用原始构型的箭弹的俯仰力矩系数、压力中心系数、参考长度和长度增量来表示，即可以通过原始构型的箭弹的俯仰力矩系数和压力中心系数修正得到改进构型的箭弹的俯仰力矩系数和压力中心系数。
本申请实施例提供的箭弹俯仰力矩系数和压力中心系数修正方法能够基于原始构型的箭弹的气动特性参数，得到箭弹长度变化后的改进构型的箭弹俯仰力矩系数和压力中心系数，能够使箭弹的气动特性参数的计算摆脱对风洞试验和数值计算的依赖，大大缩短设计周期，降低设计成本，提高设计效率。
下面结合某型运载火箭的实际研制过程来说明本申请实施例提供的箭弹俯仰力矩系数和压力中心系数修正方法。
某型运载火箭方案设计阶段采用4级构型，改进构型为3级构型，火箭长度由原来的16.524m变为19.727m，长度增加3.203m。此外全箭头部外形、箭体直径、尾翼尺寸外形以及箭体上的相对位置不变，符合本本申请实施例提供的箭弹俯仰力矩系数和压力中心系数修正方法的适用范围。
以惯性力Ma＝1.5，攻角α＝2°、4°、6°，侧滑角β＝0°为例，基于 原始构型的已有全箭法向力系数C N、俯仰力矩系数C mz、压力中心系数X cp、尾翼俯仰力矩系数C mz,tail、参考长度l ref，改进构型的火箭参考长度
Figure PCTCN2020132800-appb-000035
和长度增量Δl ref，通过本申请修正方法获得改进构型火箭的俯仰力矩系数
Figure PCTCN2020132800-appb-000036
和压力中心系数
Figure PCTCN2020132800-appb-000037
其中，原4级构型的火箭的俯仰力矩系数C mz和压力中心系数X cp如表1所示。4级构型与3级构型火箭的参考长度与修正系数如表2所示。改进3级构型Ma＝1.5试验数据与本申请修正方法的计算结果对比如表3所示。
表1 原4级构型Ma＝1.5，俯仰力矩系数C mz，压力中心系数X cp统计表
Figure PCTCN2020132800-appb-000038
表2 4级构型与3级构型参考长度与修正系数
Figure PCTCN2020132800-appb-000039
表3 改进3级构型Ma＝1.5试验数据与修正算法计算结果对比
Figure PCTCN2020132800-appb-000040
从表3、图3和图4可以看出，在原4级构型的火箭的已有数据的基础上，通过本申请修正方法得到的俯仰力矩系数C mz、压力中心系数X cp与改进3级构型的火箭的试验数据对比可知，俯仰力矩系数的误差约为5％～10％，压力中心系数误差约为1.3％～3.2％，修正误差随着攻角的增大有增加趋势，攻角不大于6°时，通过本申请修正方法能够得到较好的数据。攻角大于6°时，箭体背风面分离区扩大，粘性分离产生的非线性升力导致火箭的法向力 和俯仰力矩变化量不可忽略。考虑到工程计算和使用中，气动特性数据精度一般在10％～15％。在攻角小于或等于6°时，采用本申请修正方法可以得到比较好的计算结果；在攻角大于6°时，尽管修正计算得到的数据精度下降，但在工程应用中仍有较强的参考价值和指导意义。
在示例性实施例中，本申请实施例还提供了一种计算机存储介质，是计算机可读存储介质，例如，包括计算机程序的存储器，上述计算机程序可由处理器执行，以完成前述箭弹俯仰力矩系数和压力中心系数修正方法中的所述步骤。
在示例性实施例中，本申请实施例还提供了一种服务器，其包括存储器和处理器，存储器存储有可执行程序，处理器在调用该可执行程序时，实现前述箭弹俯仰力矩系数和压力中心系数修正方法中的所述步骤。
上述的本申请实施例可在各种硬件、软件编码或两者组合中进行实施。例如，本申请的实施例也可表示在数据信号处理器(Digital Signal Processor，DSP)中执行上述方法的程序代码。本申请也可涉及计算机处理器、数字信号处理器、微处理器或现场可编程门阵列(Field Programmable Gate Array，FPGA)执行的多种功能。可根据本申请配置上述处理器执行特定任务，其通过执行定义了本申请揭示的特定方法的机器可读软件代码或固件代码来完成。可将软件代码或固件代码发展表示不同的程序语言与不同的格式或形式。也可表示不同的目标平台编译软件代码。然而，根据本申请执行任务的软件代码与其他类型配置代码的不同代码样式、类型与语言不脱离本申请的精神与范围。
以上所述仅表示本申请示意性的具体实施方式，在不脱离本申请的构思和原则的前提下，任何本领域的技术人员所做出的等同变化与修改，均应属于本申请保护的范围。

Claims (7)

  1. 一种箭弹俯仰力矩系数和压力中心系数修正方法，适用于轴对称旋成体外形，无尾布局或+、x尾翼布局的箭弹类飞行器，其特征在于，包括以下步骤：
    获取原始构型的箭弹的气动特性参数；所述原始构型的箭弹的气动特性参数包括原始构型的箭弹的俯仰力矩系数和压力中心系数；
    获取箭弹飞行器的外形变化数据；所述箭弹飞行器的外形变化数据包括原始构型的箭弹与改进构型的箭弹的参考长度变化量；
    构建改进构型的箭弹的俯仰力矩系数模型和压力中心系数模型；
    将原始构型的箭弹的气动特性参数和箭弹飞行器的外形变化数据输入到改进构型的箭弹的俯仰力矩系数模型和压力中心系数模型中，得到改进构型的箭弹的俯仰力矩系数和压力中心系数，以缩短设计周期，降低设计成本。
  2. 根据权利要求1所述的箭弹俯仰力矩系数和压力中心系数修正方法，其特征在于，构建的改进构型的箭弹的俯仰力矩系数模型为：
    Figure PCTCN2020132800-appb-100001
    式中，C mz,old表示原始构型的箭弹的俯仰力矩系数，C mz,old,tail表示原始构型的箭弹的尾翼俯仰力矩系数，l ref,old表示原始构型的箭弹的参考长度，l ref,new表示改进构型的箭弹的参考长度，l ref,new＝l ref,old+Δl ref，Δl ref表示原始构型的箭弹与改进构型的箭弹的参考长度变化量。
  3. 根据权利要求2所述的箭弹俯仰力矩系数和压力中心系数修正方法，其特征在于，构建的改进构型的箭弹的压力中心系数模型为：
    Figure PCTCN2020132800-appb-100002
    式中，X cp,old表示原始构型的箭弹的压力中心系数，C N表示箭弹的法向力系数，其中，原始构型的箭弹的法向力系数和改进构型的箭弹的法向力系数相等。
  4. 根据权利要求2所述的箭弹俯仰力矩系数和压力中心系数修正方法， 其特征在于，所述改进构型的箭弹的俯仰力矩系数模型的具体构建过程为：
    根据箭弹的俯仰力矩系数C mz的表达式：
    Figure PCTCN2020132800-appb-100003
    式中，M z表示箭弹的俯仰力矩，q ∞表示箭弹飞行动压，S ref表示参考面积，l ref表示参考长度；
    得到改进构型的箭弹的俯仰力矩系数C mz,new为：
    Figure PCTCN2020132800-appb-100004
    式中，M Z,new表示改进构型的箭弹的俯仰力矩，M Z,new,nose表示改进构型的箭弹的头部俯仰力矩，M Z,new,tail表示改进构型的箭弹的尾翼俯仰力矩，M Z,new,p表示改进构型的箭弹的箭体表面凸起物产生的俯仰力矩；
    原始构型的箭弹的头部俯仰力矩和箭体表面凸起物产生的俯仰力矩均不受长度调整的影响，得到：
    Figure PCTCN2020132800-appb-100005
    则进一步得到改进构型的箭弹的俯仰力矩系数C mz,new为：
    Figure PCTCN2020132800-appb-100006
    根据压力中心到力矩参考点的距离l cp与箭弹受到的法向力N和俯仰力矩M z的关系式：
    Figure PCTCN2020132800-appb-100007
    得到改进构型的箭弹的尾翼的俯仰力矩为：
    M Z,new,tail＝N new,taill cp,new,tail，
    箭弹的长度变化前后，尾翼产生的法向力系数保持不变，有：
    Figure PCTCN2020132800-appb-100008
    式中，N new,tail表示改进构型的箭弹的尾翼法向力，M Z,new,tail表示改进构型的箭弹的尾翼俯仰力矩，l cp,new,tail表示改进构型的箭弹的尾翼压力中心到力矩参考点的距离；N old,tail表示原始构型的箭弹的尾翼法向力，M Z,old,tail表示原始构型的箭弹的尾翼俯仰力矩，l ref,old,tail表示原始构型的箭弹的尾翼参考长度；
    则进一步得到改进构型的箭弹的尾翼的俯仰力矩为：
    Figure PCTCN2020132800-appb-100009
    进一步得到改进构型的箭弹的俯仰力矩系数模型为：
    Figure PCTCN2020132800-appb-100010
  5. 根据权利要求4所述的箭弹俯仰力矩系数和压力中心系数修正方法，其特征在于，所述改进构型的箭弹的压力中心系数模型的具体构建过程为：
    根据压力中心系数X cp与箭弹的俯仰力矩系数C mz和箭弹的法向力系数C N之间的关系式
    Figure PCTCN2020132800-appb-100011
    以及改进构型的箭弹的俯仰力矩系数模型，得到 改进构型的箭弹的压力中心系数模型为：
    Figure PCTCN2020132800-appb-100012
  6. 一种计算机存储介质，其特征在于，其上存储有计算机程序，所述计算机程序被处理器执行时实现权利要求1至5任一项所述箭弹俯仰力矩系数和压力中心系数修正方法的步骤。
  7. 一种服务器，其特征在于，包括存储器和处理器，所述存储器存储可执行程序，所述处理器在调用所述可执行程序时，实现权利要求1至5任一项所述箭弹俯仰力矩系数和压力中心系数修正方法的步骤。
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