Derivation of a Revised Tsiolkovsky Rocket Equation That Predicts Combustion Oscillations

Our study identifies a subtle deviation from Newton’s third law in the derivation of the ideal rocket equation, also known as the Tsiolkovsky Rocket Equation (TRE). TRE can be derived using a 1D elastic collision model of the momentum exchange between the differential propellant mass element (dm) and the rocket final mass (m1), in which dm initially travels forward to collide with m1 and rebounds to exit through the exhaust nozzle with a velocity that is known as the effective exhaust velocity ve. We observe that such a model does not explain how dm was able to acquire its initial forward velocity without the support of a reactive mass traveling in the opposite direction. We show instead that the initial kinetic energy of dm is generated from dm itself by a process of self-combustion and expansion. In our ideal rocket with a single particle dm confined inside a hollow tube with one closed end, we show that the process of self-combustion and expansion of dm will result in a pair of differential particles each with a mass dm/2, and each traveling away from one another along the tube axis, from the center of combustion. These two identical particles represent the active and reactive sub-components of dm, co-generated in compliance with Newton’s third law of equal action and reaction. Building on this model, we derive a linear momentum ODE of the system, the solution of which yields what we call the Revised Tsiolkovsky Rocket Equation (RTRE). We show that RTRE has a mathematical form that is similar to TRE, with the exception of the effective exhaust velocity (ve) term. The ve term in TRE is replaced in RTRE by the average of two distinct exhaust velocities that we refer to as fast-jet, vx1, and slow-jet, vx2. These two velocities correspond, respectively, to the velocities of the detonation pressure wave that is vectored directly towards the exhaust nozzle, and the retonation wave that is initially vectored in the direction of rocket propagation, but subsequently becomes reflected from the thrust surface of the combustion chamber to exit through the exhaust nozzle with a time lag behind the detonation wave. The detonation-retonation phenomenon is supported by experimental evidence in the published literature. Finally, we use a convolution model to simulate the composite exhaust pressure wave, highlighting the frequency spectrum of the pressure perturbations that are generated by the mutual interference between the fast-jet and slow-jet components. Our analysis offers insights into the origin of combustion oscillations in rocket engines, with possible extensions beyond rocket engineering into other fields of combustion engineering.

A new method for evaluating the firing precision of multiple launch rocket system based on Bayesian theory

How to effectively evaluate the firing precision of weapon equipment at low cost is one of the core contents of improving the test level of weapon system.A new method to evaluate the firing precision of the MLRS considering the credibility of simulation system based on Bayesian theory is proposed in this paper.First of all,a comprehensive index system for the credibility of the simulation system of the firing precision of the MLRS is constructed combined with the group analytic hierarchy process.A modified method for determining the comprehensive weight of the index is established to improve the rationality of the index weight coefficients.The Bayesian posterior estimation formula of firing precision considering prior information is derived in the form of mixed prior distribution,and the rationality of prior information used in estimation model is discussed quantitatively.With the simulation tests,the different evaluation methods are compared to validate the effectiveness of the proposed method.Finally,the experimental results show that the effectiveness of estimation method for firing precision is improved by more than 25%.

Identification of Backflow Vortex Instability in Rocket Engine Inducers

Bayesian estimation is applied to the analysis of backflow vortex instabilities in typical three-and four bladed liquid propellant rocket(LPR)engine inducers.The flow in the impeller eye is modeled as a set of equally intense and evenly spaced 2D axial vortices,located at the same radial distance from the axis and rotating at a fraction of the impeller speed.The circle theorem and the Bernoulli’s equation are used to predict the flow pressure in terms of the vortex number,intensity,rotational speed,and radial position.The theoretical spectra so obtained are frequency broadened to mimic the dispersion of the experimental data and parametrically fitted to the measured pressure spectra by maximum likelihood estimation with equal and independent Gaussian errors.The method is applied to three inducers,tested in water at room temperature and different loads and cavitation conditions.It successfully characterizes backflow instabilities using the signals of a single pressure transducer flush-mounted on the casing of the impeller eye,effectively by-passing the aliasing and data acquisition/reduction complexities of traditional multiple-sensor cross correlation methods.The identification returns the estimates of the model parameters and their standard errors,providing the information necessary for assessing the accuracy and statistical significance of the results.The flowrate is found to be the major factor affecting the backflow vortex instability,which,on the other hand,is rather insensitive to the occurrence of cavitation.The results are consistent with the data reported in the literature,as well as with those generated by the auxiliary models specifically developed for initializing the maximum likelihood searches and supporting the identification procedure.

火箭风暴:2024 Triumph Rocket 3 Storm R

2020年,凯旋推出了巨无霸“火箭三缸”Rocket 3 R,以排量高达2458mL的水平并列三缸发动机震惊世人,当仁不让地成为最大的量产摩托车。4年过去了,“火箭三缸”依然是寂寞的王者。能超越“火箭三缸”的,只有“火箭三缸”的自我进化。2024年,凯旋再次重磅出击,推出了新一代“火箭风暴”Rocket 3 Strom R,功率更大,扭矩更强,技术更先进,安全性能更好,掀起声势浩大的公路风暴!

China Accelerating Development of Two Large Reusable Rocket Models

BEIJING,March 12(Xinhua)——China′s development of both 4⁃meter⁃diameter and 5⁃meter⁃diameter reusable rockets is being accelerated,with their inaugural flights scheduled for 2025 and 2026,respectively.The manufacturing of these two new large reusable launching vehicle models is a response to growing demand in the commercial space market,said the China Aerospace Science and Technology Corporation.

基于RocketIO的SATA物理层实现

以Virtex-5系列FPGA内嵌的RocketIO收发器模块为平台,分析SATA(串行高级技术附件)协议的物理层功能,把RocketIO收发器的内部结构特点与协议要求相结合,设计了基于RocketIO收发器的SATA物理层电路。

基于RocketI O的高速光收发器的设计与实现

基于Xilinx公司的Virtex-6系列FPGA的Rocket IO,设计了包含高速收发器和高速串行接口的高速串行通信模型及Virtex-6系列FPGA的硬件平台。以Rocket IO为编码工具,实现了速率达6.25Gb/s的高速串行通信,给出了仿真结果和Chipscope在线调试实验结果,误码率低于10-12。

Ultra-tight GPS/INS integration based long-range rocket projectile navigation method

Accurate navigation is important for long-range rocket projectile＇s precise striking. To obtain stable and high-per- formance navigation result, a ultra-tight global positioning system/inertial navigation system （GPS/INS） integration based nav- igation approach is proposed. The accurate short-time output of INS is used by GPS receiver to assist in acquisition of signal, and output information of INS and GPS is fused based on federated filter. Meanwhile, the improved cubature Kalman filter with strong tracking ability is chosen to serve as the local filter, and then the federated filter is enhanced based on vector sharing theory. Finally, simulation results show that the navigation accuracy with the proposed method is higher than that with traditional methods. It provides reference for long-range rocket projectile navigation.

Active Control of Initial Disturbances for Rockets and Missiles

The active control theory and methods of initial disturbances for rockets and missiles are investigated. The rocket or missile/launcher is simplified as a flexible beam excited by a moving varying velocity rigid body which has two points in contact with the beam. The control force is applied at the supporting point on the beam. Active control strategies based on optimal control theory are proposed and computer simulation is carried out. Simulation results are consistent with the theoretical results, and show that the active control strategies proposed can accomplish the purpose to control the initial disturbances actively. The results show that active control of initial disturbances for rockets and missiles is feasible for application.

Experimental and Theoretical Research Review of Hybrid Rocket Motor Techniques and Applications

A hybrid rocket motor combines components from both solid fuel and liquid fuel rocket motors. The fuel itself is a solid grain, (often paraffin or hydroxyl-terminated polybutadiene, known as HTPB) while the oxidizing agent is liquid (often hydrogen peroxide or liquid oxygen). These components are combined in the fuel chamber which doubles as the combustion chamber for the hybrid motor. This review looks at the advances in techniques that have taken place in the development of these motors since 1995. Methods of testing the thrust from rocket motors and of measuring the rocket plume spectroscopically for combustion reaction products have been developed. These assessments allow researchers to more completely understand the effects of additives and physical changes in design, in terms of regression rates and thrust developed. Hybrid rocket motors have been used or tested in many areas of rocketry, including tactical rockets and large launch vehicles. Several additives have shown significant improvements in regression rates and thrust, including Guanidinium azotetrazolate (GAT), and various Aluminum alloys. The most recent discoveries have come from research into nano-particle additives. The nano-particles have been shown to provide enhancements to many parameters of hybrid rocket function, and research into specific areas continues in the sub-field of nano-additives for fuel grains.

一种基于Rocket I/O的视频数据采集和高速串行传输系统的设计与实现

介绍了一种以VIRTEXⅡPRO系列FPGA中RocketI/O为核心的视频数据采集和高速串行传输系统的实现方案。分析了串行器和解串器的结构,给出了RocketI/O进行高速串口通信的同步方法,采用Verilog语言描述了一种保护帧同步的状态机。在此基础上,自定义了一种简单的数据帧结构,完成了数据率为1.25Gb/s的1500m点对点链路的高速传输。分析了高速差分信号的阻抗匹配方案和抗干扰措施。最后给出了收发方向上的后仿真波形,整个设计在Xilinx公司的XC2VP4fg456上实现,占用资源量为7360等效门。

Application of adaptive Kalman filter in rocket impact point estimation

In order to measure the parameters of flight rocket by using radar,rocket impact point was estimated accurately for rocket trajectory correction.The Kalman filter with adaptive filter gain matrix was adopted.According to the particle trajectory model,the adaptive Kalman filter trajectory model was constructed for removing and filtering the outliers of the parameters during a section of flight detected by three-dimensional data radar and the rocket impact point was extrapolated.The results of numerical simulation show that the outliers and noise in trajectory measurement signal can be removed effectively by using the adaptive Kalman filter and the filter variance can converge in a short period of time.Based on the relation of filtering time and impact point estimation error,choosing the filtering time of 8-10 scan get the minimum estimation error of impact point.

基于RocketIO的多路相机数据传输系统的设计

数字/模拟图像数据传输一直是测控设备数据通讯中的重点和难点。针对Xilinx的Virtex-ⅡPRO系列FPGA内嵌的RocketIO收发器模块,设计了用于测控设备多路图形数据的高速传输系统。该系统充分利用了FPGA中集成的RocketlO收发器模块,采用BREFCLK差分输入参考时钟,8B/10B编码,预加重处理等技术。实现了多路图像高速、实时、远距离传输。单通道传输速率可以达到3.125Gb/s。

New System to Measure the Yaw and PitchAngles of Rocket in Launch Phase

Aim To describe a news system for measuring the and pitch angles of rocket during the launch phase Methods Optical system was to reflect the spot that represents the angular movement of rocket to the position sensitive detector that can convert analogue signal into digital one.Results Compared with conventional optical lever test system which had been applied to measure rocket attitude angle,the new system used the position sensitive detector to replace the screen and high-speed photographic instrumentation as grapher,which can avert photointerpretive data reduction and apply to field experiment more easily and pre- cisely .Conclusion Experimental results show that the test system can be used in measuring the yaw and pitch angles of rocket effectively.

Computation of Electromagnetic Properties of Mildly Overexpanded and Underexpanded Rocket Exhaust Plume

An improved near far field divided coupled method was established to investigate the electromagnetic properties of mildly overexpanded and underexpanded rocket exhaust plumes. Firstly, axisymmetric Navier Stokes equations incorporated with k ε two equation turbulence models were solved using time dependent approach to calculate the pressure of the near filed. Secondly, parabolized axisymmetric Navier Stokes equations incorporated with finite rate chemical kinetics models were marching on the detailed pressure map of the near field. The termination of the near field would yield the initial line for the far field. In addition, in the far field, the spatial marching method was directly used under the constant pressure condition, but considering more complicated chemically reacting process. Finally, the electromagnetic parameters of the whole plume were calculated with the electron conductive model. The calculated results of the overexpanded and underexpanded rocket exhaust plume were discussed. The predicted microwave attenuation accorded with the experimental results. This improved method is feasible for calculating the microwave attenuation characteristics of mildly non fully expanded rocket exhaust plumes.

A New Simulation Method for 3D Propellant Grain Burn Analysis of Solid Rocket Motor

Describes a new computer program (Regress-3D) to simulate the regression of complex 3D grain cavity and calculate the burning surface area. It has a large region of applicability in solid rocket motor design and has made new improvements compared with other available codes. User can easily and rapidly build his initial grain shapes and then obtain geometric information of his design. Considering with the calclulting results, redesigning can be performed as desire until reaching at the satisfied result. Advantages and disadvantages of this method are also discussed.

Characteristics analysis of rocket projectile based on intelligent morphing technology

Nose deflection control is a new concept of fast response control model.The partial nose of projectile deflects a certain angle relative to the axis of projectile body and then pressure difference emerges on the windward and leeward sides of warhead.Consequently,aerodynamic control force is generated.This control way has high control efficiency and very good application prospects in the ammunition system.Nose deflection actuator based on smart material and structure enables projectile body morphing to obtain additional aerodynamic force and moment,changes the aerodynamic characteristics in the projectile flight process,produces the corresponding balance angle and sideslip angle resulting in motor overload,adjusts flight moving posture to control the ballistics,finally changes shooting range and improves firing accuracy.In order to study characteristics of self-adaptive control projectile,numerical simulations are conducted by using fluid dynamics software ANSYS FLUENT for stabilized rocket projectile.The aerodynamic characteristics at different nose delectation angles,different Mach numbers and different angles of attack are obtained and compared.The results show that the nose deflection control has great influence on the head of rocket projectile,and it causes the asymmetry of the flow field structure and the increase of pressure differences of the warhead on the windward and leeward surface,which results in a larger lift.Finally,ballistics experiments are done for verification.The results can offer theoretical basis for self-adaptive rocket projectile design and optimization and also provide new ideas and methods for field smart ammunition research.

一种基于Rocket I/O的视频数据采集和高速串行传输系统的设计与实现

介绍了一种以VIRTEX Ⅱ PRO系列FPGA中Rocket I/O为核心的视频数据采集和高速串行传输系统的实现方案。分析了高速串口通信的同步方法,自定义了一种简单的数据帧结构,完成了数据率为1.25Gbps的点对点高速传输。

开源处理器Rocket的自定义指令研究与测试

Rocket是基于RISC-V指令集架构的开源处理器,其实现了RISC-V的三条自定义指令custom0、custom1、custom2,在分析Rocket中自定义指令的处理过程后,编写测试程序,验证了自定义指令的实现。

开源处理器Rocket的分支预测机制与性能评估

Rocket是基于RISC-V指令集架构的开源处理器,具有分支预测功能,其实现了GShare分支预测机制,在分析Rocket处理器分支预测处理过程、分支预测实现原理的基础上,利用模拟器进行了性能测试,并依据测试结果,对Rocket处理器分支预测参数配置给出建议。