Normal Accelerations Research Articles

Data-driven optimization of nose profiles for water entry impact load reduction

The prediction and reduction of impact loads during water entry are critical in various engineering applications, such as ship slamming and seaplane landings. Traditional methods, including theoretical models, computational fluid dynamics (CFD), and experimental approaches, often suffer from limited applicability, lengthy processing times, and high costs. To address these challenges, this study explores the use of Deep Neural Networks (DNNs) for predicting peak impact loads during the oblique water entry of cylinders with different nose profiles. Optimized Latin Hypercube Sampling (OLHS) and Sobol sequences are employed to generate dataset inputs from a 7-dimensional parameter space that governs impact dynamics. These inputs are then fed into OpenFOAM solvers to compute the peak impact accelerations, serving as dataset outputs for training and testing the DNN. Experiments are conducted to validate the numerical method, confirming that the resulting dataset outputs can be considered as ground truth. With Bayesian hyperparameter optimization, the well-trained DNN model demonstrates reliable accuracy in predicting peak axial and normal accelerations. Further, this study integrates the DNN model with the Non-dominated Sorting Genetic Algorithm II (NSGA-II) to optimize the nose profiles, resulting in a maximum weighted reduction of 48% in the combined axial and normal accelerations.

Real-time position path smoothing for robotic manipulators by constructing Composite Trajectory Spline

Aiming at smoothing discontinuous corners in robotic tool paths, a novel spline named “Composite Trajectory Spline”(CT-Spline) is proposed in this paper. Based on CT-Spline, the real-time position path smoothing for robotic manipulators is realized. CT-Spline enables analytical trajectory planning and interpolation without curve length computation, significantly enhancing trajectory generation efficiency and avoiding numerical errors. By directly controlling resultant trajectory acceleration, CT-Spline avoids decomposing it into tangential and normal accelerations, ensuring adherence to the maximum acceleration constraint while fully utilizing acceleration potential. The geometric shape of CT-Spline is determined by three control points and a trajectory model. This paper further develops C1 and C3 continuous CT-Splines based on two different trajectory models, combined with a velocity look-ahead algorithm to achieve real-time local smoothing of path corners. Additionally, an adaptive control algorithm of smoothing error is introduced to dynamically maximize trajectory velocity. Simulations and experiments validate the effectiveness of CT-Spline, and demonstrate that the proposed C3 continuous trajectory smoothing method has several advantages over the method based on Pythagorean-hodograph splines in terms of kinematic constraints, velocity, smoothing errors, and real-time performance.

Theoretical and experimental study on combustion response of aluminized solid propellant under acceleration effects

The combustion performance of solid propellants is significantly affected by the external operating parameters of rocket motors. In this paper, the combustion response characteristics of aluminized solid propellant under acceleration conditions have been studied theoretically and experimentally. A theoretical model of unsteady burning for aluminized solid propellant, considering transient heat transfer and acceleration effects, is developed based on the Zel'dovich-Novozhilov solid-phase energy conservation. The pressure-coupled responses of the solid propellant are also measured experimentally under different normal accelerations using the T-burner and centrifuge. The model is well validated by comparison with literature and experimental results. The unsteady burning of propellants is analyzed in detail, and the effects of acceleration and propellant properties on combustion response are investigated. The results show that there is a significant difference between the transient and quasi-steady burning rate under dynamic environments. As normal acceleration increases from 0 g to 1000 g, the fluctuation amplitude of the net heat flux on the burning surface continues to decrease, the magnitude of the pressure-coupled response peak decreases significantly by 69 %, and the frequency of the response peak shifts from 140 Hz to 230 Hz. Moreover, the pressure exponent and thermal conductivity plays a positive role in the pressure-coupled response. The model presented in this paper can be helpful for predicting the differences between flight and ground test performance and evaluating the combustion stability of solid rocket motors.

New transition curves maintaining constant normal accelerations for vehicles

New transition curves maintaining constant normal accelerations for vehicles

Distributed Trajectory Planning for a Group of UGVs Carrying a Load Considerting Terrain Properties

The article studies a trajectory planning task for a group of UGVs with a consideration of wheels-terrain adhesion variation. Within this paper a brief analysis devoted to existing trajectory planning is done. It outcomes with a conclusion of a necessity to produce additional research within this topic. This paper suggests to use a Sampling-based method to solve this trajectory planning task. An algorithm of rapidly exploring random tree (RRT) is used as a basic algorithm. An advantage of this method (typical for Sampling-based methods) is a simplicity of various non-linear restrictions introduction (e.g. obstacles, differential restrictions etc.). In addition we should mention good potential for algorithm parallelization, because of tree structure of the algorithm. However there exists a shortage of the proposed methods — a high consumption of computational resources, and as an outcome a long calculus duration. This paper proposes to overcome this shortage via distributing of computation among UGVs — actors of a group. This is followed by a comparative analysis of distributed and centralized methods. Analysis shows that the main advantage of proposed method is that it can use almost all models of interaction between wheel and terrain. The latter can act a component for calculation of restrictions for motion acceleration over certain types of terrain. Within this paper we did not study models of interaction between wheel and terrain, but instead used empirical data of allowed values of tangential and normal accelerations for specific UGVs in particular conditions. In final part we present results of simulation witch confirm effectiveness of proposed methods.

Symmetry analysis of the constant acceleration curve equation

Abstract Lie group theory is applied to the curve equation which maintains constant normal accelerations for a vehicle with constant deceleration. The curve equation is a third order nonlinear ordinary differential equation for which the symmetries are calculated. It is shown that the equation possesses four-parameter Lie group of transformations including scaling, rotation and translational symmetries. In the case of constant velocity, the algebra increases to a six-parameter Lie group of transformations. Using the symmetries of the differential equation, the group invariant solutions are determined first. The conditions for group invariant solutions to exist are given. By employment of the symmetries, a solution is obtained by reduction of order also. It is found that the nontrivial solutions are of implicit complex forms.

Nonlinear curve equations maintaining constant normal accelerations with drag induced tangential decelerations

Abstract A nonlinear curve equation is derived for a vehicle exposed to drag force only. At each point on the curve, the vehicle maintains constant normal acceleration component. The resulting curve equation is a highly nonlinear third order ordinary differential equation. By defining dimensionless coordinates, the equation is cast into a non-dimensional form and a special path parameter is defined. Two different perturbation type solutions as well as a series solution are constructed as approximations to the curves. The three approximate solutions are contrasted with the numerical solution of the problem. The validity range of the approximate solutions is discussed. The curves may be used in determining the routes of land, marine and aerial vehicles.

Investigation on energy-effective guidance-to-collision strategies for exo-atmospheric interceptors

This paper aims to investigate energy-effective guidance-to-collision strategies for an exo-atmospheric interceptor producing the normal and axial accelerations independently. According to the utilization of the two accelerations, three interception strategies are possible from the collision geometry and the nonlinear engagement kinematics. A unified form of guidance-to-collision laws realizing these interception strategies is then determined by solving a nonlinear finite-time tracking problem for the heading error based on a specific form of the error dynamics. The characteristics of the proposed guidance-to-collision laws for different interception strategies are analytically analyzed. The results show that the guidance-to-collision strategy using normal and axial acceleration simultaneously is always advantageous in control energy efficiency. Additionally, the characteristic of the guidance-to-collision law for this interception strategy is compared with existing guidance laws. It turns out that the guidance-to-collision law behaves like the true proportional navigation (TPN) guidance in a near-collision course. This fact could provide new insight into the behavior of TPN in the nonlinear engagement kinematics from the collision geometry standpoint. Additionally, analysis results also show that the proposed law is effectively working even in the presence of a large initial heading error compared to TPN due to the nonlinear nature of the proposed method in the collision geometry. Finally, our findings are verified through numerical simulations.

MATHEMATICAL EXPANSION OF SPECIAL THEORY OF RELATIVITY ONTO ACCELERATIONS

The special theory of relativity (STR) is operationally expanded onto orthogonal accelerations: normal and binormal that complement the instantaneous tangential speed and thus can be structurally extended into operationally complete 4D spacetime without defying the STR. Thus the former classic Lorentz factor, which defines proper time differential can be expanded onto within a trihedron moving in the Frenet frame (T,N,B). Since the tangential speed which was formerly assumed as being always constant, expands onto effective normal and binormal speeds ensuing from the normal and binormal accelerations, the expanded formula conforms to the former Lorentz factor. The obvious though previously overlooked fact that in order to change an initial speed one must apply accelerations (or decelerations, which are reverse accelerations), made the Einstein’s STR incomplete for it did not apply to nongravitational selfpropelled motion. Like a toy car lacking accelerator pedal, the STR could drive nowhere. Yet some scientists were teaching for over 115 years that the incomplete STR is just fine by pretending that gravity should take care of the absent accelerator. But gravity could not drive cars along even surface of earth. Gravity could only pull the car down along with the physics that peddled the nonsense while suppressing attempts at its rectification. The expanded formula neither defies the STR nor the general theory of relativity (GTR) which is just radial theory of gravitation. In fact, the expanded formula complements the STR and thus it supplements the GTR too. The famous Hafele-Keating experiments virtually confirmed the validity of the expanded formula proposed here.

Three-dimensional impact angle constrained distributed cooperative guidance law for anti-ship missiles

This paper investigates the problem of distributed co-operative guidance law design for multiple anti-ship missiles in the three-dimensional (3-D) space hitting simultaneously the same target with considering the desired terminal impact angle constraint. To address this issue, the problem formulation including 3-D nonlinear mathematical model description, and communication topology are built firstly. Then the consensus variable is constructed using the available information and can reach consensus under the proposed acceleration command along the line-of-sight (LOS) which satisfies the impact time constraint. However, the normal accelerations are designed to guarantee the convergence of the LOS angular rate. Furthermore, consider the terminal impact angle constraints, a nonsingular terminal sliding mode (NTSM) control is introduced, and a finite time convergent control law of normal acceleration is proposed. The convergence of the proposed guidance law is proved by using the second Lyapunov stability method, and numerical simulations are also conducted to verify its effectiveness. The results indicate that the proposed cooperative guidance law can regulate the impact time error and impact angle error in finite time if the connecting time of the communication topology is longer than the required convergent time.

Normal and extreme aircraft accelerations and the effects on exposure to expiratory airborne contaminant inside commercial aircraft cabins

A novel dataset based on satellite observations of aircraft positions was utilized to estimate normal accelerations of commercial aircraft during climb and descent legs. Further, these accelerations are used to simulate the effects on exposure to expiratory airborne contaminant inside commercial aircraft cabins. Compared to previous studies, which reported exposures more than twice due to high aircraft accelerations during the climb leg, the new findings suggest lower aircraft accelerations that result in exposures on par with steady level flights during climb and descent legs. The new findings place previous studies in context to be interpreted as extreme conditions only while they call for more detailed experimental investigations.

Distributed multi-munition cooperative guidance based on clock synchronization for switching and noisy networks

This paper proposes a novel three-dimensional guidance method based on clock synchronization algorithms, creatively solving the problems of randomized change, non-connection and even communication outage caused by packet loss and delay in the co-guidance of loitering munitions. The proposed method is characterized by fast convergence of the aspect angle rate in the longitudinal plane, and the attack time constrains in the lateral plane. Normal accelerations on the two sub-planes are thereby calculated, so as to control the munitions’ co-attack. Simulation experiments show that the proposed method can ensure reliable and stable asymptotic agreement of attack time expectation for the cooperative multiple munitions under the switching and noisy networks.

Phase-field–lattice Boltzmann simulation of dendrite growth under natural convection in multicomponent superalloy solidification

The thermosolutal convection can alter segregation pattern, change dendrite morphology and even cause freckles formation in alloy solidification. In this work, the multiphase-field model was coupled with lattice Boltzmann method to simulate the dendrite growth under melt convection in superalloy solidification. In the isothermal solidification simulations, zero and normal gravitational accelerations were applied to investigate the effects of gravity on the dendrite morphology and the magnitude of melt flow. The solute distribution of each alloy component along with the dendrite tip velocity during solidification was obtained, and the natural convection has been confirmed to affect the microsegregation pattern and the dendrite growth velocity. In the directional solidification simulations, two typical temperature gradients were applied, and the dendrite morphology and fluid velocity in the mushy zone during solidification were analyzed. It is found that the freckles will form when the average fluid velocity in the mushy zone exceeds the withdraw velocity.

Effects of non-Newtonian lubricants and elastic coating on transient elastohydrodynamic lubrication at impact squeeze loading

This study explores the effects of non-Newtonian lubricants on elastohydrodynamic lubrication with coating at impact and rebound loading using power law lubricants. The coupled transient modified Reynolds, rheology, elasticity deformation, and ball motion equations are solved simultaneously, thus obtaining the transient pressure profiles, film shapes, normal squeeze velocities and accelerations. The effect of the flow index ( n) is equivalent to enhancing the lubricant viscosity, also enlarging the damper effect. The simulation results reveal that the film thickness, the primary peak, and the secondary peak increase with increasing the flow index. The greater the flow index is, the earlier the dimple form, and the smaller the maximum value of the impact force is. The rebounding velocity and the peak value of acceleration increase with decreasing the flow index. Moreover, this research possesses academic innovation and industrial application.

Flight Loads Spectra of a Fleet of Heavy Air Tankers

In-flight recorded data from eight BAe-146s and eight RJ-85s flown in support of the United States Forest Service aerial firefighting operations have been analyzed. Flights have been divided into firefighting, ferry, and maintenance/training missions. Firefighting flights have been divided into five separate phases. The recorded normal accelerations have been filtered to remove the frequencies due to structural vibration and have been divided into gust and maneuver loads using the two-second rule. Using the method of peaks-between-means, exceedance spectra for gust and maneuver loads have been developed for ground-air-ground cycles, as well as for specific flight phases. The results have been compared with those of the legacy air tankers and other aircraft flown in support of firefighting missions and as civil transport. The maneuver load factor spectra are shown to indicate smaller loads than those of legacy air tankers, but exceeding considerably in frequency those of civil transport.

Galileo’s Parabola Observed from Pappus’ Directrix, Apollonius’ Pedal Curve (Line), Galileo’s Empty Focus, Newton’s Evolute, Leibniz’s Subtangent and Subnormal, Ptolemy’s Circle (Hodograph), and Dürer-Simon Parabola (16.03.2019)

Galileo’s Parabola describing the projectile motion passed through hands of all scholars of the classical mechanics. Therefore, it seems to be impossible to bring to this topic anything new. In our approach we will observe the Galileo’s Parabola from Pappus’ Directrix, Apollonius’ Pedal Curve (Line), Galileo’s Empty Focus, Newton’s Evolute, Leibniz’s Subtangent and Subnormal, Ptolemy’s Circle (Hodograph), and Dürer-Simon Parabola. For the description of events on this Galileo’s Parabola (this conic section parabola was discovered by Menaechmus) we will employ the interplay of the directrix of parabola discovered by Pappus of Alexandria, the pedal curve with the pedal point in the focus discovered by Apollonius of Perga (The Great Geometer), and the Galileo’s empty focus that plays an important function, too. We will study properties of this MAG Parabola with the aim to extract some hidden parameters behind that visible parabolic orbit in the Aristotelian World. For the visible Galileo’s Parabola in the Aristotelian World, there might be hidden curves in the Plato’s Realm behind the mechanism of that Parabola. The analysis of these curves could reveal to us hidden properties describing properties of that projectile motion. The parabolic path of the projectile motion can be described by six expressions of projectile speeds. In the Dürer-Simon’s Parabola we have determined tangential and normal accelerations with resulting acceleration g = 9.81 msec-2 directing towards to Galileo’s empty focus for the projectile moving to the vertex of that Parabola. When the projectile moves away from the vertex the resulting acceleration g = 9.81 msec-2 directs to the center of the Earth (the second focus of Galileo’s Parabola in the “infinity”). We have extracted some additional properties of Galileo’s Parabola. E.g., the Newtonian school correctly used the expression for “kinetic energy E = ½ mv2 for parabolic orbits and paths, while the Leibnizian school correctly used the expression for “vis viva” E = mv2 for hyperbolic orbits and paths. If we will insert the “vis viva” expression into the Soldner’s formula (1801) (e.g., Fengyi Huang in 2017), then we will get the right experimental value for the deflection of light on hyperbolic orbits. In the Plato’s Realm some other curves might be hidden and have been waiting for our future research. Have we found the Arriadne’s Thread leading out of the Labyrinth or are we still lost in the Labyrinth?

Investigations on formation mechanisms of out-of-round wheel and its influences on the vehicle system

The railway wheels are invariably subjected to the uneven wear owing to the wheel/rail interaction, and always tend to be an out-of-round wheel. Such wear on the wheel circumference can be classified into the local defect and the periodic uneven wear. The local defects, including the wheel flat and wheel shell, have been well documented, while the formation mechanisms of wheel polygonalizations, especially for high-order polygonal wear, have not yet been explained clearly. The formation mechanisms of wheel polygonalizations are thus initially reviewed and discussed in this study, and the metal cutting theory is also employed to explain the formation procedure of wheel polygonalization. A coupled vehicle/track dynamic model integrating with the flexibilities of the wheelset, bogie and car body is subsequently formulated to investigate the influences of wheel polygonalization on the dynamic responses of vehicle system, in terms of wheel/rail normal forces, lateral forces and accelerations of wheelset and bogie frame. A maintenance strategy for wheel polygonalization considering the different peak-to-peak amplitudes and the number of harmonic waves is proposed on the basis of limit values of wheel/rail vertical force.

Maneuvering Acceleration Estimation Algorithm Using Doppler Radar Measurement

An algorithm to estimate the tangential and normal accelerations directly using the Doppler radar measurement in an online closed loop form is proposed. Specific works are as follows: first, the tangential acceleration and normal acceleration are taken as the state variables to establish a linear state transition equation; secondly, the decorrelation unbiased conversion measurement Kalman filter (DUCMKF) algorithm is proposed to deal with the strongly nonlinear measurement equation; thirdly, the geometric relationship between the range rate and the velocity direction angle is used to obtain two estimators of the velocity direction angle; finally, the interactive multiple model (IMM) algorithm is used to fuse the estimators of the velocity direction angle and then the adaptive IMM of current statistical model based DUCMKF (AIMM-CS-DUCMKF) is proposed. The simulation experiment results show that the accuracy and stability of DUCMKF are better than the sequential extended Kalman filter algorithm, the sequential unscented Kalman filter algorithm, and converted measurement Kalman filter algorithms; on the other hand they show that the AIMM-CS-DUCMKF can obtain the high accuracy of the tangential and normal accelerations estimation algorithm.

Application of neural-networks and neuro-fuzzy systems for the prediction of short-duration forces acting on the blunt bodies

Present studies deal with application of finite element method and intelligent soft computing techniques viz. neural network (NN) and adaptive neuro-fuzzy inference system (ANFIS) for the prediction of short duration impulse, ramp and hat forces. Two blunt bodies viz. a hemisphere and a blunt cone with cylindrical aft body have been considered in these investigations. Training of the NN and ANFIS has been carried out using one axial acceleration and two normal accelerations obtained from known input forces and a moment. It is shown here that the NN is unable to recover the unknown forces and moment. However, ANFIS-based strategy is found better for prediction of the same forces and moment. Thus, novelty of these studies exists in the assessment and successful implementation of the soft computing techniques like NN and ANFIS for prediction of the unknown short-duration force and moment time histories. These predictions are also cross-checked for the error, and it has been observed that the ANFIS can be used for short-duration force prediction in high-speed aerospace applications.

Three-dimensional impact angle constrained distributed guidance law design for cooperative attacks

In this paper, a novel cooperative guidance law is proposed to make multiple missiles in the three-dimensional (3-D) space hit simultaneously the same target at pre-specified impact angles. Firstly, the normal accelerations which change the velocity direction (flight-path and heading angle) are designed such that all missiles will fly along the desired line of sight (LOS) after a given time which ensures the hit-to-kill interception at the desired impact angles; then the consensus variable is constructed using available information and can reach consensus under the proposed tangential acceleration which determines the velocity magnitude. Hence simultaneous hit-to-kill attack is achieved. Finally, some simulation studies are performed to verify the effectiveness of the proposed scheme.