Estimation of the Effect of a Parameter Change on the Roots of Stability Equations

1949 ◽  
Vol 1 (1) ◽  
pp. 39-58 ◽  
Author(s):  
K. Mitchell
Keyword(s):  
Secular Equation ◽  
Probable Error ◽  
Typical Case ◽  
Lateral Stability ◽  
Parameter Change ◽  
Longitudinal Stability ◽  
Quartic Equation ◽  
Spiral Motion ◽  
The Stability

SummaryA method is given for calculating approximately the changes in the roots of a stability secular equation caused by a change in any of the parameters involved. General formulas are given applicable to any quartic equation, and special formulae are also given applicable to the stability of an aeroplane: lateral stability in the text, and longitudinal stability in an appendix. The method of using the formulae is illustrated by applying them to a particular calculation of the lateral stability of an aeroplane, and a check of the results is made by comparing the predicted approximate changes with those calculated by solution of the modified period equations. It is shown that the formulae are reliable, for this typical case, for any reasonable changes in any parameter other than nv. If the changes in the derivatives are made equal to the probable error with which they can be measured, the formulae enable us to evaluate the probable errors of the roots. These are found to be considerable, and to arise mainly from uncertainties in yv, nv and nr: if these could be reduced to 0.03 in yv and 0.006 in the others, the uncertainties in the roots would be reduced to some ten per cent, of their values, except for a larger uncertainty in the root corresponding to the slow spiral motion.

A Study of the Lateral Stability of Railroad Vehicles Using a Nonlinear Constrained Multibody Formulation

2001 ◽  
Author(s):  
Davide Valtorta ◽  
Khaled E. Zaazaa ◽  
Ahmed A. Shabana ◽  
Jalil R. Sany
Keyword(s):  
Stability Analysis ◽  
Linear Stability ◽  
Linear Theory ◽  
Linear Stability Analysis ◽  
Numerical Study ◽  
Operating Conditions ◽  
Lateral Stability ◽  
Railroad Vehicles ◽  
Contact Formulation ◽  
The Stability

Abstract The lateral stability of railroad vehicles travelling on tangent tracks is one of the important problems that has been the subject of extensive research since the nineteenth century. Early detailed studies of this problem in the twentieth century are the work of Carter and Rocard on the stability of locomotives. The linear theory for the lateral stability analysis has been extensively used in the past and can give good results under certain operating conditions. In this paper, the results obtained using a linear stability analysis are compared with the results obtained using a general nonlinear multibody methodology. In the linear stability analysis, the sources of the instability are investigated using Liapunov’s linear theory and the eigenvalue analysis for a simple wheelset model on a tangent track. The effects of the stiffness of the primary and secondary suspensions on the stability results are investigated. The results obtained for the simple model using the linear approach are compared with the results obtained using a new nonlinear multibody based constrained wheel/rail contact formulation. This comparative numerical study can be used to validate the use of the constrained wheel/rail contact formulation in the study of lateral stability. Similar studies can be used in the future to define the limitations of the linear theory under general operating conditions.

Vehicle Lateral Motion Control Based on Estimated Stability Regions

2017 ◽  
Author(s):  
Yiwen Huang ◽  
Yan Chen
Keyword(s):  
Measurement Errors ◽  
Local Stability ◽  
Stability Region ◽  
Control Method ◽  
Linearization Method ◽  
Stability Control ◽  
Lateral Stability ◽  
Shortest Distance ◽  
The Stability ◽  
Yaw Moment

This paper presents a novel vehicle lateral stability control method based on an estimated lateral stability region on the phase plane of vehicle yaw rate and lateral speed, which is obtained through a local linearization method. Since the estimated stability region does not only describe vehicle local stability, but also define the oversteering and understeering characteristics, the proposed control method can achieve both local stability and vehicle handling stability. Considering the irregular geometric shape of the estimated stability region, a stability analysis algorithm is designed to determine the distance between vehicle states and stability region boundaries. State estimation or measurement errors are also incorporated in the distance calculation. Based on the calculated shortest distance between vehicle states and stability boundaries, a direct yaw moment controller is designed to maintain vehicle states stay within the stability region. CarSim® and Simulink® co-simulation is applied to verify the control design through a cornering maneuver. The simulation results show that the proposed control method can make the vehicle stay within the stability region successfully and thus always operate in a safe manner.

The Characteristics of Certain Resisting Surfaces and Screws

1916 ◽  
Vol 20 (77) ◽  
pp. 3-9
Author(s):  
G. H. Bryan
Keyword(s):  
General Idea ◽  
General Character ◽  
Lateral Stability ◽  
Wind Gusts ◽  
The Stability ◽  
The Way

In the stability investigations which the late Captain Ferber published in the Revue d'Artillerie, the sustaining and other surfaces of an aeroplane were in certain cases taken to be represented, for dynamical purposes, by a system of three plane resisting laminæ fixed mutually at right angles. Unfortunately, however, such a system cannot in general be made equivalent to a collection of surfaces, such as those of an aeroplane, with the result that Captain Ferber's investigation failed to give the correct conditions of lateral stability. At the same time, Ferber's system of three orthogonal planes is so convenient, especially for forming a general idea of the effects of wind gusts on an aeroplane, that it is desirable to investigate conditions and limitations under which such a representation is valid. The desirability of a further investigation of the forces and couples acting on a system of resisting surfaces of a general character was foreshadowed in “Stability in Aviation,” and a more detailed discussion of the problem has now become necessary in order to prepare the way for further studies in the rigid dynamics of the motions of aeroplanes or of systems resembling them.

Normal form method for large/small amplitude instability criterion with application to wheelset lateral stability

2014 ◽  
Vol 14 (03) ◽  
pp. 1350073 ◽  
Author(s):  
H. Dong ◽  
J. Zeng
Keyword(s):  
Normal Form ◽  
Small Amplitude ◽  
High Speed ◽  
Order Approximation ◽  
Algebraic Approach ◽  
Instability Criterion ◽  
Lateral Stability ◽  
Subcritical Bifurcation ◽  
Large Amplitude Oscillation ◽  
The Stability

Subcritical and supercritical bifurcations are two typical behaviors that exist in high speed railway vehicles. In the presence of instability, the former and the latter behaviors may lead to large amplitude oscillation and small amplitude swaying, respectively. The normal form (NF) method of Hopf bifurcation provides a way to study the supercritical and subcritical bifurcation. The wheelset is a key component in the vehicle system and it plays an important role in vehicle lateral stability. To study the lateral stability problems, three wheelset models are considered, which involve the NF theory. This method is an algebraic approach as opposed to the integration approach. Like the sign of Re (λ) that determines the stability of linear system, the sign of Re c1(0) determines the two bifurcation modes, meaning that Re c1(0) > 0 for supercritical bifurcation and Re c1(0) < 0 for subcritical bifurcation. Furthermore, if the ordinary differential equation (ODE) is local linear near the equilibrium position, it leads to the condition of Re c1(0) = 0, resulting in the jumping phenomenon. Besides, the expression of the 1/2-order approximation of limit cycle can be further obtained.

A Comparison of the Stability and Curving Performance of Radial and Conventional Rail Vehicle Trucks

1981 ◽  
Vol 103 (3) ◽  
pp. 191-200 ◽  
Author(s):  
D. Horak ◽  
C. E. Bell ◽  
J. K. Hedrick
Keyword(s):  
Shear Stiffness ◽  
Bending Stiffness ◽  
Lateral Stability ◽  
High Shear ◽  
Wear Properties ◽  
Rail Vehicle ◽  
Curving Performance ◽  
Conventional Rail ◽  
The Stability ◽  
Total Shear

This paper compares the lateral stability and steady-state curving performance of radial and conventional rail vehicle trucks. The radial truck has two unique features, it allows direct elastic coupling between the wheelsets and it allows greater total truck shear stiffness for a given bending stiffness. It is shown that the first property allows the radial truck to achieve up to a 40 percent higher critical speed than the conventional truck for equivalent truck total shear and bending stiffness since the direct coupling between the wheelsets allows decoupling of the truck mass from the hunting wheelset masses. The second feature, i.e., greater shear stiffness capability, allows the radial truck to have improved wear properties during the negotiation of tight curves. It is shown that the high shear stiffness property combined with a low bending stiffness reduces the lateral flange force and wheelset angle of attack during flange contact. It is concluded that for routes where the majority of curves are less than 4 deg (greater than 400 m radius) the truck optimized for off-flange performance should have intermediate values of shear stiffness, bending stiffness, and conicity. On the other hand, for routes where the majority of curves are greater than 4 deg, the truck optimized for on-flange performance should have a high shear stiffness and low values of bending stiffness and conicity.

Lateral Stability of Cable Structures

1997 ◽  
Vol 12 (1) ◽  
pp. 19-27 ◽  
Author(s):  
Pál Tomka
Keyword(s):  
Parametric Study ◽  
External Load ◽  
Lateral Stability ◽  
Structural Behaviour ◽  
Cable Structure ◽  
Cable Structures ◽  
The Stability ◽  
Cable Dome ◽  
Simplified Procedure ◽  
Geometric Arrangements

The structural behaviour of pre-stressed cable-and-post structures has recently drawn the attention of the researchers. The aim of this paper is to focus on some practical aspects of the problem. The investigation concentrates on the stage of the erection, especially on the stability of cable structures when subjected to no external load. The analysis of bifurcation of equilibrium is based on the method presented here. The advantage of this method is that practical quantitative conclusions can be drawn concerning the measure of stability. As an example, the stability of a cable structure (a modified version of the Geiger cable dome) is investigated. Critical loading conditions in the state of pre-stress are analyzed. Using a simplified procedure based on a detailed parametric study, practical conclusions are drawn for different geometric arrangements.

Lateral Stability of Freight Cars With Axles Having Different Wheel Profiles and Asymmetric Loading

1979 ◽  
Vol 101 (1) ◽  
pp. 1-16 ◽  
Author(s):  
J. M. Tuten ◽  
E. H. Law ◽  
N. K. Cooperrider
Keyword(s):  
Dynamic Response ◽  
Strong Influence ◽  
Lateral Stability ◽  
Loading Conditions ◽  
Stability Behavior ◽  
Rail Freight ◽  
Rail Vehicle ◽  
Asymmetric Loading ◽  
Left And Right ◽  
The Stability

The majority of studies of rail vehicle lateral dynamic response have utilized models wherein it is assumed that the loading and geometry of the vehicles are symmetrical left and right and fore and aft. It has been observed that with use North American rail freight vehicles develop transverse wheel profiles that may be different for wheels on a given axle and that may also differ from axle to axle on a given vehicle. As the transverse wheel profiles exert a strong influence on lateral dynamic response by affecting the effective conicity and gravitational stiffness of the wheelset, models capable of having different wheel profiles on the same axle as well as on different axles were developed to investigate the stability behavior. Additionally, these models were formulated so that the effects on stability of asymmetric fore and aft loading conditions, as manifested through gravitational stiffness effects and creep coefficients, could be examined. Results of studies using these models are presented that display characteristics markedly different from those of completely symmetric models. A particularly interesting result is that, in most cases, the lateral stability of vehicles with different wheel profiles on the various axles is strongly sensitive to the direction of motion with results for each direction of motion which may differ radically from symmetric cases.

scholarly journals Boosting Aircraft Efficiency by Reversing the Load on the Horizontal Stabilizer

2019 ◽  
Vol 8 (3) ◽  
pp. 112-119
Keyword(s):  
Control Theory ◽  
Air Force ◽  
Cost Savings ◽  
Longitudinal Stability ◽  
Longitudinal Dynamics ◽  
Modern Control Theory ◽  
Model Based ◽  
Aircraft Performance ◽  
The Stability ◽  
Modern Control

This work aims at finding how reversing the direction of THS force improves aircraft performance. In most airplanes, the trimmable horizontal stabilizer (THS) is subjected to downward air force. This downward force acts in the same direction as the weight and opposite to the lift. The produced extra lift can be used to increase the payload or extend the range of the aircraft by carrying more fuel. The proposed design is based on shifting the wings location forward in order to make the force on the THS upward instead of downward. However, the stability of the airplane will be adversely affected. To address this issue, modern control theory is applied to the airplane elevator so as to maintain longitudinal stability. An airplane model based on longitudinal dynamics was used to investigate the stability of the airplane. Both current and proposed designs are simulated first without controllers and then with active controllers. The longitudinal dynamics’ equations are used to design the controllers so as to make the aircraft stable. The payload gain due to the proposed design is calculated; For a typical airliner, it is found that up to 21% increase in payload can be achieved using the proposed design. The proposed design where the load on the THS becomes upward instead of downward results in improving flight efficiency; that is, we can choose between increasing payload, extending the range, reducing the thrust, or using a smaller wing, or any combination of these benefits. In all these cases, there is an operational advantage. This advantage is translated to cost savings or higher revenues.

scholarly journals Preliminary calculation of the landing gear of a military training aircraft

2020 ◽  
Vol 12 (4) ◽  
pp. 241-247
Author(s):  
Ilie NICOLIN ◽  
Bogdan Adrian NICOLIN
Keyword(s):  
Calculation Method ◽  
Military Training ◽  
Landing Gear ◽  
Lateral Stability ◽  
Preliminary Calculation ◽  
The Stability

The paper presents a preliminary calculation method, which is easy to apply for pre-dimensioning the landing gear. Preliminary calculation of the landing gear includes estimating the loads on landing and determining the position of the nose landing gear and the main landing gear of a military training aircraft. Another purpose of the preliminary calculation is to ensure the stability of a military training aircraft on landing and take-off, as well as to ensure the lateral stability of the aircraft during ground operations such as taxiing, landing or take-off.

scholarly journals Influence of four modern Flettner rotors, used as wind energy capturing system, on container ship stability

2020 ◽  
Vol 180 ◽  
pp. 02003
Author(s):  
Mihail-Vlad Vasilescu ◽  
Ionut Voicu ◽  
Cornel Panait ◽  
Violeta-Vali Ciucur
Keyword(s):  
Wind Energy ◽  
Container Ship ◽  
Ship Stability ◽  
Longitudinal Stability ◽  
Stability Calculation ◽  
Power Generators ◽  
The Stability ◽  
Metacentric Height

This article is presenting the influence on the stability of a container ship, by connecting four modern Flettner rotors, as wind energy capturing system. Modern Flettner rotors, are energy power generators. They are one of the various equipment used to capture and harness wind energy. By reading the article, the reader can discover what are the forces which influence the modern Flettner rotors and how they influence the ship stability.This article major points are: calculation the influence of the modern Flettner rotors on the ship transverse and longitudinal stability, calculation of the ship new displacement, new draft, new metacentric height and period of rolling.

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