An analysis of gravity model distance exponents

This study examines variations in the basic parameter of the gravity model: the distance or travel time exponent. In a conceptual examination of the exponent under ideal conditions, it is noted that the exponent will be low if either production or consumption of the phenomena is geographically concentrated. It is further noted that if all regions produce and consume the phenomena, this generally implies a large number of substitute regions, and therefore a large exponent. These three variables are made operational and related to a set of eighty exponents for 1967 commodity flows in the United States. A multiple regression model is derived and utilized to estimate the exponents. The latter are then used to reestimate the flows. The root mean squared errors are quite similar for the fitted and estimated exponents. Implications of the research appear to be consistent with variations of the exponent in the urban context.     

The Application of Linear Optimal Control Theory to the Design of Active Automotive Suspensions

Some linear stochastic control theory relevant to the design of active suspension systems subject to integrated or filtered white noise excitation is reviewed, and application of the theory to a particular problem is considered. The problem considered is the well known quarter car problem in which a control law which minimises a performance function representing passenger discomfort, suspension working space, and tyre load fluctuations is required. With full state feedback, the requirement for a formulation of the problem which leads to the system under consideration being observable and controllable is referred to, and it is shown how a well known coordinate transformation enables this requirement to be satisfied. With limited state (or output) feedback, problem formulations which will avoid potential numerical problems in deriving the optimal control are described. Example solutions are included in order to illustrate the methods.     

Marginal cost pricing of ferry transportation: a practical application

In this paper, in which the author attempts to redress the lack of attention by economists to ferry operation, a simple pricing model, based on marginal cost pricing, is developed.     

Dynamic and Vibration Analysis of a Vehicle Rear Axle System

A detailed finite element model for the rear axle system of a sport utility vehicle is developed in this investigation. The axle system is treated as a multibody system that consists of nine bodies that include the input shaft, two output shafts, the carrier and tube system, four control arms and a track bar. The rotating input and output shafts are mounted on the carrier and tube system using six bearings. The four control arms and the track bar are connected to the carrier system and the frame of the vehicle using rubber bushings. In the model developed in this investigation, three dimensional beam elements are used to develop the finite element model for the input and output axle shafts, the control arms, and the track bar. A non-conventional finite element formulation is used to develop the equations of motion of the rotating input and output shafts in order to account for the effect of their angular velocities. These equations are expressed in terms of inertia shape integrals that depend on the assumed displacement field. The inertia shape integrals are first evaluated for each finite element. The inertia shape integrals of the rotating shafts are obtained by assembling the inertia shape integrals of its finite elements using a standard finite element assembly procedure. A conventional finite element formulation is used for the control arms and the track bar. The model developed in this investigation includes the effect of the bearing stiffness, the effect of the stiffness of the helical springs of the suspension system, and the effect of the stiffness of the tires. Using the Lagrangian dynamics and the finite element method, the equations of motion of the axle system are developed and expressed in terms of the nodal coordinates of the shafts, the control arms and the track bar as well as the degrees of freedom of the carrier. This finite dimensional model is used to determine the mode shapes and the natural frequencies of the axle system. The discrepancies between several of the natural frequencies predicted using the dynamic model developed in this investigation and natural frequencies determined experimentally are found to be less than 2%. A parametric study is performed in order to investigate the effect of the axle system parameters on the natural frequencies and mode shapes. Using the modal transformation, a set of differential equations of motion of the axle system is developed and used to examine the system dynamics under given loading conditions. The solutions of the resulting equations of motion are obtained using numerical methods.     

Effect of Frame Compliance on the Lateral Dynamics of Motorcycles

The lateral dynamics of an uncontrolled motorcycle, running on a straight, level road surface, is investigated in this paper. The structural compliances in the front and the rear frames of the motorcycle are taken into account by introducing additional degrees of freedom in the analysis. The kinematics of the tires is represented by linear differential equations which are based on the taut-string model of pneumatic tires. The linear differential equations of motion are solved to yield the eigensolutions of the system. Numerical results, obtained for parameters corresponding to a Honda CB750 motorcycle, are presented and discussed.     

The Influence of Tire Factors on the Stability of Trucks and Tractor Trailers

The mechanical properties of tires and trucks are contrasted with comparable properties of the motor car to explain why the motor truck and the tractor-trailer can exhibit fixed-control instability at moderate levels of lateral acceleration. The (1) rearward bias in the distribution of roll stiffness, (2) large ratio of e.g. height to track, and (3) low torsional stiffness of the parallel-rail frame (as typically employed in heavy commercial vehicles) are found to be the major factors implicated in this phenomenon. Experimental and analytical evidence is provided to show how tire inflation pressure and mixes of (a) tire-carcass construction and (b) tread design also influence stability at moderate levels of lateral acceleration. Conclusions relating to the safety of commercial vehicle operations are drawn.     

Aerodynamics of Road- and Rail Vehicles

The technical state-of-the-art of aerodynamics of ground transportation vehicles is reviewed. Currently available theoretical calculation methods and experimental simulation techniques as well as typical results illustrating the impact of aerodynamics on vehicle performance and running characteristics are summarized and the interactions between vehicle system dynamics and aerodynamics are adressed. Correlation of theoretical and experimental data show the present potential of vehicle aerodynamics and point to fields in which further research work is necessary.