Alta velocidad ferroviaria en California(USA): cuarta parte (IV) Fresno-Sacramento (Roseville) = High speed railway in California (USA): fourth part (IV) Fresno-Sacramento (Roseville)

Implantación de la Red de Alta velocidad Ferroviaria en California. Tramo Fresno-Sacramento. El presente articúlo es la cuarta parte de la serie "Alta Velocidad Ferroviaria en California (CHSRS)". Recoge la Alternativa "Stockton Arch", que el Proyecto FARWEST presenta a la prevista por la Authority (CHSRA), para la Línea HSR Fresno-Sacramento, en programación y en trazado. Éste discurre, desde la gran Terminal de Fresno (implantada en las afueras al suroeste de la ciudad) por el segmento sur del "mar interior" (que en el Terciario Superior ocupaba el actual Valle Central), hasta Stockton, y por el segmento norte, hasta Sacramento. El Paet de Ripperdan (~ pK 40) queda conectado por carretera con el PAET de Oroloma de la Línea HSR Fresno-San Francisco (Golden Gate Alternative). La última parte del trazado de la Línea HSR Fresno-Sacramento (Stockton Arch Alternative), coincide en alineación y rasante con la Línea HSR San Francisco-Sacramento (Crossing Bay Alternative) a la altura de Roseville, donde se emplaza la gran terminal norte de la red de California, desde la que se unirá ésta con la de Nevada, por Reno. This article forras the fourth part of the series entitled "High Speed Railway in California (CHSRS)". It addresses the "Stockton Arch" alternative, which the FARWESTProjectpresents in scheduling and in alignment as to that provided for by the Authority (CHSRA) for the Fresno-Sacramento HSR Line. The latter runs from the grand Fresno Terminal (located in the outskirts to the southwest ofthe city) through the south segment ofthe "inland sea" (which oceupied the current Central Valley in the Upper Tertiary) to Stockton and through the north segment to Sacramento. The Ripperdan TSAP (post ofpassing and stabling trains), — kilometer point 40, conneets with the Oroloma TSAP ofthe Fresno-San Francisco HSR Line (Golden Gate Alternative) by road. The last part of the Fresno-Sacramento HSR Line alignment (Stockton Arch Alternative), coincides in alignment and grade with the San Francisco-Sacramento HSR Line (Crossing Bay Alternative) at Roseville, where the great north terminal ofthe California network is located, from which the latter will be linked with Nevada s network through Reno.

Alta velocidad ferroviaria en California(USA): tercera parte (III) Fresno-Los Ángeles-San Diego = High speed railway in California(USA): third part (III) Fresno-Los Ángeles-San Diego

Implantación de la Red de Alta velocidad Ferroviaria en California. Tramo Fresno-Los Angeles-San Diego. Este artículo, tercera parte de la serie que describe la red de Alta Velocidad Ferroviaria de California (CHSRS), se ocupa de la línea Fresno-Los Angeles Airport-San Diego Airport, con el trazado propuesto en la Alternativa Missions Trail del Proyecto FARWEST, caracterizada por el paso directo de las montañas de Tehachapi, mediante dos grandes túneles de 27,5 Km (17 mile) y 25,6 Km (15,9 mile) de longitud. También por el emplazamiento de la estación terminal de Los Angeles, junto al Aeropuerto Internacional de Los Angeles y la sustitución de la circunvalación ferroviaria de la aglomeración urbana de Los Angeles, a través de Inland Empire, por el ramal Anaheim-Riverside, que da acceso a esa región, y que es cabecera de la futura Dessert Express a Las Vegas. The third of a series describing the California High Speed Railway (CHSRS), this article refers to the Fresno-Los Angeles Airport-San Diego Airport line, with the alignment as proposed in the Missions Trail Alternative of the FARWEST Project, characterized by the direct Tehachapi mountain pass through two large tunnels 27.5 Km (17 miles) and 25.6 Km (15.9 miles) long and also to the siting of the Los Angeles terminal station next to the Los Angeles International Airport and the replacement of the Los Angeles urban conglomeration railway by-pass through Inland Empire, by the Anaheim-Riverside branch providing access to that region and which is the head of the future Desert Express to Las Vegas.

Great roof marquee in the new railway station for high speed trains of Málaga

The new railway station of María Zambrano for AVE (Spanish high-speed trains) located in Malaga, has been inaugurated in November 2006, just on the site of the former railway station. The new railway station with an investment of 134.7 million Euros occupies a surface of 51.377 m2, five times the surface of the former station. The enclosure is the biggest intermodal transport and commercial center of Spain which comprises a parking of 21,000 m2 for 1,300 parking places, one commercial area and a hotel of 35 m height, with a total extension constructed of approximately 100,000 m2.

A low-mass impact sensor for high-speed firmness sensing of fruits.

A low-mass impact sensor for high-speed firmness sensing of fruits was built and tested. Results of tests with a rubber ball indicated that the impact measurement was not sensitive to the distance between the impactor and the impacting surface of the sample within the range of 8 to 23 mm, and was not sensitive to how the sample was held. Tests with kiwifruits and peaches show good correlation between firmness readings obtained with the impact sensor and those obtained with the penetrometer. The best correlation was between the slope of the impact curve (at mid-point) and the force-deformation firmness. Preliminary test showed that the sensor could sense fruit firmness at a speed of 5 fruits/s.

Aerodynamic Optimization of the Nose Shape of a High-speed Train

La influencia de la aerodinámica en el diseño de los trenes de alta velocidad, unida a la necesidad de resolver nuevos problemas surgidos con el aumento de la velocidad de circulación y la reducción de peso del vehículo, hace evidente el interés de plantear un estudio de optimización que aborde tales puntos. En este contexto, se presenta en esta tesis la optimización aerodinámica del testero de un tren de alta velocidad, llevada a cabo mediante el uso de métodos de optimización avanzados. Entre estos métodos, se ha elegido aquí a los algoritmos genéticos y al método adjunto como las herramientas para llevar a cabo dicha optimización. La base conceptual, las características y la implementación de los mismos se detalla a lo largo de la tesis, permitiendo entender los motivos de su elección, y las consecuencias, en términos de ventajas y desventajas que cada uno de ellos implican. El uso de los algorimos genéticos implica a su vez la necesidad de una parametrización geométrica de los candidatos a óptimo y la generación de un modelo aproximado que complementa al método de optimización. Estos puntos se describen de modo particular en el primer bloque de la tesis, enfocada a la metodología seguida en este estudio. El segundo bloque se centra en la aplicación de los métodos a fin de optimizar el comportamiento aerodinámico del tren en distintos escenarios. Estos escenarios engloban los casos más comunes y también algunos de los más exigentes a los que hace frente un tren de alta velocidad: circulación en campo abierto con viento frontal o viento lateral, y entrada en túnel. Considerando el caso de viento frontal en campo abierto, los dos métodos han sido aplicados, permitiendo una comparación de las diferentes metodologías, así como el coste computacional asociado a cada uno, y la minimización de la resistencia aerodinámica conseguida en esa optimización. La posibilidad de evitar parametrizar la geometría y, por tanto, reducir el coste computacional del proceso de optimización es la característica más significativa de los métodos adjuntos, mientras que en el caso de los algoritmos genéticos se destaca la simplicidad y capacidad de encontrar un óptimo global en un espacio de diseño multi-modal o de resolver problemas multi-objetivo. El caso de viento lateral en campo abierto considera nuevamente los dos métoxi dos de optimización anteriores. La parametrización se ha simplificado en este estudio, lo que notablemente reduce el coste numérico de todo el estudio de optimización, a la vez que aún recoge las características geométricas más relevantes en un tren de alta velocidad. Este análisis ha permitido identificar y cuantificar la influencia de cada uno de los parámetros geométricos incluídos en la parametrización, y se ha observado que el diseño de la arista superior a barlovento es fundamental, siendo su influencia mayor que la longitud del testero o que la sección frontal del mismo. Finalmente, se ha considerado un escenario más a fin de validar estos métodos y su capacidad de encontrar un óptimo global. La entrada de un tren de alta velocidad en un túnel es uno de los casos más exigentes para un tren por el pico de sobrepresión generado, el cual afecta a la confortabilidad del pasajero, así como a la estabilidad del vehículo y al entorno próximo a la salida del túnel. Además de este problema, otro objetivo a minimizar es la resistencia aerodinámica, notablemente superior al caso de campo abierto. Este problema se resuelve usando algoritmos genéticos. Dicho método permite obtener un frente de Pareto donde se incluyen el conjunto de óptimos que minimizan ambos objetivos. ABSTRACT Aerodynamic design of trains influences several aspects of high-speed trains performance in a very significant level. In this situation, considering also that new aerodynamic problems have arisen due to the increase of the cruise speed and lightness of the vehicle, it is evident the necessity of proposing an optimization study concerning the train aerodynamics. Thus, the aerodynamic optimization of the nose shape of a high-speed train is presented in this thesis. This optimization is based on advanced optimization methods. Among these methods, genetic algorithms and the adjoint method have been selected. A theoretical description of their bases, the characteristics and the implementation of each method is detailed in this thesis. This introduction permits understanding the causes of their selection, and the advantages and drawbacks of their application. The genetic algorithms requirethe geometrical parameterization of any optimal candidate and the generation of a metamodel or surrogate model that complete the optimization process. These points are addressed with a special attention in the first block of the thesis, focused on the methodology considered in this study. The second block is referred to the use of these methods with the purpose of optimizing the aerodynamic performance of a high-speed train in several scenarios. These scenarios englobe the most representative operating conditions of high-speed trains, and also some of the most exigent train aerodynamic problems: front wind and cross-wind situations in open air, and the entrance of a high-speed train in a tunnel. The genetic algorithms and the adjoint method have been applied in the minimization of the aerodynamic drag on the train with front wind in open air. The comparison of these methods allows to evaluate the methdology and computational cost of each one, as well as the resulting minimization of the aerodynamic drag. Simplicity and robustness, the straightforward realization of a multi-objective optimization, and the capability of searching a global optimum are the main attributes of genetic algorithm. However, the requirement of geometrically parameterize any optimal candidate is a significant drawback that is avoided with the use of the adjoint method. This independence of the number of design variables leads to a relevant reduction of the pre-processing and computational cost. Considering the cross-wind stability, both methods are used again for the minimization of the side force. In this case, a simplification of the geometric parameterization of the train nose is adopted, what dramatically reduces the computational cost of the optimization process. Nevertheless, some of the most important geometrical characteristics are still described with this simplified parameterization. This analysis identifies and quantifies the influence of each design variable on the side force on the train. It is observed that the A-pillar roundness is the most demanding design parameter, with a more important effect than the nose length or the train cross-section area. Finally, a third scenario is considered for the validation of these methods in the aerodynamic optimization of a high-speed train. The entrance of a train in a tunnel is one of the most exigent train aerodynamic problems. The aerodynamic consequences of high-speed trains running in a tunnel are basically resumed in two correlated phenomena, the generation of pressure waves and an increase in aerodynamic drag. This multi-objective optimization problem is solved with genetic algorithms. The result is a Pareto front where a set of optimal solutions that minimize both objectives.

Simulation, Design and Analysis of Air-Breathing Combined-Cycle Engines for High Speed Propulsion

Desde la aparición del turborreactor, el motor aeróbico con turbomaquinaria ha demostrado unas prestaciones excepcionales en los regímenes subsónico y supersónico bajo. No obstante, la operación a velocidades superiores requiere sistemas más complejos y pesados, lo cual ha imposibilitado la ejecución de estos conceptos. Los recientes avances tecnológicos, especialmente en materiales ligeros, han restablecido el interés por los motores de ciclo combinado. La simulación numérica de estos nuevos conceptos es esencial para estimar las prestaciones de la planta propulsiva, así como para abordar las dificultades de integración entre célula y motor durante las primeras etapas de diseño. Al mismo tiempo, la evaluación de estos extraordinarios motores requiere una metodología de análisis distinta. La tesis doctoral versa sobre el diseño y el análisis de los mencionados conceptos propulsivos mediante el modelado numérico y la simulación dinámica con herramientas de vanguardia. Las distintas arquitecturas presentadas por los ciclos combinados basados en sendos turborreactor y motor cohete, así como los diversos sistemas comprendidos en cada uno de ellos, hacen necesario establecer una referencia común para su evaluación. Es más, la tendencia actual hacia aeronaves "más eléctricas" requiere una nueva métrica para juzgar la aptitud de un proceso de generación de empuje en el que coexisten diversas formas de energía. A este respecto, la combinación del Primer y Segundo Principios define, en un marco de referencia absoluto, la calidad de la trasferencia de energía entre los diferentes sistemas. Esta idea, que se ha estado empleando desde hace mucho tiempo en el análisis de plantas de potencia terrestres, ha sido extendida para relacionar la misión de la aeronave con la ineficiencia de cada proceso involucrado en la generación de empuje. La metodología se ilustra mediante el estudio del motor de ciclo combinado variable de una aeronave para el crucero a Mach 5. El diseño de un acelerador de ciclo combinado basado en el turborreactor sirve para subrayar la importancia de la integración del motor y la célula. El diseño está limitado por la trayectoria ascensional y el espacio disponible en la aeronave de crucero supersónico. Posteriormente se calculan las prestaciones instaladas de la planta propulsiva en función de la velocidad y la altitud de vuelo y los parámetros de control del motor: relación de compresión, relación aire/combustible y área de garganta. ABSTRACT Since the advent of the turbojet, the air-breathing engine with rotating machinery has demonstrated exceptional performance in the subsonic and low supersonic regimes. However, the operation at higher speeds requires further system complexity and weight, which so far has impeded the realization of these concepts. Recent technology developments, especially in lightweight materials, have restored the interest towards combined-cycle engines. The numerical simulation of these new concepts is essential at the early design stages to compute a first estimate of the engine performance in addition to addressing airframe-engine integration issues. In parallel, a different analysis methodology is required to evaluate these unconventional engines. The doctoral thesis concerns the design and analysis of the aforementioned engine concepts by means of numerical modeling and dynamic simulation with state-of-the-art tools. A common reference is needed to evaluate the different architectures of the turbine and the rocket-based combined-cycle engines as well as the various systems within each one of them. Furthermore, the actual trend towards more electric aircraft necessitates a common metric to judge the suitability of a thrust generation process where different forms of energy coexist. In line with this, the combination of the First and the Second Laws yields the quality of the energy being transferred between the systems on an absolute reference frame. This idea, which has been since long applied to the analysis of on-ground power plants, was extended here to relate the aircraft mission with the inefficiency of every process related to the thrust generation. The methodology is illustrated with the study of a variable- combined-cycle engine for a Mach 5 cruise aircraft. The design of a turbine-based combined-cycle booster serves to highlight the importance of the engine-airframe integration. The design is constrained by the ascent trajectory and the allocated space in the supersonic cruise aircraft. The installed performance of the propulsive plant is then computed as a function of the flight speed and altitude and the engine control parameters: pressure ratio, air-to-fuel ratio and throat area.

Does high speed rail compete fairly with other transportation modes? Madrid-Barcelona case study

Transportation modes produce many external costs such as congestion, accidents, and environmental impacts (pollution, noise and so on). From the microeconomic theory it is well known that in order to maximize social welfare, transportation modes should internalize the marginal costs they produce. Allocative efficiency is achieved when all transportation modes are priced at their social marginal cost. The objective of this research is to evaluate to what extent different passenger transport modes internalize their social marginal costs. This analysis is important since it affects the competitiveness of the different transport modes for a given OD pair. The case study analyzed is the corridor Madrid-Barcelona in Spain and the different transport modes have been considered (cars, buses, high-speed train and air). The research calculates the marginal social cost per user for each transportation mode, and it compares it with the average fare—allowing for the effect of discriminatory taxes—currently paid by the users. The external costs are calculated according to the guidelines established by the European Union. The gap between the marginal social cost and the price paid by users will provide the extra cost per passenger that each transport mode should have to pay for internalizing the external cost it produces. The research shows that external costs already produced by road and air transport modes are much higher than those produced by rail. However, the results show that road transport already internalizes every external costs it produces because users pay high fuel taxes. In other words, although rail transportation produces lower external costs, road transportation pays more than it should on the basis of the social marginal costs. The results of this work might be of help for Europ ean policy actions to be undertaken in the future.

High speed railroad bridges. Conception, bases of design, typological possibilities and construction methods

Diseño conceptual de puentes de alta velocidad ferroviarios. Railroad bridges, in general, and those for high speed railways, in particular, demand very special conditions. The traffic loads are much higher than for road bridges. Loads due to braking and acceleration determine, due to their magnitude, the structural layout. Because of the speed of the vehicles there are specific dynamic effects which need to be considered. In order to ensure passenger comfort, compatible with speeds of up to 350 km/h, it is necessary to meet very demanding conditions with respect to stiffness, displacements and dynamic behavior. In this paper these conditions are briefly described and different typological possibilities to satisfy them are presented as well as the main construction methods applicable to this kind of bridges.

Multi-objective Aerodynamic Optimization of High-speed Trains in Tunnels

A genetic algorithm (GA) is employed for the multi-objective shape optimization of the nose of a high-speed train. Aerodynamic problems observed at high speeds become still more relevant when traveling along a tunnel. The objective is to minimize both the aerodynamic drag and the amplitude of the pressure gradient of the compression wave when a train enters a tunnel. The main drawback of GA is the large number of evaluations need in the optimization process. Metamodels-based optimization is considered to overcome such problem. As a result, an explicit relationship between pressure gradient and geometrical parameters is obtained.

Fórmulas para el cálculo del factor de impacto de estructuras semienterradas en líneas de ferrocarril de alta velocidad = Dynamic factors for underpasses in high speed train lines

Los pasos inferiores son muy numerosos en las líneas de ferrocarril. Su comportamiento dinámico ha recibido mucha menos atención que el de otras estructuras como los puentes, pero su elevado número hace que su estudio sea económicamente relevante con vista a optimizar su forma, manteniendo la seguridad. El proyecto de puentes según el Eurocódigo incluye comprobaciones de estados límite de tensiones bajo carga dinámica. En el caso de pasos inferiores, las comprobaciones pueden resultar tan costosas como aquellas de puentes, pese a que su coste es mucho menor. Por tanto, se impone la búsqueda de unas reglas de cálculo simplificado que pongan en consonancia el coste de la estructura con el esfuerzo necesario para su proyecto. Este artículo propone un conjunto de reglas basadas en un estudio paramétrico = Underpasses are common in modern railway lines. Wildlife corridors and drainage conduits often fall into this category of partially buried structures. Their dynamic behavior has received far less attention than that of other structures such as bridges, but their large number makes their study an interesting challenge from the viewpoint of safety and cost savings. The bridge design rules in accordance with the Eurocode involve checks on stresses according to dynamic loading. In the case of underpasses, those checks may be as much as those for bridges. Therefore, simplified design rules may align the design effort with their cost. Such a set of rules may provide estimations of response parameters based on the key parameters influencing the result. This paper contains a proposal based on a parametric study.

Influence of the Second Bending Mode on the Response of High-Speed Bridges at Resonance

This paper deals with the assessment of the contribution of the second bending mode to the dynamic behavior of simply supported railway bridges. Traditionally the contributions of modes higher than the fundamental have been considered of little importance for the computation of the magnitudes of interest to structural engineers (vertical deflections, bending moments, etc.). Starting from the dimensionless equations of motion of a simply supported beam subjected to moving loads, the key parameters governing the dynamic behavior are identified. Then, a parametric study over realistic ranges of values of those parameters is conducted, and the influence of the second mode examined in detail. The main purpose is to decide whether the second mode should be taken into account for the determination of the maximum displacement and acceleration in high-speed bridges. In addition, the reasons that cause the contribution of the second bending mode to be relevant in some situations are highlighted, particularly with regard to the computation of the maximum acceleration.

Big bridge in pérgola for high speed trains to the northwest of Spain

Big bridge in pérgola for high speed trains to the northwest of Spain

Aeroacoustics in high speed trains

Este trabajo se centra en el estudio de problemas aeroacústicos en los trenes de alta velocidad. Se han considerado dos escenarios en los que las ondas de presión generadas son críticos para el confort de los pasajeros. Uno es el debido a las ondas de presión que genera el tren cuando entra y sale de un túnel, que a su vez producen saltos de presión de baja frecuencia en el tren (cuando se cruzan con él) y en los alrededores del túnel cuando alcanzan la salida. Se estudia este fenómeno, y se propone un sistema aeroelástico basado en el galope transversal para disminuir la energía de estas ondas, y se analiza la energía extraíble de las ondas utilizando cuerpos con diferentes secciones transversales [Sorribes-Palmer and Sanz-Andres, 2013]. La influencia de la geometría de los portales en la energía radiada hacia el exterior de túnel es analizada experimentalmente, prestando especial atención a las boquillas porosas. Las ondas de presión en el interior del túnel se han analizado mediante el método de las características. Se han realizado ensayos experimentales para estimar la energía reflejada hacia el interior del túnel al alcanzar las ondas de presión el portal de salida del túnel. Se ha estudiado la formación e interacción entre el portal del túnel y la onda de choque generada en los túneles de gran longitud y pequeña fricción. Se propone un método para describir de forma aproximada el ruido radiado al exterior. Por otro lado se ha estudiado el ruido de media y alta frecuencia de origen aerodinámico. Se ha estudiado la influencia del desprendimiento de la capa límite sobre el tren. Se propone una metodología basada en una sección de tren característica para predecir rápidamente el nivel de presión de sonido dentro y fuera del tren para todo el rango de frecuencias. Se han realizado medidas experimentales en vía de los espectros de presión sobre la superficie del tren, y de la transmisibilidad de las uniones entre estructura y revestimiento. Los resultados experimentales se han utilizado en los modelos vibroacústicos. El método de la sección del tren característica es especialmente útil a altas frecuencias cuando todo el tren se puede modelar mediante el ensamblaje de diferentes secciones características utilizando el análisis estadístico de la energía. ABSTRACT This work is focused on the study of aeroacoustic problems in high speed trains. We have considered two scenarios in which the pressure waves generated are critical for passengers comfort. The first one is due to the pressure waves generated by a train entering in a tunnel. These waves generate pressure gauges inside the train (when they find each other) and outside of the tunnel portals. This phenomenon has been studied, and an aeroelastic system based on transverse galloping to reduce the energy of these waves is proposed. The maximum extractable energy by using bodies with different cross-section shapes is analyzed. The influence of the portals geometry in the energy radiated outwards the tunnel is analyzed experimentally, with particular attention to the porous exits. The pressure waves inside the tunnel have been analyzed using the method of characteristics. Experimental tests to estimate the energy reflected into the tunnel when the pressure waves reach the tunnel portal have been performed. We have studied the generation and interaction between the tunnel portal and a shock wave generated in long tunnels with small friction. A method to describe in an approximated way the pressure radiated outside the tunnel is proposed. In the second scenario, middle and high frequency noise generated aerodynamically has been studied, including the influence of the detachment of the boundary layer around the train. A method based on a train section to quickly predict the sound pressure level inside and outside the train has been proposed. Experimental test have been performed on board to evaluate the pressure power spectra on the surface of the train, and the transmissibility of the junctions between the structure and trim. These experimental results have been used in the vibroacoustic models. The low frequency pressure waves generated with the train during the tunnel crossing has been identified in the pressure spectrum. The train characteristic section method is especially useful at high frequencies, when the whole train can be modeled by assembling different sections using the statistical energy analysis. The sound pressure level inside the train is evaluated inside and outside the tunnel.

On the Analytical Approach to Present Engineering Problems: Photovoltaic Systems Behavior, Wind Speed Sensors Performance, and High-Speed Train Pressure Wave Effects in Tunnels

At present, engineering problems required quite a sophisticated calculation means. However, analytical models still can prove to be a useful tool for engineers and scientists when dealing with complex physical phenomena. The mathematical models developed to analyze three different engineering problems: photovoltaic devices analysis; cup anemometer performance; and high-speed train pressure wave effects in tunnels are described. In all cases, the results are quite accurate when compared to testing measurements.

Territorial cohesion impacts of high-speed rail under different zoning systems

Large-scale transport infrastructure projects such as high-speed rail (HSR) produce significant effects on the spatial distribution of accessibility. These effects, commonly known as territorial cohesion effects, are receiving increasing attention in the research literature. However, there is little empirical research into the sensitivity of these cohesion results to methodological issues such as the definition of the limits of the study area or the zoning system. In a previous paper (Ortega et al., 2012), we investigated the influence of scale issues, comparing the cohesion results obtained at four different planning levels. This paper makes an additional contribution to our research with the investigation of the influence of zoning issues. We analyze the extent to which changes in the size of the units of analysis influence the measurement of spatial inequalities. The methodology is tested by application to the Galician (north-western) HSR corridor, with a length of nearly 670 km, included in the Spanish PEIT (Strategic Transport and Infrastructure Plan) 2005-2020. We calculated the accessibility indicators for the Galician HSR corridor and assessed their corresponding territorial distribution. We used five alternative zoning systems depending on the method of data representation used (vector or raster), and the level of detail (cartographic accuracy or cell size). Our results suggest that the choice between a vector-based and raster-based system has important implications. The vector system produces a higher mean accessibility value and a more polarized accessibility distribution than raster systems. The increased pixel size of raster-based systems tends to give rise to higher mean accessibility values and a more balanced accessibility distribution. Our findings strongly encourage spatial analysts to acknowledge that the results of their analyses may vary widely according to the definition of the units of analysis.