Advances in travel geometry and urban modelling

Urban travel geometry is a generalization of patterns of movement in cities and regions where route configuration and prevailing traffic speeds constrain or direct movement in distinctive and repeatable patterns. In this paper we use these properties to construct time surfaces on which distance equates to the time of travel in the urban plane. Such surfaces can be two- or three-dimensional and are useful in the study of urban structure, locational analysis, transport planning and traffic management. A particular niche addressed in this paper is non-conformal time surface transformations in which speed or the cost of travel is constrained according to co-ordinate directions. It is argued that such models may be more suited to gridded and orbital-radial cities than previously used conformal transformations. After explaining the rationale behind the approach, a mathematical basis is developed and several calibrated examples are provided based on regions in the UK. The paper concludes with some examples of potential applications, and an annex provides a detailed mathematical framework. This revised version was published online in August 2006 with corrections to the Cover Date.