Contents lists available at ScienceDirect Progress in Planning journal homepage: www.elsevier.com/locate/progress The shape compactness of urban footprints Shlomo Angel ⁎ , Sara Arango Franco, Yang Liu, Alejandro M. Blei The Marron Institute of Urban Management, New York University, USA ARTICLE INFO Keywords: Compact city Urban footprints Shape compactness Urban expansion Sample of cities Climate change Population density ABSTRACT Urban population density has featured in a large body of literature on the Compact City paradigm as the key compactness attribute of cities, yet the shape compactness of urban footprints has hardly deserved a mention. This essay seeks to correct that. We review the literature on the Compact City Paradigm with a special focus on the relationship between urban form and climate change, and focus on twelve physical attributes of cities that make them more or less compact. Other things being equal, both population density and shape compactness help determine the average travel distances in cities, and hence affect their energy consumption and their greenhouse gas emissions. They also affect the length of infrastructure lines and the length of commutes. In principle, therefore, increasing either the shape compactness or the population density of cities can contribute—in dif- ferent yet similar measure—to mitigating climate change. There are strong forces that push urban footprints to become more compact—that is, circular or near circular in shape—and these forces have evolved over time. There are also powerful forces that have pushed urban footprints to become less compact over time. We in- troduce these forces and illustrate their effects on particular cities. We then focus on a small set of metrics for measuring the shape compactness of cities. We use them to measure urban footprints obtained from satellite imagery in a stratified global sample of 200 cities in three time periods: 1990, 2000, and 2014. We find that the shape compactness of urban footprints the world over is independent of city size, area, density, and income and that, not surprisingly, it is strongly affected by topography. We also find that it has declined overall between 1990 and 2014 and explain some of the sources of this decline. We conclude the paper by assessing the ways in which the shape compactness of cities can be increased to make them better able to mitigate climate change in decades to come. Of all the attributes that characterize a city, there can be little doubt that proximity is the most crucial. Fanis Grammemos, 2011 The circle is the most compact of shapes because the proximity of all points to all other points within it is at a maximum. A yet to be proven mathematical conjecture 1. Introduction 1.1. The conceptual framework The central objective of this essay is to broaden and deepen our understanding of the compact city paradigm by introducing readers to a number of new compactness attributes of cities that have not been extensively discussed in the literature before, essentially those that have to do with the geographical shape of urban footprints, rather than with their densities or with their internal spatial structure. We begin this section by reviewing the emerging interest in compact cities in the last 25 years and then focus on an integrated conceptual framework for understanding, studying, and acting upon the various compactness at- tributes of urban forms. More specifically we introduce, define, and give real-world examples of twelve compactness attributes of cities and discuss the relationships between them and later measure the correla- tions between most of them, using data from a global sample of 200 cities. In this manner, we aim to provide the reader with a novel and rigorous understanding of a subset of these attributes, the compactness attributes of urban footprints, and of what can be done and needs to be done to make cities more compact—and in many instances possibly more productive, more inclusive, and more sustainable as well—by making their urban footprints more compact. Since the Earth Summit of 1992 (United Nations, 1993), there have been worldwide efforts to address environmental challenges—be they the depletion of natural resources, the loss of cultivable lands, air and water pollution, or greenhouse gas emissions—by changes in urban form. Proposed changes have ranged from the design of energy-efficient https://doi.org/10.1016/j.progress.2018.12.001 Received 16 July 2018; Received in revised form 30 November 2018; Accepted 2 December 2018 ⁎ Corresponding author at: The Marron Institute of Urban Management, New York University, 60 5th Avenue, 2nd Floor, New York, NY, 10011, USA. E-mail addresses: sangel@stern.nyu.edu (S. Angel), saf537@nyu.edu (S. Arango Franco), yl3371@nyu.edu (Y. Liu), ablei@stern.nyu.edu (A.M. Blei). Progress in Planning xxx (xxxx) xxx–xxx 0305-9006/ © 2018 Elsevier Ltd. All rights reserved. Please cite this article as: Angel, S., Progress in Planning, https://doi.org/10.1016/j.progress.2018.12.001