We studied the structure of the 15-minute city by measuring the distances from the services on spatial graphs. While the concept of the 15-minute city is rapidly spreading, its operative definition can be of help for planning and understanding the possibilities of the general idea. For three European cities (Rome, Paris, and London), we developed a method to calculate pedestrian travel time to reach services for all the possible paths on urban graphs, finding that the 15-minute city generally has multiple connected components and that the services have not necessarily been part of it. This algorithm was used to to make a quantitative comparison between the cities, showing that Paris and London have a stronger 15-minute characterization than Rome. By generalizing the method, it was possible to define a 15-minute urban index, which quantitatively characterizes this city feature. The results seem to be promising because, at the cost of the massive use of computational time, a digital model for the city can be generated: a planning tool to simulate urban solutions and a rigorous criterion for evaluating how much a city can be considered a 15-minute city.

A large part of the stock of Italian educational buildings have undertaken energy retrofit interventions, thanks to European funds allocated by complex technical-administrative calls. In these projects, the suggested retrofit strategies are often selected based on the common best practices (considering average energy savings) but are not supported by proper energy investigations. In this paper, Italian school buildings’ stock was analyzed by cluster analysis with the aim of providing a methodology able to identify the best energy retrofit interventions from the perspective of cost-benefit, and to correlate them with the specific characteristics of the educational buildings. This research is based on the analysis of about 80 school buildings located in central Italy and characterized by different features and construction technologies. The refurbished buildings were classified in homogeneous clusters and, for each of them, the most representative building was identified. Furthermore, for each representative building a validating procedure based on dynamic simulations and a comparison with actual energy use was performed. The two buildings thus singled out provide a model that could be developed into a useful tool for Public Administrations to suggest priorities in the planning of new energy retrofits of existing school building stocks.

Among the super insulating materials, aerogel has interesting properties: very low thermal conductivity and density, resistance to high temperatures and transparency. It is a rather expensive material, but incentives in the field can improve its economic attractiveness. Starting from this, the thermal behavior of a test building entirely insulated with aerogel panels was investigated through an extended experimental campaign. A dynamic simulation model of a case study building was generated to better comprehend the energy savings obtained through aerogel in terms of energy demand over a whole year. The investigation was completed by computing the carbon and energy payback times of various retrofit strategies through a life cycle assessment approach, as well as by a cost-benefit analysis through a probabilistic financial framework. Compared to conventional insulation materials, aerogel is characterized by a higher energy and carbon payback time, but it guarantees better environmental performance in the whole life cycle. From an economic-financial perspective, the aerogel retrofit is the best in the current tax incentive scenario. However, due to its higher lump-sum investment, aerogel’s net present value is very sensitive to tax deductions, and it is riskier than the best comparable materials in less favorable tax scenarios.