Abstract

Firstly we amend for buildings the traditional terms of Surface to Volume ratio) formulating a Weighted Form Factor (FF*= A*/V) in which the surface areas of the geometric envelope are pondered by the corresponding thermal transmission coeffi-cients. This parameter is shown to be equal to the unitary (by degree of temperature) and specific (by unit of volume) flow of heat due to the transmission through that envelope, and it is an adequate parameter to compare the preliminary efficacy of different design solutions on an homogeneous basis. Then it is unveiled a Geometrical Law (mathematically formalised in an Identity Theorem), that establishes that for certain typologies of elongated buildings (eg. An-nular types of building, and also long Blocks and Towers), the Form Factor of their three-dimensional shape is identical to the Form Factor of the mean cross section. The corresponding dimensional reduction from 3D to 2D, implies that many prob-lems of analysis and design become extremely easy in a variety of fields: urban planning, building projects, and in general morphology. The Practical Implications are clear: applied for example to the task of achieving a greater energy efficiency (by thermal transfer) of long building blocks and towers, there is no need for considering the whole exterior envelope; it is enough to ensure the optimisation of the cross section (in the tower is the floor plan), trying to obtain the most adequate, compact and large 2D figure, and the most insulated perimeter for it. In order to achieve those goals, we establish new criteria and methodology, and give hints for developing two-dimensional morpho-thermical models. Using these prodedures, design tasks not restricted by volume, can focus only on the section of elongated buildings, and their plan layouts can be freely adapted to what is more appropriate in relation to other important aspects: street guide-lines, sunlight & wind orientation, lighting, etc