The Mathematical Foundation of Shelter Design Decisions

 

A correlated set of floor quantity and site plan area decisions determines gross building area, shelter capacity, intensity, intrusion, and context for any given buildable land area and building design category. A collection of these parcel decisions determines the physical context, but not the appearance, of shelter projects, blocks, tracts, zones, districts, cities, regions, and conurbations. The quantitative correlation of these quantity decisions has been overlooked for centuries because the evolution from shelter concept to completion has required drawings to define direction. The final style and appearance of the result has distracted us from a mathematical foundation that can be classified to consistently lead the choices that consume land to produce shelter capacity for any activity.

Shelter capacity evaluation focuses on the mathematical correlation of site plan area and floor quantity decisions. These decisions produce gross building area options and shelter capacity, intensity, intrusion, and context implications that range from sprawl to excessive intensity, but these relationships remain to be mathematically defined in terms of consistent measurement, evaluation, and leadership potential.

The absence of shelter capacity measurement, evaluation, and mathematical expression has prevented the accumulation of knowledge and the formation of a leadership language that can consistently guide shelter decisions for the activities of growing populations toward choices that protect their quality and source of life in limited geographic areas.

I have written about building design categories, design specification templates, and the shelter capacity implications of specification value choices on many occasions using forecast models to illustrate the mathematical correlation required for consistent shelter capacity leadership. I have made the effort to put the discussion of shelter capacity and its relationship to quality of life on an equal footing with the languages of real estate law and economics.

The debate can only begin on an equal footing when a mathematical language of shelter capacity built on measurement, evaluation, prediction, and knowledge accumulation can forecast the implications of land area, building design category, and specification value choices. These are the choices that lead to the formation of urban context and appearance. The nascent awareness of the need for this leadership language and knowledge has been referred to as urban design, or city design in the words of my deceased but prescient professor Rudolf Frankel.

I self-published “The Equations of Urban Design” on Amazon.com in 2020 to summarize and improve my work in three previous books entitled, “Land Development Calculations”, editions 1 and 2 published by McGraw-Hill in 2001 and 2010, and “The Science of City Design” self-published in 2016. They represent my continuing effort to explain the site plan allocation that precedes architectural design, urban design, city design and landscape architecture. It is the quantity allocation of building cover, parking cover, pavement, unpaved open space, and floor quantity in a site plan that determines shelter capacity options, context, and quality of life in mathematical terms equal to the leadership debate involved with city planning, real estate law, zoning regulation, economic development, and private enterprise. The mission is to establish a consistent leadership language for shelter debate and land consumption decisions on a planet that does not compromise with failure to anticipate.

Walter M. Hosack, July 2025