PURSUING URBAN DESIGN and ZONING KNOWLEDGE

I first began considering the capacity of land to accommodate gross building areas when I began studying architecture. At the time the land area given for the problem was always adequate. The site plan issue was one of parking, pavement, and unpaved open space quantity arrangement in relation to the building floor plan needed for the shelter activity assignment, and the floor plan could reduce its footprint by increasing its floor quantity. The problem included consideration of the assets and liabilities on and around the site. The amount of land consumed for shelter capacity was never an issue.

Land area adequacy became an issue in practice, but it was a function of what was available. Tailoring land consumption to productive capacity was a rural, agricultural concept. Eventually I realized that the urban concept of approximate land consumption based on prior land surveys and current availability was at the heart of arbitrary consumption, sprawl, and excessive intensity that was slowly consuming agriculture and the Natural Domain, but I was not prepared to accurately evaluate the land needed to shelter the activities of an owner.

This became more apparent when I confronted density regulation. I became aware that density and all other zoning regulations were not mathematically correlated with each other or with the land available. The combination of density, parking, floor quantity, setbacks and so on, were often irreconcilable because they were independent requirements. In many cases, the conflict could not be resolved without variance approval for regulation exceptions that were considered arbitrary by the opposition, and virtually impossible to track as precedent-setting standards by the arbitrators. I realized that the difference between the independent regulations of zoning law and the correlated, interrelated demands of shelter design decisions represented a collision of two different languages.

The problem became more acute in multi-family residential zones when an ordinance led land owners to believe that they could reach a permitted density when it was not correlated with their average dwelling unit size objectives and parking requirements, not to mention correlation with all other applicable, independent regulation topics. This inevitably led to suspicion, mistrust, variance requests, and wildly different interpretations of leadership intent in some cases.

THE FIRST EXPERIENCE

The issue crystallized for me when I was asked to evaluate a multi-family housing proposal and responded that the site plan appeared too compressed or “tight”. My opinion was based on the visual impression of a site plan based on years of exposure and experience, but the density regulation permitted more than was requested and the quantity had already been reduced. At this point it became clear to me that the debate revolved around regulations without correlation. They often permitted excessive shelter capacity, intensity, intrusion, and context compression in my opinion, and the method of density measurement was unequal to the correlation of design decisions required for adequate leadership guidance. Unfortunately, the implications in bold above had no quantitative definition. My interpretation had been learned as a product of trial-and-error education, and the intuitive lessons learned could be easily contradicted by the demands of an owner and the representations of legal counsel.

I came away knowing that the issue was mathematical, and that opinion needed a more quantitative and correlated mathematical foundation of experiment, evaluation, prediction, and conclusion before it could become a consistently credible leadership language. It had to be based on knowledge accumulation that recognized the interrelated, mathematical nature of design specification topics, values, and shelter capacity design decisions.

SEARCH FOR CONSISTENCY

My search for consistency began with the recognition that all human shelter falls into a limited number of building design categories when they are distinguished by their method of providing parking, including one that provides no parking. The result was six building design categories whose gross building area potential was a function of a given land area and a standard template of design specification topics and assigned values. I called the gross building area alternatives that could be achieved with optional floor quantities and design specification values shelter capacity.

Shelter capacity is equal to predicted gross building area options in sq. ft. per buildable acre of land occupied. The predictions are based on the values entered in the design specification template of the category. These gross building area options have shelter capacity, intensity, intrusion, and context implications that are calculated with separate, universal equations.

The collection of building design categories represents a set of forecast models with a consistent measurement system, predictive shelter capacity format, and related implication calculations comparable across all design categories and project installations. This is the measurement format I felt was needed to evaluate the shelter capacity of land and regulate its growth in a Built Domain geographically limited to protect its source of life – agriculture and the Natural Domain.

ACTIVITY GROUPS

Gross building area can be occupied by any permitted activity. Its internal capacity for activity varies with the specification values entered in a companion activity group template. The addition of an activity group template to a building category forecast model correlates the predicted gross building area options for land with each option’s internal capacity for the activity based on the specification values entered in the companion activity group template. The results have economic potential related to the scope of activity predicted within the gross building area options predicted.

I’ve illustrated the building design category-activity group relationship with the Residential Activity Group of specification templates in several previous essays. A more complete presentation is included in my book, “The Equations of Urban Design” available from Amazon.com.

CONCLUSION

Shelter capacity results have social, psychological, environmental, and economic implications that remain to be correlated with measurement and evaluation that can lead to knowledge regarding the quality of life implied by measurable alternatives.

Currently the Shelter Division of the Built Domain is served by Movement, Open Space, and Life Support Divisions in both the Urban and Rural Phyla of a Built Domain that is currently a parasitic threat to the Natural Domain. This threat cannot be addressed with debate over the details of independent, conflicting zoning regulations that require arbitrary adjustment, or land use master plans that depend on annexation of agriculture and the Natural Domain to address budget deficiencies based on land use activity and shelter capacity misallocation.

Shelter capacity evaluation is a measurement language capable of evaluating options and guiding decisions toward the goal of shelter for the activities of growing populations within limited geographic areas designated and designed to protect their quality and source of life, the Natural Domain. It is simply a classification and measurement language that can be used to pursue research and define conclusions capable of consistent leadership, however.

The Latin word for shelter, roof, or cover is “tegimen”. I pronounce it “tejimen”, even though this may offend Latin scholars, and would like to suggest the word “Tegimenics”, “Tegimenistics”, or "Tegimenology" as a label for those interested in pursuing the issue of shelter capacity and quality of life for growing populations in limited geographic areas on a planet in a universe that expects us to anticipate its unwritten Law of Limits. It is a language intended to give a quantitative voice and credible support for emerging but also ancient topics many refer to as urban design or city design with roots in architectural design.

SITE PLAN EXPLANATION

The forecast models I have discussed on many occasions depend on the site plan terminology I presented long ago. Figure 1 is an introduction for those who may be unfamiliar with site plans in general. There have been a few additions and adjustments along the way, but Figure 1 has been the foundation for all design specification topics and templates associated with a building design category. It is not comprehensive but can be a useful introduction.

PS:

This is a repeat of previous essay paragraphs.

“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 on Amazon.com 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 involving private enterprise and architecture, landscape architecture, government, city planning, real estate law, zoning regulation, and economic development. 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.

I also maintain a blog entitled, “Cities and Design” at www.wmhosack.blogspot.com that began in September 2010. It currently contains 258 essays for anyone interested in following the topic. The more recent essays are also included on LinkedIn.” 

Walter M. Hosack, July 2025

FIGURE 1

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

Shelter Capacity Design Dissection

 

The identification and definition needed to shelter the activities of growing populations within economically stable and geographically limited communities.

 

The term “dissection” in the title of this essay means the comprehensive, consistent identification, measurement, and evaluation of the design specification topics that define building mass and the related site plan features of a building design category. They do not operate independently. The values assigned to these topics must be mathematically correlated before their shelter capacity, intensity, and intrusion implications can be calculated and guided toward context results that represent a desirable quality of life and coexistence with our source of life.

There is no divine guidance that directs the growth and anatomy of shelter toward adequate organization, context, and coexistence. Master plans and zoning ordinances have been our attempt to provide guidance, but conflicting regulations, rezoning, variance requests, and annexation have randomly diluted their intent. This has often left us with sprawl, excessive intensity, diminishing agriculture, and a threatened natural source of life. The results have confirmed our inability to identify and evaluate the building design categories, activity groups, design specification topics, and topic values that must be mathematically correlated at the project level to consistently produce shelter capacity for the activities of growing populations within limited areas of the planet.

SHELTER CAPACITY

Shelter capacity evaluation involves the capacity of land to accommodate gross building area options, their related site plan features, and their shelter capacity, intensity, intrusion, and context implications. The shelter options are three-dimensional. The site support options are two-dimensional. Population density and activity options per square foot of gross building area measured or predicted are separate social issues.

Density has been an inadequate measure for the shelter capacity of land. It has not been able to bridge a gap that requires mathematical correlation of many related shelter capacity decisions before we can learn to protect the activities of growing populations within geographic limits defined to guard both their quality and source of life.

The dissection of a shelter project identifies the specification components and mathematical decisions that lead to the formation of shelter capacity, intensity, intrusion, and context in a limited land area long before appearance becomes an issue. Identification is not enough, however. Measurement, evaluation, and correlation are needed to define and predict the mathematical parameters that have physical, social, psychological, environmental, and economic leadership potential. The knowledge acquired can help us step beyond the random results produced by isolated and often conflicting zoning ordinance regulations.

BUILDING DESIGN CATEGORIES and ACTIVITY GROUPS

A building design category is distinguished by the parking system chosen to serve its occupants such as (G1), (G2), (S1), and so on. An activity group is the generic occupant activity historically referred to as “land use” such as (R) for residential. A shelter type is a unique form and arrangement of shelter for an activity group member such as a single-family home (R1); a townhouse (R2), or an apartment (R3). An activity group member is identified by the specification characteristics related to its building design category, occupant activity, and shelter type.

The first seven chapters in Table 1 address six generic building design categories that may be occupied by any permitted activity. Chapters 9-17 explain how these categories are used to accommodate the Residential Activity Group.

For example, a G1 or G2 Building Design Category is typically used to accommodate single-family occupancy members of the Residential Activity Group that are designated (R1) in Chapters 9-12. The characteristics of this group member are defined in the specification templates of its G1.R1 and G2.R1 forecast models. The values entered in the templates are either measurements or value entries used to predict gross building areas and building cover options for the land area given. The implications calculated for these predictions indicate the suitability of the values for the purpose intended. These shelter capacity, intensity, intrusion, and context implications are found using the secondary equations above the relevant columns in the model.

The G1 and G2 building design categories are also used to shelter the townhouse occupancy members of the Residential Activity Group that are designated (R2) in Chapter 13 of the Residential Activity Group. The characteristics of this group member are defined in the specification templates of its G1.R2 and G2.R2 forecast models. The values entered in the templates are either measurements or value entries used to predict gross building areas and building cover options for the land area given. The implications of these predictions indicate the suitability of the values for the purpose intended. These shelter capacity, intensity, intrusion, and context implications are found using the secondary equations above the relevant columns in the model.

Any building design category may be used to shelter apartment occupancy members of the Residential Activity Group designated (R3) in Chapters 14-17 of Table 1. The characteristics of this group member are defined in the specification templates of its G1, G2, S1, S2, S3, and NP forecast models. The values entered in the templates are either measurements or value entries used to predict gross building areas and building cover options for the land area given. The implications of these predictions indicate the suitability of the values for the purpose intended. These shelter capacity, intensity, intrusion, and context implications are found using the secondary equations above the relevant columns in the model.

The point is that the gross building area of a building design category may be occupied by any permitted activity, but subdivision of the gross building area for occupant activity may require additional design specification topics and values to define or predict the internal capacity of the building for the activity under consideration. The shelter capacity of the land for gross building area is a constant function of the building design category, site plan specifications, and floor quantity options that pertain to the generic building design category under consideration.

DESIGN SPECIFICATION TEMPLATE

Table 2 is an example introduced in many previous essays. It is included to show that the values assigned to the shaded cells in a design specification template are mathematically correlated by an architectural algorithm to predict their core area implications in cell F33 and G33.

The Design Specification Template in Table 2 is an example related to the generic G1 Building Design Category. The gray cells in the template represent a dissection of the category’s essential specification topics. The value assignments entered in the gray cells above cell F33 are mathematically correlated to determine their combined core area implications in cell F33 and G33.

The master equation in cell B39 combines this core value found in cells F33 and G33 with the additional specification values entered to find gross building area implications in cells B44-B53. These vary with the floor quantities entered in cells A44-A53 of the model. The gross building area options become the basis for all other predictions in the Planning Forecast Panel and Implications Module of the forecast model.

QUESTIONS and CHOICES

Our ability to shelter the activities of growing populations within geographic limits that protect our quality and source of life is the question that the equations in Table 1 have been derived to address. The forecast models and design specification templates involved with the answer offer the ability to measure, evaluate, and predict the implications of quantitative choices that have the potential to lead future shelter capacity, intensity, intrusion, and context debate and decisions. The templates do not make decisions. The intent is to improve the discussion by defining questions and potential answers with a common, quantitative language based on consistent measurement and evaluation. This can make it possible to express options and decisions with a credible leadership vocabulary and language equal to the challenge.

ECONOMIC IMPLICATIONS

A building can shelter any permitted activity. The correlation of shelter capacity, intensity, activity, and location of a building has context, quality, and economic implications.

Private investment implications are limited to the specific project costs involved and the profit per square foot potential of the activity, location, and scope anticipated.

Public implications concern the combined revenue potential per acre of municipal land consumed by a city’s combined shelter capacity, intensity, intrusion, and activity decisions for all projects in the city, since the average revenue received from all taxable acres must equal a city’s annual cost per acre for operations, maintenance, improvement, and debt service. In other words, land use allocation for shelter capacity, intensity, intrusion, activity, and context represents the content of a city’s investment portfolio and the yield available to serve its population.

To my knowledge, no city can comprehensively monitor and adjust the relationships between shelter capacity, land use allocation, and revenue potential at the parcel, block, tract, or zone level of the community. In the absence of this ability to monitor and correlate, a city must rely on annual budget estimates and random economic development initiatives. These initiatives represent hope without the data, evaluation, knowledge, and vision required to increase revenue for the quality of life desired, and hope is not a strategy.

FINAL COMMENT

An improved method of definition, measurement, evaluation, and expression is needed before leadership debate can credibly address the issue of shelter capacity for the activities of growing populations within land areas limited to protect their source of life and improve their quality of life.

Walter M. Hosack, July 4, 2025

 

LEARNING TO LEAD SHELTER CAPACITY DESIGN DECISIONS

 The G1 Building Design Category includes all buildings with a surface parking lot adjacent to, but not under, a building on the same premises. The maximum gross building area that can be provided to shelter permitted activity is a function of the core land area remaining for parking cover and building cover after all other demands and/or land deficiencies are subtracted from the gross land area given.

When the core area is multiplied by the coefficient in parentheses in Equation (1), the result is a maximum gross building area forecast (GBA) that increases with the floor quantity considered. The equation for this G1 shelter capacity relationship is:

Equation (1):

G1 Building Design Category 

GBA = ((a/f) / (a + (fs))) * CORE

 When: 

GBA = gross building area

a = total parking lot area per parking space in sq. ft.

f = floor quantity

s = parking lot area per parking space in square feet

CORE = land area remaining in square feet for parking cover and building cover after all other demands and/or land deficiencies are subtracted from the gross land area given. 

The values (a), (f), and (s) in Equation (1) are variable design decisions. The importance of accurately defining the core area available for use in this equation is imperative and will be discussed.

The forecast model for Equation (1) is included as Table 1. Lines 3-33 are devoted to the derivation of the core area (CORE) remaining in cells F33 and G33 for parking cover and building cover after all other demands and/or land deficiencies are subtracted from the gross land area given. This includes the percentage of unpaved open space (S) to be subtracted from the buildable land area in cell F11. It is a critical decision because it offsets the amount of building cover, parking, and pavement (impervious cover) that produces storm water runoff; and that must be accommodated by the storm sewer capacity planned or present. It is also a critical factor contributing to the amount of physical intensity introduced to a given land area. These Table 1 decisions produce the shelter capacity, intensity, intrusion, and context implications calculated in cells F44-J53.

Table 1 has been discussed many times. It is used to find the G1 shelter capacity of land based on the design specification variables entered in the shaded cells of its G1.L1 forecast model. It has been customized for this example by entering one acre in cell F3 and zero in all other shaded cells except F3, F11, A35, A36 and A44-A53. The combination represents a land area unencumbered by land deficiencies and miscellaneous pavement provisions.

In other words, the core land area (CORE) found in cell F33 is equal to the gross land area given minus the unpaved open space quantity specified in cell F11. This is the greatest the core area can be, unless the unpaved open space percentage entered in cell F11 is reduced.

The values entered for (s), (f), and (a) in cells A35, A36, and A44-A53 are needed to calculate the coefficient in parentheses in Equation (1). A change to one or more of the values entered changes the coefficient and the gross building area options calculated. Since no miscellaneous pavement area percentages are subtracted, the gross building area predictions in cells B44-B53 are maximum forecasts based on the values entered and the core area defined.

The point is that G1 shelter capacity on a given land area is the product of its core area multiplied by a coefficient that is formed from three design decisions. When a gross land area of one acre is given and an unpaved open space percentage is subtracted from the buildable land area to find the core area remaining, the coefficient indicates the percentage of the core area that will equal the gross building area capacity of any given land area when considering the G1 building design category. Table 2 has been created to illustrate the point along with a few observations below. Be careful to note in this example that the core area example is equal to the one acre given minus the unpaved open space percentage noted with each schedule of the table.

The values entered in the gray cells of Table 2 indicate given information. The coefficients calculated in the white cells of each schedule in the table indicate the fraction of any core land area that can become G1 gross building area given the conditions chosen to identify the coefficient multiplier at their intersection. Obviously, the accurate definition of core area for use with the coefficients in each schedule is critical, and the temptation to reduce unpaved open space (S), increase the gross building area planned or permitted per parking space (s), and increase the floor quantity (f) under consideration will increase potential gross building area. The temptation to overlook unbuildable, unstable, environmental, historic, archeological, woodland, water, public roadway, wetland areas and so on can also increase since their subtraction reduces the core area available for building footprint area. However, considering any of these areas as part of the core area available represents an attempt to artificially inflate the shelter capacity of a given land area. The increasing intensity and intrusion calculations that result would represent a decline in the context anticipated.

Keep in mind that Table 2 is meant to display maximum possibilities based on a core area that has no miscellaneous pavement percentage estimate subtracted. It has been omitted because it cannot be consistently predicted, but an estimate should be subtracted from the core area available before gross building area prediction when a specific project makes a more accurate forecast possible.

Table 3 has been included to illustrate the increase in gross building area percentages of core area (coefficients) that occur when the incremental unpaved open space allocation declines from 40% to 20%.

A comparison of the coefficients in Tables 2 and 3 should illustrate a very limited picture of the tug-of-war that has occurred between architects, planners, urban designers and real estate interests when the shelter capacity, intensity, intrusion, and context implications of design specification decisions could not be measured, predicted, and evaluated on a uniform scale for comparison, and leadership direction. Equation (1) has made it possible to find common ground.

Tables 2 and 3 are a very small window into the spectrum of shelter capacity decisions that can lead us to shelter the activities of growing populations on geographic areas scientifically limited to protect their quality and source of life. I have written “The Equations of Urban Design” to crack the window for those who may be interested in pursuing the measurement, evaluation, knowledge, and decisions required to lead us in a direction that will respect the planet’s unwritten Law of Limits. Opinion without measurement and evaluation on a consistent, comparable physical scale of shelter capacity evaluation will not get us there.

Walter M. Hosack, June 2025

PS: Density is a social measurement that has attempted to lead physical decisions without the comprehensive shelter capacity specifications and mathematical correlation required. This essay has attempted to offer a glimpse of the building design categories, design specifications, algorithms, master equations, and implication predictions involved with urban design decisions and discussed in detail in the book just mentioned. I am leaving research, measurement, evaluation, knowledge acquisition, and leadership decisions to those interested in applying the vocabulary and language provided.

Eliminating Hope as a City Design and Zoning Strategy

 Shelter capacity is provided for activity on an intensity scale that ranges from minimal to life threatening; but perception, intuition, and approximation have had to substitute for correlated mathematical guidance capable of consistently reproducing success and avoiding failure or variance compromise. The result has often been low-intensity, sprawling consumption of agriculture and the Natural Domain, or excessive intensity attempting to improve return on investment with the physical concentrations of building mass and pavement on limited land areas.

The challenge is to derive accurate, consistent measurements of shelter capacity, intensity, intrusion, and context that can lead the design and construction of shelter capacity in a Built Domain served by movement, open space, agriculture, and life support systems that must coexist with its source of life -- the Natural Domain.

SHELTER CAPACITY and INTENSITY

To begin with, shelter capacity is gross building area in square feet per buildable acre occupied. It is a mathematical function of a building design category choice, values entered in its design specification template, and a category master equation that predicts gross building area options in sq. ft. based on the specification values and floor quantity alternatives entered. These options, when divided by the land area consumed in buildable acres, form mathematical increments of shelter capacity. When shelter capacity is multiplied by the impervious cover percentage present or planned and divided by 10,000, the result is a measurement of physical intensity.

THE ECONOMIC IMPLICATIONS of SHELTER CAPACITY, INTENSITY, and ACTIVITY DECISIONS

Real estate profit and public revenue implications vary with the shelter capacity, intensity, and activity planned or present on a given land area. Activity produces income per square foot of gross building area occupied. Shelter capacity is the gross building area present or planned per buildable acre in square feet. The product of shelter capacity in sq. ft. times the expected income or revenue per sq. ft. of activity divided by the buildable acres occupied produces an estimate of the total income or revenue that can be expected per acre by the combination. This result has quality of life implications when the average revenue received per buildable acre from a city’s total shelter capacity, intensity, and activity allocation is less than the city’s total cost to provide the operational, maintenance, improvement, and debt management services required to maintain a desired quality of life per acre. This mathematical relationship adds economic meaning to the rather ambiguous planning term “balance”. A negative balance means that a city’s quality of life can be compromised, or even blighted, by the budget reductions required.

OUR LIMITED ABILITY TO MONITOR LAND USE ALLOCATION IMPLICATIONS

A city’s allocation of land for shelter capacity, intensity, and activity defines the composition of its physical investment portfolio and the annual income (revenue) it will receive from these decisions. Annexation of more land for new income with deficient revenue potential over time is a short-term Ponzi solution, but difficult to predict with the paucity of relevant data and processing ability available to lead a city’s long-term land investment portfolio.

Community satisfaction with the scope of services being provided is a political issue beyond the scope of this essay. In any case, the annual cost per acre for the public services provided must be less than, or equal to, the total revenue a city receives from its land use allocation of shelter capacity, activity, and intensity. Unfortunately, most if not all cities do not have the shared data, relational databases, algorithms, and geographic information systems required to measure, evaluate, debate, correlate, and adjust their land use allocation of shelter capacity, intensity, and activity in relation to their fluctuating annual operating, maintenance, improvement, and debt service expense.

THE OBJECTIVE

The challenge is to define and monitor a sustainable balance between the Natural and Built Domains on a limited planet, AND the sustainable correlation of shelter capacity, intensity, and activity needed to produce a desirable physical, social, psychological, environmental, and economic quality of life for growing populations within a limited Built Domain.

THE LEADERSHIP NEEDED

The spectrum of shelter capacity and intensity possibilities is vast. Sprawl is at one end of the spectrum and excessive intensity at the other. These extremes have been too-frequent results from market experimentation that continues to promiscuously consume available urban, rural, and natural land with annexation and rezoning that thrives on a city’s deficient analytical ability.

Experimentation without a mathematical language of measurement, prediction, and evaluation equal to the leadership evaluation and guidance needed will leave us without the correlation required to produce the coexistence expected by the planet’s unwritten Law of Limits. It directly contradicts our pursuit of unlimited growth.

THE SPECTRUM of SHELTER CAPACITY and INTENSITY CHOICES

It is possible to mathematically define the shelter capacity and intensity spectrum of possibilities along with their intensity, intrusion, and context implications. The graduated increments can be measured and predicted with the building design categories, design specification templates, master equations, and forecast models of Shelter Capacity Evaluation. They have been introduced in “The Equations of Urban Design” that I self-published on Amazon.com in 2020. Leadership choices will involve the correlation of project options and implications predicted by these equations.

RESEARCH

The consistent measurement of existing examples and evaluation of their implications is needed to improve our knowledge and leadership decisions regarding shelter capacity in a Built Domain because its sprawling expansion must be limited by public policy to prevent consumption of its source of life.

THE MEANING of ARCHITECTURAL INTENSITY

The concept of “physical intensity” has often been associated with extreme relationships perceived but not defined with an adequate mathematical vocabulary.

In the context of this essay, and all others I have published, the term “intensity” (INT) is not an extreme condition. It is a mathematical spectrum, or range of building mass, pavement, parking, and unpaved project open space relationships that range from non-existent to life-threatening. Its implications are measured with the following sequence of equations when a gross land area, building design category, and template of design specification values is given as illustrated in Table 1.

(1)   Gross building area potential GBA = ((af) / (a+(fs))) * CORE. The value (a) is equal to the gross building area in sq. ft. permitted per parking space provided. The value (f) is a floor quantity option. The value (s) is the parking lot area in sq. ft. per space provided. The value (CORE) is the gross land area remaining for building and parking cover after all other existing and/or anticipated unbuildable areas, rights-of-way, impervious cover, shared spaces, reserve areas, unpaved project open space quantities, and so on are subtracted from the gross land area given. This core area quantity varies with the design specification template topics and values associated with a given building design category and specification values entered.

(2)   Shelter capacity implications SFAC = GBA / BAC. The gross building area GBA found in equation (1) is divided by the buildable acres BAC derived in the design specification template of a given building design category to find the shelter capacity options under consideration.

(3)   Intensity implications INT = SFAC * IMP% / 10,000. The shelter capacity SFAC found in equation (2) is multiplied by the total impervious cover percentage present or planned for the project area. The product is divided by 10,000 to find the intensity represented.

(4)   Intrusion implications INTR = f / 5. The effect of floor quantity (f) on the relationship of building mass, parking, pavement, and unpaved project open space is considered by equation (1), but its influence can be buried in the result without the attention provided by equation (4).

(5)   Context implications CTX = INT + INTR. The spatial impact of a shelter project on pedestrians at street level, without considering building façade appearance, is defined by combining the intensity found in equation (3) with the intrusion found in equation (4). This purposely emphasizes the impact of floor quantity on the spatial context represented by the measurement since floor quantity is also a factor in equation (1).

The point is that shelter capacity, intensity, and intrusion combine to produce physical context on a scale that ranges from excessive shelter concentration to natural absence. The range is intuitively perceived but has never had an accurate method of measurement and evaluation that could identify a desirable shelter intensity range within specified land areas for all seven building design categories.

TABLE 1

Table 1 is included to point out the context measurements CTX in cells J44-J53. They are a function of all the design specification values entered into the shaded boxes of the table, the cascading equations in the design specification template, and the implication calculations presented in cells B44-J53. There are no judgments assigned to these context calculations.

OPPORTUNITY

The use of shelter capacity evaluation for consistent measurement and evaluation of existing shelter projects can produce the knowledge needed to successfully correlate shelter capacity, intensity, activity, and economic decisions within a sustainable Built Domain. This is the future challenge associated with the seven primary building design categories and the shelter capacity evaluation system of urban design. 

ECONOMIC DEVELOPMENT

The mathematical correlation of shelter capacity, intensity, and activity on every parcel within a city has revenue implications that combine to affect a city’s physical, social, psychological, environmental, and economic quality of life.

I doubt that any city has recorded its shelter capacity, intensity, and intrusion measurements with the context and total revenue per acre it receives per parcel, block, tract, or zone. This, however, would permit it to compare the total average revenue per acre received per parcel, block, tract, or zone with its total expense per acre. The comparison could not help but contribute to the debate and decisions needed to produce an advanced comprehensive strategy for improvement.

The alternative has been piecemeal economic development hoping for “big scores” to offset revenue deficiencies. This includes mistaken annexation for “new money per acre” that cannot keep pace with a city’s increasing average annual expense per acre. It results from an inadequate ability to accurately monitor and understand the shelter capacity, intensity, activity and revenue relationships present per block, tract, and zone within its boundaries. This prevents comprehensive adaptation and adjustment with the knowledge required to eliminate hope as a strategy.

FUTURE WORK

There are no current examples of the effort I suggest to my knowledge. All my work has been a theoretical attempt to answer the question: “How do we shelter the activities of growing populations within geographic limits that protect their quality and source of life?” 

During this effort I have suggested the question and a method of pursuing the answer with shelter capacity evaluation based on proposed building design categories and equations for urban design definition of leadership solutions. It represents a new vocabulary and language. The use of these tools to build and apply leadership knowledge will not be proven without technical applications pursued by interested readers around a planet we cannot pollute and consume without consequence.

Walter M. Hosack, June 2025

PS: Don’t be distracted by legal solutions that overlook the mathematical, architectural fundamentals required for shelter correlation and urban design leadership. Annexation and variance approvals attempting to reconcile a lack of mathematical correlation have never been an adequate, comprehensive answer to the issues of population growth, land consumption, encircled cities, budget deficits, and deterioration.

Hosack Blog Index: 10.2.2010 to 6.6.2025

I recently published a list of essays. The list, however, was buried in another essay. I also didn’t make it clear that the essays posted to LinkedIn began in June 2016, but the first essay was posted in October 2010 on my blog at this location. The entire list has had quite a few additions since my last update and is indexed by date below.

The Relationship of Shelter and Space to Survival

 I asked Google for the essential elements of survival and got the following response:

“The fundamental requirements for survival include air, water, food, shelter, sanitation, sleep, space, and touch.”

I assume that “space” was chosen because “land” can be excessively occupied to threaten survival, but “adequate space on land” was too cumbersome in context. In fact, the unmentioned assumption throughout the sentence is “adequate quantity and quality”. Space on land, however, is my point of reference in this essay.

I expected to see “shelter” but was surprised by the presence of “space” in the Google sentence. Shelter and space are the building blocks of architecture and urban design. They have been associated with fine art rather than survival because we have been distracted by their final appearance. The importance of shelter and space to survival seems self-evident, but the fundamental issue is their quantity and quality on a planet that must share its space with the shelter we need and the environment our source of life requires.

SHELTER CONTEXT

Shelter mass combines with pavement and unpaved open space in quantities that produce a spectrum of physical intensity options. They range from “sprawl” to “excessive intensity” in defined project land areas. The issue of survival enters the picture because excessive shelter sprawl threatens to consume our source of life and excessive shelter intensity is a threat to our health, safety, and quality of life. The devil is in the definition of “excessive” and “intensity” because the terms have simply been undifferentiated ranges on the missing yardstick of “intensity”. We have been distracted from these measurements by the appearance of a shelter result that has always begun with these intuitive, unwritten intensity decisions for the land available. Google has reminded us that survival is at stake. Literature warns us to avoid judging a book by its cover. Architecture, urban design, city design, and city planning should judge both – in my opinion.

The relationship between shelter and space in the Built and Natural Domains is the least understood among the survival topics mentioned by Google. It involves a rather simple commandment, however. We must provide adequate shelter capacity for growing population activity within space that must be limited to coexist with that required by a Natural Domain that is its source of life.

The issue we face is the “quantity and quality” of space that must be provided for both the Built and Natural Domains, and the shelter capacity of the space allocated for the Built Domain, since it must also accommodate the arteries of movement, open space, and life support that serve its urban and rural phyla. The Natural Domain requires space to serve the ecology that is our source of life. The relationship is inherently unstable when human motivation remains growth without limits on limited land area.

SHELTER INTENSITY and CONTEXT

Shelter capacity options produce a spectrum of physical intensity results with “sprawl” at one end and “excessive intensity” at the other, but the spectrum of shelter capacity, intensity, and context has never been mathematically defined. These conclusions have remained matters of perception, intuition, and unsubstantiated opinion. In fact, sprawl is simply a degree of intensity, and the spectrum can be mathematically measured and predicted.

SHELTER CAPACITY

The “equations of shelter capacity evaluation” have been derived to produce intensity, intrusion, and context measurements from design specification values entered in their forecast models. The equations and models are included in a book of the same name. They represent the leadership vocabulary needed to mathematically measure, evaluate, predict, and lead the shelter capacity of land and the economic organization of activity for growing populations within geographic limits scientifically defined to protect their quality and source of life.

Shelter demand for activity has often been answered with unlimited sprawl or excessive intensity. One threatens our source of life and the other threatens our quality of life. Improvement will require the correlation of shelter capacity, intensity, and activity options to consistently produce economic stability and a desirable quality of life within limited geographic areas.

Shelter capacity is the amount of gross building area in square feet present, planned, or possible per buildable acre of designated project land area. It can be occupied by any activity permitted in a zoning district. It can be measured, predicted, and evaluated based on a building category forecast model and values entered in the category’s design specification template. The values entered can be measurements or design options correlated by the forecast model algorithm to produce consistent shelter capacity, intensity, intrusion, and context measurements. 

LEADERSHIP DECISIONS

Leadership decisions based on mathematical evaluation are the only way to emerge from the morass of undisciplined, emotional opinion that continues to promiscuously consume the land while overlooking the fundamental correlation and mathematical allocation required to achieve a desirable, economically sustainable quality of life– in my opinion.

In this discussion, “space” has meant land used for the construction of shelter, movement, open space, and life support in the Built Domain. It has also meant land in the Natural Domain that is our source of life. Defining the relationship between these two spatial domains, and the adequate quantities needed to serve each, will demand far more accurate attention, evaluation, and leadership than presently committed. Fortunately, the foundation for leadership opinion can be mathematical evaluation.

A FORECAST MODEL

I’ve discussed the building design categories, forecast models, design specification topics/values, and master equations related to shelter capacity measurement, evaluation, prediction, allocation, and land consumption in many essays. The discussions have focused on mathematical values entered to define topic quantities in the design specification module of a building design category forecast model. These project value options are correlated by the model’s algorithm to calculate their combined planning and design implications. These shelter capacity, intensity, and context implications can then be evaluated for their potential to establish correlated physical, social, psychological, environmental, and economic stability within neighborhoods, districts, cities, and regions. The caveat for the process is that the shelter capacity of the Built Domain cannot be permitted to consume its source of life.

Forecast Model G1.L1 in Table 1 illustrates the primary mathematical terms and equations associated with shelter capacity evaluation for the G1 Building Design Category when gross land area is given. The forecast model, given information, forecast objective, and design premise are explained in the first four lines of the model.

Optional design specification values have been entered into the 26 gray cells of Table 1 to illustrate the operation of the model. The equations in cells H3-H33 convert these percentage values to their equivalent sq. ft. values in cells G3-G33. The objective is to find the CORE value in cell G33 for use in the master equation located in cell B39. The master equation combines this value with the parking quantity (s), parking area (a), and floor quantity (f) values entered in cells A35, A36, and A44-A53 to find the gross building area (GBA) options listed in cells B44-B53. These gross building area options are key to the forecast and are a function of the floor quantity options (f) entered in cells A44-A53. All remaining planning and design implications predicted in cells C44-J53 are a function of the gross building area options predicted in cells B44-B53.

The measurement predictions in the Implications Panel of Table 1 have physical, social, psychological, environmental, and economic implications that can be organized and evaluated in relation to these measurements to build knowledge and leadership direction. This can assist in forming the knowledge needed to consistently improve context results without dictating appearance.

CONCLUSION

I was gratified to see “shelter” and “space” mentioned as essential elements of survival, but these elements are topic titles. They do not indicate the essential quantities and intensity levels required for the survival of growing populations on a limited planet with a desirable, sustainable quality of life.

The building design category classification system, specification topics, and equations supporting Shelter Capacity Evaluation are also topic names that require quantity and quality evaluation. The results can be used to build leadership knowledge. Knowledge itself will remain a mystery until consistent measurement, evaluation, correlation, and prediction produce desirable shelter capacity and activity allocation within sustainable geographic limits. This is the foundation needed to support the fine art and quality of life that can emerge - in my opinion.

Walter M. Hosack, June 2025