Design Decisions That Determine Apartment Density

 

An apartment is a one floor leased or rented dwelling unit that may be subdivided from any one of six building classification categories. The apartment activity group is designated R3 and often referred to as a land use category.

Land use is social activity that occupies a physical shelter classification, and social activity is served or subjected to the intensity of the physical shelter and surroundings provided.

A building design category is classified by the primary method of parking used to serve its occupant activity.

A G1 Building Design Category includes all buildings served by a grade parking lot around, but not under, the building on the same premise.

Apartment density is the product of 42 initial design decisions when a G1 Building Design Category is subdivided to create R3 dwelling units. Ten of these decisions are often limited by local zoning regulations. The remaining 32 are discretionary. The combined decisions may not produce a dwelling unit quantity greater than that specified by a density limit in a zoning ordinance (without public variance approval). Density does not lead these 42 decisions however. It is a product of them, and correlation of these decisions to respect a density limit depends on instinct, intuition, and opinion referred to as talent at the present time. Consistent success will remain arbitrary and elusive until we can accurately predict the results produced by these 42 decisions and lead them to produce shelter for growing populations within limited geographic areas defined to protect their quality and source of life.

The 42 apartment decision topics are identified in Table 1 with a gray tone. Ten zoning requirement topics are designated with solid black lines around their respective gray cells, but the values entered are not consistently mandated in all zoning ordinances. The values entered in the 32 remaining gray cells are discretionary. The 42 values involved have been mathematically correlated in the Table 1 forecast model to produce results in its Planning Forecast Panel, Implications Module, and Dwelling Unit Forecast Panel. If one or more of the gray cell values is modified, the results calculated will adjust in response.

If we look at the 3 story building specified in cell A58 of Table 1, the correlation of the 41 related gray cell values entered above produces the results summarized on line 58 and the density calculated in cell N58. Any change to one or more of the gray cell values entered will produce a revised set of implications in the forecast model.

Density is a very inaccurate measure of the shelter capacity, intensity, intrusion, and dominance produced on a given land area by the 42 correlated design decisions itemized in Table 1, however; because the number of dwelling units permitted may be any size and pavement may be permitted in many required yard areas. The result can easily become excessive quantities of impervious cover threatening existing storm sewer capacity and surrounding quality of life. These lifestyle outcomes can now be measured with the equations in cells H50 and H51. Their conclusions are presented in columns K and L of the Implications Module based on the values entered in the gray cells of Table 1.

Zoning intent has been to leave at least 32 of the values entered in the gay cells of Table 1 flexible as long as the density limit is not exceeded, but this sacrifices the leadership needed to ensure that shelter capacity, intensity, intrusion, and dominance do not become excessive on the land area subject to these 31 decisions, since the intent behind these decisions is not necessarily in the public interest.

The combination of building mass, pavement, and unpaved open space quantities that emerge on a given land area are a function of the 42 site planning / massing design decisions entered in the gray cells of Table 1. This collection of decisions could be called a quantity recipe for an urban design site plan. These quantities are mathematically correlated by the equations in the forecast model to produce the intensity calculations included in the Implications Module of Table 1; and many different levels of density and intensity can be created by adjusting the values assigned to these 42 topics. The lack of itemization and correlation of these values has led to the random and often excessive intensity levels we attempt to escape in every sprawling Built Domain we have created.

POSTSCRIPT

It would be a simple matter to discuss any project values entered in the gray cells of Table 1 with all public and private parties involved at a common round table. The established mathematical relationships of the forecast model would quickly determine the development capacity of the land based on the mandatory and discretionary values entered. The focus would then center on the alternatives created and the implications produced by adjusting the discretionary values entered. The mandatory values could also be examined for variance opportunities. Decisions would be based on accumulating knowledge formed by measuring and evaluating these topics at existing locations to determine shelter capacity, intensity, intrusion, dominance, and density to be emulated or avoided with reasonable assurance that success could be duplicated and failure avoided. This would convert contentious disputes over isolated zoning requirements to a common focus on the correlated site plan / massing values that can correlate the development capacity of land with its intensity, intrusion, dominance, density, and quality of life potential.

I have deleted most of the equations in Table 1 to simplify the illustration and have omitted a detailed discussion of the Building Design Category and Residential Activity Group classification mentioned in this brief essay. If you are interested, these equations and discussions can be found in my book, The Equations of Urban Design, which is available from Amazon.com. (I discovered an error the cell N55 equation of Table 14.2 and Table 14.5 that will be corrected in future editions to conform to this essay.)

Measuring the Intensity of Place

The spaces surrounding building mass in a project include varying amounts of service pavement, social pavement, and unpaved landscape open space. The spaces combine with building mass to form the physical intensity of the places we traverse. The intensity present produces a spectrum of emotional response that ranges from phobia through ambivalence to inspiration. The levels of stress created have not been correlated with the levels of intensity introduced, however; because the intensity of place has remained a perception without calibration. Density and the floor area ratio are the closest we have come to methods of measurement, but both have failed to completely hold the reins of leadership required. They are symptoms that result from more fundamental decisions. These decisions are the quantity choices that combine to form the intensity of mass and space that we find in our neighborhoods, districts, cities, and regions.

Dimensions have been used to measure building mass and space, but their percentage equivalents have often been overlooked as the project recipe involved. These quantities measure the intensity of place while dimensions are limited to the shape and size of the land available. I’d like to begin explaining myself by introducing Table 1. It itemizes the topics whose quantities are currently correlated by trial and error to produce the shelter capacity and intensity implied by illustrated site plans.

Table 1 applies to all buildings served by a grade parking lot around but not under the structure when gross land area is given. The measurements entered in the gray cells of Column G are those of the project entitled Bradenton Office. They are the traditional square foot measurements of architecture and subtraction is used to define a new area I’ve referred to as “shelter area remaining” in cell G17. It is composed of impervious cover in cell G19 and unpaved open space in cell G20. The amount of impervious cover available in G19 is found by subtracting the amount of unpaved open space in cell G11 from the buildable land area available in cell G10. It also represents the storm sewer runoff capacity required. The corresponding percentages in Column F track the quantity allocations measured in Column G. These percentages represent a project recipe that could be applied to a land area of any size.

The objective of the first seven gray boxes in Column G of the Core Module of Table 1 is to identify all miscellaneous pavements that reduce the impervious cover remaining for parking lot and building footprint area. The sum of these miscellaneous impervious areas is located in cell G30. It is subtracted from the impervious area available in cell G19 to find the impervious area remaining in cell G33. This is the core area that is available for surface parking and building footprint area.

The Bradenton footprint consumed 21,667 square feet of its core area as noted in cell C46. The three floors noted in cell A46 transformed the footprint into 65,000 square feet of gross building area as noted in cell B46. The remaining 109,330 square feet of core area was used for the parking lot measured in cell D46. Two-hundred and sixty parking spaces were provided in this area for an average of 420.5 square feet per space as calculated in cell A35. The parking space quantity provided was equal to a provision of one space for every 250 gross square feet of building area as calculated in cell A36.

Gross building area in this context is a generalized measurement referred to as building mass. Mass is equal to floor plan area times floor quantity when floor plan area is defined by a simplified building perimeter that ignores architectural articulation. The result is an indication of building volume, or mass that encloses all detail and combines with pavement to form impervious cover. It is offset by the unpaved landscape open space quantity provided.

The implications of the massing just measured are calculated by the equations in cells F43–J43 of the Implications Module. The first of these equations explains that the specification values entered in the gray cells of Table 1 combine to produce 12,428 square feet of shelter area per buildable acre. This is referred to as shelter capacity. The second explains that the shelter capacity calculated represents an intensity of 0.752 in cell G46. The third explains that the 3 story height produces an intrusion value of 0.6, and the fourth explains that the sum of intensity and intrusion produces a dominance value of 1.352. This is the point where evaluation can begin based on an objective classification system for the place or places created.

The project I chose for this example is located on a street with low pedestrian and vehicular volumes. If the volumes were greater, the intensity of 0.752 could have been multiplied by a factor greater than 1 for each mode and level of adjacent traffic. In fact, the basic intensity value could be multiplied by a number of related factors such as sound pressure level and air quality to refine the sophistication of the measurement.

I do not intend to offer an evaluation of the measurements presented. My objective is to demonstrate that it is possible to classify the places we create for evaluation, knowledge accumulation, and leadership consistency. Conclusions will always remain in the realm of opinion, but there are few verdicts that do not rest on this foundation. The challenge is to give them greater credibility with the method of knowledge formation employed.

The values entered in the gray boxes of Table 1 were primarily square foot areas. The values calculated in the white cells of Col. G were also square foot areas based on the equations in Col. H. These areas had their percentage equivalents calculated by equations that were not displayed to avoid confusion. These percentages are the keys to much greater planning and urban design potential that I will explain with Table 2.

Table 1 presented the capacity and intensity implications of one set of project measurements related to a given land area and three story building. Table 2 uses the same given land area, but illustrates the options that can be predicted when percentage values replace the square foot measurements entered in the gray cells of Table 1. These percentages are entered in the Table 2 gray cells of Col. F. Their square foot implications are forecast in Col. G by the equations in Col. H.

The master equation entered in cell B39 of Table 2 applies to Building Design Category G1 and has been added to predict gross building area options for the floor quantity options entered in cells A44-A53. The ability to accurately predict gross building area options in cells B44-B53 will become increasingly important as we attempt to coordinate shelter capacity with intensity in geographic areas that are limited to protect our source of life. I will show in Tables 3 and 4 that the gray box specifications in Table 2 can easily be modified to evaluate shelter capacity options for a limited land area based on the intensity and quality of life desired.

The master equation in cell B39 of Table 2 applies to Building Design Category G1 and indicates the pivotal points of shelter capacity discussion when gross land area is given. The core area in this equation is a function of the values entered in the gray cells of Col. F. It is found in cell G33 and will adjust whenever one of its constituent values is modified. The second and third factors in the discussion are parking related and entered in cells A35 and A36. The value in cell A36 is a zoning regulation that varies with the land use activity involved. The value in cell A35 reflects the total parking lot area that will be provided per space. It is discretionary above a minimum standard and indicates the extent of landscaping that will be included with the parking spaces provided within the parking lot perimeter. The fourth factor in the discussion is floor quantity. Options are entered in cells A44-A53 and related gross building area alternatives are calculated in cells B44-B53 by the master equation in cell B39. Related building footprint and parking design implications are predicted in the remaining columns of the Planning Forecast Panel.

The existing Bradenton Office project is classified by the data on line 46 of Table 2, but the table illustrates that an unlimited number of shelter capacity options were available during the planning stage since the calculations will change whenever one or more of the gray cell specifications is modified. Rapid calculation of these options will become increasingly helpful as we attempt to balance the shelter demand of growing populations with the quality of life produced by the increasing intensity required to avoid the sprawling consumption of land. Tables 3 and 4 have been created to illustrate how these options can be created with a few keystrokes.

I haven’t changed the land area under consideration in Table 3 in order to facilitate comparison with Tables 1 and 2, but have adjusted the three remaining points of primary discussion. The amount of unpaved open space planned in cell F11 has been reduced to 25%. The amount of parking lot area per space has been reduced to 400 in cell A35 (This means that little landscape area will be provided within the parking lot perimeter), and the parking requirement in cell A36 has been reduced to one space for every 300 square feet of gross building area. The result is an increase in gross building area potential from 65,000 square feet to 97,435 square feet and an increase in shelter capacity from 12,428 square feet to 18,630 square feet per acre when the same three story floor quantity is considered. Intensity increases from 0.752 to 1.397, however; and dominance increases from 1.044 to 1.997.

I don’t mean to imply that the intensity increase above is desirable. I am simply trying to illustrate the efficiency of land use evaluation that can be produced with a standard classification and measurement system for the Shelter Division of our Built Domain. For instance, Table 4 can be produced with a few keystrokes if the previous intensities are considered too high.

The open space value in cell F11 of Table 2 has been revised to 50% in Table 4. This single change means that intensity has dropped to 0.444 from 0.752, but three-story gross building area potential has also dropped to 46,398 square feet from 65,000 square feet because more unpaved open space is being provided. In fact, Table 4 predicts that the 65,000 square feet of gross building area in Table 2 cannot be reached with a ten-story building when the unpaved open space increases from 39.5% to 50% and all other specification values remain the same.

The Bradenton Office first appeared on pg. 219 of my book Land Development Calculations published in 2001 by The McGraw-Hill Companies, but the measurements were disorganized compared to those in the attached tables. It also contained no shelter capacity, intensity, intrusion, or dominance measurements and no master equation. The measurements in this essay document what we know intuitively. This is a suburban office building with more than average unpaved open space allocation and a modest three–story building height. The picture tells you that some attention has been paid to the grading and plant material added along the street frontage, and additional open space remains to the rear along a stream and its floodplain, but it will win no architectural design awards.

It will take thousands of these project measurements and evaluations to build a library of knowledge that can successfully lead real estate development toward shelter for the activities of growing populations on land areas that do not sprawl to threaten our quality and source of life.

There is much to learn about the shelter capacity, intensity, intrusion, and dominance of the places we create, and sprawl reveals our current lack of knowledge and leadership ability. When rigorously classified, there are only six building design categories providing shelter for activity across the planet, and a limited number of master equations that control the capacity, intensity, intrusion, and dominance they produce. If you would like to learn more, and become one of the knowledge-builders, please see my book, Equations of Urban Design, published in 2020 on Amazon.com.

CONTRIBUTING KNOWLEDGE

 

I have recently self-published The Equations of Urban Design: Leading the Evolution of Shelter Capacity, Context and Intensity within Cities, 2020. It has taken me three books to arrive at the final building design classification system, architectural algorithms, and master equations that make the prediction of shelter capacity for any given land area mathematically predictable and scientifically consistent in my fourth. (Shelter capacity is gross building area in sq. ft. divided by the acres of buildable land occupied.) This is significant for two reasons: (1) Every acre we consume to expand the shelter, movement, open space, and life support divisions of the Built Domain is an acre we remove from our source of life; and (2) The scope of activity on every acre we consume must produce revenue that combines to produce an average yield per acre equal to a city’s average expense per acre to provide a desired quality of life.

The percentage of each activity sheltered within a city determines its economic potential to support a desired quality of life, but excessive building mass, pavement and movement can compromise the pedestrian spaces remaining with oppressive intensity. Economically stable proportions of shelter for activity can now be measured and predicted at the cellular level of the urban anatomy. This means we can write our own DNA for the sustainable urban aggregations we must form with the equations of urban design.

I’ve added a second book entitled, Symbiotic Architecture: Collected Essays on Architecture, Urban Design and Development Capacity Evaluation, to contain essays that have been stepping stones on my path to the completion of “Equations”. It contains 63 of the 178 essays that have appeared on my blog. Some have also appeared at various other receptive sites such as Linked-In and Facebook. The essays in this book have been left along the path I have traveled. I hope they stimulate the work we need to undertake. Both books are available from Amazon.com.

ZONING DESIGN SPECIFICATIONS: Expanding the Language of Urban Design

Note: Table 1 is located at the end of this text. The complete book can be found on Amazon.com.

Zoning ordinances attempt to lead the increment-

al growth of urban areas with a vocabulary that has not consistently produced success and avoided failure. It addresses the Shelter Division of a Built Domain that is served by its Movement, Open Space, and Life Support Divisions, but its success to date can be summarized with the terms “sprawl” and “over-development”. Random success has received awards that hope to encourage similar results, but these awards struggle with inadequate measurement, evaluation, and direction toward the success pictured but not adequately defined. This arbitrary pattern of success and failure can be improved with an amended vocabulary of zoning specification and the design leadership it enables.

The gray boxes in Table 1 combine to define the characteristics of a building served by grade parking around, but not under, the building. The shelter design alternative is referred to as G1. In this example, gross land area is given and its capacity to accommodate gross building area is to be found. Answers depend on the values and floor quantity options entered in the gray design specification boxes of Table 1. The values entered are processed by the algorithm noted in the Planning Forecast Panel of Table 1. Optional line item answers are related to the floor quantity alternatives entered in cells A44-A53. The line item implications of each gross building area option are calculated in the adjoining Implications Module.

Shelter capacity, or gross building area per buildable acre, is calculated in Col. F of the Planning Forecast Panel and may be occupied by any activity. It is a critical piece of planning information that will determine our ability to shelter the activities of growing populations, without excessive intensity, within geographic limits that do not expand to consume our source of life.

The G1 design values entered in the gray specification boxes of Table 1 define the relationship of building mass and service pavement to the amount of offsetting unpaved open space provided. The master equation in cell B39 is used to predict the gross building area options presented in Col. B of the Planning Forecast Panel. When the forecasts are divided by the buildable acres occupied, the shelter capacity options in Col. F are produced. The intensity of these options is measured in Col. G to compare increasing shelter capacity with its intensity implications.

Gross building area alternatives produce measurable levels of shelter capacity, intensity, intrusion, and dominance within the neighborhoods, districts, cities, and regions they combine to create. These implications are calculated at the cellular level in the Implications Module of Table 1. A change to one or more of the values entered in the gray specification boxes of a design specification template will produce a new set of planning forecasts and implication measurements.

A chosen shelter capacity and intensity alternative can be defined by the specification values that are correlated to create the option. Thousands of technical form, function, and appearance decisions ensue to define a final product, but the foundation is established with these initial urban design decisions. The G1.L1 forecast model presented in Table 1 enables measurement, evaluation, prediction, and definition. The topics and values involved create an urban design vocabulary that can be used for knowledge formation and leadership improvement within a Built Domain that must be limited to coexist with its source of life – the Natural Domain.

When values are entered in the gray boxes of Table 1, they define the contents of a G1 cell in the urban anatomy. An algorithm correlates these choices to calculate leadership information. The correlation produces a prediction of options in a Planning Forecast Panel and a prediction of implications in an Implications Module. These predictions will change whenever one or more of the values in the specification are modified. The process offers the opportunity to measure existing conditions and predict future capacity and intensity options with a consistent set of criteria that permit comparison and evaluation of the implications calculated. As a result, success can be measured, failure can be avoided, and knowledge can be accumulated on a track parallel to that of traditional aesthetic criticism.

A zoning ordinance attempts to consistently produce the results intended by the master plan it supplements based on a concept of minimum standards that are written to protect the public’s health, safety, and welfare. The problem has been that these standards have not been mathematically correlated. The resulting contradictions have been one source of “hardship” variance requests and inconsistent judgments by appointed residents from the community. Table 1 resolves this issue for the G1 Building Design Category by mathematically correlating the design topics and items that interact to produce gross building area results for any given land area; and it calculates the capacity, intensity, intrusion, and dominance implications produced by a set of value entries. The fact that these values can be modified to produce alternative results presents the opportunity to evaluate and define correlated sets of minimum standards with the confidence that they will produce the implications forecast.

Table 1 illustrates the use of one fail-safe measure that deserves special mention. The total unpaved open space percentage of a buildable land area must be specified in cell F11. This can be either a planned, present, or required percentage; but the entire topic is often overlooked, ignored, or marginalized in an effort to maximize the gross building area and parking potential of a given land or lot area. When it is ignored, the intensity added to the neighborhood is unknown and the runoff produced by excessive impervious cover is rarely correlated with the storm sewer capacity present or planned. Cell F11 in Table 1 ensures that unpaved open space is included as a conscious decision and correlated within a complete design specification.

The aggregation of unpaved cellular open space can lead to open space arteries that let urban anatomies breathe. Its absence adds to the suffocation of body and soul; but if this argument does not resonate, the absence of unpaved open space has also led to serious flooding implications. A conscious consideration of unpaved open space as a portion of cell content on every lot in a city will be one step toward the arteries of open space needed to breathe life into the urban forest of building mass and pavement we travel seeking the green places we left.

DENSITY and the CORONA VIRUS

NOTE: Tables 1 and 2 are located at the end of this text

I'm writing this during the Covid-19 plague because discussion has begun over the role of density and social distance in its propagation and prevention. We made progress during the 20^th century in addressing density’s relationship to health, safety, and welfare; but our ability to lead density toward a desired quality of life has been severely hampered by our inability to comprehensively define and correlate the components of its definition. I hope to add a few suggestions with this brief essay.


The term “density” has many meanings. In this case it refers to both population and dwelling unit quantity per acre. Excessive amounts have produced terms like “overdevelopment”, “excessive intensity”, and “congestion”. Low density has produced “suburban sprawl”. None of these terms indicate desirable results. They imply threats to either our quality or source of life.

Density is a product of correlated design specification decisions. It does not lead them and it cannot consistently produce desired results when the components of its definition are randomly and incompletely addressed.


Building Design Categories


Shelter density is produced by choices that begin with the selection of one building design category from a universe of six. The six are classified by the method of parking they employ and are: (1) G1 buildings served by grade parking around but not under a building; (2) G2 buildings served by grade parking around and under a building; (3) S1 buildings served by structure parking adjacent to a building on the same premise; (4) S2 buildings served with structure parking underground on any percentage of the buildable land area; (5) S3 buildings served with structure parking beneath a building footprint that may be above, below, or at grade; (6) NP buildings with no parking required. A building design category for parking that is not intended for human habitation is designated PG.


Shelter Capacity Specifications


A building design category choice leads to a specification template in a forecast model related to the choice. Values assigned to items and topics in the specification template are correlated by an architectural algorithm. Summations are used by a building category master equation to predict either: (1) Gross building area options for a given land area; or (2) Buildable land area options for a given gross building area objective.


G1 Building Design Category


As an example, Table 1 applies to the G1 Building Design Category when gross land area is given and gross building area options ae to be forecast. The values entered in its gray boxes define the land area and design concept under consideration. Any value or combination of values in the gray boxes may be modified to test alternate design decisions, but they cannot be isolated from their combined influence.


The values entered in the gray boxes of Table 1 define pavement, unpaved open space, parking, and floor quantity options that are correlated by an architectural algorithm to serve the master equation in cell B39. The equation predicts gross building area options in cells B44-B53 based on the floor quantity options entered in cells A44-A53. Companion building footprint and parking lot area options are predicted in the remaining columns of the Planning Forecast Panel. The secondary equations at the top of each column have been used for these predictions. A change to one or more of the values entered in the 27 gray boxes of Table 1 would produce a new table of gross building area predictions in its Planning Forecast Panel.


Implications


The results predicted in the Planning Forecast Panel have the shelter capacity, intensity, intrusion, and dominance implications forecast in cells F44-J53 of the table’s Implications Module. These implications vary with the floor quantity options in cells A44-A53 and are the measurable characteristics of density produced by correlating the 27 specification values entered in the Design Specification Template of Table 1. 


The first thing to notice in Table 1 is that there is no mention of dwelling unit quantity in the Implications Module. The calculation is not included because a G1 building is a “shell building”. It may be occupied by any permitted activity. In this discussion, the term “density” applies to gross building area per acre, or shelter capacity, and represents measurable quantities of intensity, intrusion, and dominance.


The values entered in the gray boxes of Table 1 represent the building design decisions associated with G1 density; and they must be correlated to lead the relationship of buildings, parking, pavement, and unpaved open space toward a desired objective. These are the site planning decisions that set the stage for all ensuing building form, function, occupancy, and appearance decisions. The extent of topics involved explains the broad spectrum of design possibilities that can be created, since one or more value changes will produce a new forecast of options - and not all are desirable.


Intensity


Physical intensity is created by the extent of building mass, pavement area, and floor quantity introduced per acre. It is offset by the amount of unpaved open space provided. Social density is produced by population quantity per acre. In other words, shelter capacity, intensity, intrusion, and dominance are created by building mass and its surrounding site plan support. Implication topics are the measurable characteristics of shelter density that can be led by a master equation that is served by design specification value decisions. Occupancy may vary over time, but the physical impact of building mass, pavement, open space, and floor quantity remains constant until physically modified, and I repeat that not all options are desirable.


Population density is a separate issue that is enabled by shelter capacity. Excessive population density and shelter intensity eventually produced the planning, zoning, and building regulations of the twentieth century; but the partial, uncorrelated regulations written to address over-development and blight have been unable to arrest the flight from excessive density and oppression. Flight from congestion and intensity continues to create sprawl that threatens our source of life. It has been relatively easy to ignore these conditions for the sake of population growth and economic development in the past because the planet was considered a “world without end”, but the corona virus is forcing us to consider the issue of physical and social distance more carefully. This will require an improved leadership language capable of correlating the design decisions that combine to determine the physical capacity, intensity, intrusion, and dominance of shelter that is served by movement, open space, and life support within cities.


We use the term “over-development” to describe physical excess when we see it, but have not been able to define the condition with leadership precision. Table 1 has just illustrated the 27 design specification items and topics associated with the definition when the G1 Building Design Category is involved. It illustrates the design specification quantities, architectural algorithm, and master equation that combine to calculate the three dimensional implications of correlated G1 shelter capacity design decisions. The issue of social distance and density is inextricably associated with these intensity decisions. When correlated, they represent a leadership recipe for the shelter capacity, intensity, intrusion, and dominance that emerges. These initial massing decisions are then shaped by thousands of additional form, function, and appearance choices. There is no “world without end”, and we must adjust our definitions of growth and intensity to protect a source of life that we currently threaten with our limited awareness.


Population density is enabled by the physical intensity of building mass, pavement, and unpaved open space that serves the population. Building design categories, design specification quantities, and master equations produce shelter capacity, intensity, intrusion, and dominance options for these populations. These are the physical components of intensity that can be measured without reference to the occupant activity involved. In other words, it is a universal measurement system for the impact of shelter capacity within cities. This means that capacity can be led to produce the intensity and distance objectives we must define to achieve our public health, safety, and quality of life objectives. 


Our leadership language must improve before we can begin to guide shelter capacity in our Built Domain toward a relationship with the Natural Domain that protects our quality and source of life.


Apartments – the G1.R3 Activity Group


Table 2 introduces an apartment module on lines 34-48 to illustrate what happens when a G1 Building Design Category or “shell building”, is occupied by an R3 Apartment Use Group. The apartment occupancy proposal is added to Table 1 in cells A34-J47 of Table 2. I won’t go into great detail concerning this table because I have a limited objective.


My first point is to illustrate that the traditional residential density calculations in Col. N of the Implications Module result from the 51 design specification values entered in the gray boxes of Table 2. A density calculation does not lead the 51 decisions. It is a product of them. Random results will always occur when there are too many specification options without leadership direction. This is the case when a density limit is used without further correlated specification. 


My second point is that gross building area options predicted in cells B44-B53 of Table 1 have increased in cells B56-B65 of Table 2 because residential occupancy specifications have been added to the shell building specifications entered in Table 1. The intensity implications in cells J56-N65 of Table 2 have increased in response because reduced residential parking has permitted building mass to increase on an increased building footprint area. If you compare the “a” value entered in Cell A36 of Table 1 to the calculated apartment value “a” in cell J47 of Table 2, the reason for the increase becomes apparent. The value “a” defines the building square feet per G1 grade parking space planned, permitted, or required. A higher value permits more gross building area per parking space, and a reduced number of parking spaces permits greater land area for the building footprint. The value “a” in Table 2 has changed because the apartment occupancy defined in Table 2 has replaced the general occupancy statistics in Table 1. It is the only shell specification value that has changed, but the parking revision enabled by apartment occupancy has increased gross building area potential and had a significant impact on potential shelter capacity, intensity, intrusion, and dominance.


Table 2 shows that there are 51 interrelated design decisions that affect gross building area potential when a G1 Building Design Category is occupied by R3 apartment activity. A density range from 28 to 68 dwelling units per shelter acre is possible, as shown in cells N56-N65, given the design specification values entered in Table 2 and the floor quantity options in cells A56-A65. The shelter capacity, intensity, intrusion, and dominance implications vary as noted in cells J56-M65. None of the shelter intensity values calculated in cells K56-K65 may contribute to a desired quality of life on the gross land area specified in cell K3 however, since the social distance implied may contribute to a condition we have nebulously referred to as “over-development” and “congestion”. The point is that we don’t know without further measurement and research.


Summary


The Covid-19 plague has brought the issue of shelter intensity, over-development and social distance to our attention once again and exposed our continuing lack of knowledge. We do know that lower density produces sprawl that expands with population growth to consume increasing quantities of agriculture and the Natural Domain. We also know that excessive density produces intolerable congestion, but our efforts to define acceptable levels have failed to correlate the many building design categories and specification topics that combine to form a definition. We can’t manage what we can’t measure, and this leaves us with a concept of social distance and shelter density that is poorly formed with an inadequate definition. This, in turn, leaves us waiting for a vaccine that will allow us to revert to our old definitions of growth and economic success on a world without end. 


Density has measureable shelter capacity, intensity, intrusion, and dominance implications that are produced by the quantities of building mass, parking, pavement, and unpaved open space introduced. Occupant activity may add social congestion, but a physical pattern is established by design decisions that begin at the site planning stage of shelter creation.


Shelter is served by divisions of movement, open space, and life support within the urban and rural phyla of our Built Domain. Shelter is capable of protecting any social activity and is governed by design specification values that can threaten our physical, social, psychological, environmental, and economic quality of life when uncorrelated and unrestrained.

Covid-19 has given us a glimpse of the threat posed by inadequate social distance and excessive physical intensity occupied by social congestion, but sprawl is not a solution. It is a threat to a Natural Domain that is our source of life. The dilemma is forcing us to face public policy issues of growth, density, intensity, and geographic limits on a planet that is no longer a world without end.

A Farmer Knows More Than a City

A farmer's field is like any city zoning district. The yield per acre from both must be subsidized when less than the cost of support per acre. (To visualize municipal yield, divide the total revenue received per lot, block, zone, or tract by the taxable acres within these boundaries. Compare this revenue per acre to a city’s total annual expense divided by its taxable acres.) The municipal revenue imbalance found in many cases will make it apparent that “big data” is required to provide the information needed to manage the city as a farm, since each must become productive within geographic limits that protect our source of life.

The fact that acreage is a divisor in this yield equation conveys a serious message. If a taxable acre is providing $1,000 to local government, its yield is $1,000 per acre. If the same total tax is provided by 0.1 acre, its yield is $10,000 per acre. This simple arithmetic explains the importance of land use, since a city has a limited number of acres and the activity located on each determines a city’s ability to support its lifestyle. Annexing land to increase these acres can be self-defeating when the activity planned provides new money that proves inadequate to meet a city’s average expense per acre over time. New revenue can be deceptive since it isn't reduced by public maintenance expense that increases with age.  It can be a mirage that declines for later governments and is one source of the disease we call "sprawl". 

I doubt that a city knows the total revenue per acre produced by its individual lots and parcels, census tracts, census districts, or zoning district areas. In this context, a farmer knows more about the productivity of his land and crops, and a city cannot easily change the crops it has planted. A city cannot manage what it has not measured. “Big data” is needed to visualize the city as a farm that must become a productive part of a symbiotic future.


It doesn’t take much to visualize the city as a farm.

·        Every lot, block, zone, and tract produces revenue per acre that is a function of its shelter capacity, intensity, and activity.

·        Total yield divided by taxable acres produces average municipal revenue per taxable acre.

·        Total expense divided by taxable acres produces average municipal expense per taxable acre.

·        Some taxable municipal acres produce less revenue than the minimum required to equal expense and must be subsidized by others.

·        The objective is to improve the average yield from all municipal acres to support a desirable quality of life.

·        The misallocation of land use areas, activity, capacity, and intensity can easily disrupt the fragile physical, social, psychological, environmental, and economic balance a city must maintain to ensure a reasonable quality of life that exceeds a minimum standard of survival.

A few related thoughts have come to mind while writing this.


Property Value. Property value is determined by a city’s ability to deliver basic public services. Value is compromised by crumbling curbs and sidewalks, potholed streets, flooding basements, sewer backups, deficient water quality, failing bridges, traffic congestion, maintenance deferral, government conflict, budget reductions, inadequate social services, and so on. 


The rate of property value appreciation is a function of a city’s school system. A school system has very limited ability to offset the physical decline fought by government, but consumes the greatest share of local tax revenue. Sacrificing basic government services to meet the increasing cost of public education leads to a market-timing exodus as residents become aware that they are investors in a depreciating asset with deficient physical, social, and economic equilibrium.


Minimum Standards. The concept of minimum standards began with Hammurabi for some and with the Ten Commandments for others. The definition of “minimum” has been a battlefield ever since. Protection of public health, safety, and welfare with minimum standards became a grudgingly accepted objective in the 20^th century, but is still seen as an infringement on individual freedom to achieve at the expense of others by those who object to the definition of “minimum”. 


Services defined as “minimums” by some are considered excessive by others; but I doubt that any resident can recite the full list of his or her city departments, let alone the services provided by each. Under these circumstances, it is no wonder that residents often consider the cost of government excessive for the benefit received since many apply to limited segments of the population. A simple list with related costs might help to create a more informed discussion.


Quality of Life. The term “quality of life” has become a frequent substitute for the term “welfare” in an attempt to refine the intent of the term, but in either case I believe the intent has always been to protect the physical, social, psychological, environmental, and economic interests of entire populations from domination by a few under the banner of “freedom”.


Quality of life is compromised by municipal deficits per acre that must be offset with annual budget reductions. We will continue to assume that budget reductions are improvements without the assistance of “big data” evaluation; and will continue to flee decline with metastasizing sprawl in the absence of more informed diagnoses and treatment.

Summary. The expansion of internal urban decline and fringe area sprawl over the face of the planet are visible symptoms of our inability to manage the city as a farm within geographic limits that protect its source of life – The Natural Domain. The Agricultural Phylum of the Built Domain and the entire Natural Domain will remain at risk until cellular content classification, “big data” collection, and leadership language formation improve to support knowledge assembly, diagnostic success, and leadership direction. Science has already taught us that an ignorant parasite will consume its source of life and a symbiotic parasite will survive. City design of the future will reveal if we have learned to live this lesson.

UNSTABLE LAND USE ALLOCATION

Gross building area can be occupied by any land use activity. A combination of gross building area per acre and occupant activity per square foot sets the stage for municipal income per taxable acre. When this primary source of revenue is added to other investment income, it must equal a city’s total annual expense per acre. It is a fairly simple relationship complicated by our inability to accurately and rapidly predict shelter capacity options per buildable acre and the revenue per sq. ft. that can be expected from occupant activity alternatives. This has made it impossible to correlate urban pattern with urban form and occupant activity to produce yield that supports a desired quality of life within geographic limits. Our inability to correlate has led us to repeatedly consume our source of life with annexation in a vain search for economic stability. Few are aware and fewer have paid attention to this unwitting Ponzi scheme. It requires new money from increasing amounts of land consumption to compensate for the increasing cost of past land use allocation mistakes. The problem appears over generations of budget reductions, slow decline, tax resistance, and community complaint; and the mathematical correlation required to correct the condition is just emerging to face its political opposition. 


Annexation for more shelter capacity and activity with less than the average yield per acre appears to solve immediate budget problems with new money until its expense exceeds the revenue provided over time. At this point annexation again appears in vain pursuit of stability with hope as a strategy and Ponzi as its companion - when additional land is available. “First ring” suburbs have no room to expand and have been the first to confront this problem without the knowledge, commitment, and equipment that is equal to the threat. 


The shelter capacity of land is a function of a building design category choice and the values assigned to its design specification topics. These values are correlated by an architectural algorithm and processed by a category master equation to produce gross building area options that are a function of the floor quantity alternatives entered. A change to one or more specification values produces a new forecast of gross building area options that can be occupied by any desired activity. Prior to this, the number of options that could be considered in a reasonable time frame was severely limited by time-consuming graphic evaluation. The introduction of mathematical analysis makes it possible to evaluate hundreds of options and economic forecasts before graphic analysis focuses on the most promising. These cellular content solutions represent design decisions at their most fundamental level. They aggregate to produce shelter form that is served by a pattern of movement, open space, and life support within the Built Domain.


Municipal financial stability will remain an elusive goal stimulating random annexation until we understand the current productivity of each acre within a city’s corporate limits. At this point, we can accurately predict the adjustments needed to equate average yield with the expense required per acre for a desired quality of life within city limits. The effort will require relational databases of acquired knowledge combined with evaluation models and treatment decisions at the cellular level of city formation. Keep in mind, however, that excessive capacity options produce intensity, intrusion, and domination that detract from our quality of life. Fortunately, they can be measured and evaluated to build the knowledge needed to lead future city design decisions.

SHELTER SPRAWL

Sprawl is a disease consuming the Natural Domain with building mass, pavement, and open space in both the Urban and Rural Phyla of the Built Domain. When sprawl is seen as a cancer expanding with population growth, there will be a search for a cure to treat this threat to our source and quality of life. The cure will begin at the cellular level of sprawl formation called a lot. A primary building providing shelter for human activity is its nucleus. A cell and its aggregation is where architecture can help by focusing on the building categories, cell content, design specification values, and master equations that produce gross building area options within each cell of currently sprawling urban form.


Gross building area can be occupied by any activity. These area and activity options combine with pavement and social open space to produce levels of shelter capacity, intensity, intrusion, and domination in each cell of the Shelter Division of the Urban and Rural Phyla of the Built Domain; but capacity and intensity have not been measured or compared with occupant activity. This combination has municipal revenue and expense per acre implications that affect its physical, social, psychological, environmental, and economic quality of life; but this lack of correlation means that the relationship of building mass, intensity, and activity to economic stability and quality of life cannot be predicted at the present time. This, however, is the key to a cure for sprawl vainly seeking financial stability and shelter for growing populations.


Shelter capacity is gross building area per acre. It produces a level of intensity, intrusion, and domination in a cell based on the building design category chosen and the values entered in its design specification template. These values have had partial recognition and conflicting specifications in zoning ordinances. This has led to uncorrelated, unsuccessful attempts to consistently lead the emergence of urban form to physical, social, and economic success that protects our health, safety, welfare, and source of life.


Architecture intuitively understands the correlation required but has never classified building design categories, comprehensively listed their design specification topics, or written algorithms to correlate design specification values for use by master equations that accurately predict shelter capacity and intensity options for any given land area. This leadership language was not needed by anyone when the planet was “a world without end” and we were encouraged to be “fruitful and multiply”. These exhortations have led to promiscuous consumption of land vainly searching for economic stability with hopeful annexation. Public participation has kept everyone busy within the city, but its focus on detail has failed to recognize sprawl and the knowledge needed for correction. 


The cure is city design of urban form for growing populations that contains shelter capacity, intensity, intrusion, and dominance decisions balanced for economic stability and quality of life within sustainable limits. New relational databases are needed to produce knowledge that can defend the decisions required. Decisions in turn must be expressed in a language that can lead. It must correlate the mathematical design specification decisions that are the hidden foundation of shelter formation. This is the language needed to repeat success and avoid failure on a very finite world in a universe without end.


A city design recipe for urban form is not a replacement for traditional architectural priorities. It is a massing prelude that requires further architectural refinement to produce shelter composition, context, and appearance. These results will symbolize the logical foundation needed to achieve sustainable cities and symbiotic survival on a planet that does not compromise with ignorance. 



If you have read my books you should have a thorough understanding of what I mean by the mathematical language of city design, building design categories, design specifications, gross building area, shelter capacity, intensity, intrusion, dominance and urban form correlation. The first two contained forecast models based on the incremental approach to calculation historically used by architects. The third translated this approach into architectural algorithms that correlated comprehensive sets of design specification values to serve a building design category master equation. The equation predicted gross building area options based on these design specification decisions and floor quantity alternatives. A change to any specification value or floor quantity alternative produced a new set of options, but a forecasting CD was not included because of previous copyright infringement. This book has been replaced by an unpublished fourth that simplifies the third and contains far better organization. All final forecast models will be placed in the cloud if someone takes up the baton.

A Collision of Architectural Opinion

The first two paragraphs are excerpts from comments that have prompted my response.


Mark Wigley: “…If you could say what the problem is you wouldn’t hire an architect…You call an architect in when you have a very complex situation in which you have a lot of information that doesn’t really connect, and the architect just goes in there and sees or projects or imagines a possible form of organization that allows that complexity to continue…naiveté is crucial…because to know that you don’t know, to have a sense that you don’t know and therefore to be in awe of what you are experiencing and full of love and respect for complexity, this I think is the genius of architects and why I think they have an enormously important role in society.”

Ujjval Vyas, Ph.D., J.D. Strategic Advisor | Attorney | Entrepreneur | Scholar | Principal of Alberti Group | Founder, FDI-AEC

“Are you kidding me? This is the clarion call of obfuscatory mumbo jumbo. The endless excuse-making about a serious lack of thinking, deep respect for learning and knowledge, and the final recourse of the scammer. The idea that ignorance is a qualification … is bizarre... No wonder the idea that architects have some special design thinking to contribute is only of interest to those trying to bail water out of this Titannic (sp). Architecture is too great a discipline to be permanently held down, but the jury is still out if this recovery is just over the horizon or only where there be dragon’s (sp).

Walter Hosack:


Architecture records complex owner requirements and desires in a document it calls a program. It solves the puzzle defined by the program with logic it calls schematic design. In the military the program would be called a policy and schematic design would be called strategic planning. Architecture has made the mistake of calling its entire effort fine art.


Mr. Vyas talks about seeing over the horizon to reach a remote destination, but the skill required an abstract ability to calculate latitude and longitude. Unfortunately, architecture earns a living from its project orientation and has no incentive to consider a horizon beyond the cell it calls a lot, or the cells that are combined to form a larger project area. It will take a different form of calculation to pursue an attempt to cure metastasizing sprawl that is consuming our source of life.


A building is the shelter nucleus of a cell we call a lot. Cells collect to create a Built Domain that is expanding through annexation of the Natural Domain. The form created is called sprawl to shelter the activities of growing populations, and there is no correlated mathematical language or political priority that can lead to healthy, symbiotic urban form within geographic limits.


Zoning is a collection of uncorrelated, conflicting design specifications that cannot predict the shelter capacity of cells and their aggregations. As a result, it cannot lead to the formation of healthy urban anatomies that avoid excessive intensity with correlated shelter capacity and economic activity. At the present time, zoning contradictions combine with activity misallocation to abet sprawl searching in vain for elusive economic stability through annexation. 


Land use planning is a two dimensional exercise that cannot correlate the shelter capacity, intensity, and activity of urban form. This is critical because shelter capacity measures the gross building area per acre present or planned. Shelter is occupied by activity and the combination determines revenue yield per acre of land area consumed. When thought of collectively, average economic yield per acre consumed must equal a city’s average expense per acre to avoid budget cuts and a declining quality of life.


Since shelter capacity can be occupied by any activity, the ability to predict shelter capacity per acre and the economic yield per square foot from occupant activity is crucial to economic stability. At the present time, a city cannot balance the shelter capacity of its land with occupant activity to meet the average yield per acre it needs for operations, maintenance, improvement, and debt service.

This is a problem that begins with architectural inability to comprehensively and accurately predict and compare shelter capacity, intensity, intrusion, and dominance options at the cellular level of urban aggregation, but it is not a problem that can be assigned to architecture as we know it. It is a problem for city design leadership with a new version of latitude and longitude prediction.

The goal is shelter capacity, intensity, and activity in proportions that will protect a growing population’s economic stability and quality of life within geographic limits that protect their source of life. This is our new destination over the horizon. It will require the ability to calculate another version of latitude and longitude and the power of a captain sailing in a universe without end.

Pete Pointer

Science is good but principles, values applied in process locally is more important.

Like "Pete" Pointer FAICP, ALA, ITE’S comment

Walter Hosack

A strategic plan to correlate shelter capacity, intensity, and activity for economic stability throughout a city begins at the cellular level of building mass, pavement, and open space. Conversion of this cellular recipe to composition, context, and appearance is a more detailed, tactical level of physical design that you refer to as "local". I would not prioritize the effort. It is all needed to contribute to our quality of life within sustainable cities that are capable of contributing to our symbiotic survival.

Drake Waters

The world needs good architecture more than ever by a factor of 100. So much is changing and has to change and the brilliance and creativity good architecture brings is priceless. Good architecture is not wasteful useless and comatose through aesthetics alone. It is a way of thinking that encompasses everything to support society. We are done for if current trends in architecture continue. We must enable AI to force multiply our impact and integration of disciplines has to be the norm. None of that is possible in gate keeper lock down, our status quo. Sink or swim? We are sinking fast.