The Equations of Urban Design: A new language for an ancient topic

I have self-published The Equations of Urban Design after completing two prior books with McGraw-Hill. The content of “Equations” is the culmination of an effort I’ve pursued over a lifetime, but have only been able to resolve with the derivation of equations that are included in the book. I’ve always believed that improved credibility was needed to lead us toward shelter for growing populations within geographic limits that protect our quality and source of life. The equations of urban design are my answer to this search for a language that can increase the credibility of planning design recommendations. They empower the measurement, evaluation, prediction and definition of results that can consistently improve the quality of the places we create and preserve more of the land they depend on for survival.

I included a CD with my first two books. It included forecast models to predict the shelter capacity of land. Growing populations are building increasing amounts of shelter to protect their activities on land that is not inexhaustible, and has always had a more fundamental purpose. A better method of measurement, evaluation, prediction, and direction has been needed to reconcile the shelter demands of a population with the capacity of land that is its source of life. Historic approximations were not based on algorithms serving master equations, however. They were based on the centuries-old method of incremental architectural calculation that has been one step short of integrated derivation and algebraic expression. The geometric emphasis has prevented the formation of a scientific language capable of measuring, evaluating, and predicting the spectrum of shelter intensity and its impact on our physical, social, psychological, environmental, and economic quality of life.

Before I go any further, I should explain that shelter capacity is the sq. ft. of gross building area planned or present per acre of buildable project area. It is produced by specification values assigned to the topics in a building category template but this has not been documented or correlated in the past. You will discover that there are only six building classification categories on the planet, and that this makes shelter capacity and intensity measurement, prediction, evaluation, and direction feasible.

The mathematical correlation of specification values for each building category and location is the missing link needed to correlate capacity, intensity, activity, and context on limited land areas; and we must improve our knowledge of intensity before we can begin to preserve land and understand the implications of choices within the intensity spectrum. The Equations of Urban Design has been written to support the research needed to improve this knowledge - and introduce the leadership language needed to guide the formation of shelter on a planet with limited capacity and diminishing patience.

Shelter form, function, and appearance decisions are built upon building category choices and specification decisions that determine the building mass, pavement, intensity and intrusion that will be offset by unpaved open space and placed on land; but the intensity of these choices cannot be evaluated with our current incomplete methods of classification, measurement, evaluation, prediction, and correlation. This has contributed to excessive intensity, expanding deterioration, sprawling reaction, unlimited consumption, and inadequate planning credibility.

A new language is needed, and this is the objective of the building classification system, design specification menus, mathematical algorithms, master equations and forecasting panels of shelter capacity and intensity prediction. This language can define the massing options and intensity implications of shelter formation decisions within the urban form of city design.

The design specification topics associated with a building design category and its forecast model are the key to shelter capacity measurement, evaluation and intensity prediction, but the complete list of topic values for each category has been incomplete and mathematically uncorrelated in zoning ordinances. This has contributed to the random, arbitrary, conflicting, and uncertain leadership symbolized by the excessive intensity and profligate sprawl we find at both ends of the shelter spectrum in our cities. This has often been referred to as a city’s pattern and its harmony as discordant.

The topics listed in a forecast model can be measured at existing building locations to build the topic knowledge needed to repeat success and avoid failure. This is the knowledge needed for planning leadership, and it will not compromise traditional design efforts associated with the form, function, appearance, and internal subdivision of the buildings that follow.

A research emphasis based on the consistent measurement and evaluation of existing building specification topics will inevitably lead to correlated topic parameters for each building category, activity, and location. This is critical knowledge, since building categories aggregate to form the shelter anatomy of cities and the quality of life within their neighborhoods. These are served by a city’s arteries of movement and life support but remain unrelieved by arteries of open space in most cases.

The allocation of activity within a city’s total shelter capacity is a major determinant of financial stability. Unfortunately, the successful balance of land use allocation for capacity, intensity, activity and economic stability will require more than the random results produced by conflicting opinion and competing market forces. The data required to build credibility and convince others of the critical decisions needed to balance land use allocation, economic stability and quality of life within geographic limits has yet to begin in earnest.

It may be helpful to realize at this point that a building is currently defined by the activity present or proposed such as a drugstore, bank or gas station; but the activity may change over time. This naming convention by activity has distracted us from a more fundamental building classification system that supports the equations of urban design. This has limited our ability to correlate shelter capacity and activity with economic stability, quality of life and environmental preservation.

The values assigned to the specification topics of a building classification category determine the shelter capacity and intensity that will be produced on the project’s buildable land area. The type and scope of occupant activity determines its economic productivity. Its appearance may change with the activity sheltered, but its gross building area is a more permanent feature of the percentage values assigned to its design specification topics. These are the decisions that determine capacity, intensity, context, and economic potential; and these quantities can be measured at existing locations to build knowledge. They are also the values that can be correlated and prescribed as a foundation for the form, plan, appearance, context and economic stability of the project that follows.

The forecast models mentioned are available and could be provided on a web site for international use, but they await someone with the business interest, initiative, capital and skill required to make a prototype into a product.

The Shelter Components of Capacity, Intensity, Intrusion and Dominance

 NOTE 1: This essay was originally published in September, 2010 as “Replacing Density” but has undergone such significant change that it deserves a separate title. This essay is based on the information provided in the book entitled, The Equations of Urban Design, by Walter M. Hosack, 2020 and available from Amazon.com.

NOTE 2: All tables in this essay are located at the end of this text. 

 

Density is an oversimplified indication of building intensity that only applies to the shelter provided for residential land use activity. It is produced by a number of decisions it does not correlate. It is a product of their often contradictory collision. This will continue until we recognize the design specification topics and values that must be correlated to reach any shelter objective with certainty and consistency. It is a critical issue because shelter is survival and sprawl is a disease driven by population growth and uncertainty that threatens to consume our source of life with a parasite’s lack of anticipation. 

Intensity can be an emotional response to pressure that is prompted by the degree of our confinement within space. In the case of shelter, intensity is produced by the relationship of building mass, pavement, and unpaved open space quantities that surround us in a project area, not to mention adjacent influences. In these projects, and the districts, cities, and regions they combine to produce, it is possible to both predict and measure the shelter capacity, intensity, intrusion, and dominance that will be, or has been, produced. Our previous inability to define and correlate these relationships has led to a flight from intensity and decline to our current experimentation with suburban sprawl. Unfortunately, the results have not consistently balanced land use activity with shelter capacity to produce economic stability within geographic limits. Physical, social, psychological, environmental, and economic experiments continue to randomly consume our source of life without evidence that the land consumed has produced measurable shelter capacity, intensity, intrusion, and dominance results that symbolize success. 

This is a brief essay about the design specification topics and values that define shelter intensity at the project level of city formation. Each topic is contained in a design specification template that is related to one of the six building design categories listed below. They shelter most, if not all, human activity on the planet. Each topic value has been intuitively correlated by a designer to determine the physical presence of buildings and spaces that surround and serve our daily activities throughout history. The physical results have been called “massing” when building appearance has been ignored. It combines to form the texture of cities and is served by arteries of movement, life support, and pockets of public open space. It is produced by one or more of the following six building design categories that emerge from site plans to form the places we inhabit: 

1)      G1: Buildings with surface parking around, but not under the building

2)      G2: Buildings with surface parking around and/or under the building

3)      S1: Buildings with structure parking adjacent to the building on the same parcel

4)      S2: Buildings with underground parking

5)      S3: Buildings with structure parking at grade under the building

6)      NP: Buildings with no parking required 

Design specification values define quantities that combine to produce shelter capacity, intensity, intrusion, and dominance results for each building design category listed. 

Design specification topics and values define the gross building area quantities that can be introduced per acre at the project level of city formation. The quantity introduced combines with the impervious cover percentage defined to determine the intensity level present. The combination of intensity and activity determines the project’s revenue potential per acre -- and its ability to meet a city’s total annual cost per acre. The physical, social, psychological, environmental and economic impact of this “improvement”, therefore, begins with the gross building area introduced per buildable acre to shelter occupant activity. 

OCCUPANCY 

Gross building area has nothing to do with occupancy. It may be occupied by any activity that conforms to local zoning and building code regulations; and occupancy often changes over time. Relating gross building area to occupancy requires a secondary template of topics that are tailored to the specific activity. A gross building area prediction remains constant, given the same set of design specification values; but its capacity to shelter a given activity is modified by the values entered in a companion activity template. Table 1 illustrates the prediction of gross building area alternatives for a given land area using the G1 Building Design Category without the influence of a companion activity template. 

TABLE 1 

The values entered in the gray boxes of Table 1 represent one set of potential building design decisions within a broad universe of options. They could just as easily represent the measurements of an existing building. There are 26 gray boxes and each value entered represents a design decision that can be modified to test options. The percentages and values entered have been converted to their square foot area implications in Col. G. The objective of the algorithm is to identify the shelter area available in cell F17 and the core buildable land area remaining for building footprint and adjacent parking lot in cell F33. 

A master equation correlates the specification data in the Land and Core Modules of Table 1 with the floor quantity options entered in cells A44-A53. Gross building area alternatives are predicted in cells B44-B53 of the Planning Forecast Panel based on these floor quantity options. The remainder of the panel predicts the implications of the gross building area forecasts in Col. B using the secondary equations on line 43. The panel illustrates a few of the many implications that can be forecast after the gross building area capacity of buildable land area can be accurately predicted. 

Table 1 illustrates that 16 gray box design specification decisions are correlated with one floor quantity options in cells A44-A53 to forecast the gross building area options in Column B. A change to one or more of the gray box specification values in Table 1 will produce a new forecast of options in Col. B of its Planning Forecast Panel, and hundreds of options can be predicted in a very short time. The point is that gross building area predictions can be occupied by any permitted activity, and the combination of intensity and activity per buildable acre determines our physical, social, psychological, environmental, and economic quality of life. 

The gross building area options forecast in Col. B of the Planning Forecast Panel have been used to produce the shelter capacity forecasts in Col. F. These capacity options have then been used to calculate their intensity, intrusion, and dominance implications in Columns G- J. These four implication measurements are like our first blood pressure readings. They indicate the impact level present or proposed. I can only hope that continued measurement, evaluation, and prediction will lead to parameters that can improve our symbiotic chances of survival. 

TABLE 2 

I have mentioned that design specification topic and value decisions have nothing to do with occupancy and everything to do with gross building area potential. Occupancy involves a secondary template of topics and adjustable values that are tailored to a specific activity. The template is used to calculate the capacity of gross building area options to accommodate the activity. This means that land has a given shelter capacity that is related to the building design category chosen and the design specification values assigned. These choices determine the physical form of the cities we inhabit. Its capacity to shelter activity is a function of this capacity. 

The Table 2 forecast model is based on the same G1 Building Design Category as Table 1. The difference is that an R3 Apartment Module has been inserted beginning on line 34. The 28 gray cell design specification values entered in this module define how the gross building area predictions in cells B56-B65 will be subdivided to create the apartment mix specified in the R3 Apartment Module. The remainder of the Planning Forecast Panel provides additional design predictions regarding building footprint area, dwelling unit quantity, parking quantity, and so on that are related to the gross building area predictions in cells B56-B65. 

The Implications Module calculates the shelter capacity, intensity, intrusion, and dominance implications of the gray cell specification values. When intensity and density are based on the same design specification values, they have equal implications. The difference is that density only applies to residential activity. Intensity calculation applies to the six basic forms of shelter on the planet and is a universal measure of its presence. The way we use land to shelter the activity of growing populations will reflect our progress toward a sustainable future. 

CONCLUSION 

Architecture has always sheltered the activities of its period and correlated the knowledge available. It is no accident that the current sprawl of shelter reflects our current confusion. Opinion has produced indiscriminate regulation and the land is compromised by the process. We are distracted by the details of compatibility, construction and appearance — not to mention ownership and sovereignty; but intuition is looking beyond the environment we build to include the environment we consume. Balancing these two worlds will depend on our ability to understand implications and offer options within limits that meet strategic goals that can only be defined with anticipation.

Our responsibility is to recognize that symbiotic survival is the goal. Intuition is again required – and leadership is needed when anticipation must substitute for proof. When shelter without sprawl is the survival issue, our knowledge is limited. Our vocabulary is inadequate. Our language is inarticulate. In my opinion, this means that our vision must restrain an instinct to control or be dominated that has become a threat to the planet. Nothing less than symbiotic survival is at stake, and we must again prove that we are equal to the threat success has produced by providing the leadership required. 

A SIMPLE URBAN ECONOMIC QUESTION

 

This is an addendum to my essay, “The Implications of Land Use & Urban Design Decisions”.

 

What does the taxable land in a city’s inventory yield in average revenue per acre -- and what should it cost the city per acre to operate, maintain, improve, and finance a desirable quality of life without continuing budget costs and tax increases? The municipal budget must balance each year, but this is no indication of physical, social, or economic success.

If there is a municipal budget deficit, an economic development strategy is needed for all of the acres in a city’s inventory; since this is a primary source of revenue and not all acres will be productive. If a city does not understand its average revenue productivity per block and per acre of land use and shelter capacity allocation, it will continue pursuing random economic development projects without understanding the comprehensive economic strategy needed to lead its physical decisions to foreseeable financial improvement in the balance between its revenue and expense per acre of its inventory.

Land Use & Development Capacity Correlation

 

It should be obvious that many different gross building areas can be created on the same buildable acre, and that they may be occupied by many different activities. (Assuming these activities comply with all related zoning and building code regulations.) It should also be obvious that different activity generates different taxable revenue per square foot of shelter, and that larger buildings containing the same activity on the same acre have greater shelter capacity and revenue potential. Unfortunately, we have been unable to correlate these self-evident principles across all taxable acres of a city. This has limited our ability to produce shelter capacity and activity relationships that yield average annual revenue per acre equal to, or exceeding, a city’s average annual expense per acre to deliver a desired quality of life over time.

A city cannot successfully plan its economic future and continuing quality of life until it can correlate the shelter capacity of land with the revenue implications per sq. ft. of its occupant activity. Until then, it cannot evaluate the activity and intensity options that will improve its average revenue production per acre. We have called our partial efforts economic development; but our project-oriented focus has been too limited, our knowledge too undeveloped, and our tools too inexact to produce consistent leadership correlation at the strategic level of effort implied by the term city planning.

We are not ready to plan cities without annexation as a crutch and sprawl as a result. Improvement will require the ability to correlate the economic potential of activity per square foot of shelter with the gross building area options available per buildable acre. Unfortunately, many of these gross building area options produce excessive physical intensity, intrusion, and dominance in the pursuit of profit. This result has prompted more than a century of flight to the suburbs, but our limited knowledge has produced rings of sprawling land consumption in a search for solutions on a planet that is no longer a world without end.

The physical intensity of shelter within cities has been a term without an adequate definition. It has been exacerbated by movement and life support systems that have magnified the condition and been inadequately offset by quantities of dedicated open space. The condition worsens when a city becomes surrounded and economically suffocated by its inability to adjust shelter capacity, activity, and revenue within its limited boundaries. Improvement requires a delicate balance among these topics, but we have not been able to address them with the knowledge and tools available.  Our only choices have been annexation and sprawl for new revenue that often proves inadequate over time; tax increases; or budget reductions that can prompt decline when the status quo cannot be maintained.

My efforts have focused on the algorithms and forecast models needed to consciously and consistently correlate the shelter capacity of land with the revenue potential of its occupant alternatives – and on the consistent measurement of the physical intensity, intrusion, and dominance produced by shelter alternatives that can compromise our quality of life when ignored.

The economic potential of gross building area is a function of the occupant activity present or planned. Therefore, if the shelter capacity options for a given land area can be accurately predicted in sq. ft. per buildable acre and the revenue potential of occupant activities is known in dollars per sq. ft. of building area, the economic contribution of the potential combinations can be predicted. In other words, taxable land area represents a primary financial resource for every city. Its potential depends on the shelter capacity and activity introduced on every buildable acre.

If a city knows its expense to operate, maintain, improve, and finance its services per acre, it can subtract all known sources of revenue that are unrelated to land use in order to find the remaining expense that must be served by its average revenue per acre. If I borrow the word “productive” from farming, urban revenue per acre that equals or exceeds a city’s remaining average municipal cost per acre is productive. All acres will not be productive with this definition, however. Every city’s challenge is to make the average yield per acre from all of its crops (zones, census blocks, census districts, lots, parcels and so on) equal to or greater than its remaining expense to provide a desirable quality of life. This means it must learn much more about its shelter capacity, activity, and intensity alternatives.

Revenue data per parcel, block, or tract is a simple matter of relational database creation, information assembly and correlation -- if political cooperation can be found. Geographic mapping systems based on this data can reveal existing conditions and strategic alternatives for ensuring economic independence based on land use and shelter capacity correlation. It is a concept a farmer describes with terms like crop allocation, yield, and productivity per acre. Urbanists will be threatened by a fear of geographic discrimination, but it is already a problem to be resolved.

A farmer knows that his/her revenue per acre depends on both yield and quality. We have referred to yield as “density” and quality as “health, safety, and welfare” in the history of city planning; but density and welfare have proven to be inadequate leadership terms and measurement yardsticks.

Density is a function of shelter capacity per acre. Capacity is produced by the correlation of design specification topics and values entered in one of six building design category templates. These templates classify most, if not all, shelter we construct on the planet. Welfare is influenced by the physical intensity, intrusion, and dominance of shelter capacity. It surrounds and contains activity that we pursue on a daily basis. It is initiated with a combination of design specification decisions that have been partially recognized and independently addressed. Unfortunately, they function together like the sections in an orchestra and produce similar dissonance when uncorrelated. A focus on isolated shelter design topics and items has frustrated our efforts to produce a symphony.

Building design categories can be classified at existing locations. Their design specification topics can be identified and their values can be measured. The shelter capacity, intensity, intrusion, and dominance of the project can be calculated from the measurements taken using the new equations in its related forecast model. These measurements represent the correlated starting point for every shelter capacity project. Few are aware, however, that excessive intensity and profligate land consumption can be produced by many uninformed design specification decisions. The discovery of these measurements will produce the knowledge needed to begin considering the implications of symbiotic urban pattern and form. It can provide the shelter we need to survive as a parasite on a planet that does not compromise with ignorance.

We have been preoccupied with land use relationships and the word “compatibility” since we began to recognize that some relationships were unhealthy, unsafe, and detrimental to a quality of life that we originally called “welfare” -- until it became associated with poverty. We have fled the intensity of cities in a search for answers but have produced sprawl that threatens our source of life. This will continue until we recognize that the quantities of activity protected by the square feet of shelter provided per acre must be correlated to produce average revenue per acre that equals a city’s annual expense per acre for a desired quality of life over time -- without excessive physical intensity that dominates the quality desired and within geographic limits that protect our source of life.

Quality of life is influenced by the capacity, intensity, intrusion, and dominance of shelter we construct to protect activity. These are terms that have consistent mathematical definitions as noted on line 43 of Table 1. They can be measured, evaluated, and correlated to lead and limit the results implied by their titles. Their intuitive definitions, partial recognition, and lack of correlation have led to the contradictions and sprawl we face today.

I have written extensively about this topic in my blog at www.wmhosack.blogspot.com; on my page at Linked-In; and in my books entitled: Land Development Calculations, editions 1 and 2, The Equations of Urban Design, and Symbiotic Architecture. They are available from Amazon.com and I will not attempt to repeat their content in this brief essay.

I would also like to mention one essay in Symbiotic Architecture in particular. It is entitled, “The Least a Smart City Should Know”. It is not the easiest to read, but contains a blueprint for the relational database content that can be used to build knowledge regarding the values needed by the equations and forecast models of urban design.

I’ll close by including Table 1 as an example of an urban design forecast model that applies to all buildings served by an adjacent parking lot on the same premise. It is called the G1 Building Design Category and is the most common category used to shelter non-residential activity in many parts of the world -- when parking is required.

The gray cells in Table 1 indicate design specification variable locations. The values entered are mathematically correlated to produce the results shown in the Planning Forecast Panel. A change to one or more of the design specification values entered will modify the results produced in the panel. The point is that these specification values are not independent and isolated. They represent combinations that must be correlated -- and illustrate the interactive relationship of building design decisions.

The ten floor quantities entered in gray cells A44-A53 complete a set of gray cell specification options. The Planning Forecast Panel predicts their design implications using the equations on line 43. The impact of these options is classified by shelter capacity, intensity, intrusion, and dominance with the equations on line 43 of the Implications Module. I am not providing an evaluation of these impact measurements since this is a hypothetical example; but measurement, evaluation, and accumulated knowledge is the leadership promise offered by this system of building classification, design specification, planning prediction, and implication measurement.

The public revenue implications of the development capacity forecast in Table 1 is easiest to explain by looking at the gross building area options predicted in cells B44-B53. If $10 of revenue were expected per sq. ft. of gross building area, the total annual revenue would range from $48,843 to $73,511 depending on the floor quantity chosen. Since the buildable land area noted in cell F10 is 100% of the gross land area given in cell F3, the total revenue projections would be divided by 5.230 acres to find the revenue potential per acre consumed from the city’s inventory. This would range from $9,339 to $14,055 per acre. A simple comparison with the city’s annual expense per acre would indicate the contribution or subsidy implications of the project.

The results that evolve from fundamental design specification decisions have been overlooked for centuries; and claims of overdevelopment and oppression are not easily overcome in the face of economic hardship claims -- until the examples become too extreme to ignore during the debate that ensues. The Implications Module in Table 1 illustrates one method of measuring the impact of shelter composition on our quality of life within the urban fabric we create. When these measurements are combined with the financial evaluation mentioned in the paragraph above, it will become easier for a city to evaluate the combined impact of urban design decisions. A city that understands these implications for every parcel within its jurisdiction is a city that is prepared to evaluate the land use and urban design decisions that will affect its future.

Two Simple Questions

Question 1: What does the taxable land in a city’s inventory yield in average revenue per acre? A city knows its taxable acres per lot or parcel and the answer is as simple as dividing its total annual revenue by the total number of these acres.

Question 2: What does it cost a city to operate, maintain, improve, and finance a desirable quality of life per taxable acre? It knows its total annual expense and the answer is as simple as dividing this expense by the taxable acres served. However, a city is required to balance its budget each year. This means that its revenue per acre must equal its expense per acre, but this does not mean that the city is providing a desirable physical, social, psychological, environmental, and economic quality of life. If it isn’t, the only solution is to improve the total revenue produced by the sum of the acres available, and this is a function of the taxable activity present on each parcel within its corporate limits.

A city’s historic, and current, solution is annexation to increase the taxable acres within expanded corporate limits. This provides new money to meet current obligations when land is available, but the new revenue per acre can prove inadequate to meet increasing expense as the annexed area ages. The problem is exacerbated when a city has no land to annex and decline increases as redevelopment meets extensive opposition. It is rooted in a lack of knowledge concerning the revenue per buildable acre that can be expected from the spectrum of land use activity options available. This makes it impossible to equate urban land with its estimated revenue productivity per acre, and to allocate these acres to achieve a desired balance that is economically sustainable over time.

The acres in a city’s inventory are a primary source of its revenue, but all do not produce the income needed to equal a city’s average expense per acre. If a city does not understand the economic implications of land use and development capacity allocation, it will continue pursuing random economic development projects without the comprehensive strategy needed to lead its physical decisions to foreseeable financial improvement in a revenue and expense equation that determines its quality of life.

Design Decisions That Determine Single-Family Subdivision Density

I have written three essays entitled, "Design Decisions That Determine Apartment Density”; “Design Decisions That Determine Townhouse Density”; and “Design Decisions That Determine Single-Family Detached Housing Density”. They were written to identify the design topics whose values must be mathematically correlated to lead residential shelter capacity toward intensity combinations that avoid overcrowding and sprawl.

Houses provided in subdivisions have led to the term “sprawl”, but the design decisions that produced this reaction to overdevelopment have remained ambiguous, or isolated when partially recognized by zoning ordinance regulations. This essay is about the complete vocabulary of design decisions that combine to produce the shelter capacity of subdivisions -- and the implications of these choices.  

There are 27 gray cell entries in Table 1 that represent decisions collected in 3 modules entitled, “Land”, “Lot”, and “Building”. Gross land area is given in cell F3 and the objective of the table is to predict the average number of lots and gross home area options that can be constructed on the land area given under the conditions specified by the gray cell values entered and mathematically correlated. These predictions can be found in the Planning Forecast Panel at the bottom of the table, and they will change whenever one or more of the gray cell values are modified in the spreadsheet.

The Land Module in Table 1 pertains to traditional subdivision plans that provide no common open space for shared public amenities as noted by the 0% values entered in cells F13 and F14. If percentages had been entered in these cells, the remaining shelter area would have declined as a percentage of the buildable area available, but the impervious cover limit calculated in cell F12 would have remained for every lot subdivided from the smaller shelter area.

The 10 gray cell values entered in the Lot and Building Modules of Table 1 are used to find the first floor footprint area remaining on the lot area given in cell F23 after all other allocation is subtracted. This footprint area is found in cell F46. It is multiplied by the floor quantity alternatives entered in gray cells A55-A63 to find average gross home area options for the given lot area in Column B of the Planning Forecast Panel.

This footprint, or first floor area in cell F46 may seem low for a 9,000 sq. ft. lot, but it is a function of the 30% storm sewer capacity calculated in cell F12 from the 70% unpaved open space entered in cell F11. It is not only low. The area is a limit that includes all future expansion. This should indicate the critical importance of a subdivision feature that is often overlooked until storm sewer flooding produces a need to supplement the developer’s limited contribution with a public relief sewer. I cannot overstate the need to take the value entered in cell F11 seriously for this reason, along with the implications calculated in cell F12 and the related implications in the Planning Forecast Panel of Table 1. If the storm sewer capacity calculated in cell F12 had been greater, the lot area entered in cell F23 could have been reduced while producing an equal or greater footprint area. This would have produced greater shelter capacity per buildable acre and reduced land consumption for the most desired dwelling unit configuration on the planet. The downside is that too great a decrease in the value entered in cell F11 would increase the intensity calculated in Column H of the Implications Module until it prompted a flight similar to that of the original suburban migration.

Estimated lot quantity for the recipe entered in Table 1 is found in cell C55 of the Planning Forecast Panel by dividing the average lot area given in cell F23 into the shelter area remaining in cell G17. Three additional columns of predictions are also included in the Planning Forecast Panel.

The Implications Module in Table 1 is the last feature of the Table 1 forecast model. The shelter capacity of the land area given is related to the floor quantity options entered in Column A. The results are used by the formula in cell H53 to produce the related intensity values in Column H. These calculations measure the relationship of building mass and pavement to unpaved open space when floor quantity options change in Column A and the remaining gray cell values entered are constant. Any change to one or more of the gray cell values entered will produce a revised planning forecast and set of implication measurements.

The intrusion measurements calculated in Column J translate the floor quantity options entered in Column A to a compatible four-part measurement system.

The measurements calculated in Column K of the Implications Module combine the capacity, intensity, and intrusion measurements of Columns G-J into a consolidated statement of project dominance options. In other words, a project dominance value in this example is produced by correlating 18 design decisions that do not exist in isolation and must be coordinated to provide correlated leadership direction for the three physical fronts of shelter design.

From a city design perspective, land use planning with design specification correlation can optimize the use of land to shelter any activity, and is the key to correlating capacity, activity, intensity, and economic stability within limited geographic areas.

CONCLUSION

I hope that I have made the significance of comprehensive, coordinated design value decisions apparent. Our current concept of minimum, independent zoning regulations cannot lead us toward the shelter capacity and activity allocation needed to protect the physical, social, psychological, environmental, and economic welfare of growing populations within geographic limits that protect their source of life. We depend on shelter for survival but it consumes land that is our source of life. We are expected to discover the correlation required.

I have deleted most of the equations in Table 1 to simplify the illustration and have omitted a detailed discussion of Building Design Categories and Residential Activity Group classification that I have mentioned in earlier essays. 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. The subdivision chapter in this book considers two fundamental Traditional and Clustered subdivision questions in depth:

1)      What lot quantity and average home area options can be accommodated in a subdivision when gross land area and minimum lot area are given? 

2)      What minimum lot area, shelter area and buildable land area is needed for a subdivision when lot quantity and average home area objectives are given?

A third question is a variation of Question 1.

3)      What average lot area and home area options are available to a subdivision when gross land area and lot quantity objectives are given?

A fourth question is solely devoted to cluster subdivisions.

4)      How is average home size affected when lot quantity remains constant in traditional and clustered subdivision plans for the same gross land area?

The answers to these questions can be examined in spreadsheets I have called forecast models. The values assigned are like a musical score. The symphony produced will remain a function of the talent available. The objective is to eliminate the dissonance produced when a score and conductor are missing.

Design Decisions That Determine Single-Family Detached Housing Density

This discussion concerns the land required for single family detached residential activity when it occupies the G1 Building Design Category. The combination is referred to as the G1.R1 Activity Group. It may be the most desirable form of residential shelter on the planet, but the scope of demand and amount of land it consumes is becoming a serious concern. It needs an improved method of measurement, evaluation, and prediction to ensure that its land area allocation within city limits contributes to a city's average economic yield per acre that is equal to, or greater than, the average municipal expense per acre required to provide a desirable quality of life for its residents.

TABLE 1

Table 1 pertains to single family detached homes when lot area is given. It contains twenty-five gray cell locations for design value decisions / entries. These entries are mathematically correlated within the table to accurately measure or predict shelter capacity and its implications. This is more significant than may be realized because capacity per acre multiplied by revenue per sq. ft. determines the financial contribution provided by every acre in a city; and inadequate contributions produce average revenue per acre deficits that can plague our efforts to improve the quality of life provided.

The objective of the Lot Module in Table 1 is to identify the buildable lot area remaining from the gross lot area given in cell F4 after 5 design value decisions are entered and subtracted.

The value entered in cell F12 of the Lot Module deserves special mention. It is based on the storm sewer capacity planned or present for the branch line serving the area in which the lot is located. In this example 70% unpaved open space has been entered. This means that storm sewer capacity equals 30% impervious building and pavement cover when additional detention and/or retention systems are not provided. This 30% has been calculated in cell F13 from the 70% unpaved open space entered. In my experience this is one of the most overlooked issues in city planning. I have tried to draw your attention to this topic by requesting that you enter this percentage rather than the 30% impervious cover that is derived from its provision. Variances are routinely granted for building cover and pavement percentage increases that reduce the unpaved open space remaining on a given lot. These are granted with the best of intentions, but can exceed the impervious cover capacity of the adjacent storm sewer or drainage system. This often occurs because impervious cover limits are rarely recorded on plats for recall and review after the initial civil engineering installation. In these cases, variance requests can be approved to expand building cover and pavement percentages along branch storm sewer lines that were not designed to handle the increase requested when it begins to occur on multiple lots over time. The result can become a source of basement flooding, disease, decline, and decay.

DENSITY

The net density calculated in cell F14 of Table 1 also needs explanation. The discretionary values entered in cells F5-F7 and F9 have been subtracted from the gross lot area given in cell F4 to find the buildable lot area remaining in cell F11. If an unbuildable percentage of the lot had been entered in cell F5, the buildable lot area calculated in cell F11 and G11 would be less than the total lot area given in cell F4. If the total lot area were used to calculate density in this case, density would appear to be less than a calculation based on the buildable land area remaining and more lots would be permitted.

A conscious decision has been made to calculate density based on the buildable land area available because it reflects the amount of useful space available. If there had been an unbuildable ravine on the lot, for instance, it would have enhanced the view but condensed the activity present. In other words, the larger lot size would have produced a lower density calculation but increased the intensity of activity on its remaining buildable area. The bottom line is that density is only affected by the first 6 discretionary value decisions entered in Table 1 and 10 more correlated values are required to improve leadership guidance. Density can be a deceptive calculation for many reasons based on these omissions and lack of correlation.

PAVEMENT MODULE

The Pavement Module in Table 1 contains 4 discretionary design decisions that serve to further reduce the impervious cover area remaining for primary building footprint on the buildable lot. These calculations are included in cells F22 and G22.

BUILDING MODULE

The Building Module contains 5 discretionary design decisions that continue to reduce the impervious cover area available for building footprint within the buildable lot area. This continued subtraction leads to the first floor impervious area remaining in cell F32 and B41. Multiplication of the nine floor quantity options entered in cells A41-A49 by the first floor area remaining in cell F32 produces the 9 home size options calculated in column B of the Planning Forecast Panel.

PLANNING FORECAST PANEL

Column D in the Planning Forecast Panel presents total building area options that include primary home, garage, and accessory building areas. Column E presents the buildable lot area percentages consumed by the total building area options in column D. It may be a surprise to see the low percentage calculated.

It may also be a surprise to see on line 43 of the Planning Forecast Panel in Table 1 that a 60 x 120 foot lot served by a storm sewer with 30% impervious cover capacity can only support a 2 story home with 990 sq. ft. of habitable area and 1,590 sq. ft. of total building area. Cell B41 also shows that the first floor area of this home would only be 495 sq. ft. based on the 15 discretionary design values entered above. For the uninitiated this is about the size of a two car garage. The motive behind variance requests for building and pavement expansion should be apparent from this low number, as well as the threat of variance requests to installed storm sewer capacity. The mathematical justification for home size limits in relation to storm sewer capacity, unpaved open space, and 15 other variable percentages has rarely, if ever, been available, however; because the measureable implications of correlated shelter design decisions have been unavailable. They will become important considerations as populations continue to grow and consume the land like locusts of old.

IMPLICATIONS MODULE

The Implications Module beginning on line 51 calculates that the 2 story, 990 sq. ft. home mentioned above represents a shelter capacity of 9,621 sq. ft. of total building area per acre; an intensity of 0.066; intrusion of 0.400; and dominance of 0.466. These statistics are like the first blood pressure readings, however. We have an intuitive sense of the implications measured based on professional experience, but no accumulated knowledge that adds credibility to leadership recommendations.

THE 3,150 SQUARE FOOT LOT

The previous discussion involved a 60 x 120 foot lot, but the 495 sq. ft. floor plan area that emerged reminded me of a 3,150 sq. ft. lot created in 1907 that I examined in my latest book, The Equations of Urban Design. I’m quoting it here because I think its comparison to the statistics just calculated may be helpful.

“The home and lot in Diagram 9.3 was built in 1907. It represents one of the first rings of migration from the central city and is an early form of an evolving suburban lot that is now part of the inner city.

The alley and detached garage represent a transition from stables, outbuildings, and remote kitchens to the automobile. Small rear yards became replacements for ample kitchen gardens. Alleys provided inadequate turning radii into garages and extended driveways consumed remaining open space for access to the garage from the street. Parking in the street was prompted by narrow lots, constrained driveways and alleys of inadequate width and turning radii. Their relative invisibility encouraged hidden behavior and indefensible space.

The home had a gravity coal furnace, electric power, public water supply, one bathroom, and was served by a public sewer that combined sanitary effluent with storm water runoff to open street inlets. At the time, it represented a significant improvement to public health and welfare, but combined sewers now tell us a different story.

Table 9.4 recites the design specification values that originally applied to this lot. Private, unpaved open space UOSL is 43.21% of the lot as noted in cell F12, but the percentage does not indicate a minimum area requirement. It is a measurement of existing condition. This means that 56.79% of the buildable lot area is impervious cover.

Impervious cover increased to 64.41% after a building addition was approved as shown in Diagram 9.4. The result was increased storm water runoff that exceeded the capacity of the combined sewer during moderate to heavy rainfalls. This increased basement and street flooding with storm water and sanitary effluent.

The driveway and garage represented 27.73% of the lot. This is an overlooked statistic but was a greater impervious area than the original building footprint. In other words, an attempt to accommodate the car and driveway reduced the alley to a garbage collection service while providing inadequate sewer capacity and sacrificing unpaved social open space. The result encouraged unsafe, on-street parking but was a step in the right direction. It provided the population with a home of their own, but did not adequately anticipate the continuing need for relief from overcrowding. Eventually, the car permitted escape to suburban areas and the migration has led to invasive sprawl as inner city homes are left to decline.

Open space on this historic lot was originally minimized to increase density within walking distance to employment since the car was a luxury. Overcrowding was exacerbated by a fifteen-foot front yard adjacent to parked cars along the street; side yards that could be as small as six inches; and a small rear yard surrounded by buildings, fence, and alley that served to complete the encirclement.

So what do the measurements tell us when entered in Table 9.4? First, the forecast of a 513 sq. ft. footprint for a two-story, three-bedroom home in cell F32 represents a floor plan equal to many two car garages today. The home area potential in Column B of the Planning Forecast Panel shows that increased floors in Column A would produce increased area in Column B, but would also produce increased levels of intensity and dominance in Columns E and G of the Implications Module. This overwhelms the open space provided in my opinion. The density calculated in cell F14 is constant because the lot area per dwelling unit does not change, but density is an inaccurate measure of the shelter capacity, intensity, intrusion, and dominance produced by increasing floor quantities as I mentioned earlier. The shelter capacity provided was 21,929 sq. ft. per acre, but the design specifications that produced this capacity also produced an intensity of 0.286 and a dominance level of 0.686. This was for a two-story building. The Implications Module shows that a five story building would produce a dominance level of 1.563 based on the values entered in the design specification template.

Design specification values are the ingredients that produce shelter capacity, intensity, intrusion, and dominance. These were intuitive design decisions in 1907 regarding lot size, home size, impervious cover, open space, and shelter capacity. The relationship of these decisions to public health, safety, and welfare could only be anticipated based on comparison to truly inadequate historic conditions. The relationship of these decisions to physical, social, psychological, environmental, and economic quality of life was not even an issue when health and safety were at risk. These evolving decisions caused residents to seek relief from health and safety solutions that still did not reach the quality of life desired. In response, market experiments with lot size and customer preference began to consume farm land and the Natural Domain in earnest.

Table 9.5 and Diagram 9.4 are included to show the implications of a 480 sq. ft. building addition that was approved for the 3,150 sq. ft. lot. The addition reflects the occupant’s desire to increase a small habitable footprint, but the additional impervious cover reduces already inadequate combined sewer capacity. It also increases intensity from 0.286 to o.422; dominance from 0.686 to 0.822; and decreases the unpaved open space percentage from 43.21% to 35.59%. The result is increased overcrowding behind an identical façade that conceals the decline in desirability. This is the path to blight that encourages sprawl.

In other words, inadequate initial home area encouraged expansion that further compromised infrastructure capacity and increased intensity pressure levels that were already excessive. These conditions were eventually abandoned by those who could afford to search for an improved quality of life with the automobile. It has been a random search for an unmeasurable “quality of life”, and experiments have been compromised again and again by well-meaning but intuitive lot sizes, variance approvals, and rezoning requests. Experiments will continue to consume the planet with sprawl and decline until we can measure, evaluate, and forecast shelter capacity, intensity, and dominance options with the power to protect our quality of life within a limited Built Domain.

I’m only telling you what you already know. The difference is that I’m translating tacit knowledge with mathematical accuracy. It adds credibility to the debate; improves the ability to evaluate options; improves the opportunity to create knowledge; and offers the vocabulary needed by leadership during the formative stages of strategic shelter, movement, open space, and life support design. When city design evaluation and decision is documented, it becomes easier to adjust and defend the result from random requests from special interest for modifications that have long range implications for our health, safety, and quality of life.”

COMPARISON

The most relevant measurements from Tables 1, 9.4, and 9.5 are summarized in columns D-F of Table 2, but measurements need observations to become useful. The first and most important is the abstract observation that the results presented in the Planning Forecast Panel and Implication Modules of these tables were produced by correlating the measurements entered in them. The second is that the unpaved open space percentages on line 12 decrease significantly as impervious areas increase on line 13 because the total cannot exceed 100%. The third is that density remains constant in cells E14 and F14 even though intensity increases in cells E42 and F42 because the number of dwelling units does not increase. It is dwelling unit area that increases. The fourth is that driveways on line 29 of Table 2 consume a great deal of the impervious lot area allocation. The fifth is that first floor area on line 32 remains low for all examples when the impervious cover limit on line 13 is not exceeded. This encourages expansion requests over time that places further demand on a sewer system that often has inadequate capacity. The sixth is that intrusion on line 43 remains constant because floor quantity on line 35 remains constant. The seventh is that intensity and dominance increase on lines 42 and 44 because of the impact produced when all design decisions entered in the gray cells of Table 1, Table 9.4, and Table 9.5 are correlated. This means that a focus on a few independent topics of zoning can easily lead to the wrong conclusions.

A growing home market will continue to experiment by consuming more land for shelter, movement, open space, and life support until: (1) Measurement, evaluation, and correlation is recognized as an essential prerequisite for shelter design leadership; and (2) Land consumption for shelter is limited to force adjustment to the geographic boundaries of a sustainable, symbiotic shelter domain. Growing shelter sprawl seeking ideal single-family dwelling unit lot sizes over the face of the planet will continue to deplete our source of life until we recognize this self-evident truth.

From a shelter capacity perspective, the quantities in cells E41 and F41 provide the most for the land consumed, but the intensity levels in E42 and F42 and the dominance levels in E44 and F44 are inner city characteristics that have prompted flight to suburban sprawl in the twentieth century.

The lot in column D of Table 2 could be considered a minimum size if it weren’t for the 30% impervious cover limit in cell D13. This limits the first floor area predicted in cell D32 and the limited home area predicted in cell D36. (I should also mention that these are maximum first floor areas that include future expansion potential.) The obvious solution is to reduce the unpaved open space percentage and increase the impervious cover percentage planned. This would increase the shelter capacity predicted in cell D41, but also increase the intensity and dominance calculated in cells D42 and D44 - as well as the cost of the storm sewer. At this point in time it is anyone’s guess if these intensity and dominance measurements represent desirable single-family detached residential lifestyle relationships -- much less a land allocation for these units that can yield revenue per acre equal to the average revenue per acre a city requires for its desired lifestyle.

The relationships in Table 2 will vary every time one or more discretionary decision values are modified in the gray cells of its parent tables. The search for values that can be a foundation for a desirable quality of life is what is meant by the search for “balance”. The fact that every building design category and occupant activity group is affected by different sets of value decisions makes the search for an economically stable and desirable quality of life a far more complicated city design challenge than presently envisioned.

CONCLUSION

I hope that I have made the significance of comprehensive, coordinated design value decisions apparent. Our current concept of minimum, independent zoning regulations cannot lead us toward the shelter capacity and activity allocation needed to protect the physical, social, psychological, environmental, and economic welfare of growing populations within geographic limits that protect their source of life. We depend on shelter for survival but it consumes land. We are expected to discover the correlation required.

I have deleted most of the equations in the attached tables to simplify the illustrations 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.

POSTSCRIPT

A house is the third category of shelter within the Residential Activity Group. The other two are townhouses and apartments. It is a detached building for single-family use on a legally defined lot and became governed by minimum requirements for health, safety, and welfare in the 20^th century. Early plans failed to adequately anticipate the automobile however, and early houses were tightly packed to enhance pedestrian accessibility. An intuitive response to intensity and deteriorating physical conditions produced sprawling flight to suburbs providing more space for shelter, parking, movement, open space, and life support. Lot size grew to consume increasing amounts of land as populations grew to increase the need in a limited Natural Domain that was no longer a land without end.

The unanswered question that prompts sprawl remains and is not limited to housing. It seeks to understand the area required to shelter growing human activity without excessive physical intensity. The lack of an answer has led us to consume greater amounts of land that is vaguely recognized as our source of life.

Design Decisions That Determine Townhouse Density

 

 

A townhouse is a dwelling unit attached to but not stacked above others in a common building shell. It is often called a rowhouse for this reason. The physical shell, however, may be converted and occupied by any other activity when in conformance with local building and zoning codes.

The capacity of land to accommodate gross building area for any activity begins with the primary parking system adopted. Based on this definition, there are only six building classification categories on the planet.

1)      G1: Buildings with adjacent surface parking on the same premise

2)      G2: Elevated buildings over surface parking

3)      S1: Buildings with an adjacent parking garage on the same premise

4)      S2: Buildings with an underground parking garage

5)      S3: Buildings over a parking garage

6)      NP: Buildings with no parking required

These 6 categories constitute the Shelter Division in the Urban and Rural Phyla of a Built Domain that is one of two worlds on a single planet.

All residential land use activity falls into one of three classification categories and occupies one of the 6 building design categories mentioned above.

1)      R1: Single-family detached dwelling units

2)      R2: Single-family attached and spread dwelling units that are not elevated above a garage. (townhouses, twin-singles, four-family, and so on)

3)      R3: Single-family attached and stacked dwelling units (apartments)

The combination of the R2 occupant arrangement within the G1 building category shell is referred to as the G1.R2 Activity Group.

The purpose of this discussion is to illustrate that site planning decisions involve too many correlated variables to be led by a few uncorrelated zoning regulations.

The design decisions that determine G1.R2 townhouse density are identified by the 68 gray cells in the Table 1 forecast model. Only 4 of these topics and 15 gray cell items are generally addressed by a zoning ordinance. The remaining 53 are discretionary. This encourages arbitrary leadership decisions that have never been measured or evaluated for the physical, social, psychological, environmental, and economic quality of life that results. We only know that we are creating sprawl in an attempt to escape the excessive intensity, deteriorating conditions, and market acceptance of decline within our cities; but cannot determine with our current measurement tools if revised percentages of shelter capacity, activity occupancy, and intensity will produce lifestyle improvement over time as maintenance expense increases.

Table 1 applies to the G1.R2 Activity Group and illustrates that the density calculated in cell J55 is a function of the 68 mathematically correlated gray cell values entered above. The only values typically led by zoning regulation can be found in the 15 gray cells of columns D, H, and L of the Townhouse Module. The remaining 53 are discretionary but needed to find the density value in cell J55. Unfortunately, density does not clearly explain the shelter capacity, intensity, intrusion, and physical dominance implied by these decisions. These measurements are unknown; and they cannot be related to a reference library of accumulated knowledge until consistent measurement and evaluation of existing conditions is compiled.

In fact, under current zoning regulations, it is possible to decrease density to meet a requirement while increasing the physical intensity created. For instance, if I increased the habitable areas planned in column C of the Townhouse Module and held all other values constant, the total number of dwelling units predicted in cell K53 for the land area given would decline from 147 to 137. This would reduce the density calculated in cell J55 from 8.98 to 8.34 but increase the total building area planned in cell L53 from 205,284 to 219,039 sq. ft. This increases the physical intensity calculation from 0.115 to 0.123 in cell D61. In other words, the number of families would decline but the physical proximity of the buildings would increase on the same land area. This indicates the social nature of density measurement and its inability to lead the physical characteristics of shelter intensity within cities. Confusion over this distinction has left innumerable loopholes in zoning ordinances illustrated by the 53 discretionary gray cells values mentioned. The values in these cells can be adjusted to increase profitability while ignoring the unknown consequences of excessive intensity. This lack of leadership simply encourages our intuitive, sprawling search for relief.

The percentage of unpaved open space requested in cell F11 of Table 1 and the dwelling unit mix specified in columns B and C of Its Townhouse Module are two design decisions topics that often remain unspecified in a zoning ordinance. I’ve prepared Table 2 to explain the random implications associated with this degree of flexibility. The examples are only a few of the many that could be made by exploiting the loopholes a zoning ordinance creates with the omission of pivotal design topics, decisions, and correlation.

The omission of dwelling unit area specifications in a zoning ordinance created the opportunity described above and recorded in column D of Table 2. Gray cell D2 in this table notes the change made in Table 1 to produce the results in cells D5-D8. Columns E-H in Table 2 record the results produced in Table 1 by the unregulated changes noted in the gray cells of Table 2. Density and intensity vary in unison in Table 2 because all 68 design decisions are mathematically correlated in Table 1. In reality, density could vary to a much greater degree in Row 5 because current zoning regulations are not complete or mathematically correlated. This arbitrary approach was the best we could do for decades and was justified by our inability to comprehensively classify, itemize and mathematically correlate the design decisions involved with schematic site planning.

I hope I’ve made it clear that anything can happen when one or more values related to any of the gray cell design decisions in Table 1 are modified without prior understanding. This has compromised our ability to lead change because we have not been able to classify results within a spectrum of intensity that can be used to shelter growing populations within geographic limits that protect their source and quality of life.

The challenge is to correlate a city’s land areas with the building capacity, intensity, and activity needed to produce an average economic yield per acre equal to the total average expense per acre it needs to provide the quality of life it desires. A mismatch simply produces decline and sprawling attempts to adjust revenue without an understanding of the economic yield per acre produced by combinations of shelter area, capacity, intensity, and activity within cities. It cannot be done without mathematics and relational databases.

I’ve previously written an essay entitled, “The Decisions That Determine Apartment Density”. This essay has addressed townhouses. They’re both part of the Residential Activity Group, but these references can be confusing without an overview of the building classification system. I’m including the Table of Contents of my new book, The Equations of Urban Design, to provide this overview. (Keep in mind that a land use activity may occupy any building design category when both comply with local building and zoning codes. The fact that there are many activities but few building design categories makes shelter capacity and intensity measurement, evaluation, and prediction useful, since shelter capacity must be present before occupant activity can contribute revenue per sq. ft. of shelter and economic yield per acre of incorporated area.)