NOTE: All exhibits and tables are located at the end of this text.
We call the growth of cities “sprawl”, but know little about the cellular content of this pathogenic organism as it spreads across the face of the planet. We call these cells lots, parcels, acreage and so on. They are created by an army of investors and specialists led by incremental plans for land use, property acquisition, subdivision, engineering, architecture, and sales. The plans produce new cells that multiply to slowly consume their source of life, the planet. There has been no realistic discussion of geographic limits for cities because there has been no mathematical ability to predict, evaluate and correlate the shelter capacity and activity of cells within these limits. This has made shelter sprawl a default condition based on annexation that produces new cells and revenue to repeat old mistakes at its leading edge of growth - with declining cells multiplying in an expanding core of blight. Single-family detached housing has been on the front line of this random advance, and it has been led with incomplete, uncorrelated direction that has frustrated leadership credibility and authority.
Shelter capacity is gross building area per acre that can be occupied by any activity, assuming zoning and building code compliance. Sprawl results from population growth that cannot survive without shelter for its many activities, and an inability to correlate shelter capacity and activity with average public revenue and expense per acre over defined municipal areas. This prevents our ability to achieve a desired quality of life within areas that are limited to protect their source of life.
My focus in this brief essay is to discuss: (1) the anatomy of cities, (2) the cellular category we call single-family detached housing, (3) the list of single-family cellular contents I refer to as design specification topics, (4) the mathematical relationship of single-family design specification topics, (5) the shelter capacity options produced when topic values are modified, and (6) the measureable intensity levels produced by correlated topic value decisions. The effort is based on my belief that we must begin to understand, predict and correlate shelter capacity with activity, revenue, and expense before we can lead the combination to form cities with a desirable quality of life that are limited to protect their source of life.
One of two building design categories can be chosen to shelter single family residential activity. In order to proceed, I need to explain these categories and their fit within a Built Domain classification hierarchy that permits shelter measurement, evaluation, prediction and knowledge to be accumulated, organized and taught on a consistent, comparable basis that has the potential to improve our leadership performance.
THE ANATOMY of CITIES
Population growth has produced two worlds on a single planet: The Built Domain and The Natural Domain.
The Built Domain is divided into Urban and Rural Phyla that contain Shelter, Movement, Open Space, and Life Support Divisions. Each phylum is distinguished by the significantly different areas associated with the same divisions. (See Exhibit A for a more complete classification outline.)
The Shelter Division in both phyla is served by its supporting Movement, Open Space and Life Support Divisions. Each cell in the Shelter Division contains one of the eight building design categories listed on lines 1-31 of Exhibit B. These categories are classified by their method of parking supply, not their internal activity or external appearance. This makes it possible to reconcile unique buildings into a common, limited set of classification categories. The residential activity groups listed below line 33 in Exhibit B represent six of the many activity groups that can occupy a limited list of building design categories.
Single-family detached residential activity is designated R1 and can occupy either the G1 or G2 Building Design Category. Table 1 applies to the G1 Building Design Category when it is occupied by R1 activity and gross land area is given. This table will be used to address discussion topics 2-6 previously mentioned.
SINGLE-FAMILY DETACHED HOUSING
The Reference Panel on lines 2-5 of Table 1 recites the characteristics of seven common single-family lot sizes in columns C-J. These lot sizes will be used as references for the remainder of this essay. Column C represents an escape from earlier 15-30 by 100 foot or less lots created when land ownership and the automobile made flight from a high density urban core feasible. These small lots are now part of inner cities. They could not compete with the larger 50x120, or 6,000 sq. ft., lots created in first ring suburbs and noted in Column C.
The 6,000 sq. ft. lot typically contains a one-car detached garage in the rear yard with a long access driveway that passes by the house and through the rear yard. Social activity in the rear yard is compromised by the garage and driveway presence. Fences often magnify rear yard insufficiency in an effort to improve privacy.
The 60x120 foot lot in column D was an attempt to offer an alternative to the smaller lots in Column C. It typically contains a two-car garage that is either attached or detached. Detached garages still require extended driveways and both still detract from a slightly larger rear yard. Attached garages preserve the rear yard and require shorter driveways. Both still seek to introduce rear yard privacy with fences on occasion.
Variance requests to expand home sizes with additions, add outdoor social pavement, or connect to detached garages are often requested by owners of Col. C-E lots. These variance requests reflect attempts to adapt to changing lifestyle expectations with over-development and excessive impervious cover on inadequate lot areas. This in turn can overwhelm storm sewer capacity when repeated along a shared storm sewer line.
The 90x120 or 12,000 sq. ft. lot in Column G seems to provide enough land area to meet current mainstream expectations regarding home size, garage capacity, social pavement, service pavement, and privacy but variance requests to expand can still reduce the unpaved open space percentage that serves installed storm sewer capacity. Fence installations decline in quantity when not prohibited.
The lot sizes in Columns G-J indicate increased affluence and privacy. In general, increasing lot size increases the scope of sprawl per dwelling and the movement, open space, and life support systems that must be extended to serve it.
All lot sizes are subject to the impervious cover percentage limits associated with installed storm sewer capacity. It is in a developer’s interest to minimize initial sewer capacity and impervious cover potential to serve only the initial installation in an effort to reduce cost. When this occurs, it eliminates future home expansion potential and places unpaved open space at risk of future expansion requests that seek to exceed the impervious capacity of the storm sewer. It is in the public interest to record initial impervious limit information for future reference when variance requests are submitted, but this critical information is often overlooked, rarely compiled on a city-wide basis, and unavailable for comparison with measured impervious cover requests during variance proceedings.
The bottom line is that unpaved open space percentages and impervious cover percentages are critical planning topics that must be recognized and will be included with this discussion.
Table 1 illustrates the G1.R1.L1 Forecast Model listed on line 36 of Exhibit B. Sixteen variable specification topics are identified with boxes in three design specification modules. The Lot Module begins on line 9. The Garage and Accessory Building Module begins on line 21. The Pavement Module begins on line 31. Each box in a module must receive a specification value to define the two-dimensional site planning characteristics of a housing proposal. Nine specification boxes are provided in Col. A of the Planning Forecast Panel to receive floor quantity options. These values complete the information needed by the master equation in cell A44. It converts the maximum first floor area found in cell G40 into nine home area options in cells B50-B58 based on these values. In other words, sixteen two-dimensional specifications in the Land, Garage and Pavement Modules of Table 1 are correlated with the nine floor quantity options in the Planning Forecast Panel to produce the line item options presented in the forecast panel. A change to one or more of the design specification values in the three modules, or a change to one of the floor quantity options in the Planning Forecast Panel, will produce a new forecast of implications in the Planning Forecast Panel.
The Lot Module in Table 1 is based on a given lot size of 6,000 sq. ft. or 0.13774 acres in cell F10. The module subtracts a number of potential demands on the gross lot area given to arrive at the buildable lot area calculated in cell F17. An unpaved open space percentage is entered in cell F18 and the remaining impervious cover is automatically calculated in cell F19. The impervious cover percentage is used to calculate the amount of buildable land that can be devoted to building and pavement cover in cell G19.
Garage and Accessory Building Module
The five specification values entered in this module are used to calculate the amount of impervious cover that is, or will be, consumed by garage and accessory buildings in cell G29. This reduces the amount of impervious cover remaining for first floor home area.
The five specification values entered in this module are used to calculate the amount of social and service pavement planned or present around the home. The total pavement area is calculated in cell G38 and it too reduces the amount of impervious cover remaining for first floor home area.
When the available footprint area in cell G40 is multiplied by the floor quantity options in cells A50-A58, the master equation in cell A44 calculates gross home area options in cells B50-B58, including any bonus area above the garage. If cells F25-F27 are zero, there is no bonus area and the reduced home area options calculated in cells C50-C58 will match the home area options calculated in cells B50-B58.
The buildable land area remaining for building footprint was found in cell G40 by subtracting the total support building and pavement areas found in cell G39 from the total impervious area available in cell G19. The remaining first floor or footprint area of 528 sq. ft. was the first indication of an outdated lot area. The footprint was a function of the 30% impervious cover available and the design specification values entered. The impervious cover percentage limits future expansion, and I’ve seen more than 60% permitted by variance approval when the storm sewer capacity is unknown. It’s very difficult to say no to your neighbors when opinion cannot be answered with fact.
Shelter Capacity Options
Shelter capacity (SFAC) is equal to total building area (TBA) in sq. ft. divided by buildable lot area in acres (BLAC). When buildable lot area (BLA) is expressed in sq. ft.:
SFAC = TBA / BLA / 43560. This can be reduced to:
SFAC = TBA * 43,560 / BLA
Home capacity per buildable acre (HCAC) does not include garage and accessory building area. It is presented in Column G of the Planning Forecast Panel of Table 1 but does not give an accurate impression of the total building area contribution to site plan intensity. Total building area (TBA) includes garage and accessory buildings in col. D and is used for this purpose. Shelter capacity options are based on total building area (TBA) and presented in Column H as one element of the intensity equation in cell J48. Both capacity and intensity statistics are related to the floor quantity options in Column A.
As an example, a home with 2,000 sq. ft. of total building area on ¼ acre equals a shelter capacity of 8,000 sq. ft. per acre. The same total building area on 1/8 of an acre represents shelter capacity of 16,000 sq. ft. per acre. This correlates land consumption with its shelter potential, and is one element of the intensity equation in cell J48. If the occupant activity on both land areas produced equal revenue per sq. ft., the 1/8 acre lot would produce greater yield per acre but introduce much greater intensity.
The acres within a city are its raw material. The shelter capacity potential of each acre combines with occupant activity to determine the productivity of each acre. From a public perspective, the average yield per acre of municipal land area must equal or exceed its average expense to avoid budget reductions. The push to increase shelter capacity per acre to increase yield can produce excessive intensity that detracts from the quality of life a city is attempting to afford, however. This means we need an improved method of measuring, evaluating and correlating shelter capacity with occupant activity because decisions at this land allocation level produce intensity, revenue and context quantities that represent leadership decisions awaiting refinement by talent.
Intensity (INT) is the relationship of building mass and pavement to unpaved open space on a given land area in the Shelter Division of both the Urban and Rural Phyla of the Built Domain. The intensity equation is noted in cell J48 of Table 1. There is no attempt to pass judgement on the intensity statistics presented in Col J of this table, but I have mentioned that the lot size given in cell F10 is less competitive than the other options available to this activity group on line 2 of the Reference Table. It also has the highest density as shown on line 5.
Two and one-half stories has been a commonly accepted limit for building height on suburban residential lot areas. Table 1 presents the intensity produced by a 2.5 story building in cell J53 based on the sixteen values entered in the design specification boxes above. The history of this lot size and the intensity produced by the 2.5 story home specified provides a glimpse of the measureable specification topics that can be compared, evaluated and used to build leadership knowledge in the pursuit of sustainable cities with symbiotic potential and a desirable quality of life.
I hope Table 1 has made it clear that it takes at least sixteen correlated design specification values and one building height value to accurately predict a single-family detached housing option with the master equation in cell A44, and that this knowledge opens up a vast number of square foot related predictions. A few of these have been included in the Planning Forecast Panel of Table 1.
Incomplete, independent and uncorrelated specifications called zoning regulations often require choices among contradictions. When this occurs, it requires variance approval to reconcile the choices made. The variances approved are considered precedent setting, but they simply add confusion when there is no comprehensive correlation of all regulations that combine to affect shelter capacity and intensity. Contradictions in any endeavor simply frustrate consistent leadership direction.
Home sizes and lot sizes represent fixed decisions that can last for centuries. Changing circumstances require adaptation that cannot be accommodated easily, if at all. I chose the 6,000 sq. ft. lot in Table 1 to add this point to the discussion. I could have chosen the 3,150 sq. ft. lot on page 23 of my book, The Science of City Design, but this would have been too extreme for a brief discussion. The point is that both were desirable escapes from the punishing density of central cities at one point in time. Time passes however, and outdated home size can combine with outdated movement, open space, and life support infrastructure to introduce intransigent decline. In some limited cases this has been reversed when old neighborhood attributes become desirable again; but for most, cities are saddled with decline they have yet to solve with improved tools, knowledge and political determination.
Encircled cities without annexation potential often face budget reductions and decline or increased taxation. The consequences of encirclement have become apparent and have encouraged others to protect their annexation corridors into agriculture and the Natural Domain. It is an unhealthy formula that begins with a lack of data correlation that can lead to knowledge and adjustment. Improvement will require that currently isolated data centers be linked to a relational database with shelter forecast models that make land management evaluation feasible and defensible.
Comparison of Intensity Implications
I’m introducing Table 2 to make another point. The land area given is 0.34435 acres, or 15,000 sq. ft. and is generally referred to as a 1/3 acre lot. The impervious cover limit calculated in cell F19 is 4,500 sq. ft. when 70% unpaved open space is required in cell F18. This is the same open space percentage entered in Table 1, but the percentage produces a significantly higher impervious cover limit than the 1,800 sq. ft. in Table 1 because the lot size is greater.
The same number of garage spaces and garage cover is provided in Table 2, but a bonus habitable area over the attached garage has been provided in cell F27 based on the specification values entered in cells F25-26. After building cover and pavement are subtracted, the remaining impervious cover available for home footprint is 2,718 sq. ft. in cell F40.
Based on the values entered in the design specification template of Table 2, the 2.5 story home noted in cell A53 has a total home area potential of 7,034 sq. ft. This is calculated in cell C53 using the master equation in cell A44, and is significantly greater than the maximum home area calculated in Table 1 for a 2.5 story home on a 6,000 sq. ft. lot.
A 7,034 sq. ft. home on a 15,000 sq. ft. lot would be far greater than normal, but the 15,000 sq. ft. lot permits home expansion over time with a 30% storm sewer capacity. It simply permits too much. If, or when, the maximum home size is constructed; it would produce an intensity of 0.613 as calculated in cell J53 of Table 2 and be compatible with its neighbors. The intensity calculated for the 6,000 sq. ft. lot in cell J53 of Table 1 is only 0.287, but the 1,319 sq. ft. maximum home size is now considered less desirable.
The maximum home size permitted by 30% impervious cover on the 6,000 sq. ft. lot in cell B53 of Table 1 may be less than desirable; but if the neighborhood is desirable, it can prompt variance requests for building additions and pavement that exceed 60% impervious cover. Under these circumstances, shelter capacity will increase to 44,714 sq. ft. per buildable acre, intensity will increase to 2.535, and the potential for flooding will increase when adjacent neighbors demand equal treatment along the same sewer line.
If low intensity on a small lot produces less intensity when the impervious cover limit is respected, but much greater intensity when variances are granted to exceed this limit, how should lot size be addressed for a building design category and activity group that consumes the most land per occupant sheltered in urban areas? Keep in mind that lot size has been a major contributor to both inner city blight and suburban sprawl. A free market has sought relief from excessive intensity with this residential concept, but it rarely produces enough revenue per acre to offset a city’s average expense per acre over an extended period of time without increased taxation and budget cuts.
Unpaved Open Space Implications
If I prepared tables for ½ acre and 1 acre lots with similar 30% unpaved open space specifications, theoretical shelter capacity and intensity for a 2.5 story home would continue to increase from the 15,000 sq. ft. lot in Table 2. The ½ acre lot would produce 24,381 sq. ft. per acre and an intensity of 0.731. The one acre lot would produce 26,892 sq. ft. per acre and an intensity of 0.807, but these intensity measurements are going in the wrong direction. An increasing lot size is expected to produce less intensity.
The intensity increase occurs because the 70% unpaved open space provision has not been increased with the increasing lot sizes. If it isn’t, 30% impervious cover on a larger lot size will permit greater potential shelter capacity and intensity per acre. This doesn’t happen because maximum potential home sizes are rarely built on larger lots, but the intent to decrease intensity by increasing lot size is left to chance.
I’m including Table 3 to illustrate an obvious design principle. The table is based on a given home area with an unknown lot area to be found. The Lot Module explains that the land area basis for calculation is 70% unpaved open space and 30% impervious cover. A number of specification values have been entered in the Building Module to arrive at a total home area objective of 2,148 sq. ft. in cell F23. The 100 sq. ft. accessory building area entered in cell F24 is added to the home area to find the total building area of 2,728 sq. ft. in cell F25. The specification values entered in the Pavement Module are used to find the driveway and parking pavement areas in cell F34. These values complete the information needed by the master equation in cell A37. (I should mention that this master equation is equal to the equation on page 48, line 56 of my book, but it does a better job of differentiating building cover from pavement cover.)
The Planning Forecast Panel predicts that a one story home with the specification values entered would require a 12,000 sq. ft. lot in cell B43, and that this would produce an intensity of 0.297 with a shelter capacity of 9,901 sq. ft. per acre. A 2.5 story home would only need a 7,761 sq. ft. lot as shown in cell B46, but would produce an intensity of 0.362 and a shelter capacity of 12,054 sq. ft. per acre. In other words, the trade-off for greater shelter capacity per buildable acre is increased floor quantity and greater intensity. The choice is a very serious issue because the management of shelter capacity, intensity and context for all building design categories and activity groups will determine our ability to correlate our presence on a planet with limited capacity.
Someone may comment that intensity hasn’t been left to chance because front, side and rear yard setback requirements increase with lower density zoning districts, and this hasn’t been taken into account. I have empirically found that setbacks increase yard areas with increased dimensions, but these dimensions do not consistently reduce shelter capacity and intensity. They only appear to be correlated and may be occupied by buildings and pavement that reduce their off-setting benefit. From a designer’s perspective, setbacks are primarily useful for building alignment when desired, fire separation when adequate, and privacy when generous. They are no substitute for adequate unpaved open space quantities defined and correlated with design specifications that establish the format for shelter capacity, intensity and context refinement.
Table 4 shows how intensity increases in cells F12-17 when shelter capacity per acre increases in cell B12-17. The intensity noted in cell F12 is related to the 6,000 sq. ft. lot introduced by Table 1. Cell F17 is based on a similar specification when a one acre lot is given. The intensity statistics are going in the wrong direction because the design specifications for all lots have been held constant, and a larger lot with the same impervious cover percentage will produce greater building and pavement area that results in greater potential intensity. This can be easily corrected when an unpaved open space percentage is increased with lot size in a design specification template, or when other adjustments are introduced to reflect the lifestyle associated with increased lot sizes. This resolves one issue, but it does not begin to address the excessive consumption of agriculture and the Natural Domain for increasing lot sizes.
This essay has focused on site plan quantities defined by the values entered in a design specification template. This is a tactical project issue. The strategic question involves the cellular aggregations that combine to form neighborhoods and districts within a city. The land use allocation of shelter capacity, activity and intensity must produce average revenue per acre that meets or exceeds its average expense per acre for operations, maintenance, improvement, and debt service without excessive intensity. Strategic answers will require data accumulation, correlation, and land management that is beyond the scope of this brief essay. Physical, social and financial balance is feasible, however, when specification templates are linked to each parcel of land within a city and correlated with other data sources to form a complete picture of a city’s current physical, social, and financial condition. This will permit comprehensive evaluation and adjustment with the credibility required to convince others. Planning leadership for a sustainable future cannot proceed without a scientific bridge language capable of relating population and activity to its shelter imperative on a planet with limited resources that demands symbiotic relationships.
We have been preoccupied with growth to counter risk and threat since the beginning of time. This is the origin of the admonition to be fruitful and multiply. We have been successful. It is time to recognize that success from growth is the enemy of balance, and we must adapt to a new level of symbiotic responsibility. The planet is programmed to seek its own balance. I think we intuitively understand that the same law applies to us, but it requires anticipation without proof by extinction. This is a requirement of faith by any name. In fact, faith-based names have distracted us from reality. God has given us the planet. This power has not assigned ownership. It has assigned responsibility. It is up to us to define what that means and adapt accordingly.
Copyright: Walter M. Hosack, 2017. All Rights Reserved