Search This Blog

Wednesday, August 30, 2017


We will compete to consume until we realize that our definitions of growth and success confuse winning with losing on a planet that demands symbiotic solutions from all of its tenants.

QUESTION: Is sprawl responsible (at least partially) for the flooding in Houston?  

ANSWER: Yes, but it is a term without adequate definition that indicates an inability to correlate the many decisions that lead to failure when independently considered and randomly applied.

Saturday, August 19, 2017

Core Area Restrictions on Shelter Capacity

This is the third essay in a trilogy. The first two were entitled “The Future of Cities” and “Understanding a Building Footprint”.

NOTE: All tables referenced are located after the text 

When parking is required, core area is the buildable land area remaining for shelter and parking after a number of support areas are subtracted from gross land area. Shelter capacity is affected by the building design category chosen, the core land area available, and the building height contemplated. This essay is based on a G1 Design Category that depends on surface parking and building footprint areas that combine to equal the total core land area available. The emphasis here is on available quantity.  It has nothing to do with preliminary or final site plan configuration. This definition of core area makes the formation of shelter capacity equations feasible.
In some cases an architect will know the gross land area available and the objective will be to calculate its gross building area potential - Case 1. (I’ve covered Case 1 in two previous essays entitled, “The Future of Cities” and “Understanding a Building Footprint”.) In other cases the architect will know the gross building area desired and the objective will be to calculate the buildable land area required - Case 2. In some cases the gross land area available and the gross building area objective is known, but this essay is based on Case 2. The answer in both cases depends on the core land area remaining. In Case 2 it is an unknown to be discovered.
Table 1 is related to Case 1. It illustrates the subtraction that leads to the definition of core area in cell F32 and G32 based on the gross land area given in cell F3. (The percentage estimates and calculations in cells F3-F31 lead to the core area estimation in cell F32.)
Table 2 is related to Case 2 and does not begin with a given gross land area. It illustrates the distillation of core area in cell F32 based on the percentage estimates and calculations in cells F3-F31. No square foot land areas are given or calculated.
I introduced the G1 Building Design Category and its Case 1 master equation entitled G1.L1 in “The Future of Cities”.
GBA = CORE * af / (a + (fs))

a –              gross building area square feet permitted per parking space provided

CORE –     buildable land area available for building and parking cover in square feet

f –               floor quantity

GBA –       gross building area potential in square feet

s –              gross parking lot area provided per parking space provided in square feet
The equation solves for an unknown gross building area (GBA) when land area is given, but can be transposed to solve for the core land area needed when a gross building area objective is given:
1)      CORE = GBA / af / (a + (fs))  Transposing master equation G1.L1

2)      CORE = GBA / (a2f + af2s)  Reducing line 1

3)      CORE = GBA / (af * (a + fs))  Reducing line 2
Defining core land area is not the answer to the question posed, however. It is the first step in the derivation:

4)      CORE = CORE% * SHA  When shelter area (SHA) in sq. ft. is known

5)      SHA = SHA% * BLA  When buildable land area in sq. ft. is known

6)      CORE = CORE% * SHA% * BLA  Substituting line 5 for SHA in line 4

7)      CORE = GBA / (af * (a + fs))  Repeat line 3

8)      GBA * ((a + (fs)) / af) = CORE% * SHA% * BLA  Substituting line 7 for CORE in line 6

9)      GBA * (a +(fs)) = CORE% * SHA% * BLA * (af)  Reducing line 8

10)    BLA = (GBA * (a + (fs))) / (CORE% * SHA% * (af))  Transposing line 8 to find Equation G1.B1.BLA
Equation G1.B1.BLA on line 10 is located in cell A38 of Table 2. It is used to calculate the buildable land area options in cells B43-B52 of the table. At this point, the equations in cells C42-L42 are used to calculate additional option columns related to the floor quantity options in cells A43-A52. Shelter capacity, intensity, intrusion, and dominance measurements related to each option are calculated in Columns G-L of the Planning Forecast Panel.
I should again point out that floor quantity above 5 produces rapidly declining gains in gross building area per floor when the G1 Design Category is chosen for shelter construction. This was discussed in “The Future of Cities”.
The buildable land area in cell F9 of Table 2 is estimated to be 82% of the gross land area needed (GLA). An estimate of this gross land area can be simply expressed as:
              GLA = BLA / BLA%
In other words, a GLA estimate can be defined with the following revision to Equation G1.B1.BLA
              GLA = (GBA * (a + (fs))) / (CORE% * SHA% * BLA% * (af))  Master Equation G1.B1
Master Equation G1.B1 is one of 25 related to the building design categories listed in Table 3 and presented in my book, The Science of City Design, CreateSpace, 2016. The derivation of Equation G1.B1.BLA can be found on page 154, lines 62-67. The book, and the second edition of my earlier book entitled Land Development Calculations, can be found on at the following address:

Wednesday, August 16, 2017

Understanding a Building Footprint

I recently wrote an essay entitled "The Future of Cities" that introduced the G1 Building Design Category and its master equation for gross building area that I called (G1.L1):
GBA = CORE * af / (a + (fs))


a –              gross building area square feet permitted per parking space provided

CORE –     buildable land area available for building and parking cover in square feet

f –               floor quantity

GBA –       gross building area potential in square feet

s –              gross parking lot area provided per parking space provided in square feet

The essay explained that when (GBA) is divided by (f), the result is gross building cover area (BCA), also known as building footprint or floor plan. It also noted that (BCA) was equal to 0.1111 of the core land area, but it did not mention the obvious. Eleven percent (0.1111) of a core area is a very small percentage when you consider that core area is the area that remains for building and parking cover after a number of related land areas are subtracted from the gross land area available. It is a surprising statistic, but the formula for maximum potential building floor plan area is one that can give design leadership a simple site planning tool. If maximum floor plan area can be predicted, design results can be easily measured to ensure compliance with leadership intent.

The formula for building cover can be easily derived from the G1.L1 master equation noted above:

Given: BCA = GBA / f

Find: BCA when CORE area is equal to 1.0 in Equation G1.L1:

GBA = af / (a + (fs))                          Equation G1.L1 coefficient

BCA = (af) / (a + (fs)) / f                  Substitute GBA in BCA

BCA = af / ((af) + (f2s))                     Reduce BCA

BCA = a / (a + (fs))                          Reduce BCA to coefficient equation

BCA = CORE * a / (a + (fs))            Reintroduce CORE to form Equation G1.L1.BCA

Remember that Equation G1.L1.BCA only applies to the G1 Building Design Category. When core area is defined by subtraction of estimated land area quantities in a G1 design specification template, the maximum footprint area (BCA) can be found when values are assigned to (a), (f), and (s) in Equation G1.L1.BCA. (The coefficient equation can be useful when presenting options. A sample G1 design specification template explaining the subtraction the leads to core area definition can be found in my essay, “The Future of Cities”. A sample of coefficient evaluation can be found in Table 2 of this essay.)
If you use Equation G1.L1.BCA you will find what every building designer has intuitively observed since automobiles became a G1 site planning topic; but if you are like me, the small percentages will still be a surprise.

Saturday, August 12, 2017


NOTE: All exhibits, tables and figures referenced are located at the end of this text.

The future of a city is directly related to the intelligent use of land within its corporate boundaries. These acres produce yield in the form of revenue - and intensity in the form of perception. Yield per acre has often been inadequate to meet a city’s average cost per acre to operate, maintain and improve. Excessive intensity has often produced physical, social, psychological, environmental, and economic stress generally referred to as inadequate quality of life. Stress has produced sprawl in search of quality at an expanding suburban perimeter.
Expansion often involves annexation, and it can repeat past land use allocation and shelter capacity mistakes in its search for new revenue to solve immediate problems. The increasing cost of maintenance and improvement over time for the new land is ignored until age requires more annexation for new money to balance increasing budget demand. The result can be an unbalanced allocation of shelter capacity and activity within a municipal land area that unwittingly multiplies the burden on an increasingly deficient public revenue stream, or yield per acre. This parasitic growth pattern is a Ponzi scheme that is slowly consuming and polluting its source of life – a limited Natural Domain that does not compromise with ignorance.
The source of the disease we call sprawl is our inability to predict levels of shelter capacity per acre that contain activity producing enough revenue to support municipal expense, even when introducing excessive intensity in some cases. Our ability to accurately predict the shelter capacity of land per acre and correlate this capacity with its revenue and intensity implications remains a random result of marketing decisions based on individual interpretation. This has produced sprawl that will not be contained without a bridge language that can correlate shelter capacity, activity and revenue with its intensity and its quality of life implications. This does not mean that every acre within a geographically limited municipal area must meet or exceed its average cost per acre for municipal operations, maintenance, and improvement. It means that we need a bridge language to correlate average revenue from all shelter capacity and activity present or planned per acre with its average municipal expense per acre. In other words, we need an accurate ability to measure, predict, and lead shelter capacity decisions toward the goal of balanced activity within a geographically limited Built Domain that protects its quality and source of life. We now have a bridge language capable of correlating shelter capacity measurement and prediction with its physical, social, psychological, environmental and economic implications.
Project site plans and building mass combine to produce shelter capacity. The relationship of shelter capacity to movement, open space and life support within a city determines the physical intensity, intrusion, and dominance perceived at any scale of city design. Physical intensity combines with social activity to produce economic performance. This performance supports the quality of life present or planned for a city. The aggregation of cities produces a Built Domain that is currently sprawling to consume its source of life - The Natural Domain. Sprawl is produced by an arbitrary and expanding demand for shelter from a growing population. These populations consume excessive amounts of land and resources to satisfy the demand because they have not been able to accurately correlate shelter capacity with activity to form beneficial, balanced physical, social, and economic relationships.
The purpose of this essay is to introduce one equation from a portfolio of 26 listed in Exhibit A. They are bridge equations that can be used to link shelter capacity measurements, predictions, options, and decisions to a wide variety of implications related to their square foot measurements and predictions such as, but not limited to, shelter capacity, cost, yield, population, traffic, open space, life support, return on investment, and so on. They can also be used to link a wide variety of disciplines influenced by shelter capacity options such as city planning and design, architecture, landscape architecture, civil engineering, urban geography, sociology, psychology, ecological science, real estate investment, traffic engineering, and so on. In other words, the series of bridge equations listed in Exhibit A, and their related design specification templates, can be used to guide city design measurement, evaluation and prediction toward the formation of city planning and design decisions that will produce knowledge when results are evaluated.
The bridge equation to follow is listed in Exhibit A. It is one in a series written to fill a measurement, evaluation, conclusion, and prediction gap. This gap has prevented more rapic accumulation of city design knowledge and the formation of options that can be chosen to lead our efforts toward a symbiotic future.
Shelter capacity is gross building area in square feet divided by the total number of buildable acres occupied. I have referred to these acres as gross, net, buildable, shelter, and core areas. Table 1 begins with gross acres in cell F3 and illustrates the subtraction that leads to net area in cell G7, buildable area in cell G10, shelter area in cell G17, and core area in cell G32. Core area is the land area remaining for building floor plan and parking support when parking is required.
Gross building area in a project is converted to shelter capacity per buildable acre, but should not be confused with land use activity. Activity can occupy any gross building area, assuming building code compliance. The scope of activity that can be sheltered is a function of the gross building area present of planned per acre. If building capacity per acre does not shelter enough activity to produce adequate revenue per acre, capacity must either increase or be offset by the revenue from other activities to meet a city’s annual cost to operate, maintain, and improve. In other words, the scope and type of activities sheltered per acre within a city must combine to meet or exceed the average revenue required per acre to support a city’s desired quality of life. If the relationship is inadequate, budget cuts will ensue and the conversion of agriculture through annexation will be considered. Building capacity is shelter capacity and it is a function of building design category and design specification decisions that produce gross building area options. Revenue is a function of the activity sheltered within gross building area in addition to the real estate value introduced.
The downside to a capacity-activity relationship occurs when excessive capacity produces excessive intensity in a project or larger urban area. Cells G42-J51 calculate the intensity, intrusion, and dominance implications of the shelter capacity options in cell F42-F51. (These capacity calculations are a function of the gross building area options predicted in cells B42-B51.) I have no idea if the intensity options in Column (G) are excessive. This definition is a challenge for future research. I have simply provided a method of measuring physical intensity, predicting gross building area options at the cellular (project) level of city formation, converting gross building area measurements to their shelter capacity implications, and calibrating perception with capacity, intensity, intrusion, and dominance statistics that have physical, social, psychological, environmental, and economic implications.
When a surface parking lot around, but not under, one or more buildings is used to satisfy parking demand on a given land area, the building design category is referred to as “G1” and gross building area options for the land area given can be defined with Equation G1.L1.

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

a –              gross building area square feet permitted per parking space provided
CORE –     buildable land area available for building and parking cover in square feet
f –               floor quantity
GBA –       gross building area potential in square feet
s –              gross parking lot area provided per parking space provided in square feet

The detailed discussion surrounding this equation can be found in Chapter 6 of my book, The Science of City Design, published by CreateSpace in 2016 and available on (The derivation of the equation can be found on page 154. It permits shelter capacity options to be accurately predicted for any given land area when the G1 Design Category is the shelter design choice.) The equation predicts shelter options based on the values entered in its design specification and correlated for use in this master equation. The shelter design options produced can be evaluated based on accumulated and evolving knowledge. The goal is to protect a growing population’s quality of life while limiting its consumption of land that is its source of life.
The equation depends on an accurate definition of core area, which is the land remaining for building and parking cover after percentage estimates are subtracted for all other site planning topics and quantities. An example of a G1 core area calculation is presented in Table 1. The table begins with the gross land area given on line 3. Core area is found on line 32 by subtracting percentage estimates for the intervening site planning topics listed.
Figure 1 charts the gross building area (GBA) results predicted by Table 1. It is discussed in detail in Chapter 6 of my book, and is presented here to illustrate a fundamental characteristic of the G1 Building Design Category. The increase in G1 gross building area capacity produced by increasing floor quantity on a fixed core land area rapidly declines as a surface parking lot expands to justify the increase and the core land area remaining for building footprint (BCA) shrinks in response. (A building footprint is multiplied by floor quantity to increase gross building area potential until parking lot expansion makes the footprint too small to be useful. There is also a point when the increase in gross building area per floor becomes too small to be justified given the cost of increasing the number of floors.) The point of failure is a matter of investment opinion, but appears to occur at either the 4 or 5 floor mark in Figure 1. This figure is based on the values entered in the design specification template of Table 1 and is heavily influenced by the open space percentage entered in cell F11. A change to this percentage will influence the point where the curve begins on the y-axis when all other specification values remain constant. I’ve made this point in previous essays and only repeat it here to indicate why I have limited all spreadsheets in Table 2 to a floor quantity range of 1 to 5 stories.
When the core value in Equation G1.L1 is equal to 1, the gross building area potential of any G1 core land area is indicated by the values entered in the equation coefficient, (af / (a + (fs)). This makes it possible to present a broad range of gross building area options for any G1 building on a single page. For example, spreadsheet (A) in Table 2 is based on an s-value of 400 as noted in cell C5. (An s-value is equal to the total area within a parking lot perimeter, including landscaping, divided by the number of parking spaces provided. The a-values on line 10 in spreadsheet (A) represent the total gross building area permitted per parking space provided.) The spreadsheet shows that gross building area coefficients increase as the gross building area (a) permitted per parking space increases on line 10 and floor quantity increases in cells B11-B15. It also shows in cell R15 that a 5 story building with a parking requirement of 1,000 can be 15 times the size of a 1 story building with a parking requirement of 50. This statistic and the entire spreadsheet gives a glimpse of the advantages that accrue when a parking variance to a less restrictive requirement is approved and the risk of excessive intensity is increased.
If you compare the coefficient calculated in cell G15 of spreadsheet (A) to the coefficient calculated in cell G27 of spreadsheet (B), you’ll see that the coefficient for a 5 story building declines from 0.5556 to 0.3846. This occurs because the s-value in cell C17 has increased to 600 from 400 in cell C5. This indicates that more parking lot pavement and/or landscape area has been provided per parking space introduced. A smaller gross building area is permitted by the reduced number of parking spaces that can be provided.
The coefficient in cell G27 is approximately 30% less that the coefficient in cell G15. This is a 30% decrease in 5 story gross building area potential when the parking lot area provided per space increases from 400 to 600 sq. ft. When the increase reflects additional landscape area to relieve pavement intensity, more general questions are implied.
When should shelter capacity be limited by an unpaved open space requirement (OSAU in cell F11 of Table 1) to relieve the intensity, intrusion, dominance, and impervious cover introduced by building mass and pavement, and what percentage should be required?
There is no consistent answer to this question at the present time, except for the limits required by storm sewer capacity design that are generally unknown and/or ignored. We have not accumulated the measurements and evaluation needed to distill knowledge and demand relief. The only impression I have at the moment is that the percentages will vary with the activity sheltered, but even this raises a question. When you look beyond a site plan and specific activity, how much unpaved open space should be woven into the urban fabric to relieve intensity and offset stress in the cities we build?
Building cover (BCA) is another term for building footprint or building floor plan. A building cover coefficient is equal to a gross building area (GBA) coefficient divided by the floor quantity (f) related to the coefficient. For instance, the gross building area coefficient for a 5 story building and a parking requirement (s) of 250 is noted in cell G15 as 0.5556. The maximum building cover coefficient is 0.5556 / 5, or 0.1111. If the available core area were 100,300 sq. ft. as shown in cell G32 of Table 1, the maximum GBA potential would be 55,726 sq. ft. and the maximum footprint would be 11,145 sq. ft. (These values can be calculated with a coefficient or found in Table 1.) If either area is insufficient to satisfy a client’s architectural program of rooms, spaces and relationships, the values entered in the Land Module and G1 Module of the design specification in Table 1 would have to be adjusted; and these adjustments might require zoning variance requests. In these cases, the altered values would be debated and the adequacy of their defense would depend on the logic, research, and accumulated knowledge supporting each value.
A city’s total buildable land area is restricted by corporate boundaries that make each acre a limited resource - and its permitted activity list an investment in the city’s economic future. Annexation is a losing exercise if the additional acres are not devoted to shelter capacity and activity that can maintain or improve a city’s average revenue per acre over a time period that includes the land’s increasing cost of maintenance and improvement.
The capacity, intensity, revenue and expense associated with each acre of municipal land has not been measured or predicted because a mathematical bridge has not been available to correlate shelter capacity, activity, and revenue with intensity and appearance in a timely manner. Equation G1.L1 is one example of the bridge language and science of city design that can be used to correlate reality with perception to preserve land as a source of life.