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.
SPRAWL
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.
PURPOSE
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.
LAND
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.
LAND USE ACTIVITY
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.
EQUATION G1.L1
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))
KEY:
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 Amazon.com. (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.
CORE AREA COEFFICIENTS
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.
UNPAVED OPEN SPACE
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
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.
THE BUILT and NATURAL DOMAINS
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.
