As a young architect and city planner in local government I
was asked to assist in the evaluation of a townhouse development and the
density proposed. I soon realized that my undergraduate and graduate education
in architecture and city design had left me with more opinions than knowledge,
and that these opinions were based on those of my professors. They could only
be defended with logic that often failed to persuade in the face of political,
social, psychological, and economic opposition. This led to my search for a
credible leadership language capable of accumulating knowledge that could
convince those beyond the walls of the profession. It began with my effort to replace
educated trial and error intuition with knowledge built on a mathematical
language that I knew was at the heart of initial design evaluation and decision.
If successful, I believed that this language would have more persuasive power
in the public arena of competing debate, and would form the basis for a new language
and science of city design. This science now addresses the universe of building
design categories, but this essay will only address my original question that
was formed years ago. It concerns reasonable density levels for townhouse (R2) and
apartment (R3) activity groups that occupy the G1 Building Design Category. (The
G1 category encompasses all buildings served by a parking lot adjacent to one
or more sides of a building. It does not include G2 buildings served by a
parking lot that extends under a building.) The forecast models used in this
essay represent the answer to my original struggle with density and are
entitled G1.R2 and G1.R3.
TOWNHOUSE DENSITY
As used in this discussion, townhouses are single-family
dwelling units that are attached to one or more additional units but not
stacked above a dwelling unit. Table 1 illustrates forecast model G1.R2 and
contains a Land Module, Shelter Module, Forecast Module, and Density Module. The
first three modules contain design specification boxes. The modules perform automated
calculations based on the specification values entered. The results provide the
data needed by a master equation to predict density options for evaluation in
the Density Module.
Land Module
This module begins with the gross land area entered in cell
F3. It distills the shelter area (SHA) percentage of gross land area (GLA)
remaining for building footprint, service pavement, and project open space in
cell F12 by subtracting percentage estimates for the topics represented by
cells F4-F6, F8, and F10-F11. Eighty-two percent of the gross land area remains
in cell F12 for shelter area after these topic estimates are subtracted.
Shelter Module
Values are entered in sixty Shelter Module specification
boxes, beginning on line 15 and ending on line 27, to mathematically define the
project proposal. The values entered in each box can be altered to create
proposal options for evaluation. This is also true for the seven boxes in the
Land Module and the nineteen boxes in the Density Module.
Forecast Module
The values entered in the Shelter Module are converted to
square foot predictions on lines 38-42 of the Forecast Module. Since the
townhouse proposal contains a mix of dwelling units defined in cells A23-A27 of
the Shelter Module, the objective of the Forecast Module is to convert the
values calculated for this mix to the data on lines 38-42 of the Forecast
Module, and the mix averages noted on line 45. The goal of the Forecast Module
is to calculate the total average impervious cover per dwelling unit (AVGIMPD)
in cell J43 from the mix definition areas calculated in cells A38-L42 of the Forecast
Module. The average values on line 43 are used to calculate the AVGIMPD value
in cell J43.
Density Module
The objective of the Density Module is to forecast density
options in cells F53-F71 based on the unpaved open space values entered in
cells A53-A71. The equation in cell B52 is used to calculate the average land
area required per dwelling unit (LDU) in cells B53-B71 as the unpaved open
space (UOSD) increases in cells A53-A71. The remaining shelter area calculated
in cell G12 is then divided by each succeeding LDU value in cells B53-B71 to
find the number of potential dwelling units in cells E53-E71. The shelter area densities
calculated in cells F53-F71 are based on the shelter area available in acres
and the dwelling unit quantities calculated. Shelter area is used foe he
density calculations because this is where people will live and this is the
immediate density they will experience. Density per buildable land area (BLA),
net land area (NLA), and gross land area (GLA) could also have been calculated;
but these calculations would represent increasingly ambiguous statistics.
Density Implications
The density forecast in cell F53 is much greater than the
density forecast in cell F71 because the unpaved open space percentage of land
area per dwelling unit has increased from 5% to 95% in cells A53-A71. An
increased unpaved open space percentage means that more total land is required
per dwelling unit, and a fixed shelter area (SHA) can accommodate fewer of
these larger land areas.
Impervious cover is equal to 100% minus the unpaved open
space percentages entered in cells A53-A71. It has declined from 95% to 5% in
cells A53-A71 as the unpaved open space percentage has increased. If the storm
sewer capacity available can accommodate runoff from 30% impervious cover
without storm water detention, this would mean that 70% unpaved open space
would be required and the project would be limited to a density of 6.18
dwelling units per shelter acre as noted in cell F66. Most townhouse developers
would not be satisfied with this limit. In this case, they could introduce a
storm detention system that would permit a higher impervious cover percentage;
or revise the project proposal values used to define the project in the Land
and Shelter Modules of the Design Specification Template.
If a developer wanted to reach the density of 10.3 dwelling
units per shelter acre in cell F62, cell A62 indicates that the storm sewer
system would need to accommodate 50% impervious cover based on the project
specification values entered in the Land and Shelter modules. If 50% impervious
cover sewer capacity were too demanding and the density was still an objective,
the eighty-six design specification values entered in the Land, Shelter, and
Density modules could be adjusted to produce another design option, or a storm
detention system could be introduced. The question of reasonable density that
produces a desirable quality of life would remain, however.
The underlying point is that all design specification values
entered in each box of Table 1 are correlated to produce the results in the
Density Module. A change to one or more of these values will produce a new
forecast of options. Neglecting attention to one or more of these topics and
values will produce arbitrary leadership. Neglecting correlation of these
values will produce contradiction and confusion.
There is another question. Does the shelter area density of
10.3 dwelling units per shelter acre produce undesirable intensity? The corresponding
shelter capacity (SFAC) noted in cell H62 is 13,985 sq. ft. per shelter acre.
The intensity calculated in cell J62 is 0.161. The dominance calculation in
cell L62 adds an intrusion measurement equal to floor quantity divided by five
in cell K53 to the intensity measurement in cell J62. The dominance result measures
the impact of building mass, pavement and height within the project area. The
value calculated in cell L62 is 0.499. These intensity and dominance
calculations are measurements without a quality of life scale based on research
at the present time. An acknowledged scale would begin to indicate how well the
proposal would protect the population’s physical, social, psychological,
environmental, and economic welfare. The scale does not exist at the present
time because existing conditions have not been measured and evaluated. As a
result, the intensity and dominance calculations in Columns J and L of the Density
Module are like early blood pressure measurements. They also began without an
accepted reference scale based on a database of research to explain their
meaning. The equations on line 52 make consistent measurement feasible,
however, and comparison with existing condition measurements will produce
knowledge to support negotiation and opinion in the offices and arenas of city
design debate.
APARTMENTS
As used in this discussion, apartments are one-story
dwelling units that are connected and stacked within a larger gross building
area envelope. Table 2 illustrates apartment forecast model G1.R3. It contains
a Land Module, Shelter Module, G1 Module, Apartment Module, and Density Module.
The first four modules contain design specification boxes. The modules perform automated
calculations that lead to the density options predicted for evaluation in the
Density Module.
Land Module
This module begins with the gross land area entered in cell
F2. It distills the shelter area (SHA) percentage of gross land area (GLA)
remaining for building footprint, service pavement, and project open space in
cell F11 by subtracting percentage estimates for the topics represented by
cells F2-F5, F7, and F9-F10. Eighty-two percent of the gross land area remains
in cell F11 for shelter land area after these estimates are subtracted.
G1 Module
The G1 module contains four specification boxes that receive
miscellaneous project service and social pavement percentage estimates. These
estimates are used to calculate the shelter area remaining for building and
parking cover in cell G19.
Apartment Module
Specification values are entered in twenty-eight Apartment
Module s boxes, beginning on line 23 and ending on line 33, to mathematically
define the project. The values entered in each box can be altered to create
proposal options for evaluation. This is also true for the seven boxes in the
Land Module and the twenty-nine boxes in the Density Module.
The values entered in the G1 and Apartment modules define
the mix of dwelling units proposed in cells A29-A33. The objective of the
Apartment Module is to calculate the mix averages on line 35, and in
particular, the average dwelling unit area (ADU) in cell D35.
Density Module
The objective of the Density Module is to forecast density
options in cells C42-M60 based on the unpaved open space values entered in
cells A42-A60 and the floor quantity options on line 40. The density options
calculated are based on the shelter land area available (SHA) because this is
where people live and this is the immediate density they will experience.
Density per buildable land area (BLA), net land area (NLA), and gross land area
(GLA) could also have been calculated; but these calculations would represent
increasingly ambiguous statistics.
Density Implications
The density forecast in cell C42 is much less than M42
because the floor quantity has increased from 1 to 100 stories, but a building
cover calculation would have to confirm if the remaining building footprint
area is feasible. This is beyond the scope of Table 2, since it is focused on
density; but is included in the G1.R3 spreadsheet of city design.
The density forecast in cell C42 is much greater than the
density forecast in cell C60, however, because the unpaved open space
percentage of land per dwelling unit has increased from 5% to 95% in cells A42-A60.
This means that the core land area available for building cover and parking
cover in Col. B of the Density Module has declined in response to the
increasing open space in cells A42-A60. This declining core area can
accommodate fewer average dwelling unit areas (ADU’s), which produces a decline
in achievable density. The reader should note that the core area declines in
Column B until it becomes unrealistically small for both building and parking
cover, however; and densities decline in cells C42-M60 in response to increased
unpaved open space in Column A until they no longer represent an apartment densities.
Impervious cover is equal to 100% minus the unpaved open
space percentages entered in cells A42-A60. If the storm sewer capacity available
can accommodate runoff from 60% impervious cover without storm water detention,
this would mean that 40% unpaved open space would be required. As a result, a
five story building is limited to a density of 16 dwelling units per shelter
acre for a five story building as noted in cell G49. If the storm sewer
capacity were not this great, the five story density would decline as noted in
cells C50-C60, or a storm detention system would be required to justify the
impervious cover percentage.
If a developer wanted to reach the density of 20 dwelling units
per shelter acre in cell G46, the storm sewer system would need to accommodate 75%
impervious cover based on the project specification values entered in the Land,
G1, and Apartment modules. If 75% sewer capacity were too demanding and the
density was still an objective, the floor quantity in cell G40 and the values
entered throughout the design specification template would have to be
re-examined. The 25% unpaved open space in cell A46 would also have to be
examined for excessive intensity.
The underlying point is that all specification boxes are correlated
in Table 2, and the values entered in each box are correlated with the UOSA
values in cells A42-A60 to produce the results in the Density Forecast Module.
A change to one or more of these values will produce a new forecast of options.
Neglecting attention to one or more of these topics and values will produce
arbitrary leadership. Neglecting correlation of these values will produce
contradiction and confusion.
There is another question. When does apartment density
produce undesirable intensity?
Intensity
Table 3 presents related intensity calculations for each of
the density values in cells C42-M60 of Table 2. For instance, the density of
16.0 in cell G49 of Table 2 is based on the design specification values entered
in the Land, G1, and Apartment modules above; and the 40% unpaved open space
area in cell A49. Table 3 calculates that this represents an intensity of 0.258
in cell G9. Cell G9 in Table 3 calculates that the density of 20.0 in cell G46
of Table 2 will produce an intensity of 0.403 based on the design specification
values entered in the Land, G1, and Apartment modules of Table 2 and the 25%
unpaved open space area entered in cell A46 of Table 2.
Intensity is a calculation in the dark at the present time. A
reference scale supported by a database of research measurement would indicate
how well the proposal would protect the population’s physical, social,
psychological, environmental, and economic welfare (“quality of life”). The
scale does not exist at the present time because existing conditions have not
been measured and evaluated. As a result, the intensity calculations in in
Table 3 are like early blood pressure measurements conducted to build a
database of knowledge. Consistent measurement of existing conditions is feasible
with a design specification template, however, and comparison will produce
knowledge to support negotiation and opinion in the offices and arenas of city
design debate.
Dominance
A dominance measure is equal to the sum of an Intensity
measure and an intrusion measure. Intrusion is measured by dividing floor
quantity by five. The quotient is added to the intensity calculation in Table 3
to form the dominance measurements in Table 4. If you locate cells G31 and G34
in Table 4, you will see that the intensities calculated in Table 3 have
dominance measurements of 1.258 and 1.403 when five story building intrusion is
considered.
Therefore, the densities of 16.0 and 20.0 produced by the
design specification in Table 2 have associated intensity measurements of 0.258
and 0.403 in Table 3. They have dominance measurements of 1.258 and 1.403 in
Table 4 that represent the sum of intensity and intrusion measurements.
The implications surrounding these measurements
are yet to be determined, but their significance lies in the ability to
measure, since it can lead to knowledge.
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