Ralph L. Knowles
Professor Emeritus of Architecture
University of Southern California (USC)
University Park - WAH 204
Los Angeles, CA 90089-0291
"Nothing is either too great or too small other than by comparison."
Gulliver's Travels by Jonathan Swift.
building size; density; solar access; solar design; solar envelope; surface/volume; zoning
The right size, and notably the right size of a building as discussed here, is relative. It is dependent upon the costs of construction and of maintenance. It is also proportional to the more illusory standards of livability and of choice. In order to make sense of this complex picture, a 10-year housing study has been undertaken in the USC School of Architecture Solar Studio comparing a range of sizes with reference to solar-access policy and design. Data have been systematically collected relating Density (a count of dwelling units per acre) to S/V (surface-to-volume ratio, an energy-related measure of building form). This relationship is taken as grounds for concluding that buildings of 3-7 stories generally represent the best size range for urban dwellings in Los Angeles. These figures can vary among cities; but the underlying suppositions of solar-access policy and design are broadly applicable to places of density everywhere.
ASSUMPTIONS FOR HOUSING STUDY
The housing study, conducted between 1983 and 1994, tests the notion that to conserve energy and preserve life quality in an urban setting, buildings can be neither too big nor too small. There are two assumptions: One is concerned with architectural design; the other, with public policy.
Energy conservation and life quality depend on access to sunshine and cross-ventilation. At the beginning of each project, design students in the USC Solar Studio are asked to generate the highest densities possible without losing access to sunshine or cross-ventilation for every dwelling unit on a property. (A periodic count of dwelling units is the students' only direct involvement in the research process; otherwise, they are encouraged to explore design ideas as they normally would in a studio setting.)
Los Angeles has enacted a zoning policy based on the solar envelope. The solar envelope, conceived at USC in 1976, is a container whose shape is derived from the passing sun. Development within this container will not shadow surrounding properties during critical periods of the day. (For a more complete description of the solar envelope see: Knowles, Ralph L. and Marguerite N. Villecco. "Solar Access and Urban Form," AIA Journal . February 1980: 42-49 and 70; also see other papers on this web site.)
LOS ANGELES ZONING
Los Angeles zoning regulations provide the urban housing reference for this study. First, the dwelling classifications are the actual ones used in the design studio. Second, they show in which density range the greatest variety of types is officially recognized by L.A. planners. Finally, a novel way of displaying the relationship between types reveals three distinct ranges of size that correspond with habits of energy consumption and styles of living (Fig.1).
Fig. 1. (Click images for larger versions.)
Three Ranges of Size
The graph for L.A. Zoning can be explained in three basic parts. The thin vertical part of the curve describes small buildings up to 3 stories. The similarly thin horizontal part describes big buildings of unlimited height. The broader "elbow" of the curve describes a range of mid-sized buildings. Each part of the curve represents not only different dwelling classifications, but a separate grouping of possibilities for designers, developers, and users. To evaluate these possibilities, it is useful to establish the meaning and the method of calculating S/V and Density.
S/V, measured on the vertical axis of the graph, is an important energy-related descriptor of building form that also expresses design choices. The high S/V of a small building means that energy must be expended mainly to overcome surface or "skin loads"; it also implies a strong architectural bond to sunshine, fresh air, and view. The low S/V of a large building means that more energy must be expended to handle the internal stresses of overheating; it also means less potential for the architect to "design with nature."
S/V is calculated to include exposed portions of the lot as well as the building for three reasons: First, zoning codes usually list minimum yard and lot sizes together with building dimensions as a combined basis for classification; second, energy is expended to maintain the lot as well as the building and when the lot is an acre or more, the proportion used for lawns and gardens can predominate; finally, when assuring solar access for winter heating and access to summer breezes for cooling, the lot and the building must be seen as an integral set.
Density (dwelling units/acre), measured on the horizontal axis of the graph, is based on net acreage of the land parcel. Higher densities correspond with inflated land values; units, and even whole buildings, become compact and essentially repetitive. Lower densities coincide with smaller land costs; developers usually concentrate on one-family houses multiplied over enormous tracts. But for urban housing on restricted sites in Los Angeles, developers customarily try for the highest densities the market and zoning will support.
Four projects, covering a range of settings and densities, are shown as exemplary. The design program for all projects calls for solar access and cross-ventilation to every dwelling unit. The research protocol for solar envelopes has been systematically adjusted in successive exemplars to provide shorter periods of solar access and greater shadowing impact on neighboring properties. Each successive project increases Density with a corresponding reduction of S/V.
Low-Density Hillside Housing
The first project, sited on the N-S ridge of a low hill, achieves a density range of 7-18 du/a with a corresponding S/V range of 0.3942-0.1670. Individual units are in the 2-4 bedroom range or about 1350-2500 sq.ft. The rules for generating solar envelopes call for guaranteeing six hours of sunshine on a winter day and progressively more toward summer (10 hrs) for outdoor recreation and for gardening. Shadowing is allowed at any time below 8 ft at front and rear property lines, but is unlimited at side property lines and on all public rights-of-way.
A view toward the northeast shows several lots surrounding an intersection, each with a somewhat different condition of slope and solar access (Fig.2). The results accentuate the natural topography of the hill: high on the ridge, low on the slopes where the solar access of houses further downhill must also be protected.
A detail view of the western slope shows two different siting strategies (Fig.3). One lot (right) contains two small houses separated by a stair for access to the rear of the lot. An adjacent lot (left) holds only one large house. Unlike the taller houses on the ridge, these on the slope must press harder against the solar envelope to channel sunlight either into atria or down stairways into spaces below.
Both views show great architectural variety. Partly this results from different site conditions that affect the solar envelopes. But even within a parcel, low Density and high S/V provide designers with especially rich possibilities.
Low-Mid Density Housing
The second project, sited on a more gentle eastern slope of the same hill, nearly doubles the density to 14-28 du/a with a corresponding S/V range of 0.2547-0.1625. All programmatic requirements for dwelling types, and also the solar envelope rules, are the same as for the first project. But here, as the hill flattens, densities rise markedly over what is achieved on the steeper slopes.
A view northward (Fig.4) shows characteristics similar to those seen earlier on the west side of the hill . The impact of the solar envelope can clearly be seen accentuating the downward tilt of the natural topography. Also, portions of otherwise useful volume are intentionally cut away and clerestories installed over stairwells to capture south sun for day-lighting and especially for winter heating.
Downhill, and onto the flatter portion of the site, houses become taller and their shapes are less impacted by the solar envelope (Fig.5). A view toward the northeast shows fairly typical three-story row houses lined up along a very deep lot with gardens and entry along one edge. Each house is centered by a very tall clerestory that provides light and air to an atrium or inside garden.
Both views show somewhat less architectural variety than was seen in the first project. Windows tend to be more of a size and shape. Terraces and gardens are smaller and less visible. This is not the result of less desire on the students' part for creative self-expression, but is almost entirely the result of increased Density and decreased S/V that together lower the possibilities for identifying separate units.
Mid-High Density Housing
The third project, sited on the old diagonal Spanish grid of Los Angeles, raises densities still higher to 38-72 du/a with a matching S/V range of 0.1574-0.0965. The program calls for replacing dilapidated one-family dwellings, but not existing multiple-dwellings, with a market mix of units averaging 1000 sq. ft. Parking is below grade on some lots, but is naturally ventilated.
The rules for solar envelopes meet less generous time and space constraints thus allowing more building volume here than for the first two projects. While the earlier protocol guaranteed 6 hours of direct sunshine, the rules here guarantee only 4 hours - the minimum generally recommended for passive design in this "Mediterranean" climate. Shadowing is allowed at any time below 10 ft on residences and below 20 ft on commercial properties where they exist in the surround.
Two western European prototypes have been adapted to solve the problem of solar access and cross-ventilation in apartment buildings (Fig.6). Higher densities in the U.S. generally depend on "double-loaded" corridors and mechanical systems. But in these European designs, hallways systematically skip some floors allowing units to pass freely both over and under for access to light and air in opposite directions.
Fig. 6. Fig. 7.
The two European prototypes have been applied directly where site conditions suggest an E-W exposure, but adjustments have been made to the sections where the exposure is N-S (Fig.7). Winter sunshine enters only the south-facing rooms, leaving those on the north relatively darker and colder. Since every dwelling unit is required to have a south exposure, the N-S building section becomes asymmetrical in its spatial organization.
The size of these sections depends on orientation. A building depth of 40-45 ft is about right for N-S exposures whereas the depth for an E-W exposure averages about 10 ft greater. This results from the fact that useful sunlight, especially in winter, can enter from only one side of a N-S section but two sides of an E-W section: 2-3 hrs from the east in morning, another 2-3 hrs from the west in the afternoon thus enlivening most of the space in the deeper unit. (Floor-to-floor height is maintained at 10 ft for the study.)
The use of these sections, along with tighter envelope rules, allows considerable building-height variation within a given land parcel (Fig.8). Along the central tree-lined street where the solar envelope is high, apartments can now rise 5-7 stories. Along the alley, where the envelope slopes downward, 2-3 story townhouses reflect more the scale of the first two projects. (Existing buildings appear in the photos as simple blocks, 3-5 stories high and closely spaced.)
Fig. 8. Fig. 9.
A detail view toward the southeast shows different ways to open outdoor spaces to winter sunshine (Fig.9). A broad south exposure allows one design to use a generous, plaza-like courtyard. Another design, because of its narrow lot shape and the diagonal orientation of the Spanish grid, splits open along a true N-S axis for the midday sun to enter a street-like court.
Both views show more architectural repetition than was seen in either of the first two projects. Still, for the higher densities involved, there is remarkable design variety among parcels and unit diversity within any one lot.
High Density Housing
The 4th project, located on a hillside close to Downtown, achieves a density range of 76-128 du/a and a comparable S/V range of 0.1272-0.0954. Design requirements for unit size and parking are the same as for Project #3, and the building sections diagrammed there are used here as well.
The solar-envelope rules for time constraints are the same as for Project 3, but the space constraints have been altered to provide still more volume. There are no setbacks, and neighboring parcels are allowed to share space across sidelines; in addition, overshadowing is purposely allowed on a north-facing slope that has been left open as a park.
Fig. 10. Fig. 11.
A view toward the northwest shows that, because the solar envelopes do not drop at sidelines as they do in Project #3, separate designs merge (Fig. 10)). In the foreground are actually three separate designs. The closest one is L-shaped. The middle one is very tall with a low building in the front yard facing the street (Fig. 11). The last design in the row breaks from the envelope but holds the south facade line.
A view toward the southeast and across the park again shows designs merging under shared solar envelopes (Fig.12). In the background are two separate designs that divide one envelope; in the foreground are two other designs that take the division a step further by coalescing into a single, dynamic composition.
This last project not only has the highest density of the four projects shown, but it extends the density range to the highest value attained in any of the twelve projects that comprise the study.
The housing study did not achieve the full range of densities contained in L.A. zoning, but for two different and opposing reasons. The lowest density of the study (7 du/a) was deliberate, the result of an initial decision to exclude from investigation one-family dwellings on very big lots as inappropriate for urban housing. On the other hand, the high end of the range (128 du/a) was not deliberate but the chance result of a step-by-step disclosure over the ten years of testing.
The Cut-Off Values for S/V and Density
The consistent effort to achieve both energy efficiency and life quality, while striving for higher densities, has produced a critical cut-off value of S/V = 0.1 corresponding with a density range of 80-100 du/a. A few special circumstances as, for example, the overshadowed park in Project #4, have resulted in exceptions to this rule. Otherwise, for good solar access and cross-ventilation in a compact and continuous urban fabric, the rule holds. Designers who break it lose the choice of architectural means to sustain building comfort and must depend on energy-intensive mechanical systems.
The cut-off value of S/V = 0.1 provides a simple but powerful design tool. Architects don't have to wait until a project is far advanced to evaluate its passive-design potential. Even at very early stages of planning, a simple calculation, performed on alternative massing schemes, provides an unequivocal basis for comparing the eventual character of their energy usage. If S/V is more than 0.1, designing with nature is a good option. On the other hand, if S/V drops below 0.1, reliance on energy-intensive systems is inevitable.
Latitude affects the cut-off for S/V. Los Angeles, where this study was sited, is at 34 N. At higher latitudes, where the sun is lower in the winter sky, buildings must be either shorter or spaced further apart for solar access; the result is a higher cut-off value for S/V. Lower latitudes produce the opposite effect, in which buildings can be either taller or placed closer together without losing solar access. The result is a lower S/V cut-off. Other cities, especially at significantly different latitudes, need to be studied for corresponding limits.
(Some architects and engineers may prefer to deal with whole numbers in which case the S/V ratio can be inverted and the curve rises as density increases. The critical cut-off value then becomes V/S = 10.0.)
The Fit With Los Angeles Zoning
Finally, a composite graph that includes both L.A. zoning data and values derived from the USC housing study (Fig.12) shows that points representing all 150 student designs contained in twelve separate projects cluster within the broad elbow of the original graph for L.A. zoning. This part of the curve includes a remarkable variety of ways to live in the city within a height range of 3-7 stories. The conclusion of the study is that ample opportunities do exist in this size range to provide both energy conservation and life quality without overly limiting development options for urban growth.
It is impossible to acknowledge individually each of the many students who participated in this 10-year study; without their efforts to record essential data as their designs changed and developed, this design research would be impossible.
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