Ann Arbor, Michigan:  Virtual Downtown Experiments, Part II
Sandra Lach Arlinghaus
Adjunct Professor, The University of Michigan
School of Natural Resources and Environment; Taubman College of Architecture and Urban Planning.
Member and Secretary, Board of Trustees, Community Systems Foundation (International NGO)
Member, Secretary, Vice-Chair, and Chair, City Planning Commission,* City of Ann Arbor (1995-2003);
member, Ordinance Revisions Committee (1995-2003), Master Planning Committee (2002-2003), and Environmental Commission (2001-2003), City of Ann Arbor.

For background information, please view this link to Part I:  Ann Arbor, Michigan:  Virtual Downtown Experiments

Material in this article is part of a forthcoming book by the author and William C. Arlinghaus entitled Spatial Synthesis (in press).

Thanks to:
  • Merle Johnson of the City of Ann Arbor for permission to use City of Ann Arbor base maps and aerials in this article.
  • Karen Hart, Planning Director, and Chandra Hurd, Planning Department, City of Ann Arbor, for files concerning building height in the downtown.
  • Matthew Naud, Environmental Services Coordinator and Emergency Services Coordinator, City of Ann Arbor.
  • Prof. Peter Beier, Director 3D Laboratory, Media Union, The University of Michigan and his staff members Lars Schumann and Brett Lyons.

  • Brief Background
    Ann Arbor is a small city (of just over 100,000 population) in southeastern Michigan.  It is home to the main campus of The University of Michigan, a state university with over 35,000 students on the Ann Arbor campus.  The student population composes about 1/3 of the population of the city.  Much of the rest of the population works at the university in some capacity or in research industry, businesses, government, or institutions that locate near the campus.  Most cities in the US have shapes that are topologically equivalent to a circle, in terms of paying taxes to the city:  land parcels that lie within the city boundaries pays taxes to the city.  There are, of course, cities that contain enclaves within their boundaries that are not part of the city itself.  In the case of Ann Arbor, however, and other small cities that contain large state universities, the city is more of an annulus (doughnut) in shape.  A large hole, containing the university is cut out of the city:  lands in this hole do not pay taxes to the city.  Hence, a disproportionately large property tax burden is placed on owners of non university parcels within the city (although of course the presence of the university is vital to the well-being of the city in numerous ways).  Ann Arbor is a college town.

    Thus, there is a need to have mechanisms to create continuing economic development within the city.  One way is to increase the stock of housing and space for commercial and other establishments in support of that housing.  This path is all the more attractive in light of enduring interests in reducing "sprawl" and in preserving open space in the more rural surrounding lands.  In a city with few remaining empty buildable lots, this approach seems to offer few alternatives, the most obvious of which is to increase the density of dwelling units within the city.  When density increases are proposed in established residential neighborhoods there is often loud and long public objection from residents of those neighborhoods.  There may also be serious environmental considerations, as well.  Few residents, however, seem to object to increasing density in the downtown:  many who already live in the downtown moved there with an acceptance of taller buildings. Residents of the city who do not live in the downtown often seem not to care about the idea of increasing density in the downtown.  What people do seem to care about, however, is what an increase in downtown residential density may mean to the character, appearance, and feeling of the downtown:  to its skyline and to the pedestrian experience.  To some, an 18 story building is a visual blight on the skyline that provokes negative comment every time it is viewed; yet, others note that they have become accustomed to it and view it as an old, familiar friend.  Building height can be a source of substantial dispute.

    Inventory of the Vertical City
    Prior to considering new tall buildings, it seems appropriate to create an inventory of existing buildings in the downtown area.  (In Ann Arbor, the "downtown" generally refers to the "Downtown Development Authority" or DDA:  a state-enabled authority that can capture increases in taxable value to pay for improvements within the defined boundaries.)  To create this inventory, building footprints were digitized from high quality aerial flown in 2002.  Heights were assigned to buildings based on information from the City of Ann Arbor Planning Department (only partially complete).  When the building footprints are sorted out according to height it becomes possible to visualize how the taller buildings are arranged with respect to the shorter buildings.  Figure 1 shows an animation of this pattern.  In that animation the reader has an opportunity to study different layers of downtown space in relation to a plain backdrop and finally to an aerial of the city.

    Figure 1.  Animation of existing building height in downtown Ann Arbor, Michigan.

    The evidence of Figure 1 suggests that buildings of 1, 2, and 3 stories are common in the downtown.  Indeed, casual conversations with individuals from around town suggest that no one objects to buildings of any of these heights.  One might wonder if that is because they somehow fit a sense of Ann Arbor well or if that is because they are prevalent and people become accustomed to them.  In any event, one might imagine an ordinance which allows three stories "by right" on any downtown parcel.  The question then becomes, how high elsewhere on prime parcels?  For this question one might look to the spacing pattern of existing buildings taller than three stories.  Tall buildings adjacent to other tall buildings can create wind tunnels and block wide channels of light.  Tall buildings built lot line to lot line may present those as well as other unwelcome effects.

    The Floor/Area Ratio as an Urban Planning Tool

    The problem of where to locate tall buildings, with sensitivity to existing building types on adjacent and nearby lots, is a difficult one.  In Ann Arbor, building height is currently limited by "floor area ratio" (FAR).  The FAR is calculated as the ratio of floor area in a building divided by parcel area, times 100.  If a given parcel has an FAR of 100 assigned to it, then a building footprint built lot line to lot line may have a height of 1 story.  If a parcel has an FAR of 200 assigned to it, then a building footprint built lot line to lot line may have a height of 2 stories.  Similarly, an FAR of 300, assigned to a parcel, yields a building of height 3 stories covering the entire parcel.   Thus, on a parcel with an FAR of 300, one might, instead, build a building on half of the lot area but of height six stories, or on a third of the lot area but of height 9 stories.  On the same parcel, a 30 story building could be built only if its footprint covered one tenth of the land area of the parcel.

    The FAR provides a height limit based on the size of foundation needed to support a tall building.  It also offers subtle encouragement for preserving some amount of open space and visual variation in the region to which it applies.  The drawback is that a tall building may get built with no regard to the broader context of how that new building will fit in with existing buildings on the surrounding parcels.  A possible side effect of using FAR (alone) to limit height is that it might encourage parcel amalgamation by large developers, thereby driving out desired local small business owners.  [Note:  in Ann Arbor, there are also "premiums" designed to encourage residential construction, and other uses viewed as "desirable" in the downtown; these allow an increase in FAR.  They will not be covered in this discussion as they introduce no new theoretical issues--just complexity of detail.]

    The Floor/Area Ratio, a Closer Look:  The Hyperbola as an Urban Planning Tool

    In a  recent article Claudia Iturriaga and Anna Lubiw consider the problem of labeling maps.  Because the current mapping environment is one that allows dynamic positioning of maps (zooming-in and panning), they consider the problem of non overlapping placement of text boxes to be one that is sufficient to solve with text boxes only at the perimeter of the map (with map content in the interior).  They note that if the aspect ratio of the label (ratio of height to width) is permitted to vary, with label area held constant, then labels can be fit together in a variety of patterns that will permit a balanced display of map and text boxes.  The requirement of constant label area ensures that a certain amount of text content is communicated; shape is permitted to vary.  Thus, if the label is viewed as having a fixed lower left corner, then the upper right corner varies along the track of the first quadrant of a rectangular hyperbola with origin at the lower left corner.  That is, if width is measured along the x-axis and height is measured along the y-axis, and the area of a label is fixed at K, then the equation describing the label is xy = K.  This latter equation is precisely the equation of a rectangular hyperbola in the first and third quadrants intersecting the line y = x at (K, K).

    It is not a long conceptual leap to imagine the rectangular areas arranged around the perimeter of a rectangular map as being similar to the rectangular areas of building footprints arranged around a rectangular block of a downtown based on a gridded street system.  The idea of a rectangle with an elastic aspect ratio tracing out the path of an hyperbola is similar to the idea of Floor Area Ratio (FAR) discussed above.  From an abstract viewpoint, the FAR/100, or number of stories, times the parcel area serves as an envelope within which buildings may be built.  For example, if a parcel has area 100,000 square feet and an FAR of 300, then 300,000 square feet of floor area may be built on the parcel:  as a 3 story building lot line to lot line front, back, and sideways (green building in Figure 2); or, as a 6 story building with each floor having 50,000 square feet on half the parcel (yellow building in Figure 2); or as a 12 story building with each floor having 25,000 square feet on 25% of the parcel area (magenta building in Figure 2).  What is constant is the value, K = (FAR/100)*(parcel area).  If one graphs this function, with parcel area on the horizontal axis and FAR/100 on the vertical axis, the result is a rectangular hyperbola, xy = 300,000 (Figure 2).  Different masses of building in relation to land area result depending on the height one chooses.

    Figure 2.  Rectangle with elastic aspect ratio and lower left corner fixed at the origin traces out part of one limb of a rectangular hyperbola xy = 300,000.

    When one abstracts away from the grid suggested by Figure 2, and focuses instead on the hyperbola, it is possible to extend the analysis to the more global scene of the entire DDA and to the issue of building mass in relation to land area.  Thus, consider that the x-axis units are now percent area in the downtown; then, the right-hand limit of the hyperbola is 100% of the land in the DDA.  Under these assumptions, what the hyperbola of Figure 2 now says is that 100% of the DDA may be covered with 3 story buildings:  that a 3 story building may be constructed, by right, anywhere within the DDA.  It also says that 50% of the land area in the DDA may be covered with 6 story buildings, or that one quarter of the land area in the DDA may be covered with 12 story buildings, or that 10 percent of the land in the DDA may be covered with 30 story buildings.  The use of the FAR to govern building height may play our at a regional (DDA) level as well as at a local level of the individual parcel.  The hyperbola captures the FAR in a systematic manner and it does so at all scales, from local, to regional, to global.  It does not reflect planning and geographic elements that the FAR does not capture such as (but not limited to)  heights of neighboring buildings and other adjacency considerations, historic preservation issues, shadow or wind tunnel effects and other quality of life issues, or lateral or upper story setback concerns.  Issues such as these require the human elements of judgment and common sense.  The mathematical implementation can do much, but not all; it is a tool of humans, not a replacement for human thought (although numerous abstract connections remain to be probed:  from cartography, to urban planning, to the Zipf rank-size rule and the lectures given by Michael Batty at The University of Michigan and Eastern Michigan University in the spring of 2003).

    The principles set forth here, would enable one to consider the total mass of building square footage permitted according to FAR, independent of municipality and local concerns.  Subtracting the actual built up area from that would give an estimate of the remaining mass that could be built, by right, according to code.  Within that remainder, one might calculate how many more 3 story buildings could be built; how many more 6 story buildings; how many 12 story buildings (or whatever height in whatever units).  Such a strategy can completely characterize the mass of building in relation to land area and may suggest a basis for the control of that mass, especially when one decides what future is desired and works back from that to create ordinances and code that will lead to that desired outcome (an approach similar to that take by others, as for example by people at ChicagoMetropolis2020).  It offers, however, no guidance as to where tall buildings might be placed in relation to each other or in relation to existing structures, as to which parcels might contain tall buildings, as to wind, light, and sound issues, and as to a host of other qualitative issues.  Other approaches might involve a guide to the spacing of buildings (forthcoming), buffers around existing buildings as zones of limited height, or legislated design standards.  It is for creative needs such as these, to be superimposed on measures of sheer mass or quantity that can be captured generally as mathematical and geographical propositions, that cities require the service of professional planners and a host of municipal authorities and support personnel.

    Beyond the Floor/Area Ratio:  Virtual Reality as an Urban Planning Tool.

         Virtual reality, the envisioning of alternative three-dimensional scenarios on a computer screen, offers to decision makers the capability to see how the massing of buildings and the general design of the urban landscape might look with various changes.  In the case of Ann Arbor, that might mean envisioning the downtown with new tall buildings in a three-dimensional model that can be viewed at the pedestrian level:  as a virtual landscape that can be navigated on the computer screen by City Council members as they sit with laptops in Council Chambers or by members of the public as they sit at home or in public libraries using computers with internet connections.  Part I of this topic showed virtual reality of the downtown based on

    Additional work has yielded refinements on these files.  Building footprints were digitized from an aerial of the downtown, flown for the City of Ann Arbor in 2002.  Many of the footprints had heights from the records of the Planning Department.  However, a number (over 300) did not.  Buildings with no height were assigned the height based on FAR by zoning type (using information from the City of Ann Arbor Zoning Ordinance) calculated in association with the virtual reality in Part I, above.

    The following sequence of interactive maps, made using the ImageMapper 3.3 extension to ArcView, shows the results, using maps and aerials in various combinations:

    This strategy necessarily produces error.  Buildings that do not occupy a full parcel may well be taller than indicated here (as the FAR permits them to be).  Others may be lower than what is allowed by FAR because they were not developed to the maximum permitted.  Still others may be yet another height because they were part of a Planned Unit Development (PUD). (PUD designation is a custom zoning that permits projects to be built outside the standard zoning currently present for that parcel when there are good reasons to consider such action and when there is substantial public benefit, defined in City Code, for such action.)  Finally, some parcels may not be developed for buildings:  they may house parking lots or other non-building uses.  Obviously, parcels that are empty, parcels housing parking lots, or parcels containing buildings of height less than permitted by FAR are targets for development or re-development. One block often targeted in this manner is the "Brown Block":  the block of land bounded by Ashley, Huron, First, and Washington Streets (Figure 2).   Vacant lands are easy to select from an aerial; what is not easy to see from an aerial is how new buildings might appear on them in relation to existing buildings. For that visualization, virtual reality is critical to gaining either a pedestrian's eye, or a bird's eye, view.

    On November 9, 2003, City Council Member Jean Carlberg (and Mayor ProTempore, Planning Commissioner, and member of the Ordinance Revisions Committee), City Council Member Joan Lowenstein, City of Ann Arbor Planning Director Karen Hart, and former City Attorney (on two occasions) Jerold Lax, visited the GeoWall (with the author and others, a total of 14) at The University of Michigan's 3D Laboratory at the Media Union (Dr. Peter Beier, Director).  At that time, they had the opportunity to view the files above at a scale that permitted them to feel as if they were walking among the buildings.  Each was given the map displayed in Figure 3 and an earlier version of the commentary following the map.  The red building on the map in Figure 3, at the southeast corner of Fifth and Huron Streets, is a location mentioned as a possible site for a new tall building by Ann Arbor Mayor John Hieftje (in personal communication with the author and elsewhere).  The commentary following the map enumerates the steps taken to build a virtual structural base of the downtown to use as a model to consider density/height issues in the downtown.

    Figure 3.  Map handed out to participants in the GeoWall display of November 9, 2003 at the Media Union of The University of Michigan.


    Procedure used to date to create a structural building base of downtown (no detail):
    • Building footprints were digitized using a city aerial (.tif file).  They are represented in the map above as polygons filled with color according to building height (all buildings of the same height have the same color).
    • Issues with height:
      • Over 300 polygons had a value of "0" height.  For all but 32 of those polygons, the digitized building footprints were assigned values based on the FAR for the zoning category.  Because the parcel outline generally exceeded the building footprint in area, this decision likely produces buildings that are shorter than what is permitted (although of course there may be actual buildings that have been constructed at less than what is permitted by right).
      • For the remaining 32 polygons, for which there was no data, a height of 3 stories was inserted (in later files, one was adjusted to 7 stories based on field evidence (Ashley Mews)).
      • Stories were assumed to be 12.5 feet in height.
    • Contours, with a contour interval of 5 feet, were used to create a triangulated irregular network  as a topographic base level from which to measure building height (rather than from a flat geometric base level). 
      • VR 3:  topographic base level in 3D
      • VR 4:  topographic base level with buildings extruded from that level.  This file may take a long time to load and it may be difficult to navigate because of the extended load time.
    • Actual height Virtual Reality:  digitized building footprints are superimposed on parcels in the downtown core zones. 
      • These VR experiments depict the downtown using actual building heights, where known that are extruded from a topographic base. This base is a Triangulated Irregular Network (TIN) made from a City of Ann Arbor contour map with a contour interval of 5 feet.  There are three sets of files for June 21: 
        • VR 5:  sun in the southeast (morning), 
        • VR 6:  in the south (noon), 
        • VR 7:  and in the southwest (afternoon).  
        This was done in order to suggest variation in lighting conditions with season and with time of day. The lighting scheme is designed for hill shading and is therefore really only useful for suggesting shadow location as it does not account for light reflected from impervious surface.
      • Later experiments involved inserting building heights for the 300+ parcels of unknown height, as above.  Links to 
        • VR 8:  a low sun scene (sun in the southwest) with the new building and 
        • VR 9:  a high sun scene (sun in the southwest) with the new building 
        are included here.  In these scenes parcels are extruded from topographic base level although it is not shown directly as a TIN in the scenes (in the interests of reducing file load time and map clutter).
    • A new building was added in response to comments from Mayor John Hieftje and is shown as a red block in Figure 3 and also in the attached aerial..
    • Earlier versions of files were shown to the Ordinance Revisions Committee of City of Ann Arbor Planning Commission.
    • Karen Hart and Matthew Naud, both of the City of Ann Arbor, previewed earlier files in the immersion CAVE and on the GeoWall at the 3D Laboratory (Peter Beier, Director) of the Media Union of The University of Michigan. 
      • Hart noted the utility of this tool for urban planning and mentioned one local project in particular; she agreed with the author that this tool might be useful in the context of a maximum height ordinance in the downtown; 
      • Naud noted the utility of this tool for emergency management, including as a training tool for first responders.  He expressed a desire to have building textures and other detail that would aid in building recognition introduced into scenes. Naud also suggested that knowing where hazardous materials were located would be useful to first responders.  He followed up by suggesting a connection to others and helping to arrange, and participating in, meetings with them.  These meetings have led to some proposals to fund emergency management activities linking various groups of individuals from the public and private sectors
      • Beier noted, on viewing the earliest files in the CAVE, that the buildings appeared to be too tall as one took a walk through the virtual downtown.  Later, Lars Schumann (Programmer Analyst II and Lab Manager) and Brett Lyons (Programmer Analyst I), of the 3D Laboratory, Media Union, told the author that the .vrml files used in the CAVE and on the GeoWall have units in meters.  Taejung Kwon (Ph.D. student, Taubman College of Architecture and Urban Planning and student in Engineering 477) noted (later yet) that one might calculate a z-factor to convert feet (used as the default unit in ArcView in City of Ann Arbor maps) to meters used in .vrml files.  Other students in the group, Paul Oppenheim, Adrien Lazzaro, and Aaron Rosenblum agreed with Kwon. 
    Current activities:
    • Research continues on building a "3D Atlas of Ann Arbor" designed to aid decision makers in a variety of contexts from Planning to Emergency Management.  It will also serve as a pilot project for a number of more global 3D atlases.
    • The author together with Matthew Naud  and John D. Nystuen (Professor Emeritus, College of Architecture and Urban Planning, The University of Michigan) are serving as faculty advisors in Professor Peter Beier's Engineering 477 (College of Engineering, The University of Michigan) course on virtual reality, Fall 2003.  They are working with the team of four students mentioned above.  The students have created a localized study for the "3D Atlas of Ann Arbor" at the intersection of Liberty and Main Streets.  It will serve as a pilot study for other detailed 3D urban views.

    Comments from the meeting from November 9, 2003 and subsequent follow-up:

    linked aerial

    one sees a red square on a parking lot corresponding to the location mentioned as a possible location for a tall building by Mayor Hieftje.  The buildings around it cast shadows that extend almost across the street.  A new building on the red square, of height greater than adjacent buildings would cast a shadow on both sides of the street.  Shadow position is important when considering budgetary allocations from the city's street tree escrow.  It is also important in creating a positive pedestrian experience in the downtown.
    linked map
    the mouse-over callouts shows the building address for three locations.  Click on a location to reveal elements of the database associated with each site.  In seeing all buildings simultaneously one gets an immediate picture of adjacency patterns: for example, a fire in one building may need immediate containment on the eastern edge to prevent spread to an adjacent building on the east containing volatile material. Careful database construction is critical:  the mapping, in this case, is easy in relation to the database construction.
    attached aerial

    The display below presents the final experiments in this set (given to Ann Arbor City Council in December of 2003) as the first in a series of possible 3D mapping  tools to aid in making a variety of difficult decisions:  for Ann Arbor as well as more globally.  It includes parcels extruded from building footprints, with the sun set in the south at a "low" setting, using an invisible topographic base created from a TIN made from a topographic map with a contour interval of 5 feet.  Buildings have been adjusted using a z-factor of 0.3048.  It also includes street labels that appear as one moves around at a local level as well as navigation aids (click in the lower left corner of Cosmo Player) of assigned camera viewpoints.  These, coupled with using the "driving" capability of Cosmo Player, help in getting around the virtual downtown so that one does not get lost in the space of virtual Ann Arbor!

    VR 10this virtual model of downtown Ann Arbor shows views of the downtown
    • from the south, along a corridor between Division and State streets
    • from the south, looking north along the Main Street corridor
    • from the east, looking west along the Huron Street corridor, at pedestrian level.
    Use the list of viewpoints in the lower left-hand corner to be taken to these three different camera positions.  Also, use the tools in Cosmo Player to structure your own route through the downtown at a bird's eye or human's eye level.

    Labels on the streets will appear as one zooms in.  Some graphic tasks that are easily accomplished in a GIS are not so easily accomplished in virtual reality.  The lettering for these labels was made in a polygon layer of ArcView by tracing default lettering.  Automatic labels that are easy to produce in a 2D map do not reproduce in the 3D version.  Thus, as with the building footprints, digitizing letters will make them appear.  In the process of digitizing letters such as "B" or "D," one might be reminded of converting a multiply connected domain to a simply connected domain and consequently the Jordan Curve Theorem from topology or the Cauchy-Goursat Theorem (or others) from the theory of functions of a complex variable.  It is remarkable to see that strong interdisciplinary connections between geography and geometry arise even in the most mundane of mapping tasks.

    • VR 11.1, 3 story building added at southeast corner of Huron and Fifth
    • VR 11.2, 4 story building added at southeast corner of Huron and Fifth
    • VR 11.3, 5 story building added at southeast corner of Huron and Fifth
    • VR 11.4, 6 story building added at southeast corner of Huron and Fifth
    • VR 11.5, 7 story building added at southeast corner of Huron and Fifth
    • VR 11.6, 8 story building added at southeast corner of Huron and Fifth
    • VR 11.7, 9 story building added at southeast corner of Huron and Fifth
    • VR 11.8, 10 story building added at southeast corner of Huron and Fifth
    • VR 11.9, 11 story building added at southeast corner of Huron and Fifth
    • VR 11.10, 12 story building added at southeast corner of Huron and Fifth
    This set of files shows a sequence of views, all with the same two camera angles--the first is a view of the entire downtown and the second is a view looking west along Huron Street, from a vantage point to the east of State Street. Use the navigation system in the lower left-hand corner to see the views from these preset camera positions; they offer a standard source for comparison as one switches from model to model that the free-roaming form of navigation does not. The red building in each model is a virtual building built on the southeast corner of Huron and Fifth, across from City Hall.  It is the empty spot selected by Mayor Hieftje on a number of occasions as one location to consider for building a tall building.  The sequence of files shows the virtual building with different numbers of stories:  3, 4, 5, 6, 7, 8, 9, 10, 11, and 12.  The general view of the downtown suggests how the new building might or might not fit in the overall skyline view.  The local view along Huron Street suggests what the pedestrian experience might be.
    Figures 4a and 4b below show animated sequences of screen shots from the virtual reality files.  Thus,
    • in Figure 4a, one can watch the bright red building "grow" from 3 to 12 stories, in 1 story increments, in the center of the DDA, across the street from City Hall, at the southeast corner of Huron and Fifth streets.  A view such as this one suggest the impact the new building might have on the overall skyline.  To get a good general picture, one might wish to have such animations from more than one vantage point and for change involving more than one building.  This animation suggests a style of analysis at the global level of the entire downtown.
    • in Figure 4b, one can watch the same building grow (as in Figure 4a, again in 1 story increments) but from a far more local viewpoint and from a level closer to a pedestrian's eye view.  A sequence of such animations might be helpful in understanding the impact of new structures on the pedestrian experience.


    Next steps include:

    Possible future activities

    *The author acknowledges productive meetings with and assistance from


    Software used:

    Copyright, Sandra L. Arlinghaus, 2003.  All rights reserved.