Average perimeter distance and its relation to floor plate geometry 41

Transcription

1 Lght, vews and money: Average permeter dstance and ts relaton to floor plate geometry 41 Ermal Shpuza Georga Insttute of Technology, USA Abstract Envronmental comfort n buldngs wth large floor plates s lnked to the dstance of workspaces to the buldng permeter. Ths s partcularly mportant wth regard to natural lght and vews afforded by such arrangements. In order to measure or gauge the degree of ths comfort, ths paper ntroduces the ndex of average permeter dstance for any gven floor plate. In defnton, ths ndex sums up dstances to permeter of all locatons on a gven floor plate. Locatons found lyng along polygons that are offsets of the plate permeter have equal qualtes assocated wth lght and vews, whle the length of each offset polygon determnes ther precse number. In effect, the ndex s affected by the combnaton of the geometry and confguraton of floor plate, atra and cores wthout a drect relaton to the permeter length. Therefore, by assocatng permeter length wth a consderable part of the buldng cost, t s possble to evaluate exstng floor plates or desgn schemes wth regards to mprovng natural lght levels whle reducng costs. Keywords Floor plate, average permeter dstance, permeter length, natural lght level, buldng cost, consecutve offsets 41.1 Introducton The geometry of large floor plates s of paramount mportance for the desgn of many buldng types, ncludng offces. The complex relaton between the shape of floor plate and the locaton of core and atra nfluences drectly the proxmty of workspaces to permeter, thus the probablty for natural lght and vews, whch often results n herarchcal stratfcaton of workspaces wth regard to organzaton status of employees. In general, the envronmental comfort of workspaces goes the opposte way wth the buldng and mantenance cost of the edfce. In a practcal sense, permeter length s drectly lnked to buldng cost. Assumng that the cost of buldng one unt of ndoor space does not depend upon the shape of the floor plate, whle dsregardng the nature of structural systems, modular buldng components and percentage of what can be covered wth rectangular elements, we can relate buldng cost to permeter length. At a glance, t seems that floor plates wth long permeters and concave shapes would produce shorter dstances to permeter for nternal workspaces hence a greater comfort. However, a permeter undulated n Proceedngs. 4th Internatonal Space Syntax Symposum London 2003

2 local scale wth nches and turns wll obvously have lttle mprovement on the qualty of workspaces, hence t s not clear whether the rato between area and permeter length can suffce to descrbe and evaluate the qualtes of workspaces Fgure 1: Insuffcency of characterzng floor plates wth the dstance from core to permeter only. (a) the dstance changes due to the geometry of permeter, (b) areas outsde the shaded cross cannot be descrbed Prevous studes on the geometry of floor plates have proposed descrptve measures such as dstance from core to permeter (Duffy, 1976), rato between area and permeter length, and the occurrence of hgh ntegraton spots that can gude the generaton of ntegratng crculaton systems (Shpuza, 2001). The semnal study of Duffy on offce buldngs emphaszes the metrc depth between permeter and core for characterzng the man features of the shell. A small number of depths from permeter to core can easly descrbe most of the workspace area n offce buldngs wth rectangular floor plates. However, usng such a measure s assocated wth two man ssues. Frst, n cases where the depth between permeter and core has more than one dmenson, t s not easy to characterze floor plates due to the dfferent percentages that these depths mght cover. Ths s further complcated when the permeter has a jagged or curvlnear shape, Fgure 1a. Second, even n the case of rectangular regular floor plates, depths from permeter to core account only for locatons that fall nsde the cross-lke area between core and permeter wthout coverng four corner areas, Fgure 1b. Instead of depth from core to permeter, here I propose an ndex, whch although metrc, consders any shape of permeter, and most mportantly t regards all locatons n the workspace area as contrbutors for evaluatng the floor plate rather than just those fallng nsde the regons projected from the core. How to reconcle two opposng trends of workspace comfort and buldng cost n the desgn of large floor plates? How to descrbe the complex relaton between permeter length, shape of floor plate, locaton of atra and core on one hand and proxmty to lght of workspaces on the other? To address these ssues, I propose the measure of average permeter dstance that sums up the dstance to permeter of all locaton n a floor plate. Ths measure s used n a threefold manner. Frst, t descrbes the experental qualty of locatons nsde floor plates n regard to natural lght and vews that are drectly lnked to envronmental comfort and often to the herarchcal stratfcaton of offce workspaces. Second, t characterzes the geometry of floor plate shapes n a far better way than the area to permeter rato; the latter s proved to have lttle sgnfcance for analyzng qualtes of nternal locatons. Thrd, the measure pnponts the relaton between the shape of floor plate to the buldng cost. Wthout regard to nternal parttons or corrdors, t s suggested that the qualty of floor plates as captured by the average permeter dstance nfluences drectly the probablty of any of ts locatons to have a gven dstance to permeter and thus to afford natural lght and vews. In buldngs wth open plans and contnuous condtons along the Lght, vews and money

3 buldng skn such probablty becomes a matter of fact. I suggest that the relaton between the workspace area and the floor plate geometry nvolves not only permeter length, but also somethng about ts shape. Average permeter dstance The concept for the average permeter dstance s based on the fact that any two locatons equdstant to the permeter wll have equal qualtes that derve from proxmty to permeter, such as natural lght and vews provded that we assume a contnuous dstrbuton of locatons nsde the floor plate and contnuous qualtes of the buldng envelope, such as wndow openngs. Such two locatons are found lyng along polygons that are offsets of permeter. For equal dmensons of workspaces or locatons, the length of each offset polygon shows the number of workplaces, whle the step number of each offset polygon shows ther metrc depth to permeter. I assume a contnuous state of openngs n the buldng skn dsregardng the actual locaton and dmensons of wndows and mullons as well as a contnuous state of the workspace area dsregardng the possble locaton of corrdors and cubcles. I offset consecutvely nwards from permeter untl all area to the core s covered and calculate the average permeter dstance, or else the potental dstance to permeter of any locaton n a gven floor plate, by combnng the lengths of offset polygons wth ther depth from permeter A sample of fve speculatve offce buldngs desgned by the Atlanta-based archtectural frm Cooper Carry Inc. Centura Blvd., 1825 Century Center, Cty Vew I, Glenlake Bldg. 1, Huntcrest II share common features of the rectangular shell, ncludng floor plate area, core area, and the two man permeter to core depths. A smplfed verson that ncorporates these qualtes, whch I term r-1, has a rectangular floor plate of 225 x125 and a symmetrcally postoned core of 105 x25. I use t to descrbe the method of calculatng the adp and later as a prototype for generatng a theoretcal sample. I assume a square shaped workspace wth a sze of 12 6 and I offset nwards from the permeter consecutvely wth an offset dstance od of As I shall show later, the sze of the workspace and the sze of od do not have any effect on the overall calculaton. In the frst offset polygon wth a length of 600 there are 600/ 12 6 =48 potental workplaces that are 1 step away from permeter, Fgure 2; n the second offset wth a length of 500 there are 40 workspaces 2 steps away from permeter; n the thrd one wth a length of 400 there are 32 workspaces 3 steps away; and n the last one wth a length of 300 there are 24 workspaces 4 steps away. Fgure 2: The concept of calculatng the apd. (a) 48 workspaces alongsde the 1st offset lne shown n bold, (b) 40 workspaces along the 2nd offset lne, (c) 32 workspaces located n the 3rd, (d) 24 workspaces located 4 steps deep Proceedngs. 4th Internatonal Space Syntax Symposum London 2003

4 Each workspace contrbutes ts depth to the overall depth: 48x1 + 40x2 + 32x3 + 24x4. If we dvde the total of these products 320 wth the number of all workspaces 144, we get an average dstance of all potental workspaces from the permeter of 320/144=2.22. Ths shows a step or unt dstance that when multpled wth od of 12 6 gves the real average depth of Hence, I calculate the average permeter dstance apd wth the formula below where po s the length of permeter offsets, od s the offset dstance, and d s the step depth from permeter of an offset polylne. unt average dstance uapd = (1) po average permeter dstance apd = uapd od (2) po d 41.4 Table 1: Convergence of average permeter dstance for fner offset steps od /2 uapd apd prototype r-1 r-3 r-5 r-7 e-1 e-3 e-5 e-8 c24-1 c24-3 c24-5 c24-6 c16-1 c16-3 c16-5 c16-7 c8-1 c8-3 c8-5 c8-8 Fgure 3: Calculaton of the apd ndex for famles of theoretcal floor plates derved from the prototype. Only 20 out of 36 calculated examples have been dsplayed. For clarty, only 1 out of 3 offset polygons bult wth offset dstance at 3 9 has been shown. The measure s lttle affected by the offset step dstance and converges for fner offset steps od as t s shown by calculatng the average permeter dstance three tmes wth od of 7 6, 3 9 and /2 for the floor plate c8-1, Table 1. It s also possble to automate the calculaton of the measure by summng up dstances to permeter of a large number of randomly placed postons n the workspace area. Relaton of average permeter dstance to permeter length Startng wth the prototype r-1, I generate a theoretcal sample of 36 floor plates by stretchng the permeter whle preservng the same total area and conformng to dstances allowed by fre regulatons. I stretch two sdes of r-1 nward and outward wth comparatvely equal ncrements from case to case whle preservng the orgnal area of sq and keepng the core ntact to produce a famly of rectangular floor plates r-1 to r-7. Startng from an ellptcal floor plate wth area equal to the prototype, I stretch untl the perfect crcle s reached to produce a famly from e-1 to e-8. Smlarly, I construct three more famles named c8 for the cross wth 8 corners, c16 for the cross wth 16 corners, and c24 for the cross wth 24 corners, Fgure 3, wth members whch shapes range from elongated to most compact. The theoretcal floor plates share the Lght, vews and money

5 same area, same cores, and dffer only n the geometry of permeter, ts length and number of corners. I offset nwards from permeter wth an offset dstance od of 3 9, whch s half of a common 7 5 cubcle, untl all the workspace area has been covered by offset lnes. The results for the average permeter dstance apd and permeter length for all of them are shown n Table 2 and Table 3 and ther relatonshp s expressed n Chart 1. Table 2: Average permeter dstance for famles of theoretcal shapes measured n feet r e c c c Table 3: Permeter length for famles of theoretcal shapes measured n feet r e c c c The common sense predcton about the relaton between adp and permeter length would be that the more compact shapes would produce longer average permeter dstance. Therefore, the lnes of fve famles stretch dagonally n the chart from the crcle e-8 n the lower rght corner to the cross-shaped c8-1 n the upper left corner. As the permeter becomes longer due to the makng of shape more concave, average permeter dstance tends to get smaller average permeter dstance (') e r c24 c16 c8 prototype Chart 1: Relaton between average permeter dstance and permeter length for theoretcal floor plates derved from the prototype. Lnes connect members of 5 famles of floor plates. It s mportant to note that equal permeter lengths for certan shapes produce dfferent average permeter dstances. As we move horzontally n the chart whle keepng the permeter length constant, we cross curves of dfferent famles. For nstance, a length of 700 can result n average permeter dstance as vared as 26.5 to 27.8 from r-1 to c24-6. Smlarly, dfferent permeter lengths can produce the same average permeter dstance as can be seen whle crossng curves of dfferent famles whle movng vertcally through the chart. Proceedngs. 4th Internatonal Space Syntax Symposum London 2003

6 Gven the fact that the area has been kept constant throughout the sample, the varaton of permeter length shows at the same tme the varaton of the rato between area and permeter length. Often such a rato s used to defne the compactness of a shape. For nstance, a normal cross permeter c8-5 can have almost the same permeter length of 753 as a cross wth 24 corners c24-4 wth permeter of 744, therefore the same compactness f t s defned as a rato between area to permeter length. However, as shown by the scatter chart, the average permeter dstance for these two cases dffers from 22.3 to The length of permeter can be attrbuted to ts features n both local and global scale. Both of them affect the overall length. Nevertheless, wth regard to ths dscusson, local features n the geometry of permeter have less mpact on the qualtes of ndoor space n comparson to global ones. Small turns, corners and nches n the buldng skn, whch ncrease permeter length, do not have a major effect n the qualtes of spaces nsde the buldng. On the contrary, what matters s the topology of the shape n the larger scale. Whle acceptng ths, t s possble to suggest that permeter length cannot be used as a relable measure for analyzng qualtes of ndoor spaces. Nor can compactness be defned realstcally as a rato between permeter length and area. In contrast, average permeter dstance could be assocated better wth the dea we have about compactness addressng drectly real qualtes of workspaces. Consderng that the cost of buldng one unt of ndoor area s not affected by the geometry of the floor plate, we can attrbute a consderable share of the overall buldng expendture to the cost of the envelopng skn of the buldng, thus to permeter length. Under the lght of the earler dscusson, the average permeter dstance could be used to evaluate the qualty of workspaces n relaton to buldng cost. For nstance, the costs of buldng c8-5 or c24-4 are comparable to each other, but the qualty of ndoor spaces, as measured by the average permeter dstance ndex, s potentally hgher n the case of c8-5. The apd can thus be used to evaluate how well the geometry of a floor plate performs wth regard to both buldng cost and the qualty of natural lght and vews. Evaluaton of floor plates usng the Average Permeter Dstance Index What s the best geometry of floor plate that mnmzes the dstance to permeter whle mnmzng the buldng cost for a certan bult area? I use the apd ndex to evaluate buldngs wth regard to maxmzng the proxmty to natural lght and vews and mnmzng the buldng cost of the skn. For ths, I analyze a sample of seven offce buldngs desgned by the US archtects frm SOM for corporate and speculatve clents: 444 Market Street (markt), Fourth Fnancal Center (fnancl), Lght, vews and money

7 One Magnfcent Mle (magnf), 33 West Monroe Street (monr-full) (monr-dnt) (monru), Bank of Amerca World Headquarters (boa), Bose Cascade Home Offce (bose), and Sears Tower (srs-40) (srs-50) (srs-70) (srs-100), Fgure 4. Two of the buldngs have dfferent floor plates n varous heghts, thus the sample comprses twelve offce floor plates. For a far comparson, measurements for each floor plate have been modfed wth a scalng factor that reconcles ts floor plate areas wth the bult area of the prototype at sq. scalng. factor = area prototype area (3) Fgure 4. Calculaton of apd ndex for floor plates of the prototype and offces desgned by SOM. For clarty, only 1 out of 3 offset polygons bult wth offset dstance at 3 9 has been shown 41.7 prototype srs-100 markt monr-full srs-70 fnancl monr-dnt magnf srs-50 monr-u bose boa srs-40 For the analyss, I use the BOMA standards to defne the locaton of permeter and consder ts propertes contnuous by dsregardng columns and mullons and nterruptng only when parts of the core touch the skn. Table 4 shows values of adp and permeter length modfed wth respectve scalng factors. Table 4: Modfed apd and permeter length for 12 offce buldng floor plates measured n feet prototyp markt fnancl magnf monr-full monr-dnt monr-u boa bose srs-40 srs-50 srs-70 srs-100 sc-apd sc-per Proceedngs. 4th Internatonal Space Syntax Symposum London 2003

8 I supermpose these results onto the prevous chart of the theoretcal floor plates to enable comparsons both among real floor plates and among theoretcal shapes derved from the prototype, Chart 2. Wth consderaton to short permeter length, thus low buldng cost, and low average permeter dstance, thus hgh potental of workplaces beng close to wndows, the regon n the lower left corner would nclude the favorte exemplars. Due to a combnaton of factors such as the overall shape of floor plate, the sze and poston of atra and core components, most of the cases fall n the lower left half of the chart havng n general shorter permeter lengths and average permeter dstance than the prototype and ts varatons that occupy a poor poston n the upper rght border of the scatter. Only three cases fall above the dagonal defned by the prototype varatons: monr-full, market due to havng a core that abuts the permeter, and fnancl due to an extremely stretched shape of the floor 41.8 plate average permeter dstance (') e r c24 c16 c8 markt fnancl magnf monr-full monr-dnt monr-u boa bose srs-40 srs-50 srs-70 srs-100 prototype Chart 2. Relaton between average permeter dstance and permeter length for a sample of offce buldngs desgned by SOM. Twelve cases have been supermposed on the chart 1 of theoretcal floor plates Bearng n a mnd the crteron of achevng the shortest dstance to permeter for the shortest permeter length thus lowest buldng cost, the above examples can be ranked usng the product of relatve average permeter dstance wth relatve permeter length from best to poor. Table 5 confrms the earler observaton of monroefull, market, fnancal and prototype havng the lowest performance. The best cases are bose, monroe-donut and monroe-u confrmng the benefts of atra. In a second facet, the chart enables to quantfy mprovements n average permeter dstance ndex. For nstance, for the same permeter length, thus the same expendture, usng the donut shaped floor plate lke monr-donut rather than the rectangular srs-100 wll potentally mprove the qualty of workspaces as measured by the average permeter dstance at the amount of 19%. Table 5: Ascendng order by product of relatve permeter length wth relatve average permeterdstance bose monr-dnt monr-u boa srs-70 srs-100 magnf srs-40 srs-50 prototyp fnancl markt monr-full product Lght, vews and money

9 Conclusons The desgn of floor plates for offce buldngs takes nto account a varety of determnants ncludng the constrants of ste, budgetary consderatons, organzatonal profle of clent, elevaton and tectoncs, fre regulatons and furnture standards. In any gven scenaro, the resultng geometry of the floor plate and confguratons of core and atra drectly determne the potental of ndvdual workplaces to be n proxmty to the buldng permeter thus havng access to natural lght and vews. Ths paper proposes a method to characterze floor plates through the ndex of average permeter dstance that consders the average value of the dstance to permeter of the entrety of the possble workspaces on the floor plate. The new ndex s based on the fact that locatons that le on polygons that are offsets of the permeter potentally share the same levels of natural llumnaton, whle the length of the polygons determnes ther number. Sgnfcantly, however, t has been dscovered that there s no drect relatonshp between the proposed measure and permeter length. Whle permeter length s nfluenced by features of the floor plate shape -at the global scale of atra and wngs, and at the local scale of small ndents and corners - t s the global features that have an mpact on qualtes of ndoor spaces n comparson to local ones. It s suggested that permeter length cannot be used relably to analyze qualtes of floor plates nor can compactness be defned realstcally as a rato between permeter length and area. Rather, t s the average permeter dstance that can best descrbe the dea we have about the compactness of shape of floor plate, whle drectly addressng real qualtes of ndoor spaces. Most mportantly, ths partcular measure pnponts ways of quantfyng the relaton between two opposng trends - the comfort of workplaces wth regard to natural lght and vews, and the fnancal aspect of buldng cost and mantenance of the skn. Ths s acheved through nvestgatng the varance of the average permeter dstance and length of permeter for theoretcal and real cases after reconclng the sze of ther areas, therefore gvng useful nsght for mprovng qualtes of ndoor spaces for desgn proposal schemes whle reducng cost Proceedngs. 4th Internatonal Space Syntax Symposum London 2003

10 Acknowledgments I acknowledge the encouragement and suggestons of John Pepons and Sont Bafna as well as the assstance of Pegah Zaman and Manu Sobt. The support of School of Archtecture at Georga Insttute of Technology through awardng a research assstantshp durng the academc year has been nstrumental for ths research. References Buldng Owners And Managers Assocaton, BOMA Standards, Bush-Brown, A., 1983, Skdmore, Owngs and Merrll Archtecture and Urbansm , New York, Van Nostrand Renhold Company Drexler, A., Menges, A., 1974, Archtecture of Skdmore, Owngs and Merrll, , New York, Archtectural Book Publshng Co. Duffy, F., Cave, C. and Worthngton, J.,1976, Plannng Offce Space, London, The Archtectural Press Ltd. Shpuza, E., 2001, Floor Plate Shapes As Generators of Crculaton, Proceedngs of the Thrd Internatonal Symposum on Space Syntax, Georga Insttute of Technology, Atlanta Lght, vews and money