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Linear cities in a nonlinear world
Geofonrm, Vol. 8, pp. 57-61, 1977. Pergamon Press. Printed in Great Britain.
Linear Cities in a NonlinearWorld
REID H. EWING and E. K. A. TAMAKLOE*, Ghana
Introduction
Linear cities have several advantaaes over other cities. They are rectangular which eliminates excessive congestion in central areas (BULL, ~~~~;MoRIsoN, 1970). They are open-ended which permits unlimited growth (BULL, 1967; LLEWELYN-DAVIES, 1966) and avoids land use succession. They have parallel land uses which make both central activities and the surrounding countryside more accessible to urban residents (BULL, 1967; BLUMENFELD, 1967). They have rectilinear transportation systems which provide ma~mum coverage at minimum cost (public transportation is most efficient when traffic is confined to a corridor) (BULL, 1967; LLEWELYNDAVIES, 1967).
BEAUJEU-GARNIER and CHABOT (1967) introduce linear cities with the comment, “Linear cities are now in favour”. This is an understatement. It is difficult to find a text or review article which does not tout linear cities in one form or another, and many planning reports do the same (BULL, 1967). Despite the interest they generate, linear cities seldom get beyond the drawing board. When planners critique linear cities, they critique linear cities in theory not practice. When planners opt for linear development, they do so on a purely subjective basis. This is no way to plan cities. In this paper we discuss the pros and cons of linear cities and conclude that the pros outweight the cons (at least in theory). This should come as no surprise to those who are familiar with the literature on linear cities. What may be a surprise is our analysis of Tema, the fourth largest city in Ghana. Tema’s shape, land use, and infrastructure are those of a linear city. Tema shows signs though of deviating from the linear ideal. From this we conclude that linear cities have several advantages in theory which may not be realized in practice, and that linear cities may not maintain their linearity in the long-run.
Fig. 1 l
A linear city
Linear cities have disadvantages as well. They generate some very long intraurban trips; they channel local as well as through traffic onto major arterials creating unnecessary congestion; and they fail to give proper emphasis to the automobile (KEEBLE, 1969). Whether these disadvantages are significant relative to the dJ\.int.lpej g.lf linear cities is a matter of opinion. TIY ~~II~X~II~U~ seems to be that they are not (BULL, 1967).
Linear cities Urban planners have yet to agree on what is and what is not a linear city (KEEBLE, 1969). No two linear cities are exactly alike. Compare Le Corbusier’s industrial city to Milyutin’s Stalingrad or Gide’s plan for Paris to Tange’s plan for Tokyo. We can generalize about linear cities to this extent, most linear cities are open-ended rectangles with parallel land uses and rectilinear transportation systems (see Figure 1). This is our definition of a linear city.
The real issue is not the desirability but the feasibility of linear cities. Can they maintain sufficient linearity to realize their inherent advantages? Some critics think not. Doxiadis (1967) argues that linear cities can exist only where forces act in one direction (e.g., in a valley). Where forces act in all directions, cities will be nonlinear. “Any connection with functions not situated along the axis of (a linear city) would disrupt its uniformity and linearity.” Keeble (1969) notes that some clustering of activity is inevitable even in linear cities. Transit stops and intersections will generate more activity than other points in linear cities and thus act as nuclei in polycentric development. Clustering will occur even if development is random. Activity begets more activity causing points of initial develop-
Of course, there are exceptions. Soria’s Ciudad Lineal was shaped like a ring instead of a rectangle. The Northampton-Bedford plan had land uses in series rather than parallel. London in the MARS plan had a curvilinear transportation system instead of a rectilinear one. Suffice it to say that our definition fits all linear cities in whole or in part (COLLINS, 19.59). * The authors are, respectively, a Visiting Lecturer and a Senior Lecturer in the Department of Planning at the ilniversity of Science and Technology, Kumasi. Ghana. 57
58
Geoforum/Volume
ment to grow at the expense of other points. Once again the result is polycentric development. So the question is: are cities inherently nonlinear? A close look at Tema provides a tentative answer.
81 Number
211977
near the commercial corridor. This gives the middle class maximum access to their future work places. The road to Akosombo is the backbone of Tema. It divides Tema in half with industry on one side and residence on the other. Secondary roads run parallel and perpendicular to this road (see Figure 2).
Tema -. A linear city
Land uses in Tema are arranged in parallel corridors as shown in Figure 2. There is an industrial corridor in the east, a residential corridor in the centre, and another residential corridor in the west. A narrow commercial corridor (presently under development) lies between the residential corridors. The various corridors are separated by green spaces and bounded by major roads.
q tz2l
Residential
Tema satisfies our definition of a linear city as well as any city in the world. It is an openended rectangle with parallel land uses and a rectilinear transportation system. True there is a harbour in the south running perpendicular to the major land uses, but topographical features of this sort are ubiquitous. The harbour does not detract from the essential linearity of Tema though it forces us to relax our definition of a linear city. It is also true that the original town of Tema was nonlinear, but very few linear cities develop from scratch and those which do must start somewhere. The original town of Tema has long since been assimilated into a larger linear city. All things considered, there is probably no better place to test our ideas than Tema.
Industrial
#
Commerclol (under development)
q
Urban density patterns
Population density declines exponentially with increasing distance from the centres of all cities. This was Clark’s conclusion after studying dozens of cities “from Los Angeles to Budapest” (CLARK, 195 1). In mathematical terms,
Undeveloped
4
Scale
Harbour
area -
0
5000
ft
nd=aebd
(1)
where nd is the density at distance d from the centre of a city and a and b are empirically determined constants. Clark’s study was followed by many others which confirmed his findings. To quote Berry et af. (1963) “Almost one hundred cases are now available, with examples drawn from most parts of the world for the past 150 years, and no evidence has been advanced to counter Clark’s assertion.” Not one exception to equation (1) is on record as of 1975. Clark’s “assertion” is truly a social scientific law if there are any laws in social sciences.
_I Fig. 2 l
The Accra-Tema metropolitan Associates)
area (after Doxiadis
Housing is also arranged in corridors. Low-income housing is concentrated in the east along the border of the industrial corridor. This gives laborers maximum access to their work places. High-income housing is concentrated in the west around a north-south lagoon. This is an area of considerable amenity. Middle-income housing is concentrated in the centre,
Density declines with distance from the centre of a city because non-residential activities are highly centralized. Households can reduce the cost of commuting by living near these activities and therefore are willing to pay more for sites which are centrally located. Paying more, they cannot afford as much land. This causes density to peak at the centre of a city and decline with distance from the centre. The result is a circular city (MUTH, 1961). Non-residential activities in Tema are arranged in parallel corridors. We would therefore expect density
59
Ceoforum/Volume 8/ Number 211977
patterns in Tema to be linear for the same reason they are circular in other cities. Dober (1969) says as much in his discussion of linear cities. If so, this would be the first exception to Clark’s law. There is another possibility. Private development in Tema may be restricted to certain areas but not encouraged in others, and occupancy rates may differ from their nominal values. Thus Tema may have developed a circular density pattern despite its linear design. If so, this would be virtual proof of Clark’s law.
are included in a single regression equation {see the last row of Table l), distance to Tema’s central axis fails to be significant at the 0.10 level.
Density patterns in Tema
There are at least four alternative density functions the literature. First and foremost is Clark’s in function nd = aebd
(1)
where density (nd) declines exponentia~y with distance from the centre of a city (d). The other functions are nd = aecd2 nd =ae
bd + cd2
nd = @db
(2) (3) (4)
where density declines exponentially with distance squared in equation (2) (SHERRATT, 1966) with both distance and distance squared in equation (3) (NEWLING, 1969), and with distance raised to a power in equation (4) (MILLS, 1969). a, b, and c are empirically determined constants. Being unable to choose among these functions on a priori basis, we calibrated all four of them. Our dependent variable was the gross population density in each of 41 enumeration areas of Tema according to the 1970 Census of Ghana. We had two independent variables. One was the distance from each enumeration area to the centre of Tema (see Figure 3). The centre of Tema lies near the intersection of the harbour and the industrial corridor. Development in Tema began at this point, and it is still the centre of commercial activity. The other independent variable was the distance from each enumeration area to Tema’s central axis (see Figure 3). Tema’s central axis lies along the road to Akosombo. It separates the two dominant land uses in Tema, industry and residence. More than any other point and line in Tema, density declines with distance from Tema’s centre and central axis. We derived eight regression equations, one for each independent variabie in each density function. Our results are presented in Table 1. Note that Tema has a circular density pattern. Distance to the centre of Tema in equations (I a) to (4a) accounts for -35% of the variation in intraurban density. This is typical of urban density functions. In contrast, distance to Tema’s central axis in equations (1 b) to (4b) accounts for only -15%. When both independent variables
Fig. 3
* Tema (after the Tema Development Corporation) Density in Tema is best described by equation (3). Equation (3) has higher R2 s than the other equations and avoid serial correlation in the disturbance term. Density in equation (3a) first increases and then decreases with distance from the centre of Tema. It peaks just outside the central business area where commerce is displaced by residence (see Figure 4a). Density in equation (3b) first decreases and then increases with distance from Tema’s central axis. It is a minimum in Tema’s commercial corridor {see Figure 4b). The four urban density functions are of comparable descriptive power. Distance squared does not improve on distance to the first power in an exponential function. Nor does a power function improve on an
60
l
~~forum~Volume
Table 1 Alternative Urban Density Functions*
(1) (la) (Lb) Equation (2) (2a) (2b) Equation (3) (3a) (3b) Equation (4) (4af (4b)
a
b
225.9 (15.5) 83.9 (18.7)
-1.25 (-4.4) 0.77 (m-2.3)
8/ Number 211977
c
R2
Equation
Equation
(1)
126.5 (22.5) 68.0 (22.1) 57.4 (5.3) 134.3 (12.9)
1.52 (1.1) --3.00 C--2.1)
56.8 (28.9) 36.2 (16.6)
-1.12 f- 3.7) -0.43 f 2.7)
235.1 (15.6)
0.31 0.12 ---OS6 (-4.8) ~0.41 C--1.9)
0.36 0.08
-1.18 (- 3.0) 1.47 (1.5)
0.38 0.17
1.12 C-3.6) t -0.34 C-1.1)$
0.25 0.14 0.35
* Listed above are regression coefficients, f - statistics (in parentheses), and coefficients of determination. Density is expressed in persons/acre and distance in miles. There are 41 degrees of freedom. ? Distance to the centre of Terns is the independent variable. 1 Distance to Tema’s central axis is the independent variable. exponential function. A quadratic on the others, but only slightly.
function
improves
This is to Clark’s credit. His function has never failed to describe urban density patterns in 25 years of empirical testing.
Central busmess
those of a linear city. But no city is or could be 100% linear because the world itself is nonlinear. A linear city is a theoretical construct with no “real world” equivalent. Real cities must conform to topographical features (e.g., Tema’s harbour) and develop around discrete points (e.g., the original site of Tema) which distort their linearity. The result in Tema’s case is a near-linear city with a nonlinear density pattern. It would appear that (1) Urban density patterns are inherently nonlinear - If a linear city like Tema has a nonlinear density pattern, we expect that all cities do. Studies of density in other cities add credence to this opinion.
Distance
from the centre Temo
of
Commercial
Dtstance
from temas axis
central
Fig. 4 e Best-fit urban density functions. Conclusion
Tema comes as close to being linear as any city. Its shape, land use, and infrastructure are essentially
(2) Urban development is subject to limited control Land use and infrastructure are perhaps the only factors which both can be controlled and have measurable impact on urban development. If linear land use and infrastructure fail to produce a linear density pattern, we doubt that any plan or policy would. (3) Linear cities may not realize their theoretical advantages - To benefit from their shape, land linear cities must have use. and infrastructure, linear density patterns, For example, a rectilinear transportation system is efficient only if density declines with distance from a line. If density declines with distance from a point, a radiocentric transportation system is preferable to a rectilinear one. This is the case in Tema. (4) Linear cities may not maintain their linearity - If development in Tema continues along its present lines, Tema will be nonlinear in time. Even if linearity could be maintained with strict land use controls, we doubt that planners would be willing to pay the price. Needless to say our conclusions
would carry more
GeoforumjVolume
8/Number
211977
weight if they were based on several linear cities or the same linear city at several points in time. It is conceivable that cities other than Tema have linear density patterns. It is also conceivable that Tema’s density pattern will become linear in time. Only further study can substantiate our conclusions.
References BERRY 8, SIMMONS J. and TENNANT R. (1963) Urban Populatron Densities: Structure and Change, Geograph. Rev. 53,389-405. BEAUJEUCARNIER J. and CHABOT G. (1967) Urban Geography. Longman. London. BULL D. (1967) New Town and Town Expansion Schemes: Urban Form and Structure 38, 165-186. BULL D., op.&. MORISON I. (1970) Linear growth plans: 80 years of evolution, Australian Planning Institute Jourflal8, 19-22. BULL op.&. LLEWELYN-DAVIES R. (1966) Town design, Town Plan.Rev. 37, BULL op.cit. BLUMEN~~LD H. (1967) TheModern Metropolis: MIT Press, Cambridge.
61
BULL op.&. LLEWELYN-DAVIES R. (1967) Some further thoughts on linear cities. Town Plan.Rev. 38,202-203. BULL op.cit. CLARK C. (195 I) Urban Population Densities, ..r. Roy. Statis. Sot. Vol. 114,195 1, pp. 490-496. COLLINS G. (1959) Linear planning throughout the world, $. Sot. Architect. Historians 20. DOBER R. (1969) Environmental Design, Van Nostrand, New York. DOXIADIS C. (1967) On Linear Cities, Town Plan. Rev. 38, 35-42. KEEBLE L. (1969) Principles and Practice of Town and Country Pkzning. The Estates Planning Gazette, London. KEEBLE op.&it. KEEBLE op.cit. MILLS E. (1969) The value of urban land, in The quality of the urban environment, edited by H. Perloff, Baltimore. John Hopkins Press, pp. 231-253. MUTH R. (1961)The spatial structure of the housing market, papers and proceedings of the Regional Science Association, 7, 207-220. CASETTI E. (1967) Urban density patterns: an alternative explanation, Canad. Geograph. 11,96-100. NEWLINC B. (1969) The spatial variation of population densities, Geograph. Rev. 59, 242-252. SHERRATT G. (1966) A model of general urban growth, management sciences - Models and Te~hn~ues 2, 1477159.
Linear Cities in a NonlinearWorld
REID H. EWING and E. K. A. TAMAKLOE*, Ghana
Introduction
Linear cities have several advantaaes over other cities. They are rectangular which eliminates excessive congestion in central areas (BULL, ~~~~;MoRIsoN, 1970). They are open-ended which permits unlimited growth (BULL, 1967; LLEWELYN-DAVIES, 1966) and avoids land use succession. They have parallel land uses which make both central activities and the surrounding countryside more accessible to urban residents (BULL, 1967; BLUMENFELD, 1967). They have rectilinear transportation systems which provide ma~mum coverage at minimum cost (public transportation is most efficient when traffic is confined to a corridor) (BULL, 1967; LLEWELYNDAVIES, 1967).
BEAUJEU-GARNIER and CHABOT (1967) introduce linear cities with the comment, “Linear cities are now in favour”. This is an understatement. It is difficult to find a text or review article which does not tout linear cities in one form or another, and many planning reports do the same (BULL, 1967). Despite the interest they generate, linear cities seldom get beyond the drawing board. When planners critique linear cities, they critique linear cities in theory not practice. When planners opt for linear development, they do so on a purely subjective basis. This is no way to plan cities. In this paper we discuss the pros and cons of linear cities and conclude that the pros outweight the cons (at least in theory). This should come as no surprise to those who are familiar with the literature on linear cities. What may be a surprise is our analysis of Tema, the fourth largest city in Ghana. Tema’s shape, land use, and infrastructure are those of a linear city. Tema shows signs though of deviating from the linear ideal. From this we conclude that linear cities have several advantages in theory which may not be realized in practice, and that linear cities may not maintain their linearity in the long-run.
Fig. 1 l
A linear city
Linear cities have disadvantages as well. They generate some very long intraurban trips; they channel local as well as through traffic onto major arterials creating unnecessary congestion; and they fail to give proper emphasis to the automobile (KEEBLE, 1969). Whether these disadvantages are significant relative to the dJ\.int.lpej g.lf linear cities is a matter of opinion. TIY ~~II~X~II~U~ seems to be that they are not (BULL, 1967).
Linear cities Urban planners have yet to agree on what is and what is not a linear city (KEEBLE, 1969). No two linear cities are exactly alike. Compare Le Corbusier’s industrial city to Milyutin’s Stalingrad or Gide’s plan for Paris to Tange’s plan for Tokyo. We can generalize about linear cities to this extent, most linear cities are open-ended rectangles with parallel land uses and rectilinear transportation systems (see Figure 1). This is our definition of a linear city.
The real issue is not the desirability but the feasibility of linear cities. Can they maintain sufficient linearity to realize their inherent advantages? Some critics think not. Doxiadis (1967) argues that linear cities can exist only where forces act in one direction (e.g., in a valley). Where forces act in all directions, cities will be nonlinear. “Any connection with functions not situated along the axis of (a linear city) would disrupt its uniformity and linearity.” Keeble (1969) notes that some clustering of activity is inevitable even in linear cities. Transit stops and intersections will generate more activity than other points in linear cities and thus act as nuclei in polycentric development. Clustering will occur even if development is random. Activity begets more activity causing points of initial develop-
Of course, there are exceptions. Soria’s Ciudad Lineal was shaped like a ring instead of a rectangle. The Northampton-Bedford plan had land uses in series rather than parallel. London in the MARS plan had a curvilinear transportation system instead of a rectilinear one. Suffice it to say that our definition fits all linear cities in whole or in part (COLLINS, 19.59). * The authors are, respectively, a Visiting Lecturer and a Senior Lecturer in the Department of Planning at the ilniversity of Science and Technology, Kumasi. Ghana. 57
58
Geoforum/Volume
ment to grow at the expense of other points. Once again the result is polycentric development. So the question is: are cities inherently nonlinear? A close look at Tema provides a tentative answer.
81 Number
211977
near the commercial corridor. This gives the middle class maximum access to their future work places. The road to Akosombo is the backbone of Tema. It divides Tema in half with industry on one side and residence on the other. Secondary roads run parallel and perpendicular to this road (see Figure 2).
Tema -. A linear city
Land uses in Tema are arranged in parallel corridors as shown in Figure 2. There is an industrial corridor in the east, a residential corridor in the centre, and another residential corridor in the west. A narrow commercial corridor (presently under development) lies between the residential corridors. The various corridors are separated by green spaces and bounded by major roads.
q tz2l
Residential
Tema satisfies our definition of a linear city as well as any city in the world. It is an openended rectangle with parallel land uses and a rectilinear transportation system. True there is a harbour in the south running perpendicular to the major land uses, but topographical features of this sort are ubiquitous. The harbour does not detract from the essential linearity of Tema though it forces us to relax our definition of a linear city. It is also true that the original town of Tema was nonlinear, but very few linear cities develop from scratch and those which do must start somewhere. The original town of Tema has long since been assimilated into a larger linear city. All things considered, there is probably no better place to test our ideas than Tema.
Industrial
#
Commerclol (under development)
q
Urban density patterns
Population density declines exponentially with increasing distance from the centres of all cities. This was Clark’s conclusion after studying dozens of cities “from Los Angeles to Budapest” (CLARK, 195 1). In mathematical terms,
Undeveloped
4
Scale
Harbour
area -
0
5000
ft
nd=aebd
(1)
where nd is the density at distance d from the centre of a city and a and b are empirically determined constants. Clark’s study was followed by many others which confirmed his findings. To quote Berry et af. (1963) “Almost one hundred cases are now available, with examples drawn from most parts of the world for the past 150 years, and no evidence has been advanced to counter Clark’s assertion.” Not one exception to equation (1) is on record as of 1975. Clark’s “assertion” is truly a social scientific law if there are any laws in social sciences.
_I Fig. 2 l
The Accra-Tema metropolitan Associates)
area (after Doxiadis
Housing is also arranged in corridors. Low-income housing is concentrated in the east along the border of the industrial corridor. This gives laborers maximum access to their work places. High-income housing is concentrated in the west around a north-south lagoon. This is an area of considerable amenity. Middle-income housing is concentrated in the centre,
Density declines with distance from the centre of a city because non-residential activities are highly centralized. Households can reduce the cost of commuting by living near these activities and therefore are willing to pay more for sites which are centrally located. Paying more, they cannot afford as much land. This causes density to peak at the centre of a city and decline with distance from the centre. The result is a circular city (MUTH, 1961). Non-residential activities in Tema are arranged in parallel corridors. We would therefore expect density
59
Ceoforum/Volume 8/ Number 211977
patterns in Tema to be linear for the same reason they are circular in other cities. Dober (1969) says as much in his discussion of linear cities. If so, this would be the first exception to Clark’s law. There is another possibility. Private development in Tema may be restricted to certain areas but not encouraged in others, and occupancy rates may differ from their nominal values. Thus Tema may have developed a circular density pattern despite its linear design. If so, this would be virtual proof of Clark’s law.
are included in a single regression equation {see the last row of Table l), distance to Tema’s central axis fails to be significant at the 0.10 level.
Density patterns in Tema
There are at least four alternative density functions the literature. First and foremost is Clark’s in function nd = aebd
(1)
where density (nd) declines exponentia~y with distance from the centre of a city (d). The other functions are nd = aecd2 nd =ae
bd + cd2
nd = @db
(2) (3) (4)
where density declines exponentially with distance squared in equation (2) (SHERRATT, 1966) with both distance and distance squared in equation (3) (NEWLING, 1969), and with distance raised to a power in equation (4) (MILLS, 1969). a, b, and c are empirically determined constants. Being unable to choose among these functions on a priori basis, we calibrated all four of them. Our dependent variable was the gross population density in each of 41 enumeration areas of Tema according to the 1970 Census of Ghana. We had two independent variables. One was the distance from each enumeration area to the centre of Tema (see Figure 3). The centre of Tema lies near the intersection of the harbour and the industrial corridor. Development in Tema began at this point, and it is still the centre of commercial activity. The other independent variable was the distance from each enumeration area to Tema’s central axis (see Figure 3). Tema’s central axis lies along the road to Akosombo. It separates the two dominant land uses in Tema, industry and residence. More than any other point and line in Tema, density declines with distance from Tema’s centre and central axis. We derived eight regression equations, one for each independent variabie in each density function. Our results are presented in Table 1. Note that Tema has a circular density pattern. Distance to the centre of Tema in equations (I a) to (4a) accounts for -35% of the variation in intraurban density. This is typical of urban density functions. In contrast, distance to Tema’s central axis in equations (1 b) to (4b) accounts for only -15%. When both independent variables
Fig. 3
* Tema (after the Tema Development Corporation) Density in Tema is best described by equation (3). Equation (3) has higher R2 s than the other equations and avoid serial correlation in the disturbance term. Density in equation (3a) first increases and then decreases with distance from the centre of Tema. It peaks just outside the central business area where commerce is displaced by residence (see Figure 4a). Density in equation (3b) first decreases and then increases with distance from Tema’s central axis. It is a minimum in Tema’s commercial corridor {see Figure 4b). The four urban density functions are of comparable descriptive power. Distance squared does not improve on distance to the first power in an exponential function. Nor does a power function improve on an
60
l
~~forum~Volume
Table 1 Alternative Urban Density Functions*
(1) (la) (Lb) Equation (2) (2a) (2b) Equation (3) (3a) (3b) Equation (4) (4af (4b)
a
b
225.9 (15.5) 83.9 (18.7)
-1.25 (-4.4) 0.77 (m-2.3)
8/ Number 211977
c
R2
Equation
Equation
(1)
126.5 (22.5) 68.0 (22.1) 57.4 (5.3) 134.3 (12.9)
1.52 (1.1) --3.00 C--2.1)
56.8 (28.9) 36.2 (16.6)
-1.12 f- 3.7) -0.43 f 2.7)
235.1 (15.6)
0.31 0.12 ---OS6 (-4.8) ~0.41 C--1.9)
0.36 0.08
-1.18 (- 3.0) 1.47 (1.5)
0.38 0.17
1.12 C-3.6) t -0.34 C-1.1)$
0.25 0.14 0.35
* Listed above are regression coefficients, f - statistics (in parentheses), and coefficients of determination. Density is expressed in persons/acre and distance in miles. There are 41 degrees of freedom. ? Distance to the centre of Terns is the independent variable. 1 Distance to Tema’s central axis is the independent variable. exponential function. A quadratic on the others, but only slightly.
function
improves
This is to Clark’s credit. His function has never failed to describe urban density patterns in 25 years of empirical testing.
Central busmess
those of a linear city. But no city is or could be 100% linear because the world itself is nonlinear. A linear city is a theoretical construct with no “real world” equivalent. Real cities must conform to topographical features (e.g., Tema’s harbour) and develop around discrete points (e.g., the original site of Tema) which distort their linearity. The result in Tema’s case is a near-linear city with a nonlinear density pattern. It would appear that (1) Urban density patterns are inherently nonlinear - If a linear city like Tema has a nonlinear density pattern, we expect that all cities do. Studies of density in other cities add credence to this opinion.
Distance
from the centre Temo
of
Commercial
Dtstance
from temas axis
central
Fig. 4 e Best-fit urban density functions. Conclusion
Tema comes as close to being linear as any city. Its shape, land use, and infrastructure are essentially
(2) Urban development is subject to limited control Land use and infrastructure are perhaps the only factors which both can be controlled and have measurable impact on urban development. If linear land use and infrastructure fail to produce a linear density pattern, we doubt that any plan or policy would. (3) Linear cities may not realize their theoretical advantages - To benefit from their shape, land linear cities must have use. and infrastructure, linear density patterns, For example, a rectilinear transportation system is efficient only if density declines with distance from a line. If density declines with distance from a point, a radiocentric transportation system is preferable to a rectilinear one. This is the case in Tema. (4) Linear cities may not maintain their linearity - If development in Tema continues along its present lines, Tema will be nonlinear in time. Even if linearity could be maintained with strict land use controls, we doubt that planners would be willing to pay the price. Needless to say our conclusions
would carry more
GeoforumjVolume
8/Number
211977
weight if they were based on several linear cities or the same linear city at several points in time. It is conceivable that cities other than Tema have linear density patterns. It is also conceivable that Tema’s density pattern will become linear in time. Only further study can substantiate our conclusions.
References BERRY 8, SIMMONS J. and TENNANT R. (1963) Urban Populatron Densities: Structure and Change, Geograph. Rev. 53,389-405. BEAUJEUCARNIER J. and CHABOT G. (1967) Urban Geography. Longman. London. BULL D. (1967) New Town and Town Expansion Schemes: Urban Form and Structure 38, 165-186. BULL D., op.&. MORISON I. (1970) Linear growth plans: 80 years of evolution, Australian Planning Institute Jourflal8, 19-22. BULL op.&. LLEWELYN-DAVIES R. (1966) Town design, Town Plan.Rev. 37, BULL op.cit. BLUMEN~~LD H. (1967) TheModern Metropolis: MIT Press, Cambridge.
61
BULL op.&. LLEWELYN-DAVIES R. (1967) Some further thoughts on linear cities. Town Plan.Rev. 38,202-203. BULL op.cit. CLARK C. (195 I) Urban Population Densities, ..r. Roy. Statis. Sot. Vol. 114,195 1, pp. 490-496. COLLINS G. (1959) Linear planning throughout the world, $. Sot. Architect. Historians 20. DOBER R. (1969) Environmental Design, Van Nostrand, New York. DOXIADIS C. (1967) On Linear Cities, Town Plan. Rev. 38, 35-42. KEEBLE L. (1969) Principles and Practice of Town and Country Pkzning. The Estates Planning Gazette, London. KEEBLE op.&it. KEEBLE op.cit. MILLS E. (1969) The value of urban land, in The quality of the urban environment, edited by H. Perloff, Baltimore. John Hopkins Press, pp. 231-253. MUTH R. (1961)The spatial structure of the housing market, papers and proceedings of the Regional Science Association, 7, 207-220. CASETTI E. (1967) Urban density patterns: an alternative explanation, Canad. Geograph. 11,96-100. NEWLINC B. (1969) The spatial variation of population densities, Geograph. Rev. 59, 242-252. SHERRATT G. (1966) A model of general urban growth, management sciences - Models and Te~hn~ues 2, 1477159.