Time for a bit of theorising.
Many people have noted that as cities grow, some things get bigger at a faster rate than the city’s growth overall, while some things do not grow as fast. Urban scaling effects are seen in the productivity of workers, for example, and hence their salaries (and house prices). Larger cities are more productive than smaller cities. A doubling in size sees around a 10% to15% increase in productivity.
Many people have noted that as cities grow, some things get bigger at a faster rate than the city’s growth overall, while some things do not grow as fast. Urban scaling effects are seen in the productivity of workers, for example, and hence their salaries (and house prices). Larger cities are more productive than smaller cities. A doubling in size sees around a 10% to15% increase in productivity.
One summary of these scaling effects (Michael Batty from UCL - see footnote 1 ) identifies the following effects as being consistent across most cities:
- As cities grow, the number of ‘potential connections’ increases as the square of the population (Metcalfe’s Law)
- As they grow, the average time to travel increases
- As they grow, the ‘density’ in their central cores tends to increase and in their peripheries to fall
- As they grow, more people travel by public transport
- As they get bigger, their average real income (and wealth) increases (the Bettencourt‐West Law)
- As they get bigger, they get ‘greener’ (Brand’s Law)
- As they get bigger, there are less of them (Zipf’s Law)
This is an interesting list, but not necessarily complete. An article in Nature by G West (who has written a book about scale effects) notes that as cities get bigger, per capita crime rates tend to increase faster than population growth, while infrastructure networks tend to decrease in their speed of expansion, both by the same factor. For example, doubling the population of any city requires only about an 85% increase in infrastructure, whether that be total road surface, length of electrical cables, water pipes or number of petrol stations, yet crime, traffic congestion and incidence of certain diseases all increase following the same ‘15%’ rule - see footnote 2.
The list is clearly relevant to Auckland. Our current discourse on the city seems to be stuck on some of these ‘laws’, but not others. The government seems to like the idea that as Auckland gets bigger, wealth increases at a faster rate, but they do not seem so enamoured of the need to improve public transport. Meanwhile, we struggle to sort out how to manage intensification of the core, given the constraints present. Public policy can 'bend' these scaling effects one way or another, but in simple terms the scaling effects are built into the urban system. However I do not want to discuss the above list at this point. What I want to do to is add another scaling effect. This relationship is:
“The relative multiplicity of units in a city is determined by an inverse-power law distribution.”
This scaling effect is raised in a book on cities and complexity written a while back by N Salingaros.
The basic idea that I take from this scaling effect is that as cities get larger, they need to generate more smaller ‘units’ to maintain coherence and functionality: larger buildings and open spaces should be few, and increase in number as their size decreases, for example. As humans, we tend to relate more to the numerous, lower order scales than the larger, but fewer, units higher up the scale.
These units (or elements) may be neighbourhoods, centres/hubs, connections, buildings or the components in the design of buildings and spaces. These units, places and components are important to the functioning of cities. Modernist approaches to urban planning and architecture tended to strip out the smaller units in the pursuit of order and simplicity, but at the expense of complexity that helped to off-set the effects of increased size.
Salingaros contends that: ”The inverse power-law distribution…. is found in many natural and man-made structures. Smaller elements are thus more numerous than larger elements, with a fixed balance of distribution between sizes”.
As an example, he states:
“Overall, we have two peaks in the size distribution of components in a contemporary city, one corresponding to giant office and apartment buildings, and the other corresponding to suburban houses. There is relatively little of intermediate size, and almost nothing smaller than a suburban house that forms a coherent piece of the city. This contrasts sharply with the living urban fabric as measured in historic regions of cities”.
He proposed an equation to represent this relationship between different scales.
PXM=C
P = relative multiplicity
X = size
M = 1 < m < 2
C= constant
The idea can be applied to the number and type of centres in the city. For every large centre, there needs to be many more smaller centres. Here is the link to neighbourhoods and their relative abundance that I discussed in my blog of the 5 May 2017.
If we say that centres come in three scales - sub regional, town and local (neighbourhood) and correspond to the following sizes in terms of employment - 10,000; 2,500 and 500 - then if we set M in the above equation to 1.3, we get the following distribution (hopefully my maths is right):
Centre
|
Number
|
Size
|
sub regional
|
1
|
10,000
|
town
|
6
|
2,500
|
neighbourhood
|
48
|
500
|
Now I know that the above is purely theoretical. The conceptual point is that as the larger units get bigger, there needs to be more smaller units generated to maintain a sense of coherence and stability to the urban system. If the sub regional centre increases in size to 15,000, then we need to following distribution.
Centre
|
Number
|
Size
|
sub regional
|
1
|
15,000
|
town
|
10
|
2,500
|
neighbourhood
|
83
|
500
|
Of course, the size of the other centres may also increase, while the value of M is very important to the distribution. Salingaros doesn’t say what the value of M is, except it is between 1 and 2, which is not much help.
Putting aside the detail, I think the concept of non linear scaling of urban units is a useful one that is worth looking at more closely. I think it supports my contention that we need to think a lot more about the implications of population growth for all the urban scales, but particularly the abundance of smaller scale elements and the extent to which that abundance is constrained or enabled.
- http://www.complexcity.info/files/2011/12/BATTY-Scaling-Laws-For-Cities.pdf
- A unified theory of urban living. Luis Bettencourt and Geoffrey West. NATUREl 467, 21 October 2010.
