Doubling cities

Why does a city growing a few percent a year outrun plans drawn only a decade ago?

A master plan is adopted with a twenty-year horizon. Ten years later the city has already passed the population the plan gave it for year twenty, the trunk sewer commissioned under it is at capacity on the day it opens, and the arterial road it reserved now has to be cut through eleven thousand houses that were not there when the line was drawn.

The strange part is the growth rate that did this. Not a boom — three or four percent a year, the sort of number that sounds like a rounding error. Ask yourself honestly: does three percent a year feel like something that could overwhelm a decade of professional work? Almost nobody's intuition says yes. And that mismatch, between how small the rate sounds and what it does, is the whole subject.

Start with the arithmetic, because it is short. Growth of this kind is proportional — each year's addition is a share of what already exists — and that makes the doubling time roughly seventy divided by the percentage rate. Three percent doubles in about twenty-three years. Five percent doubles in about fourteen. Seven percent doubles in ten.

Now translate a doubling into physical work, which is where the intuition breaks. Doubling means that within one doubling period you must build as much city as exists in total today. Not a bit more housing: as many dwellings as the city now contains, as many school places, as many hospital beds, as many kilometres of water main and sewer and street, as much everything — and all of it in about twenty years at a rate that sounded negligible. Every city that has ever existed had to be built once; a doubling city has to be built again, alongside itself, while the first one carries on being used.

Notice too that the increment is not constant. A city of one million growing at three percent adds thirty thousand people this year. When it reaches two million it adds sixty thousand, at the same rate. So a plan whose capacity was sized on today's annual increment — the natural thing to do, since that is what you can observe — is already too small in its first year, and gets worse every year afterwards. It does not fail at the end of its horizon. It fails immediately and quietly.

Against that, hold the timescale of the supply side. Trunk infrastructure is slow and lumpy. A reservoir, a treatment works, a main sewer, a rail line: years of study, finance and construction, and no way to build four-sevenths of one. It must therefore be sized for demand at some future date — and the demand curve it is chasing is bending upward while the works are being built.

Now the asymmetry that makes this so unforgiving. What does a road cost? On open land, reserving the right-of-way costs almost nothing: you draw it, you protect it, you build later. Through an established settlement it costs enormously more, in money, in years, and in people displaced — and the cost climbs steeply the longer the reservation is left. So the price of any given piece of infrastructure rises with delay, at the same time as the quantity needed rises with the population. Two curves both bending upward, in the same direction. That is why the gap opens rather than closing, and why a city can never quite catch up by working harder.

And the growth does not politely wait for the plan. People arrive, and they house themselves on whatever land is reachable — which is very often the land the road was going to use. The plan is not merely overtaken; it is built over.

One more piece, easy to miss. A city's built-up area has generally grown faster than its population, because average densities have tended to fall as cities expand and incomes rise. Where that holds, the footprint doubles sooner than the headcount does, and the land the city will occupy has to be thought about earlier than the population figures alone suggest.

That last point deserves to be more than a caveat, because the symmetrical error is just as real. Growth rates are not constants of nature; they decline as cities mature, and extrapolating a boom decade forward thirty years has produced empty ring roads and unoccupied new districts in more than one country. So the honest position is not "assume doubling" but "you do not know the rate, and you are badly placed to find out."

Which reframes the problem usefully. If the difficulty were simply forecasting, the response would be better forecasts. If the difficulty is that the cost of being wrong is wildly asymmetric — cheap to reserve land you did not need, ruinous to acquire land you did — then the response is a different kind of plan. Lay out and protect the skeleton: a coarse grid of arterial rights-of-way and trunk service corridors across land the city might plausibly reach, with the actual works built only as demand arrives. That is cheap if the growth does not come and decisive if it does, and it is the reasoning behind the "make room" approach to urban expansion in fast-growing regions.

The general misconception to retire is that a small rate implies a slow problem. A rate is not a speed; it is a doubling time in disguise. And the second, subtler one: the danger is not that the city grows faster than expected. It is that even at exactly the expected rate, the work required grows faster than the capacity to do it.

• How land value capture tries to fund trunk infrastructure ahead of the growth that pays for it.
• What actually happens to a city that grows without the skeleton, and how expensive retrofitting turns out to be.
• Whether falling urban densities are a preference, an artefact of transport cost, or a product of the rules.

Every term the collection defines is gathered in the glossary.