## Saturday, 10 March 2018

### Town planning - why long, narrow residential plots make sense.

When you are in a back garden and look around, the proportions seem 'about right', but what is  striking when you look at maps is how narrow and long most residential plots of land actually are.

The terraced house we lived in in London Zone 3 was on a plot about 6 yards wide x 30 yards deep. We're now out in the wilds of Zone 5 and our house is on a plot 9 yards x 40-45 yards deep (not really sure). The semi in which I grew up (fairly nice commuter suburb of Leeds) was somewhere in between. This is a ratio of about 5:1 depth to width, which I think is actually about normal for urban and suburban areas (terraced and semi-detached houses).

(Interestingly, our new house would sell for a bit more than the previous one, but if we adjust for the extra cost of the larger building, the net land value is about the same. So land values per square yard are about half as much for being twice as far from 'the centre' = Von Thünen's Law of Rent).

Using the brute force of Excel, and assuming
- an average residential plot is one-tenth of an acre,
we can work out the total amount of land you need to build X houses in a 'row' (with roads along the front and down the side of each end house), with a net plot size per home of Y (X and Y are your variables).

The spreadsheet works out the optimum width/depth of the plot to minimise the total average amount of land used (plots plus roads) per house, which is *the optimum* for the purposes of this post.

Utility connections usually run along the front, the narrower the plot, intuitively, the cheaper it is to service all those houses with water, electricity, gas, broadband/telephone etc, although I didn't adjust for that as requires too many assumptions. This means that the economically optimal answer is probably slightly narrower plots widths than the spreadsheet says.

A few things stand out (when you are changing X number of homes in a row and Y net plot size per home):

1. The more homes you have in one row, the less land you need overall. This should be pretty obvious - however many houses there are in a row, the amount of side road is fixed purely by the depth of the plots.

2. If you increase plot size, most of the increase is in depth not width. Again, fairly obvious. If you start with square plots, adding one unit of depth at the back increases the total length of side roads by two units. If you add one unit of width, that increases the total length of the front road by one units x number of homes in a row.

3. The more homes you have in one row, the narrower the optimum plot width (and the deeper the plots). So if you want to build homes in rows of ten, the optimum plot width is 10 yards (48 yards deep). If you want to build homes in rows of 20, the optimum is 7 yards wide (and 69 deep). This is because an extra house in the block means more front road but does not add to the amount of side road.

NB: I assume that most people don't value back gardens beyond a certain size. The first 50 square yards are essential, just enough for the bare essentials of a patio, a washing line and a sand pit/paddling pool for the kids. Get past 200 square yards or so and it's wasted and more bother than it's worth. Also, the further the land is from the house the less it is 'worth' to the occupants. I didn't adjust for that as it involves too many assumption - clearly a back garden 6 yards wide and 60 yards long is just daft. So I suppose there is a natural cap on the depth and/or the depth:width ratio, which appears to be about 5:1.

4. The optimum width is narrower in 'urban' areas (more homes in a row, smaller plots) and wider in 'suburban' areas (fewer homes in a row, larger plots), and with sensible inputs, plots are 5 yards wide for the former and 10 yards wide for the latter. This sort of makes sense. 5 yards is wide enough for a narrow terraced house and 10 yards is wide enough for a semi-detached house with a drive/car porch at the side. In either case, the depth: width ratio is about 5:1.

Which all leads to lots of other interesting musings, such as having council set maximum or minimum densities or plot sizes is pretty futile, these things will happen of their own accord if developers want to maximise profits/minimise amount of land used. Or that land valuations could be carried out by simply measuring frontage and assuming that most plots are the optimum depth anyway.

formertory said...

Take your point entirely as a theoretical exercise, but on a practical level it's a Victorian / Edwardian answer to housing - in this age where each house may have one, two, maybe even three cars to park. And the fun will really start when the dipshit Government (which is all of them, of any political stripe) succeeds in forcing the population to run electric cars and the pavements are covered with cables the diameter of a hosepipe. Assuming, of course, you can park near enough for your charging cable to reach :-) .

Bayard said...

"and the pavements are covered with cables the diameter of a hosepipe"

There is nothing the government likes more than forcing other people to do things and pay for doing them, so either the electricity suppliers or the local authorities or both will be forced to put in kerbside charging points, probably with some sort of electronic key arrangement so that anyone can use any point. There will then be the same turf wars about charging points as there currently is about kerbside parking space.

FT, it's not a theoretical exercise at all, look at the world around you. This is why it is how it is.

Good point about electrical cars, they really haven't thought this through have they? My other gripe is that the point of fuel duty is to make driving more expensive so that roads don't get congested. Without a similar charge on electric cars... hey ho gridlock.

Nonetheless, you can't fault the Victorians for not having predicted cars. Even a very narrow plot (5 metres) is wide enough for a car, or two small cars if you're good at parking.

The 'mistake' they made was having houses close to the road with tiny front gardens or none (done for good reasons, to make utility connections, coal deliveries easier), you are pretty much f-cked if households there want to own more than one car per home.

Having the house further back to enable off street parking in front and a smaller back garden is a quick win.

B, sounds like shit to me, I'll stick with petrol if that's OK.

Mike W said...

'forcing the population to run electric cars and the pavements are covered with cables the diameter of a hosepipe. Assuming, of course, you can park near enough for your charging cable to reach :-) .

The folks opposite us put an old bit of axminster carpet over the cable to their car - so no one even notices :)It works. Everyone blamess the carpet. But I do wonder if a coming 'trip' incident will be on their house or on a special clause on the car's insurance?

Must put my hand up here. I was into the electric bike thing, perfect for local journeys shopping etc. If that is the model folks need not worry about the roads being full. My bike spent many happy hours, indeed most of its service life, just siiting in the garage charging.

Bayard said...

Mark, AFAICS, petrol-electric series hybrid gives you the best of both worlds: the full-torque-from-standstill and the regenerative braking of the electric motor and the range of the IC engine.

MW, yes, but most terraced houses and older semi detached houses don't even have a garage. In fact even most of the detached houses on my street don't have garages. There's one block of flats with am underground car park, that is ideal for charging points.

B, on a rational level, sure, you are right. But I like to lag well behind new technology to see if it catches on, to see if it works and because the longer I wait before buying, the cheaper it will be or I can buy second hand. My cars are hopefully good for another ten or twenty years if I look after them, so no hurry.

Bayard said...

Mark, series hybrid technology is pretty old hat; the railways have been using it since the '50s. It's just a mystery that it took so long to transfer it to road vehicles. As far as being behind the curve, though, agreed, me too.