Been doing a lot of Strong Towns reading today on missing middle housing, incremental development, small developers, and such. It inspired a new calculation:
Consider a typical suburban quarter acre lot, about 1000 m2, maybe currently hosting a modern 3000 foot2 (300 m2) house. I'm not sure what the dimension of the lot are, let's say 20x50 meters. Imagine a 2 meter wide access lane down the length, leaving 18 meters width; and 5 meter wide townhouses fitting in sideways, so 10 of them (50/5). Make them 3-story. 5x18=90 m2 ground plan, 270 m2 square feet in each townhouse, putting 10 rather large houses in the space of one suburban lot. Or 30 decent sized apartments, big enough for 2 or even 3 BR without much cramping. 10-30 times the density, with no particular height, just efficient use of the land.
Maybe the lot dimensions are 25x40 meters. With a similar configuration, but 4 meter wide homes, you get 10 4x23=92 m2 buildings, and similar density increase.
Or, stick a 3 meter access lane down the middle, have 5m wide homes again, and have 8 5x11=55 m2 buildings on each side, 16 total. At 3 stories, get 16 165m2 houses, or 48 55m2 apartments, or some combination thereof.
The depth makes conventional orientation a bit problematic: at 40 meter depth, even 4 meter width gives 160 m2 ground use. Which is fine if you go all in for apartments, less fine if you want the option of reasonably sized but multi-story houses.
An article on the blocks of NYC said even their lots of 25x100 feet (30 m deep) was too deep for a modest rowhouse, thus encouraging tenements.
(The assumption is that land is valuable enough to not have yards on most housing.)
Really narrow houses are 3 meters wide! At 30 meters depth that's still 90 m2 ground plan, and 270 m2 for a whole row home.
The final message: 1/4 or even 1/8 acre lots can support far more people without building over 3 stories, but deep lots may either lend themselves to apartments or to odd orientations of row homes, and some legal flexibility if the homeowners are to own their land.