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HCoFP: parking math

(Not direct book material, but inspired by it.)

So, say a city mandates such and such space for parking; what does this do to land capacity? Let's say it's 1:1, 3 parking spaces for every 1000 sqft. If you have a 12,000 sqft lot, the easy solution is to use half of it. 6000 parking, 6000 building and floor space. How much better can you do? 4000 building lets you have two stories, for 8000 sqft floor space, and 12,000-4000=8000 parking space. Three stories can give 9000 floor space on 3000 building.

To go for the asymptotic limit, 999 stories could fit on 12 sqft of ground, giving 12*999 floor space and leaving 12*999 ground for parking. So 12,000 is the asymptotic limit we'll never reach. 1:1 means you'll never have as much floor space as the actual lot size.

How about 3:2? One story can take 40% of the land, leaving 60% for parking. More... math is helpful:
12,000-building = 1.5*n*building, where n=number of stories, and 12,000 can be A for ground area or lot size.
A=(1.5*n+1)*building; building = A/(1.5*n+1). So for n=2, A/4. 3000 sqft building, 6000 floor, parking is 12,000-3000=9000 or 3/2 the floor space.
n=3 -> A/5.5 -> 6545 sqft floor. Not much increase for the expense.

n=1000, A/1501, say A=1501 for convenience, building is 1, floor is 1000, and the floor space is almost 2/3 of the lot size.

Algebra time! A-building = p/f*n*building, p=parking fraction and f = floor fraction.
building = A/(n*p/f + 1) and we can see that the limit with large n is A*f/p. 1:1 -> A, 3:2 -> 2/3*A.

floor space = n*A/(n*p/f+1)

What about a modest requirement, like one lot per 2BR apartment? 330 sqft parking, 660 sqft apartment, p/f=1/2, can get 2A. For bigger apartments, like 1000 sqft, p/f=1/3, could get 3A, three times the lot size. But you have to build a tall narrow building to get that. 3 stories is floor space of 3A/2, only halfway to the limit, and still has parking taking half the land.

In the more likely extreme, say 9 spaces per 1000 sqft, that's p/f of 3/1, and your max usable area is A/3. Good news is that you don't have to do much to approach it; even one story gives you A/4. Two stories gives 2A/7, or 29% instead of 25%. Helps explain why there's so much one-story building; no point to doing any more given the cost of multiple stories.

By contrast, a building without parking can just pile on stories. 12,000 lot and 3 stories = 36,000 sqft, 4-12 times the floor area that real world parking requirements allow, and 3 stories is far from the limit. 4 to 12 times, just for a cheap 3 story building, never mine 20+ story skyscrapers. (12 from 3:1, 3000 sqft; 4 from 1:1 at 3 stories, 9000 sqft vs. 36,000). I think that sums up how badly parking requirements gut cities, slashing density hugely while turning half or more of the land into ugly hostile parking lots.

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Damien Sullivan

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