I don't really mean to call out u/bSchnitz for their comment here as it is probably just a throwaway comment. It is just their unlucky day that I've finally got frustrated enough to make an effort post to dispel this common nonsense. But, RI must not be violated. Although I am violating the custom of not posting somewhere I am involved but whatever, it is not a slap fight, come at me mods.

I know you guys love MSPaint drawings, but what about Excel art

The first two pictures in the link above are of a standard linear city, with a strip 1 mile wide, developed at a density of 50 foot front width and 100 foot front width centered on a downtown that contains all jobs and services in an infinitesimally small point. The third picture illustrates the lane miles required to maintain uncongested travel on the freeways in the two cities, by typical density. The fourth picture illustrates the change in freeway lane miles to maintain uncongested travel in the 100 foot front city if the second mile, and second mile only, was redeveloped at 50 foot front densities.

The lots are their labeled width and 100 feet deep¹ . The 1 mile depth means each cross street contains ~ 100 or 50 homes for the 50 or 100 foot front level of development, respectively. With a local street right of way of 50 feet the pattern repeat itself every 250 feet. At a 50 foot density there are 4200 homes per mile. At a 100 foot density there are 2100 homes per mile. This means we need a 24 mile long 1 mile wide strip of land to contain 100,000 housing units at 50 foot front level of density while we need a 48 mile long 1 mile wide strip of land to contain 100,000 housing units. Split those and half and the two cities would have 12 mile radius and 24 mile radius.

50' front

~200 homes per 250 feet from downtown

~4200 homes per mile from downtown

~12 miles = radius of city to contain 100,000 households

100' front

~100 homes per 250 feet from downtown

~2100 homes per mile from downtown

~24 miles = radius of city to contain 100,000 households

The third image illustrates lane miles and width of freeways needed if peak hour volume is 10% of daily volume (that is the 2100 homes per mile at 100 foot lot front density produce 210 peak hour trips)^2, that the width of the freeway in any given mile is based on total daily trips within or through that mile, and every household makes one trip downtown per day. Unsurprisingly, to me at least but apparently not to many others, we need half the infrastructure to support the same population at twice the density ^3.

The fourth image illustrates what happens the in the 100 foot front city if the second mile, and the second mile alone, was redeveloped at a greater density. Freeway traffic (return to ² for a discussion on local traffic) does not increase in any mile, and decreases in every location past the 2 mile stretch while 6 fewer lane miles of freeway are required to maintain congestion free travel.

This idea is not just for transportation infrastructure but infrastructure in general, and even government services.The literature finds that public expenditure per capita falls with density across a wide range of expenditure categories

"An individual police officer patrolling a square mile in a dense urban area may provide protection to many more people than his or her counterpart in a suburban area. Likewise, fewer roads are needed in high-density areas, and school systems may be operated more efficiently fewer (though larger) schools and less bussing of pupils are needed, for example"

Someone is going to not bother with reading the footnotes before responding but yeah what about in the local neighborhood, so I'll direct them to footnote 2.

¹ 100 feet is the typical depth of standard suburbia lots from about 35 foot front to about 70 foot front typically larger than 70 foot widths would start to see the deeper lots and it would be uncommon to 100 feet wide lots be 150 feet deep although I think 125 feet deep is more standard in the Houston area. But basically, I don't want to do the extra math and my point is this makes 100 foot fronts look better than they really are on the question of infrastructure.

² this part of the calculation actually really illustrates the general lie of requiring traffic demand analysis/impact studies and roadway remediation for typical developments. We've double density going 100 foot front to 50 foot front in a mile by mile section and added only 210 peak hour trips when your typical local roadway can handle 1,000 vph and it is dispersed this across 40 typical local roadways. A 300 unit apartment generating 30 peak hour trips is adding approximately fuck all demand for additional roadway capacity even on a hyper local basis.

³ In reality I think it would be even more impactful with some more realistic assumptions. For example retail would be interspersed and higher densities would allow more alternative means of travel for simple errands for more people. Assume a retail shop needs a catchment area containing XXXX households ....................

Edited to add citation to Caruthers, Ulfarson 2003