Cities Skylines Best Grid Layout

I had assumed that a 10×10 grid was best, but information technology turns out it's not.

Contents

Guide to The Optimal Square Grid
- Introduction
- Time for Mathematics
- Conclusion
- Appendix A: Medium or Large Roads
- Appendix B: Rectangles
- Appendix C: Real Cities

Guide to The Optimal Square Grid

Introduction

I ever figured that if I was going to build a nice, regular, foursquare grid that of course it should be ten×x: That fashion each of the blocks is fully zonable and the road length highlight and road guideline circles brand information technology easy to draw.

But it turns out we can do better.

Fourth dimension for Mathematics

For the 10×10 filigree, the calculation is simple: we go 8² zonable tiles in a 10² tile expanse, for a density of exactly 64%. (Hither, and in the residue of the section, we assume a minor—2u—road).

For the general case of a foursquare of side ?, the zoneable area is (?-2)²-max(0, ?-10)² — the area within the road minus the area in the eye where the zoning doesn't accomplish — and the total surface area is ?².

It'southward hard for me to grok that quotient in my caput, so let'due south just graph it and see what happens:

That shows that the "obvious" ten×x grid is actually but as good as a 15×xv grid:

It as well looks similar 12u is the best. Can we testify it? Certain, let's go back to Calculus I:

0 = d/d? (?-2)²-(?-10)² / ?²
0 = d/d? ( (?-2)+(?-x) )*( (?-2)-(?-x) ) / ?²
0 = d/d? (2?-12)*eight / ?²
0 = d/d? (xvi?-96) / ?²
0 = ( (16)*?² – (xvi?-96)*2? ) / ?⁴
0 = (16? – 32? + 192) / ?³
0 = -xvi? + 192
? = 192/16
? = 12

Then yes, it'due south a block length of exactly 12 that gives the best density.

Note: Coincidentally, that's also the maximum segment length for an centrality-aligned route in CSL.

How much better? ⅔ of the area (66.66…%) instead of just 64%.

At present, I admit that simply most 4% more zoning doesn't sound that exciting. Simply not simply is it more dumbo, but it'south also cheaper.

How's that? Well, you lot need to pay for the roads. And for the 10×10 blocks, those 64 tiles of zoning need 40u of roads (one.6tiles/u), simply with a 12×12 block you get 96 tiles of zoning out of only 48u of roads (2tiles/u). And so you're too paying xvi% less on the roads to grid the same area with more stuff.

For some physical numbers, let's compare a 60×lx area (every bit it divides evenly in a bunch of ways) using a diversity of block sizes and the basic pocket-size two-lane road:

So if you make a 10×10 grid, you'll spend l% more than yous need to for the area y'all'll get.

Notation: That table besides shows that zonable area drops slower than road cost, but don't forget that lower density is also increased toll for whatsoever service with a radius of effect.

Conclusion

If you want the densest square grid, make information technology 12×12 (using modest roads).

Yous'll fit 1⁄24 more than RICO in the same space just spend 1⁄vi less on the roads, compared to a 10×10 grid.

Appendix A: Medium or Big Roads

What if you're using a 4u-wide road, like the Medium and Big Roads?

And so the optimal-density foursquare grid is 16×16.

Merely you pay a heavy density toll for the larger roads: only 50% of the area is usable for zoning.

Appendix B: Rectangles

Rectangles, every bit they get longer and longer, tin can arbitrarily arroyo the limit† of 80% density.

The density formula for an α×β block is ((α-2)(β-ii) – (α-ten)(β-x))/(αβ), bold both sides are 10-or-longer for simplicity (it's clear that if both are smaller than 10 information technology'due south worse than the square, and I don't care what happens for giddy things like a v×50 cake).

And then there's a surprising amount of choice if you just want to do better than the x×10 block:

Merely your choices are far more than limited if you want to shell a 12×12 block:

Indeed, if you restrict yourself to integers (so you can describe information technology with Snap to Road Length), so the only things that crush the all-time foursquare block are α ∋ {10, 11}, β ∋ {13, 14, 15, …}.

How much meliorate? Well, 10×16 has a density of 70%, an extra 5% more than than the 12-square. Getting up to 75% density takes x×32, which is more than oblong than I personally like for a grid.

Is the actress density worth beingness less regular? I'll leave that upwardly to you.

The limit is parallel lines that are infinitely long and never connected, as that mode there'southward never whatever potentially-zonable area taken upwardly by a cantankerous street. A quick look at the cantankerous-section of such a road shows 4u zoneable on each side and a 2u road, for (4+4)/(4+2+four)=0.8 density.

Appendix C: Existent Cities

These are measured from satellite maps, so don't always match the "canonical" answers. For instance, the Portland Bureau of Transportation says its blocks are 200ft (≈7.6u).

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