Interstate density

[Alps]

So five minutes of my spare thought went into this idea: Measuring highway density as total roadway length (or even lane-miles) divided by area is a flawed metric, in that it's not unitless. It seems to break when you get to the smaller states, with DC having a 0.20 ratio of Interstate length to area (absurdly high) and DE having a 0.001 ratio (absurdly low). So I thought about measuring highway density as total roadway length divided by the square root of area. The outliers dropped away.

Here are the top 10 states in terms of Interstate mileage per square root area:
IL, PA, OH, NY, TX, IN, CA, FL, MA, TN

There is a clear bias toward medium-size states with a well developed highway network. Larger states like TX and CA have more open area without highways, while smaller states like MA have trouble catching up because there is less room to cram highways in.

Here are the bottom 10 states:
HI, DE, AK, DC, NV, NE, RI, ME, ID, ND

These fall into two categories: tiny, or sparsely populated.

Surprises: CT is only ranked 14th, although if you took mileage/area instead of square root of area, it would be the highest behind DC. Maryland also seems like it should be way up there, but is only ranked 18th. The metric definitely biases against small states. Also, Arizona ends up in the top 50% despite being a large state with no 3-digit Interstates.

[national highway 1]

It appears that the western x5s (I-5, I-15, I-25 and I-35), and all the other north-south routes are more spread out more than the eastern odd routes (I-55 to I-95). The same applies to the x0s and other evens in the western half of the country.

[The High Plains Traveler]

It appears that the western x5s (I-5, I-15, I-25 and I-35), and all the other north-south routes are more spread out more than the eastern odd routes (I-55 to I-95). The same applies to the x0s and other evens in the western half of the country.

You travel 2/3 of the way from the west to the east coast and you're only to I-35. Putting it another way, I used to live in Minneapolis (I-35) and two days travel east took me to I-87. Two days west would get me between I-25 and I-15. The east-west routes have constraints in the west that are more geographic than population-based but tend to be more evenly distributed (except for missing routes from the 40s to the 60s) as you move east. 

[vtk]

So five minutes of my spare thought went into this idea: Measuring highway density as total roadway length (or even lane-miles) divided by area is a flawed metric, in that it's not unitless.

Just because the metric is unitful doesn't mean it's flawed.  But slightly more intuitive is the reciprocal: area divided by total roadway length, whose unit is of length, is roughly how far one should expect to walk in a straight line before bumping into an Interstate.  Your metric of system length divided by square root of area relates more closely to how many Interstates one should expect to cross walking in a straight line across the state from border to border, I think.

[algorerhythms]

So five minutes of my spare thought went into this idea: Measuring highway density as total roadway length (or even lane-miles) divided by area is a flawed metric, in that it's not unitless. It seems to break when you get to the smaller states, with DC having a 0.20 ratio of Interstate length to area (absurdly high) and DE having a 0.001 ratio (absurdly low). So I thought about measuring highway density as total roadway length divided by the square root of area. The outliers dropped away.

Density is in general not a unitless quantity. On a 2-D geometry (such as the surface of the Earth), the units are (what is being measured)/area. In this case, it would be length/area, or 1/length. If you're uncomfortable with comparing 1-D objects (roads) to a 2-D surface, you could weight the roads by their width, so your units would be area/area (i.e. unitless), but on average that would give you a similar result.

As for your outliers, are they really that absurd? DC makes sense that it would be at top because it has a fairly large number of interstate highways in a very small area (especially because there are no rural areas). Delaware makes sense that it would be low, because although its area is small, it has very few miles of interstate highways.

[Duke87]

I would argue that interstate length divided by anything is not a fair metric since some states are more inclined to apply for interstate designations than others. What is or isn't an interstate is somewhat arbitrary.  Freeway length divided by area (or square root area) would be more reflective of reality, but even then you have some argument as to what is or isn't a freeway. Do you include parkways? And so on.

Of course, if what you're looking for is how fast it takes to get around, the better question is: what is the average speed at which traffic on all roads flows? INRIX can help with major roads but not side streets.

[NE2]

I think the idea is to give a metric that shows how gung-ho some states are about Interstates.

[Alps]

I think the idea is to give a metric that shows how gung-ho some states are about Interstates.

Yeah, pretty much. Illinois was crowing about being third in total mileage, and I found a way to make them first.

[agentsteel53]

you could weight the roads by their width, so your units would be area/area (i.e. unitless), but on average that would give you a similar result.

this indeed would be a valid modification.  though I'd weight the road not by absolute width, but by number of lanes multiplied by a constant (12 feet? whatever the width is of a standard lane), as this is a measure of the capacity.

this will cause Connecticut to rise in the rankings, since they have few four-lane interstates.  a state like North Dakota will fall because damn near all of their interstate mileage is four-lane.

[kphoger]

though I'd weight the road not by absolute width, but by number of lanes multiplied by a constant (12 feet? whatever the width is of a standard lane), as this is a measure of the capacity.

I was under the impression that highway traffic capacity is reduced as lane width is reduced.  Is this not the case?

[agentsteel53]

I was under the impression that highway traffic capacity is reduced as lane width is reduced.  Is this not the case?

it is, but given that interstates are built with a minimum standard in mind, if we use that minimum we can get a decent approximation without having to do too much math.

[Duke87]

We could also divide by population instead of area. Weren't miles in the original system allotted according to population at the time?

Though, I'd imagine this would bias towards rural states, unless you use lane-miles.