# Land area: WV vs TX

I’m here 'cause Cecil refused to answer this question (then he or one of his minions offered to sell me merchandise): If you flatten out West Virginia, would it be bigger than Texas? This is what some (West Virginians, prolly) have claimed. And if this is true, would it still hold true if you flattened out Texas, too? I would search the archives but the link didn’t work.

No. Texas is more than 10 times the surface area of WV. Even assuming WV were totally covered in mountains with an incline of 45 degrees, which is a very liberal estimate, and Texas were totally flat, Texas would still be 7 times are big as WV.

Not even if you ironed the state out?

I don’t think WV has any iron, it’s mostly coal.

Sorry.

If we treat West Virginia as a flat plate of area A (where A is equal to the “traditional” area of the state) and assume that, because it’s mountainous, it’s covered with densely-packed cones[sup]1[/sup] of earth and rock, then the area you’re asking about would be the upper surface area of all of those cones. The upper surface area of a cone is equal to Pi times the base radius times the slant-height, and the base area is equal to Pi times the base radius squared. For the mountainous surface area of West Virginia to exceed the traditional area of Texas, the slant height of the cones would need to be (A[sub]texas[/sub] / A[sub]westvirginia[/sub]) times the radius of the cones. Using Wikipedia’s numbers for state areas, that means the slant height would need to be ~11.1 times the base radius. Using cosine to find out what the angle between those sides would be, we discover that the average grade (steepness) in West Virginia would have to be about 57 degrees, which seems unrealistic.

I haven’t been to West Virginia in a while, but I remember being able to drive a car there, and seeing several towns with houses on what looked like almost-level ground. I did not see any spires of stone extending vertically into the sky, so I’m going to answer “no” to the OP’s question, and not bother “flattening out” Texas, because it scares the cattle.

1. My assumption about cones assumes large cones packed in a hexagonal grid with smaller cones filled in the gaps until you get down to fist-sized gravel. There’s probably some good way to fudge this, but I’m assuming the state is essentially jagged all over, but covered in smooth right cones.

I’ve driven through a lot of West Virginia, from Huntington in the west, to Weirton in the north, and Harpers Ferry in the east. It’s hilly, but not hilly enough to multiply the area by 10.

Do you really need all the cones? Wouldn’t it be the same if the state were flat but at an incline?

How about colorado? Bigger state and its got some pretty large mountains.

>snort<

In hindsight, sure, and the math comes out exactly the same. But modeling WV as a flat plane covered with cones is (slightly) more intuitive to visualize than modeling WV as a tilted sheet. The real prize goes to the person who can figure out that “Average slope” number so that we can claim – however facetiously – that WV actually has the same surface area as, say, Florida or Ohio.

Texas is still well over twice the area of CO (103K vs 261K, using land areas). Flattening them both out isn’t going to let CO catch up. California would probably be a better guess, as it’s bigger and also has large mountain ranges, but 163K vs. 261K still sounds like too much increase to expect. Remember that Texas isn’t entirely flat either - flattening the Guadalupe mountains will gain you some area.

ETA:

Also remember that the eastern half of CO is pretty flat - it might as well be Kansas.

You could get a much better model if you tossed the cones out and just used a topographic map of the states in question. I’d guess that using 100 ft contour intervals would be enough resolution to get a good answer.

Nice analysis; but I think you took a cosine where you wanted an arccosine. You want arccos(1/11.1) ~ 84.8°, which would make for great rock-climbing but is even more absurd.

The Guadalupes plus the Davis, Hueco, Franklin and Chisos Ranges, then there’s Palo Duro, the Balcones Escarpment, etc. The Trans-Pecos alone is about the size of South Carolina.
Maybe if you were to flatten Alaska out…

You’ll have to melt it first. It’ll probably shrink.

Seriously, Alaska is over twice the land area of Texas. It’s a given that its ranking isn’t in any danger, and our discussion concerns the rankings of the lower 48.

The eastern half of Colorado IS Kansas.

I’m a native WV’ian. Don’t debunk this myth. We are 49th in everything (thank you, MS!) and don’t need this myth busted. I live in FL now, but still have a soft spot…

You’re absolutely right, of course. :smack:

I’m sure it would be a great model, but the OP wanted a yes or no, so I went with something that would give me that answer before his guest membership expired.

Seriously, though, if the OP wants to pursue this to the bitter end, there are lots of sources he could use. If the Google Earth API is open and someone knows how to code for it, I imagine you could write a script to determine the surface area within any given boundaries pretty simply… but I’m not a coder. Seems like the slowest part would be waiting for your script to slurp down all the lat/long/alt data into a matrix. After that, Bob’s your uncle. Also, since the area is in America, you could use the USGS’s 30m National Elevation Dataset or the 90m dataset from CGIAR/CSI.

Wear a nice firm helmet and keep drinking milk, and it should heal up in no time.

Surely if West Virginia was particularly crinkly and Texas was perfectly flat, WV could in fact have a greater are than TX? Modelling WV as a slope or a collection of smooth, straight cones naturally yields a small surface area. Make those cones convex or concave, or uneven in surface texture, and the surface area rises, no?

It’s already on an incline. That’s why all the WVns looking for work wind up in southern Ohio (Ahia).