How to determine the flatness of a state? Pass the aspirin...

[ZLoth]

I keep reminding my mother who keeps stating that "Texas is as flat as a pancake" that no, there are other states that are flatter. That basis is determined by the difference between the highest point and the lowest point in the state, and from that aspect, multiple states have mean sea level as the lowest point, while both California's Death Valley and Louisiana's New Orleans having points below mean sea level. Using that criteria, Florida is the flattest as the highest land point in that state is just 345 feet above mean sea level... and multiple buildings in Florida are higher than that. Meanwhile Texas's highest point is near El Paso with Guadalupe Peak at 8,751 feet above sea level.

Ah, but there is a big problem with that methodology. You can use Interstate 35 from the Mexico border to Kansas City, then Interstate 29 from Kansas City to the Canadian border (closely following state borders) as a rough visual representation of the dividing line between the eastern and western halves of the United States. This makes fourteen of the western continental states (Arizona, California, Colorado, Idaho, Montana, Nebraska (I-29), Nevada, New Mexico, North Dakota (I-29), Oregon, South Dakota (I-29), Utah, Washington, Wyoming) plus the Alaska and Hawaii as being very large states, while Kansas, Oklahoma, and Texas are "split states" because of Interstate 35. If you look at the top 20 states in terms of land area, all of the states listed above with the exception of Hawaii would be part of that list, and the two missing states would be Minnesota (#14, and just east of the I-29 line) and Missouri (#18, and while I-29 runs through it and Iowa, most of the state is east of the line). Because of that, we have 31 states in the eastern half of the United States. All of those states are below the average land area of 70,725 square miles of the fifty states. In some cases, the land area of some metropolitan areas exceeds that land area of the smallest states. San Bernadino County in California has more land area than Rhode Island, Delaware, Connecticut, and Hawaii combined.

So, how does one normalize the data to provide a better answer? For tornadoes, it's easy. It's easy to claim that, for calendar years 2018-2022, Texas was both #1 and #30 in Tornados and be correct. How? In both the combined total (620) and averaged over five years (124), Texas tops the list, followed closely by Mississippi and Alabama. But, in terms of land area, Texas is only one of two states whose land area exceeds 250,000 square miles (261,914 to be exact), and one of eight states whose land area exceeds 100,000 square miles. When we take into account the land area, Texas drops to number 29 while Mississippi, Alabama, and Lousiana take the top three spots in that order.

Now, how does one normalize the data to provide a better and more accurate order of the flattest states? Amazing how a simple question becomes complex question. Someone pass the aspirin.

[Max Rockatansky]

A "certain" Illinois enthusiast has already made this calculus for the entire road community.

https://www.aaroads.com/forum/index.php?topic=29866.msg2672104#msg2672104

[hotdogPi]

High minus low is not the way to do it. For example, if a state touches the ocean and has a high of 500 feet, but most of the state has hills that never get above 400 and valleys that never get below 100, it's still hilly.

[wanderer2575]

Perhaps the way to do it is measure the total vertical rise from one end to the other, not simply the difference between the  lowest and highest points.  This is what I look for in dayhiking trail descriptions.  That the distance between high and low is 400 feet means little to my out-of-shape fat ass when the trail actually ascends 300, descends 250, ascends another 300, descends 300, and then ascends a final 350.

I don't know how one would apply this with an infinite number of microdirections in a 360-degree sweep of the state, but I'm just talking theory.

[bing101]

I keep reminding my mother who keeps stating that "Texas is as flat as a pancake" that no, there are other states that are flatter. That basis is determined by the difference between the highest point and the lowest point in the state, and from that aspect, multiple states have mean sea level as the lowest point, while both California's Death Valley and Lousiana's New Orleans having points below mean sea level. Using that criteria, Florida is the flattest as the highest land point in that state is just 546 feet above mean sea level... and multiple buildings in Florida are higher than that. Meanwhile Texas's highest point is near El Paso with Guadalupe Peak at 8,751 feet above sea level.

Ah, but there is a big problem with that methodology. You can use Interstate 35 from the Mexico border to Kansas City, then Interstate 29 from Kansas City to the Canadian border (closely following state borders) as a rough visual representation of the dividing line between the eastern and western halves of the United States. This makes fourteen of the western continental states (Arizona, California, Colorado, Idaho, Montana, Nebraska (I-29), Nevada, New Mexico, North Dakota (I-29), Oregon, South Dakota (I-29), Utah, Washington, Wyoming) plus the Alaska and Hawaii as being very large states, while Kansas, Oklahoma, and Texas are "split states" because of Interstate 35. If you look at the top 20 states in terms of land area, all of the states listed above with the exception of Hawaii would be part of that list, and the two missing states would be Minnesota (#14, and just east of the I-29 line) and Missouri (#18, and while I-29 runs through it and Iowa, most of the state is east of the line). Because of that, we have 31 states in the eastern half of the United States. All of those states are below the average land area of 70,725 square miles of the fifty states. In some cases, the land area of some metropolitan areas exceeds that land area of the smallest states. San Bernadino County in California has more land area than Rhode Island, Delaware, Connecticut, and Hawaii combined.

So, how does one normalize the data to provide a better answer? For tornadoes, it's easy. It's easy to claim that, for calendar years 2018-2022, Texas was both #1 and #30 in Tornados and be correct. How? In both the combined total (620) and averaged over five years (124), Texas tops the list, followed closely by Mississippi and Alabama. But, in terms of land area, Texas is only one of two states whose land area exceeds 250,000 square miles (261,914 to be exact), and one of eight states whose land area exceeds 100,000 square miles. When we take into account the land area, Texas drops to number 29 while Mississippi, Alabama, and Lousiana take the top three spots in that order.

Now, how does one normalize the data to provide a better and more accurate order of the flattest states? Amazing how a simple question becomes complex question. Someone pass the aspirin.

I always considered the number of earthquake faults and area has determines how less flat a state is until I heard of New Madrid Fault. But then again I used examples like San Andreas fault system and Cascadia subduction fault systems for that given that they are within the ring of fire.

[Rothman]

But...Texas is flat.

[dlsterner]

Mathematically, I suppose you could use the ratio of:

(1) The area of the state, as if a giant hypothetical blanket were laid upon the state, filling in all of the nooks and crannies, and using the square footage of such a blanket, and

(2) The area of the state when projected to sea level.

Since both of these are areas, the ratio would be unit-less (as long as you use the same units for both measurements).  A perfectly flat state would have a ratio of 1.0 - and the higher the ratio, the less flat the state is.

My calculus is too rusty to attempt to express this as a formula.


Or, I suppose you could just ask this guy:

[ZLoth]

I always considered the number of earthquake faults and area has determines how less flat a state is until I heard of New Madrid Fault. But then again I used examples like San Andreas fault system and Cascadia subduction fault systems for that given that they are within the ring of fire.

The measurement of how "scenic" a state is a very subjective term. From my perspective, Northern and Central California, especially along the coast and driving through the Sierra Nevadas, as well as US-101 along the Oregon and Washington Coast, was a very scenic journey which I took in September, 2013. In my subjective opinion, California is more scenic than Texas. Having said that, the reason why we have such scenic vista is because of the fault system in that area. For decades, they have been talking about "The Big One".

But...Texas is flat.

Most of Texas is fairly flat based upon my single observation driving across Interstate 10/Interstate 20 as part of move in January, 2019. Once you get west of Interstate 35 (Dallas/Fort Worth, Austin, San Antonio) in the eastern part of Texas, Texas gets drier and quite flat. Even the population density drops with few major exceptions (El Paso, Lubbock, Amarillo) although it is easier to trace Interstate 20 on a population density map than it is Interstate 10. It is because of Guadalupe Mountains National Park that is east of El Paso that we have the spike in elevation in Texas.

Or, I suppose you could just ask this guy:

While Illinois is flat, I have no desire to live there.

[Max Rockatansky]

While the vast majority of Texas is flat the extreme western part (which has more in common with New Mexico) certainly isn't. 

[thspfc]

All the plains states get heavily inflated if you use elevation range. Texas would be the 14th-least flat state. South Dakota would be 18th, Oklahoma 23rd, Nebraska 25th, Kansas 32nd, while most of Appalachia falls in the middle of the pack.

I don't think there's a mathematical way to judge it. Texas is a very flat state overall because the one mountain range is overpowered by the massive amount of flat land in the rest of the state.

[MikieTimT]

If there were a listing of grades on the Interstates of the state, per mile, or per 10 miles, or some similar metric, I would think that would make a fairly good representation of flatness to the roadgeek community.  However, there are some states that do a better job of cuts/fills than others, so maybe a better metric would be found on secondary state highways, where most states would take shortcuts on the cuts/fills compared to more major routes.  I don't know if such a list exists for any kind of road, much less secondary state highways.

There's always topographical (in Google Maps, Terrain layer at certain zoom levels) maps that have gradient lines indicating a certain change in elevation that would make a similar approximation.  The fewer the lines in a given area, the flatter the terrain.

Pretty much anywhere the glacial extent ground it's way the furthest south during the various ice ages, the flatter it tends to be with the ice sheets bulldozing their way southward over the millennia.

[Rothman]

While the vast majority of Texas is flat the extreme western part (which has more in common with New Mexico) certainly isn't.

Ok, but now we're just comparing bumpy pancakes.

[Max Rockatansky]

While the vast majority of Texas is flat the extreme western part (which has more in common with New Mexico) certainly isn't.

Ok, but now we're just comparing bumpy pancakes.

I would imagine that the likes of Guadalupe Mountains and Franklin Mountains are the lumpy pancake bumps Lorn Carhorn is envious of. 

[Rothman]

While the vast majority of Texas is flat the extreme western part (which has more in common with New Mexico) certainly isn't.

Ok, but now we're just comparing bumpy pancakes.

I would imagine that the likes of Guadalupe Mountains and Franklin Mountains are the lumpy pancake bumps Lorn Carhorn is envious of.

...on the very edge of the pancake.

[7/8]

I posted this same study before, likely in the infamous "Illinois is Flat" thread.

https://www.researchgate.net/publication/261410553_The_Flatness_of_US_States

Basic premise is dividing each state into grid boxes and measuring the "flatness" in each box (greater change in elevation over a shorter distance = steeper angle = less flat). Each box is given a rating of "not flat", "flat", "flatter", and "flattest". Rankings can than then be given based on the four rankings.

The study concludes Florida as the flattest state (has both the highest fraction of "flattest" area and the lowest fraction of "not flat" area). Note that the difference between it's highest and lowest point is irrelevant to the study's definition of flat.

[JayhawkCO]

And I think I took umbrage at the time that the study had Colorado at 25th. 

[bm7]

I posted this same study before, likely in the infamous "Illinois is Flat" thread.

https://www.researchgate.net/publication/261410553_The_Flatness_of_US_States

Basic premise is dividing each state into grid boxes and measuring the "flatness" in each box (greater change in elevation over a shorter distance = steeper angle = less flat). Each box is given a rating of "not flat", "flat", "flatter", and "flattest". Rankings can than be given based on the four rankings.

The study concludes Florida as the flattest state (has both the highest fraction of "flattest" area and the lowest fraction of "not flat" area). Note that the difference between it's highest and lowest point is irrelevant to the study's definition of flat.

Sounds similar to how I was thinking I would do it, although instead of giving somewhat arbitrary "flatness" ratings, I would get the grade of each line and find out the average and median grade of the entire state.

[US 89]

And I think I took umbrage at the time that the study had Colorado at 25th. 

Because half of your state is flatter than Kansas. 

[JayhawkCO]

And I think I took umbrage at the time that the study had Colorado at 25th. 

Because half of your state is flatter than Kansas. 

Far less than half, but still. There should be degrees of "not flat" or whatever the most "non-flat" measurement is. A seven degree slope shouldn't count the same as a forty-five.

[kphoger]

There's a whole region of Texas called "the hill country".

[fhmiii]

I posted this same study before, likely in the infamous "Illinois is Flat" thread.

https://www.researchgate.net/publication/261410553_The_Flatness_of_US_States

Basic premise is dividing each state into grid boxes and measuring the "flatness" in each box (greater change in elevation over a shorter distance = steeper angle = less flat). Each box is given a rating of "not flat", "flat", "flatter", and "flattest". Rankings can than then be given based on the four rankings.

The study concludes Florida as the flattest state (has both the highest fraction of "flattest" area and the lowest fraction of "not flat" area). Note that the difference between it's highest and lowest point is irrelevant to the study's definition of flat.

Like some others here, I'm calling BS on Colorado being "flatter" than Missouri.  Yes, we have a number of low mountains in the south and central part of the the Show Me State.  Yes, much of Colorado is flat...  but c'mon!  Does. Not. Compute.

[kphoger]

I think the question comes down to this:  are rolling hills flatter than towering mountain peaks, or are they equally non-flat?

[Rothman]

I think the question comes down to this:  are rolling hills flatter than towering mountain peaks, or are they equally non-flat?

Towering peaks.  And yet, Mount Washington in NH is more prominent than many peaks in the Rockies.

[JayhawkCO]

I think the question comes down to this:  are rolling hills flatter than towering mountain peaks, or are they equally non-flat?

Towering peaks.  And yet, Mount Washington in NH is more prominent than many peaks in the Rockies.

Prominence is so last year.

Jut is where it's at.

[7/8]

I think the question comes down to this:  are rolling hills flatter than towering mountain peaks, or are they equally non-flat?

Towering peaks.  And yet, Mount Washington in NH is more prominent than many peaks in the Rockies.

Prominence is so last year.

Jut is where it's at.

Thank you for sharing this, I've been looking for a term for this for years!