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Non-Road Boards => Off-Topic => Topic started by: ZLoth on October 15, 2023, 03:46:29 PM

Title: How to determine the flatness of a state? Pass the aspirin...
Post by: ZLoth on October 15, 2023, 03:46:29 PM
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.

Title: Re: How to determine the flatness of a state? Pass the aspirin...
Post by: Max Rockatansky on October 15, 2023, 03:51:20 PM
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
Title: Re: How to determine the flatness of a state? Pass the aspirin...
Post by: hotdogPi on October 15, 2023, 03:53:47 PM
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.
Title: Re: How to determine the flatness of a state? Pass the aspirin...
Post by: wanderer2575 on October 15, 2023, 04:27:41 PM
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.
Title: Re: How to determine the flatness of a state? Pass the aspirin...
Post by: bing101 on October 15, 2023, 04:52:28 PM
Quote from: ZLoth on October 15, 2023, 03:46:29 PM
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.
Title: Re: How to determine the flatness of a state? Pass the aspirin...
Post by: Rothman on October 15, 2023, 04:53:22 PM
But...Texas is flat.
Title: Re: How to determine the flatness of a state? Pass the aspirin...
Post by: dlsterner on October 15, 2023, 06:48:22 PM
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:

(https://uploads.tapatalk-cdn.com/20220129/2c79f44621c1701623680fec4f13008a.jpg)
Title: Re: How to determine the flatness of a state? Pass the aspirin...
Post by: ZLoth on October 15, 2023, 08:24:42 PM
Quote from: bing101 on October 15, 2023, 04:52:28 PMI 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".

Quote from: Rothman on October 15, 2023, 04:53:22 PMBut...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.

Quote from: dlsterner on October 15, 2023, 06:48:22 PMOr, I suppose you could just ask this guy:

(https://uploads.tapatalk-cdn.com/20220129/2c79f44621c1701623680fec4f13008a.jpg)

While Illinois is flat, I have no desire to live there.
Title: Re: How to determine the flatness of a state? Pass the aspirin...
Post by: Max Rockatansky on October 15, 2023, 08:37:58 PM
While the vast majority of Texas is flat the extreme western part (which has more in common with New Mexico) certainly isn't. 
Title: Re: How to determine the flatness of a state? Pass the aspirin...
Post by: thspfc on October 15, 2023, 08:58:29 PM
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.
Title: Re: How to determine the flatness of a state? Pass the aspirin...
Post by: MikieTimT on October 15, 2023, 09:20:14 PM
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.
Title: Re: How to determine the flatness of a state? Pass the aspirin...
Post by: Rothman on October 15, 2023, 11:05:06 PM
Quote from: Max Rockatansky on October 15, 2023, 08:37:58 PM
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.
Title: Re: How to determine the flatness of a state? Pass the aspirin...
Post by: Max Rockatansky on October 15, 2023, 11:28:23 PM
Quote from: Rothman on October 15, 2023, 11:05:06 PM
Quote from: Max Rockatansky on October 15, 2023, 08:37:58 PM
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. 
Title: Re: How to determine the flatness of a state? Pass the aspirin...
Post by: Rothman on October 16, 2023, 06:47:04 AM
Quote from: Max Rockatansky on October 15, 2023, 11:28:23 PM
Quote from: Rothman on October 15, 2023, 11:05:06 PM
Quote from: Max Rockatansky on October 15, 2023, 08:37:58 PM
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.
Title: Re: How to determine the flatness of a state? Pass the aspirin...
Post by: 7/8 on October 16, 2023, 09:22:51 AM
I posted this same study before, likely in the infamous "Illinois is Flat" thread. :-D

https://www.researchgate.net/publication/261410553_The_Flatness_of_US_States (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.
Title: Re: How to determine the flatness of a state? Pass the aspirin...
Post by: JayhawkCO on October 16, 2023, 10:55:20 AM
And I think I took umbrage at the time that the study had Colorado at 25th.  :)
Title: Re: How to determine the flatness of a state? Pass the aspirin...
Post by: bm7 on October 16, 2023, 11:02:40 AM
Quote from: 7/8 on October 16, 2023, 09:22:51 AM
I posted this same study before, likely in the infamous "Illinois is Flat" thread. :-D

https://www.researchgate.net/publication/261410553_The_Flatness_of_US_States (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.
Title: Re: How to determine the flatness of a state? Pass the aspirin...
Post by: US 89 on October 16, 2023, 11:58:56 AM
Quote from: JayhawkCO on October 16, 2023, 10:55:20 AM
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.  :poke:
Title: Re: How to determine the flatness of a state? Pass the aspirin...
Post by: JayhawkCO on October 16, 2023, 12:29:47 PM
Quote from: US 89 on October 16, 2023, 11:58:56 AM
Quote from: JayhawkCO on October 16, 2023, 10:55:20 AM
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.  :poke:

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.
Title: Re: How to determine the flatness of a state? Pass the aspirin...
Post by: kphoger on October 16, 2023, 03:08:56 PM
There's a whole region of Texas called "the hill country".
Title: Re: How to determine the flatness of a state? Pass the aspirin...
Post by: fhmiii on October 16, 2023, 05:15:02 PM
Quote from: 7/8 on October 16, 2023, 09:22:51 AM
I posted this same study before, likely in the infamous "Illinois is Flat" thread. :-D

https://www.researchgate.net/publication/261410553_The_Flatness_of_US_States (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.
Title: Re: How to determine the flatness of a state? Pass the aspirin...
Post by: kphoger on October 16, 2023, 05:18:28 PM
I think the question comes down to this:  are rolling hills flatter than towering mountain peaks, or are they equally non-flat?
Title: Re: How to determine the flatness of a state? Pass the aspirin...
Post by: Rothman on October 16, 2023, 05:20:00 PM
Quote from: kphoger on October 16, 2023, 05:18:28 PM
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.
Title: Re: How to determine the flatness of a state? Pass the aspirin...
Post by: JayhawkCO on October 16, 2023, 05:23:10 PM
Quote from: Rothman on October 16, 2023, 05:20:00 PM
Quote from: kphoger on October 16, 2023, 05:18:28 PM
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. (https://peakjut.com/)
Title: Re: How to determine the flatness of a state? Pass the aspirin...
Post by: 7/8 on October 16, 2023, 10:20:12 PM
Quote from: JayhawkCO on October 16, 2023, 05:23:10 PM
Quote from: Rothman on October 16, 2023, 05:20:00 PM
Quote from: kphoger on October 16, 2023, 05:18:28 PM
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. (https://peakjut.com/)

Thank you for sharing this, I've been looking for a term for this for years!
Title: Re: How to determine the flatness of a state? Pass the aspirin...
Post by: JayhawkCO on October 16, 2023, 10:35:09 PM
Quote from: 7/8 on October 16, 2023, 10:20:12 PM
Quote from: JayhawkCO on October 16, 2023, 05:23:10 PM
Quote from: Rothman on October 16, 2023, 05:20:00 PM
Quote from: kphoger on October 16, 2023, 05:18:28 PM
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. (https://peakjut.com/)

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

And it's fun that none of the 14ers get the top spot for Colorado. Intead, it's 13er Mt. Sopris that you get a really good view of in the Roaring Fork Valley, and specifically along CO133:

(https://i.postimg.cc/CxQr976t/Sopris.png)

Title: Re: How to determine the flatness of a state? Pass the aspirin...
Post by: Bruce on October 16, 2023, 11:57:12 PM
Quote from: JayhawkCO on October 16, 2023, 05:23:10 PM
Prominence is so last year.

Jut is where it's at. (https://peakjut.com/)

Washington is just swimming in juts. We should rename ourselves New Jutland.
Title: Re: How to determine the flatness of a state? Pass the aspirin...
Post by: US 89 on October 17, 2023, 12:46:25 AM
So as it seems to me, you find whatever the steepest angle is from the top of the mountain down to the surrounding terrain, pick the point that is theoretically visible from the summit that forms that steepest angle, and then find the vertical distance from that point to the summit. Fascinating. I'm a fan because it seems to include a lot of the peaks that are especially noticeable, even if they don't necessarily have a lot of topographic prominence themselves or aren't any taller than nearby peaks. Things like Big Cottonwood Twin Peaks and Lone Peak, which you won't find on any listing of tallest or most prominent mountains in Utah but are probably the two most distinctive high peaks visible from Salt Lake City.

The highest-jut mountain in Utah is not even thought of as a mountain by many people - it's the East Temple in Zion National Park, which towers over the Pine Creek branch of Zion Canyon. In fact, of the top 25 in Utah, 11 of them are in Zion. There's a reason it's a national park...
Title: Re: How to determine the flatness of a state? Pass the aspirin...
Post by: Rothman on October 17, 2023, 08:20:46 AM
Hm.  Then again, if jut is supposed to be a measure of how impressive a mountain is, I wonder how many people would think first of the cliffs in Zion over peaks of the Wasatch Front.

There was one Utahn transplant out here that was whining about how there weren't any mountains and got annoyed when I pointed out Mount Washington was more prominent than Timp. :D
Title: Re: How to determine the flatness of a state? Pass the aspirin...
Post by: US 89 on October 17, 2023, 09:41:56 AM
Quote from: Rothman on October 17, 2023, 08:20:46 AM
There was one Utahn transplant out here that was whining about how there weren't any mountains and got annoyed when I pointed out Mount Washington was more prominent than Timp. :D

I mean, Timp does tower more than 7000 feet above Utah Valley. Mt Washington isn't even that high above sea level...
Title: Re: How to determine the flatness of a state? Pass the aspirin...
Post by: JayhawkCO on October 17, 2023, 09:47:33 AM
Quote from: US 89 on October 17, 2023, 12:46:25 AM
The highest-jut mountain in Utah is not even thought of as a mountain by many people - it's the East Temple in Zion National Park, which towers over the Pine Creek branch of Zion Canyon. In fact, of the top 25 in Utah, 11 of them are in Zion. There's a reason it's a national park...

I admit being far more awe-struck by East Temple than Kings Peak.

Quote from: Rothman on October 17, 2023, 08:20:46 AM
There was one Utahn transplant out here that was whining about how there weren't any mountains and got annoyed when I pointed out Mount Washington was more prominent than Timp. :D

I've only seen Mt. Washington from the west, so I haven't seen it at its "jut-iest", so I can't compare. Anyway, Mt. Washington isn't even the highest jut in New Hampshire; Mt. Willey has that title.
Title: Re: How to determine the flatness of a state? Pass the aspirin...
Post by: kphoger on October 17, 2023, 10:28:06 AM
Another "get you thinking" question...

Which is hillier?

a.  A 70-square-mile area with one giant mountain in it surrounded by a plain

b.  A 70-square-mile area with three moderate peaks in it and a few rolling foothills

c.  A 70-square-mile area with hundreds of rolling hills blanketing the whole area

Which is flatter?
Title: Re: How to determine the flatness of a state? Pass the aspirin...
Post by: JayhawkCO on October 17, 2023, 10:38:34 AM
Quote from: kphoger on October 17, 2023, 10:28:06 AM
Another "get you thinking" question...

Which is hillier?

a.  A 70-square-mile area with one giant mountain in it surrounded by a plain

b.  A 70-square-mile area with three moderate peaks in it and a few rolling foothills

c.  A 70-square-mile area with hundreds of rolling hills blanketing the whole area

Which is flatter?

Hilliest to least hilly - C, B, A
Flattest to least flat - C, B, A

Enjoy.
Title: Re: How to determine the flatness of a state? Pass the aspirin...
Post by: webny99 on October 17, 2023, 10:46:15 AM
Quote from: JayhawkCO on October 17, 2023, 10:38:34 AM
Quote from: kphoger on October 17, 2023, 10:28:06 AM
Another "get you thinking" question...

Which is hillier?

a.  A 70-square-mile area with one giant mountain in it surrounded by a plain

b.  A 70-square-mile area with three moderate peaks in it and a few rolling foothills

c.  A 70-square-mile area with hundreds of rolling hills blanketing the whole area

Which is flatter?

Hilliest to least hilly - C, B, A
Flattest to least flat - C, B, A

Enjoy.

Agreed with C being the hilliest, but flattest to least flat should have A and C flipped.
Title: Re: How to determine the flatness of a state? Pass the aspirin...
Post by: J N Winkler on October 17, 2023, 10:48:36 AM
Wikipedia articles on the criteria that can be applied (some of which have already been mentioned upthread):

*  Prominence (https://en.wikipedia.org/wiki/Topographic_prominence) (includes discussion of isolation, parent-child relationships, cols, etc.)

*  Height above average terrain (https://en.wikipedia.org/wiki/Height_above_average_terrain)

*  Jut (https://en.wikipedia.org/wiki/Jut_(topography))

Scale is also important.  There is a water-cooler-famous scientific paper that states all of the US states are flatter than a pancake, since if the surface of the latter is inspected at a microscopic level, it has local differences between high and low that are proportionately far greater than those observed for any landform in the US (or indeed on Earth).

Colorado versus West Virginia is probably the classic example of prominence versus local variation in terrain height, but in principle any non-mountainous region with significant dissection--such as the Ozark plateau--can stand in for the latter.
Title: Re: How to determine the flatness of a state? Pass the aspirin...
Post by: JayhawkCO on October 17, 2023, 10:58:45 AM
Quote from: webny99 on October 17, 2023, 10:46:15 AM
Quote from: JayhawkCO on October 17, 2023, 10:38:34 AM
Quote from: kphoger on October 17, 2023, 10:28:06 AM
Another "get you thinking" question...

Which is hillier?

a.  A 70-square-mile area with one giant mountain in it surrounded by a plain

b.  A 70-square-mile area with three moderate peaks in it and a few rolling foothills

c.  A 70-square-mile area with hundreds of rolling hills blanketing the whole area

Which is flatter?

Hilliest to least hilly - C, B, A
Flattest to least flat - C, B, A

Enjoy.

Agreed with C being the hilliest, but flattest to least flat should have A and C flipped.

Disagree. If you take the volume of the mountain over baseline, it would contain more matter than the whole bunch of small hills over baseline. Less flat if there's more "something" above flat.
Title: Re: How to determine the flatness of a state? Pass the aspirin...
Post by: hotdogPi on October 17, 2023, 11:34:48 AM
Quote from: JayhawkCO on October 17, 2023, 10:58:45 AM
Disagree. If you take the volume of the mountain over baseline, it would contain more matter than the whole bunch of small hills over baseline. Less flat if there's more "something" above flat.

Imagine a domino-shaped state. One half of the domino is at a constant 2000 feet. The other half of the domino is at a constant 10000 feet, with a sheer cliff separating the two halves. It's entirely flat except for the very narrow strip containing the cliff, despite the huge elevation difference.

(edited to fix typo)
Title: Re: How to determine the flatness of a state? Pass the aspirin...
Post by: JayhawkCO on October 17, 2023, 11:41:55 AM
Quote from: 1 on October 17, 2023, 11:34:48 AM
Quote from: JayhawkCO on October 17, 2023, 10:58:45 AM
Disagree. If you take the volume of the mountain over baseline, it would contain more matter than the whole bunch of small hills over baseline. Less flat if there's more "something" above flat.

Imagine a domino-shaped state. One half of the domino is at a constant 2000 feet. The other half of the domino is at a constant 10000 feet, with a sheer cliff separating the two halves. It's entirely flat except for the very narrow strip containing the cliff, despite the huge elevation different.

That very narrow strip is what matters, in my opinion. If you were standing on the bottom part of the domino and wanted to walk straight forward towards the other end, you'd have to climb to get there, right? So it's not flat. It might be flat once you got to the top, but that doesn't mean that the state itself is flat.

If I remember calculus from 20 years ago, if you take the derivative of the elevation of the state, its value is not y=0.
Title: Re: How to determine the flatness of a state? Pass the aspirin...
Post by: kphoger on October 17, 2023, 01:26:01 PM
Quote from: J N Winkler on October 17, 2023, 10:48:36 AM
Scale is also important.  There is a water-cooler-famous scientific paper that states all of the US states are flatter than a pancake, since if the surface of the latter is inspected at a microscopic level, it has local differences between high and low that are proportionately far greater than those observed for any landform in the US (or indeed on Earth).

Interesting thought experiment.

Let's take the difference in elevation between 5,250 and 14,000 feet, over the course of 350 miles.  Let's label this υ for 'undulation factor'.  It works out to 25 feet per mile, or 211.2 to 1.  Now let's take a 20-cm pancake.  At υ=211.2, we should expect a difference in elevation of approximately one millimeter.  That seems rather bumpy for a pancake but, of course, the large majority of lines drawn across a mountainous state would have typical elevation changes substantially less than 8750 feet.

Seems reasonable to me.



ETA — And I'm not even considering the fact that a pancake is a bit of a dome shape to begin with.
Title: Re: How to determine the flatness of a state? Pass the aspirin...
Post by: freebrickproductions on October 17, 2023, 04:18:13 PM
I mean, I suppose, technically speaking, no state is truly "flat", given the curvature of the Earth's surface...
Title: Re: How to determine the flatness of a state? Pass the aspirin...
Post by: JayhawkCO on October 17, 2023, 04:19:43 PM
Quote from: freebrickproductions on October 17, 2023, 04:18:13 PM
I mean, I suppose, technically speaking, no state is truly "flat", given the curvature of the Earth's surface...

Even more technically, spacetime being warped by gravity and other such things...
Title: Re: How to determine the flatness of a state? Pass the aspirin...
Post by: Rothman on October 17, 2023, 04:32:41 PM
Quote from: US 89 on October 17, 2023, 09:41:56 AM
Quote from: Rothman on October 17, 2023, 08:20:46 AM
There was one Utahn transplant out here that was whining about how there weren't any mountains and got annoyed when I pointed out Mount Washington was more prominent than Timp. :D

I mean, Timp does tower more than 7000 feet above Utah Valley. Mt Washington isn't even that high above sea level...
And yet, Mount Washington has 900 feet of more prominence.
Title: Re: How to determine the flatness of a state? Pass the aspirin...
Post by: JayhawkCO on October 17, 2023, 04:42:10 PM
Quote from: Rothman on October 17, 2023, 04:32:41 PM
Quote from: US 89 on October 17, 2023, 09:41:56 AM
Quote from: Rothman on October 17, 2023, 08:20:46 AM
There was one Utahn transplant out here that was whining about how there weren't any mountains and got annoyed when I pointed out Mount Washington was more prominent than Timp. :D

I mean, Timp does tower more than 7000 feet above Utah Valley. Mt Washington isn't even that high above sea level...
And yet, Mount Washington has 900 feet of more prominence.

All that really means is that we have lots of mountains out here. You have one. :)
Title: Re: How to determine the flatness of a state? Pass the aspirin...
Post by: US 89 on October 17, 2023, 05:33:58 PM
Quote from: JayhawkCO on October 17, 2023, 09:47:33 AM
Quote from: US 89 on October 17, 2023, 12:46:25 AM
The highest-jut mountain in Utah is not even thought of as a mountain by many people - it's the East Temple in Zion National Park, which towers over the Pine Creek branch of Zion Canyon. In fact, of the top 25 in Utah, 11 of them are in Zion. There's a reason it's a national park...

I admit being far more awe-struck by East Temple than Kings Peak.

Same, but also the closest I've ever seen Kings Peak is from US 40 in the Uinta Basin and maybe also I-80 in Wyoming. The High Uinta Crest ridgeline does look cool but it's really hard to get a mountain to look impressive from that far away. Grand Teton from US 20 in Idaho is one of the few that can pull it off.
Title: Re: How to determine the flatness of a state? Pass the aspirin...
Post by: JayhawkCO on October 17, 2023, 05:42:41 PM
Quote from: US 89 on October 17, 2023, 05:33:58 PM
Quote from: JayhawkCO on October 17, 2023, 09:47:33 AM
Quote from: US 89 on October 17, 2023, 12:46:25 AM
The highest-jut mountain in Utah is not even thought of as a mountain by many people - it's the East Temple in Zion National Park, which towers over the Pine Creek branch of Zion Canyon. In fact, of the top 25 in Utah, 11 of them are in Zion. There's a reason it's a national park...

I admit being far more awe-struck by East Temple than Kings Peak.

Same, but also the closest I've ever seen Kings Peak is from US 40 in the Uinta Basin and maybe also I-80 in Wyoming. The High Uinta Crest ridgeline does look cool but it's really hard to get a mountain to look impressive from that far away. Grand Teton from US 20 in Idaho is one of the few that can pull it off.

Top 5 most awe-inspiring mountains I've seen with my own eyes, in order:

Denali
Mt. Kazbeg
Mt. Rainier
Grand Teton
Mt. Sneffels