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

[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.

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:

[Bruce]

Prominence is so last year.

Jut is where it's at.

Washington is just swimming in juts. We should rename ourselves New Jutland.

[US 89]

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...

[Rothman]

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.

[US 89]

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.

I mean, Timp does tower more than 7000 feet above Utah Valley. Mt Washington isn't even that high above sea level...

[JayhawkCO]

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.

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.

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.

[kphoger]

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?

[JayhawkCO]

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.

[webny99]

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.

[J N Winkler]

Wikipedia articles on the criteria that can be applied (some of which have already been mentioned upthread):

*  Prominence (includes discussion of isolation, parent-child relationships, cols, etc.)

*  Height above average terrain

*  Jut

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.

[JayhawkCO]

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.

[hotdogPi]

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)

[JayhawkCO]

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.

[kphoger]

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.

[freebrickproductions]

I mean, I suppose, technically speaking, no state is truly "flat", given the curvature of the Earth's surface...

[JayhawkCO]

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...

[Rothman]

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.

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.

[JayhawkCO]

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.

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.

[US 89]

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.

[JayhawkCO]

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