Can you really see five states from the summit of Pike's Peak?

Factual Questions
1

It’s often stated in tourism literature. E.g.: The Broadmoor Manitou and Pikes Peak Cog Railway

But I’ve never heard it specified which five states they are (Colorado borders on seven states: New Mexico, Wyoming, Oklahoma, Kansas, Nebraska, Utah, Arizona). So I got curious when I drove to the summit the year before last, and decided to verify it.

To calculate the horizon distance – the distance you can see from the summit of Pike’s Peak – I used the formula that the distance in nautical miles you can see to the horizon is approximately 1.2 times the square root of the height from the ground in feet. (This formula can be derived by drawing a right triangle with the right vertex at the horizon, and the other vertices at the viewer’s eyes and the center of the earth, and then applying the Pythagorean theorem. I used 3444 nautical miles as the earth’s radius. Cecil used this formula once in a column on how far you can see out to sea standing on a beach).

For the height in feet, I used the “prominence” - the height of Pike’s Peak above the nearby terrain - of 5530 feet. This seems to me the appropriate height, as opposed to the elevation above sea level of 14,110 feet.

I calculated the distance you can see from the summit of Pike’s Peak to be 89.2 nmi.

I then calculated the distances from Pike’s Peak (38.9°N, 105.0°W) to the three closest states bordering Colorado:
Wyoming: 129.6 nmi
New Mexico: 110.4 nmi
Kansas: 139.9 nmi

This was made easier by the fact that Colorado is bounded by a pair of latitude lines (41°N and 37°N) and a pair of longitude lines (102.05°W and 107.05°W.

I didn’t calculate the distances to Oklahoma or Nebraska (which are not directly north or south of Pike’s Peak, and thus further than the three states above [not to mention more complicated to calculate!]) or Utah or Arizona, which are even further.

The only thing I can think of which might invalidate my calculations is the height of points in the bordering states. You can see further from the top of Pike’s Peak to a mountain in the bordering state than you can to a low-elevation point at the same location. The formula I’ve used assumes the horizon is at a low-elevation point.

Regardless of this, it seems very unlikely that there are any mountains in Kansas (or Nebraska, or Oklahoma) high enough to make a difference.

So even if there are mountains in Wyoming or New Mexico high enough (and near enough to the border, and close enough in longitude) to be seen from the summit of Pike’s Peak, I can’t see how there are more than two states (besides Colorado) visible from the summit of Pike’s Peak.

And I’m not too sure about even these two.

Thoughts?

2

Note that Pike’s Peak is on the far east part of the mountainous area, so the topography drops off farther to the east than it does to the west. So using the prominence may not be appropriate, at least for states to the east of it.

3

I recall driving into Colorado from Nebraska and not being able to make out the Rockies on a clear, albeit hazy, day until we were at least 20 or 30 miles (st). It would follow that if you can see turf in Kansas or Nebraska, you should be able to see peaks from those states. I do not think you can.

4

Even though it doesn’t directly border Colorado, Texas is much closer to the peak than Nebraska or Wyoming. I assume they’re also counting Colorado as a state, so I’m thinking it’s CO, NM, KS, OK, TX.

5

There might not be mountains in Kansas, Nebraska, or Oklahoma high enough to make a difference, but what about radio towers? They can easily be upwards of 1000 feet high.

6

There are some pretty non-trivial buttes in the NW corner of Oklahoma.

7

You’re going to want to use the height above sea level. The extra mountains do not affect the distance you can see unless they physically get in the way of your line of sight. (If you are at sea, for example, the distance to the horizon does not change if you are standing next to a toddler.) So, this gives you a total sight distance of 143 nm.

Here are the distances between Pike’s Peak and the seven states Colorado borders that I found online using a Google Maps tool:

111 New Mexico
127 Wyoming
138 Nebraska
139 Kansas
147 Oklahoma
189 Utah
220 Arizona

Four of them are less than 143 and another is probably within the margin of error.

8

And thus we prove the fallacy. A naïve calculation of horizon difference versus sea level gives 4 states plus CO = 5 total. And that’s where the saying comes from. A naïve, i.e. wrong, calculation.

The correct calculation doesn’t use local prominence (i.e. the nearby toddler), but rather the difference in height between the terrain at Pikes Peak and the terrain at each state border e.g. NM, WY, OK, etc. That won’t be 5,500 feet as the OP asserted, but neither will it be the 14,000 feet that **RadicalPi **just used.

It’s also the case that we need to consider peaks inside NM & WY. As the OP says, there’s no significant terrain relief in the other nearby states. But there is planar terrain at significant height above sea level and that extra elevation must be accounted for.

9

I’ve been to the summit of Pikes Peak many times and they have a sign that talks about this. It boils down to “look in a generally northern direction and you see Wyoming” but I did it and I just don’t think I am that far above the surrounding plains to see that far.

If you could see any other state it would be Mount Sunflower 190 miles away just over the border and 7000’ below Pikes Peak. Yet a horizon calculator shows that the distance seen would be half of that. I called BS to the 5 states thing on top of Pikes Peak and I’m calling it BS now.

10

You do have to add atmospheric refraction. At sea level, it can be 8% farther in the right conditions. So, if you want to try it on the coldest day survivable, at sunrise, maybe you can extend your range by five or six percent and maybe glimpse Kansas. Which looks enough like Colorado that, hey, just call it Kansas, no one will know the difference.

11

If the earth were a perfect sphere, the horizon would be a circle with your eye at the center. Now, if you stand higher, then you see farther. That’s because you can see farther around the part of the earth that curves away you. In addition, if the stuff you’re looking at is higher, then it can be farther away and you’ll still be able to see it. What this means is that if you’re above sea level and the thing you’re looking at is above sea level, then you can see if at a distance farther than that between you and the horizon. Local prominence doesn’t really enter into it. Imagine one of those old tall-masted ships slowly rising above the horizon as it gets closer to you; You can see the top of it while the view of the rest of it is still blocked by the sea itself.

Now, this doesn’t mean that you’ll be able to actually see as far as the calculations will show. Air gets hazy with distance. There might be a different mountain in the way. And so on and so on.

12

I can believe it’s possible to see New Mexico from Pike’s Peak. Bartlett Mesa (near Raton) is right on the CO/NM state line and is at approx. 8,400 ft. (the highest point on the mesa reaches almost 8,900 ft. and is on the New Mexico side). There’s almost nothing in between the two points so I don’t doubt that on a clear day someone on Pike’s Peak could see Bartlett Mesa.

13

The site heywhatsthat.com will generate a panorama if you give it a location. If you believe its calculations, then this map shows that New Mexico and Wyoming (and Colorado) are visible from Pikes Peak, but that Nebraska, Kansas, Oklahoma, and Texas are not.

Kansas comes closest; but the most eastern point you can see (according to that map) is about 30 miles from the Colorado-Kansas state line, near the town of Cheyenne Wells, CO. It’s possible that with the right viewing conditions (with refraction and whatnot), one might be able to see Kansas occasionally; but not on a regular basis.

14

You need to take into account atmospheric refraction

We can actually see a fair bit further at optical frequencies than should be possible given earth curvature.

I discovered this when I was trying to set up radio links to an island that I could easily see but the radios didn’t work. It turned out that at the particular radio frequency the island was below the horizon.

So in any discussion of what you can see, take into account refraction which tends to flatten out the view.

15

Is atmospheric refraction a factor?

16

I agree completely with *almost *everything you’re saying.

The error you committed and have yet to notice was using the height of Pikes Peak above *sea level *as your height above the local horizon. And that’s wrong. Consider these two cases:

If Pike’s Peak was a small island sticking out of the sea, then yes, the distance-to-horizon visible from 14,000 feet above the surrounding surface would be a correct calculation.

But imagine Pike’s Peak was a small hill at 14,000 feet above sea level in the middle of a flat plain hundreds of miles across which plain is at 13,000 feet above sea level. The relevant height above the surface to calculate the distance-to-horizon is just 1000 feet.

In reality, Pikes Peak sits on the eastern edge of high mountains and the western edge of high plains. At the immediate base of the mountain the terrain is about 5500 above seal level, or 8500 below Pike’s summit. At the CO/KS border directly east of Pike’s Peak the terrain is around 3700 above sea level or 10,300 below Pike’s summit.

And of course, as others have noted before and since, peaks in the distance are visible from farther than the plains at their base. Which is why the calcs I’m describing are explicitly limited to discussing the distance we can see towards the flat states.
IOW, your logic is good, but you’re using the wrong inputs into your formulas.

17

To the south: Spanish Peaks.
The bow out to the east north of Pueblo so no chance of seeing the Sangre de Christos Mountains in New Mexico. Straight line distance to Raton Pass: 130 mi but it passes over the eastern foothills of the SdCs. I’d be willing to grant that if you look to the south and to the eastern part of those mountains that some ridge or peak in New Mexico is in your view.
The COMNOK tripoint is 170 miles away and the NMOKTX tripoint is 200 miles away. Absolutely flat and I just can’t buy that you see either of those states from PP because of the Mt. Sunflower scenario.

East: the Great Plains. Mt. Sunflower, the highest point is Kansas is 160 miles away just across the border and almost due east. With 7000’ relative elevation difference, I get that from Pikes Peak it is about 110mi to the horizon. Yes I get atmospheric refraction but it would have to increase almost 50% for Kansas to be visible. Likewise it is 180 miles to Nebraska.

So if Kansas isn’t visible, then Oklahoma, Texas and Nebraska can’t be seen.

North: Wyoming?
150 miles to the Wyoming border but at 6000’ unlike the 4000’ of Kansas. This actually makes it more difficult to see into Wyoming because of the smaller elevation difference. Pikes Peak sticks out to the east so you have to look back over the Rockies if you look for Medicine Bow Peak 185 miles away. I just don’t see how you can see to the plains of Wy (too far away) or the Wy Front Range (view blocked).
105 miles to my house so I will look for PP from my house and this should confirm my thinking on KS, NB, OK, and TX.

18

Mt. Sunflower has an elevation of 4039 feet, so wouldn’t the relevant elevation difference be 14,110 - 4039 = 10,061 feet?

In which case, the horizon is slightly further away (120.4 nmi).

But the verdict is the same: refraction would still have to add about 25% for Mt. Sunflower to be visible.

19

This site has calculated theoretical views for Pikes Peak, among others. I’m not sure of the method, as the technical info page was unreachable, but at a guess it’s just straight-line views with no refraction adjustment. Numbers on the map are distance in miles.

Cheyenne, Wyoming is shown, and is one of the farthest visible named points at 159 miles. To the south, there is Davis Mesa in New Mexico, and a nearby unnamed peak at 160 miles. It doesn’t look like any locations in Nebraska, Kansas, are called out and nothing is prominent in the terrain. Anything in Oklahoma or Texas looks blocked as well.

20

Looking at the distance and bearing provided, it appears to be Sierra Grande. That mountain shows up as visible in the map I linked to upthread as well.