Wednesday, July 17, 2019


--- How big is Creation Rock 2 ---

Frankly, I have no idea.

I've seen two websites that have the same statement, that both Shiprock and Creation Rock are 300 feet tall...but they're different heights. I've also seen that they're both taller than Niagara Falls.

Actually, it's hard to figure out which rock is Shiprock and which is Creation Rock, as this article at the Red Rocks Park website explains.

http://www.redrockspark.com/history/history-of-red-rocks-park

And obviously my survey wasn't correct, though I'm not as bothered about that as some might expect.

Success is an American ideal. Researchers rarely publish reports on failed experiments despite most books on research design encourages researchers to do so.

You often learn more from a well designed failure than you do from a success. A success gives you an answer. A failure gives you a bunch of interesting questions, such as, "What went wrong? Was my study design flawed?" "I was expecting this to work, it should have worked, why didn't it?"

In 1887, Albert Michelson and Edward Morley wanted to study the "stuff" that light waves flowed through. They set up and experiment that shot a stream of light in two different directions, one at a right angle to the other. They wanted to measure the difference in the speed of light through the paths. They were sorely disappointed when there was no difference.

The problem was that light doesn't propagate through "stuff" like sound or water waves, and this failure started a line of study that lead quickly to Einstein and special relativity.

So, I learned some things from my "failure" and I'll let you in on those things. And, one of the great things about adventures vs. studies is that adventures have a focus surrounded by lots of other "stuff".

I knew that Red Rocks had a concert planned that night (summer's like that at Red Rocks) and that I needed to do what I was going to do before 2:00 afternoon, so I hired a Lyft and headed straight there. The driver let me out at the Trading Post Trail trailhead.

I was delighted by the diversity of plant life on the trail.


                                                   [White Anemones and Golden Asters]

I was rather concerned by the many signs that urged visitors to stay on the trail. I certainly understood the reason - there are delicate plants and animals that live at Red Rocks Park and they don't respond well to crowds tromping all over them, but that was going to interfere with me finding a site for my survey.

As for the plants in the above photo, the anemones are easy to identify by their simple (but often brightly colored), five petaled flowers and deeply lobed leaves. The asters are a little more difficult but many similar flowers have more irregular petals and/or broader central disks.

In contrasts to the tiny flowers are the gargantuan rocks in the park. Red Rocks is justifiably famous for the huge natural amphitheater, home to internationally attended and broadcast performances, but the park itself is a geological wonder.

                                                                        [Big rock]

As the Pacific Plate crashed up against the North American continent, pushing the Colorado Plateau up to form what would become the Rocky Mountains, land around the edges were severely twisted and buckled. These layers of sediments are often tilted to right angles to the rock to the east and are sometimes turned over completely. There's evidently some debate as to whether the rock is sedimentary sandstone or gneiss. In support of the frustrated geologist that snorted and corrected me when I called the Red Rocks "sandstone", rocks this twisted are usually considered metamorphic and, therefore, gneiss. Regardless, the red is prominent and is caused by the same thing that makes old iron red.....rust.



                                                                 [Slanted rocks]

In the photos above, the big rock center stage is my target, Creation Rock. It's the largest of the three massive rocks that make up the amphitheater.

Although Red Rocks Park is the most famous display of these tilted Goliaths (and, in my estimation, the best), there are certainly others. Technically, they are called the Fountain Formation. They stretch through Wyoming and Colorado. These photos bear a strong resemblance to the Flatirons just outside Boulder, and for good reason since the Flatirons are another example of the Fountain formation. Other famous outcroppings are the Garden of the Gods in Colorado Springs. Other instances are the Red Rocks of  Eben G. Fine Park in Boulder, Roxborough State Park, and Red Rocks Canyon in Colorado Springs.

Here are some tiny blue larkspurs.

                                                                 [Blue Larkspurs]

Just behind Red Rocks is Mount Morrison and to the south is Mount Falcon.

                                                      [Mount Falcon from Red Rocks]

I was considering hiking up Falcon when I finished at Red Rocks but the brutal heat of the Colorado summer convinced me that I would be miserable and decided to hold off until cooler weather.

The Fountain Formation marches off to the south between the Front Range and the Hogback ridge to the east, From there to the Mississippi River is grassland plains.

                                                  [Slanted rocks to the south of Red Rocks]

                                               [Wavy rocks on the Trading Post Trail]

I overheard a lady telling a group of children that these waves frozen in stone were the result of erosion from the action of water. My understanding is that the rock carvings of Red Rocks Park and other parts of the Fountain Formation are mostly due to wind erosion. A little further to the north, on Dinosaur Ridge, I over heard a tour guide tell a completely different story.

As incredible as it may be, Colorado was, at one time, covered by a shallow sea. All the dinosaur activity in the area were huge beasts sunbathing at the beach (or maybe a marsh). This was before the Colorado Plateau was uplifted. So, these waves, frozen in rock were not due to erosion, but deposition - sand deposited by the gentle wave action of the inland sea, then covered by more sediment, packed down, and turned into stone under great pressure until they were uncovered millions of years later by the wind. And if you've been in any of the downslope winds in this area, that won't be a great stretch of your credibility.


                                                                 [Jumping cholla]

This is another good reason to stay on the paths at Red Rocks. The Jumping Cholla is notorious for reaching out and touching people. Still, these (cactuses) are still my favorite wildflowers and Denver area, being desert, is a natural habitat for them.

At the end of the Trading Post Trail is, of course, the Trading Post, which is also a museum of pop music. It is located to showcase some of the big rock formations, such as this huge column.

                                                                 [Big rock column]

Many of the formations are named, but there are so many....I can't find a name for this one.

I looked around the Trading Post and asked a couple of staff some questions verifying that I was going to have problems finding a place to stretch my 100 foot cord. I finally settled on a line of sight near the Trading Post for my two locations. The first is at a fire plug across from the building. Here is Creation Rock from that site. The road branching off to the left is Shiprock Road.

                                                       [Creation Rock from Site H]

The other site was a little ways up Shiprock Road to the south. I could just sight the summit of Creation Rock above the boulders to the west of the road.

                                                          [Creation Rock from Site G]

Since I knew that I would have problems with this data, I started looking for ways to double check my work, multiple ways of estimating bearings and distances. I measured the distance between my two sites using an app on my phone called Altitude (created by PyGDroid and available on the Google Play Store). The app calculates distance traveled using GPS. I found the distance between the two sites to be 0.05 miles. That converted to 264 feet and, later checking Google maps for a distance, I found it to be about 257 feet, which is the distance I ended up using.

Here is a shot from the Trading Post back down through Bear Creek Canyon where Morrison is situated. The lakes in the distance  are the Soda Lakes at Bear Creek Lakes State Park. I'll get to that later.

                                                    [Bear Creek Canyon from Red Rocks]

My altimeter reading told me that Site G was about 40 feet above Site H and I could look down on top of the tall Trading Post building from Site G, so I felt pretty confident with the phone app.

I went to work getting bearing readings from my surveyor's compass and I checked them to the nice north to south bearing of the Front Range. My bearing from Site G to Creation Rock was 313 degrees and, since I was east of the summit, that made sense. The north to south line is 360 degrees and everything to the west would be less than that. Sighting back to Site H, I found a bearing of 72 degrees. Since it was east of the north - south line, it should have been between 0 degrees and 90 degrees, and it was. I could add the difference between the bearing to Creation Rock and the north - south line (47 degrees) to the 72 degrees west to find the angle G, which was 119 degrees.

The bearing from the fire plug to Creation Rock was 257 degrees and the bearing back to Site G was 290 degrees - both were west of the north - south line, so those made sense and I could subtract them to find angle H, which was 33 degrees. That felt right. The angle of inclination from G to the summit of Creation Rock is 16 degrees and that from H to the top is 15 degrees, so I had the distance of the base of my triangle (side e) and the angles G and H, and the angles of inclination. That was what I needed. Here's my trigonometric plan diagram again.



The problem was that I had no idea what the elevation difference was between me and the base of Creation Rock. I was going to calculate the height of Creation Rock above me, not above its base. I didn't expect to be close. Well, I went with it and started back down Trading Post Trail to Morrison.

                                                     (From Red Rocks to the south]

On the way, I saw this patch of prickly poppies. That was the first western wildflower to confuse me after moving from Alabama. It looks like a thistle until it blooms and, then, that's certainly not a thistle bloom.



                                                                 [Prickly poppies]

And there was this paintbrush flower.

                                                                [Paintbrush plant]

And this rose.

                                                                             [Rose]

I didn't know that roses grew wild in Colorado.

Back on the road, I saw these huge sweet pea plants and milkweeds


                                                                    [Sweet peas]

                                                                    [Milkweeds]

I've mentioned that milkweed is one of my favorite wildflowers. I think that it grows over most of North America. I would occasionally see it in the South but it seems to like cooler climates. The further north I would travel, the more milkweed I would see.

We had a few stalks trying to grow in our back yard but one of the recent storms took them out. I was a little disappointed, there was a big flower head developing on one of them, and they are the only plant that Monarch butterflies will lay their eggs on, but then I saw all these plants in Morrison and felt better about it. I can enjoy other people's milkweed.

After a milkshake at the Mill Street Eats, I headed down Bear Creek Trail. It's been awhile and, after all, this is the Bear Creek Commentaries. I felt the need to reconnect. I also wanted to get a shot of Red Rocks Amphitheater from Mount Carbon to put it in perspective.

                                                                [Mount Carbon]

I found Bear Creek Lakes Park just as I left it, a blazing expanse of open space. By the time I reached the top, I was ready for a snack, water, and a long rest.

                                                       [Denver from Mount Carbon]

Here's Red Rocks with a magnification of X2. It may not seem so big but compare it with the prominence of Mount Morrison behind it (741 feet) and consider that this photo was taken from 3.9 miles away.

                                                       [Red Rocks from Mount Carbon]

My preferred route up or down the eastern flank of Mount Carbon is the Mount Carbon Loop Trail, which has great views of Denver and Bear Creek Valley. It also has a diversity of wildflowers such as this prickly pear cactus, certainly not a rare plant, but, like all cactuses, has an intricate, silky, showy blossom.


                                                               [Prickly Pear Cactus]
By the time I walked around the Fox Hollow Golf Course and reconnected with Bear Creek, I was whipped and spent some time on the shoulder of the trail. I would have used the bench across from me but Colorado, evidently, does not believe in shade and most park benches are situated to catch full sun. (what is that?)

Still, it allowed me to catch this bug's eye view of the grasses that line the trail.

                                                                       [Grasses]

I made it to Wadsworth Boulevard and chugged down two cans of Arizona Green Tea before calling a Lyft taxi to return home.

Now....the calculations.

Here's the geometry again.

 I know that angle G is 119 degrees, angle H is 33 degrees, and the length of side e is 257 feet. Angle E is easy because the sum of the angles in any triangle add to 180 degrees, so 180-(119+33)=28 degrees. That makes sense. Angle E is the angle between the two sites as seen from the top of Creation Rock. They are only separated by 257 feet so the angle of separation should be sorta small.

Since I have all three angles in the triangle EGH and the length of the base side, I can now use the law of sines to figure out the other two sides.

                                                                      [Law of Sines]

The length of side g, the distance from site H up to the top of Creation Rock, works out to be about 479 feet. The length of side h is about 298 feet.

Now, the diagram is a little misleading here. The point F looks like it's on the line GH, but it's not - it's way back behind the line. It is the point directly beneath the summit of Creation Rock. I calculate the length of line EF by either looking at the right triangle EGF or the right triangle EHF, and I will do both because the difference I come up with is important.

Right triangles are easy. In this case, I have the long side, the hypotenuse of the triangles (sides g and h) and the angles of inclination at G and H, and I want the length of the opposite sides. That's actually the measures that I want because it's the height of Creation Rock from the summit down to the level of my surveying sites. In other words, if I find the sine of one of the angles of inclination from the site up to the top of Creation Rock and multiply that by the distance from the site to the top, I'll have the height. I use my spreadsheet to calculate the sines and I come up with 82 feet (from site G) and 124 feet (from site H).

These results are certainly far short of the actual height of Creation Rock, but do they make sense?

Well, the difference between the two calculated heights is 42 feet. That's the difference in altitude between Site G and Site H. To walk from the Trading Post to the fire plug at site H, I had to walk slightly down the hill, then to walk to site G I had to walk around and above the tall Trading Post building. I could look down onto the roof. 42 feet works.

Also, I pulled a topographical map from the Internet site:

https://www.topozone.com/colorado/jefferson-co/locale/red-rocks-amphitheater

The contours are 40 feet elevation apart.The contour on level with the Trading Post seems to be about 3 contours above the base of Creation Rock, so that would explain the discrepancy between my measurements and the reported 300 foot height of Creation Rock. It looks like site G was about 3 contours, or 120 feet above the base. Even with that, I was off, so, no cigar.

Most likely, distance e was my most inaccurate measurement. The compass bearings seemed to agree well with the line described by the mountains.

But it was a fun and scenic adventure, so I'm happy.

The methods I used have served me well in the past. This trip was plagued by several unexpected problems - difficulty in finding two good sites being a major one. You may be able to use trigonometry in your own projects. One suggestion is to avoid angles that are too steep (within between 70 and 110 degrees) or too flat (between 340 and 20 degrees.) At these angles, a tiny difference in slant can make a huge difference in the value of a trigonometric function, or vice versa, so that can throw your precision off considerably.

There are a lot (!) of resources on the Internet about trigonometric functions and surveying methods. I can recommend CK12's Trigonometry textbook, 2nd edition by Lori Jordan, Larry Ottman, Brenda Meery, Art Fortgang, Andrea Hayes, and Mara Landers  and you may want to look at their other offerings at:

https://www.ck12.org/student

By the way, according to the topographic map, Creation Rock is either 280 feet or 400 feet tall according to where you consider the base to be.

Wednesday, July 10, 2019


--- How big is Creation Rock 1 ---

                                                    [Creation Rock from Morrison]

Surveying Creation Rock at Red Rocks....this adventure requires some planning.

I'll be using a surveyor's compass, a relatively primitive piece of equipment, a 100 foot length of cord (which I have to measure out before I go), and some surveyor flags and stakes.... and trigonometry.

I've done this kind of surveying before. In Alabama, I conceived the notion of determining the heights of waterfalls in Alabama, and did survey a couple before I realized that the number of waterfalls in Alabama would require several lifetimes. The northernmost is on the Tennessee border and the most southern is just about 20 miles north of Mobile in Mount Vernon.

One that I did survey was Falling Rock Falls near Montevallo. I hiked there with a friend, Dr. Gregory Reece, author of several books including Elvis Religion, UFO Religion, Weird Science, and Creatures of the Night. His family and a friend went with us.



                                                                [Falling Rock Falls]

This waterfall is notorious due to the number of people who have fallen from it. It's close to 90 feet tall (I calculated it to be 87 feet). The name says it all. The lip is unstable and rocks come lose from it frequently. If a person is standing on the rock....well....

So you shouldn't try to just drop a line over the edge to measure the height (although it is a popular rappelling area). I played it safe and used surveying techniques to measure the height from the bottom. In fact, I used the same surveyor's compass I plan to use at Red Rocks.

At Falling Rock, the trick was not difficult. Water falls straight down, so I had a vertical distance to measure that made a right angle with the ground. Right triangles are easy with trigonometry.

The surveyor's compass includes an inclinometer that let me measure an angle of incline from where I stood near the base of the falls up to the top. Other than the right triangle between the water and the ground, that gave me one of the other angles I needed (labeled alpha in the following diagram).

                                             [Trigonometry of Falling Rock Falls]

I needed at least one length of a leg of the triangle to figure out the rest of the triangle. The distance from me to the water would have been nice, but I would have gotten very wet trying to measure that. I could use another triangle. I struck off a line at 90 degrees from the line to the waterfall and measured 20 feet. From the end of that line, I measured the angle back to the waterfall (call that angle beta).

Now, I had all I needed.

A trigonometric function is constant for a particular angle. No matter the size of a triangle, the sine of a given angle will always be the same. The sine of a 30 degree angle, regardless of what the two sides are, is 0.5.

The longest of the sides of a right triangle is called it's hypotenuse. The other side connected to the angle is called the adjacent angle. The side opposite the angle is called the opposite side (duh!).

So, the sine of an angle is the ratio of the opposite side length to the length of the hypotenuse. I would be using another trigonometric function called the tangent, which is the ratio of the length of the opposite side to the length of the adjacent side.

I've lost my original data, but I think you can see that, having the 20 feet between my two survey points (the adjacent side) and the angle beta, I could figure out my distance from the waterfall (the opposite side). Then, knowing the distance from the waterfall and the angle of inclination, I could use the tangent again to figure out the height of the waterfall.

The point is that I can't do that with Creation Rock. I can't sight any vertical to the summit. If water was falling straight down from there, I could sight to the bottom of the waterfall but Creation Rock is dry as....well, rock.

So, what am I to do?

There is a technique used by weather watchers to determine the height of clouds (again, no vertical line to the cloud is available) that uses some of the more advanced formulas of trigonometry. A point on the cloud has to be sighted by two surveyors at the same time (clouds move). You don't have to have a right triangle to use the law of cosines and the law of sines. They apply to any triangle.

So, if I could make a sighting from one point and a point 100 feet away (the base of the triangle I'm forming is 100 feet long), then I would have two angles and the side between - enough to figure out the other angles and sides of the triangle. Here's a diagram.

                                                          [Surveying Creation Rock]

Angle G is the angle of EGH. Angle H is the angle EHG. I know the length of the base of the triangle, side e. I should be able to determine the angle E because the sum of all the angles in a triangle is 180 degrees. Knowing all the angles and one side, I can easily determine the length h or g. The law of sines states that:

                                                                  [Law of sines]

I know G, e, and E, so I can figure out the distance from my first sight to the summit, but that's not the vertical distance from the summit to the ground, so I have more work to do. If I measure the angle of inclination from the first sight up to the summit, I will have a right triangle - in the diagram, GEF (F is the point directly under the summit). I know h, the length of the hypotenuse of the right triangle,  the length of the adjacent side to angle G, and the angle G. The sine of G is the length of the opposite side (the distance I want) over the hypotenuse (h). So, I can find the height of Creation Rock.

That's all pretty jumbled but I'll go through the calculations in How Big is Creation Rock 2 and it should make more sense.

So, I will need to measure the angle of inclination at one point (G), the angle from the summit to that point to a point 100 feet away, and the angle from the summit to the second point back to the first point.

The surveyors that determine property lines, areas of lots, paths for roadways and power lines use an array of complicated equipment but, essentially, they measure angles and distances and they use trigonometry to figure out everything else. The tools they use are just elaborations on the compass, which measures angles in respect to the earth's magnetic field, and a cord stretched between two stakes. The elaborations improve the convenience of the tools in the field and their precision.

Here is my compass, a Konustar surveyor's compass that I got for less than thirty dollars.



                                                                    [My compass]

The compass would be recognized by any Boy Scout as the navigation tool that aligns itself with the earth's magnetic field to point toward the magnetic north and south poles. The dials around the compass mark off the 360 degrees of the circle. The reticle and sights help to line up land features and surveying markers with the compass.

This compass has an added bubble level to indicate when it's....well, level, and an inclinometer which can measure angles of sight upward or downward. The inclinometer is just a little pendulum that drops straight down to show the direction to the center of the earth. The scale, then measures the tilt of the pendulum to the vertical.

The eyepiece is a cool addition. It focuses on the edge of the compass disk, which is graduated from 0 to 360 degrees, 0 degrees indicating a north bearing. That means that, once I get a sighting, I can drop my eye a little to get it's bearing in relation to north. Here's what it looks like.

                                                   [What I see in the compass eyepiece]

For a right triangle, all I need is one angle (other than the 90 degree angle) and one side length to figure out the lengths of all the other sides and the measure of the other angle. For all other triangles, I just need two angles and a side. That's the core of surveying. How do I measure distance at Red Rocks?

I have a 100 foot length of cord.

I placed two stakes in my yard 20 yards across (as measured by a tape measure) and wrapped the cord five times around it.

I suspect that my calculated height of Creation Rock will be somewhat off the known height because real surveyors figured that out using much more precise equipment than what I will use. There are several places where imprecision enters my measurements and calculations. Can you see some of them?

Surveying is the way of measuring inaccessible measurements such as widths of rivers or the distance between the rims of a canyon, heights, or outlines of a plot of land that is longer than a tape measure. Even though the surveyor's compass and tape measure are not nearly as precise as the tools that a professional surveyor uses, they are precise enough for many uses. You might want to buy a set and play around with them. Neither the compass or tape are expensive.


Monday, July 1, 2019


--- Terminus: Wheat Ridge ---

I'm not going to recommend the Wheat Ridge/Ward Road Station for tourism. The G Line that services the station is rather unspectacular with the exception of the Arvada Olde Town Station that looks like a nice place for shoppers that like quaint little villages. It has that feel. But my target was the terminus in northwestern Wheat Ridge, the only RTD light rail station in Wheat Ridge.

The G Line runs through a corridor of industrial zones and the Wheat Ridge/Ward Station is no different. It is surrounded by industry, but it does have some interesting points.

The station itself has parking for 290 cars and is a clean, attractive site. It isn't far from the foothills of the Rockies and especially offers some nice views of North Table Mountain. I was tempted to hike on over to the mountain but I'm not as familiar with that area as I am some parts of the Denver Metro area and I might have been disappointed by the real distance (as contrasted with the apparent distance) and lack of access to the mountain. Anyway, I am planning to visit the mountain in a couple of years when I look at the geology of the area.





                          [Photos of Wheat Ridge/Ward Station and the Rocky Mountains beyond]

One thing that I like about Colorado is the variety of showy wildflowers here. In the Southeast, most of the nice indigenous plants were woodland flowers and one had to do some hiking to see them. Here, any vacant lot may be a home to some pretty plants. One common plant with showy flowers is the thistle. Colorado has 15 native species and 5 non-native species, loved by bees and butterflies, browsing wildlife and wildflower enthusiasts. The one I found in the grassy burm of the light rail station is (I think) a nodding thistle (or musk thistle), considered a non-native, noxious weed.


                                                                     [Thistle]

As much as Denver is associated with the mountains, it's still a plains city and the great variety of grassland grasses are represented here. This foxtail barley is pretty common in the area. We have lots of it in our back yard.

                                                                  [Foxtail barley]

The stations of the RTD are micro-museums. Many of them display narratives of their neighborhoods. At Wheat Ridge/Ward Road you can read about the relationship between Denver and the mountains....and gold. G, in the G Line stands for "gold". The windscreens at the stations on the G Line tells the story of gold.

The artwork at Wheat Ridge/Ward Station is a modernist sculpture called "Anchored by Place". It was created by artist and art educator Michael Clapper.

                                                                [Anchored by Place]

You can read a lot about the stations of the RTD light rail, their art, including the windscreens, and stories connected to the stations and their neighborhoods at the FastTrack website, http://www.rtd-fastracks.com/main_1 .

If you follow me in my adventures and want to check out any of these places, you can prepare by going to the FasTrack site.

After wandering around the station, I walked down to Ward Road and a convenience store where I picked up a snack and then returned to wait for a train for my trip back home.

Along the way, I noticed this clump of a favorite wildflower, milk weed. Despite it's name, it's a gorgeous flower. Monarch butterflies will only lay their eggs on this plant. Check out the Fish and Wildlife website (https://medium.com/usfws/spreading-milkweed-not-myths-5df8c480912d ) to clear up misconceptions about this valuable plant.
                                                                        [Milkweed]

Ward Road has some nice views of North Table Mountain. The two Table Mountains are the exposed innards of an ancient but dead volcano. Their volcanic origin is made quite clear by the basalt deposits around the crown. Basalt is a dark, fine grain rock that is formed close to the earth's surface. It hardens too quickly for the melted magma to form large crystals like granite. These unearthed bones of dead volcanoes are sometimes called "fossil volcanoes". Luckily, they're as volcanic as the Denver area gets.


                                                            [North Table Mountain]

Regardless of how boring any area looks, if you look a little closer, you can usually find fascinating facts right in front of you.