Introduction

When BBC Earth published their Presenter Search video, I set out to apply. And I wanted to do it right.

I did not need to think about what “fact” I wanted to present: I wanted to do the mass of something big.

Mount Timpanogos (“Timp”) is an imposing sight on the Northeast end of Utah Valley, and since it is more well-known than the only other mountain in the Wasatch Range that is taller (Mount Nebo), I chose it as my target.

However, I was not happy with just using Timp; after all, this was BBC Earth I was going to apply to. I decided to go even bigger: the entire Earth. But I decided that I could use Timp as a sort of yardstick (meterstick?) to give my viewers some idea of how big the Earth really is.

Script

The first step was writing a script. Since I did not know the mass of Timp yet, I had to use blank lines as placeholders. And while writing, I felt that I could not talk about a mountain without talking about its height, which is why I added the section about height and the horizon.

Estimating Mass

Next was the hard part: estimating the mass.

I know from high school physics that density = mass / volume. From the Wikipedia article on Timp, I knew what it was made of (mainly limestone and dolomite), and I knew the density of both from searching on the Internet.

So I just needed volume.

Area

Because mountains do not have really clear boundaries, I first needed to figure out what I area I would include in my estimation. I decided to include the area bounded by State Highway 189, State Highway 92 (Alpine Loop), and the boundary of developed land on the front (southwest) of the mountain. I also decided to calculate the height and volume based on the elevation of Provo, since that is technically the city that touches the mountain where State Highway 189 goes into Provo Canyon.

The area is outlined in red in the image below.

The area I included in my analysis of Timp.

This area meant that I was estimating a weight for what was technically more than one mountain, but personally, I have always felt that Timp was not just one mountain, but it included all of the area I mentioned. And I wrote this post, so I am being honest about my process.

Estimating Volume

It took me several attempts to find a way to estimate the volume, but in the end, I found this video.

3D Modeling

I downloaded Sketchup Pro, and using the free 30 day trial, I began importing all of the terrain data in, one square kilometer at a time (it took about an hour). Then I exported the data into a .obj file and imported it into Blender, my 3D application of choice.

From there, I joined all of the terrain data together into one model. However, it was not a manifold mesh, which was required to calculate volume, so I needed to make it so.

I eventually created a plane with over 4 million vertices (for good resolution), and used Blender's Shrinkwrap Modifier to get my plane to match the terrain data. I used the “Project” mode, along the Z axis (which is vertical in Blender), and in both the negative and positive direction. I also had to set the limit at 25 because after scaling the terrain data down to a usable size, Blender thought that Timp was 22 units tall, and I gave it a bit extra, just in case.

From there, I had to cut off all of the cruft around the edges, which took close to two hours. Then I extruded every vertex downward and scaled all of the new vertices to 0 in the Z axis only. In Blender, this has the effect of making all of the vertices flat (compared to each other), which gave the mountain model a flat bottom.

Then I cleaned up the model and made sure that its volume could be calculated.

Calculating the Volume

(For those of you who would like to check my work, unfortunately, I cannot upload the model because it was over 300 MB. However, all data from the model that I will report is exactly as Blender gave it to me. Also, I used this arbitrary precision calculator, set to calculate up to 50 decimal places, to run the math.)

Next was figuring out how much I had scaled the model down. I used Google Earth to calculate the distance between Timp's summit and the peak of Robert's Horn. That is shown below.

How I calculated the distance between the peaks.

The true distance is 122,603.69 cm, and the distance in the model was 4688.41 cm, which meant that the model was 1:26.150377 size.

Blender's 3D printing addon calculated the volume to be 7,620,186,500,000 cm^3. Converting that to m^3 yielded 7,620,186.5 m^3. Then multiplying by 26.150377^3, I got 136,269,754,597.1518 m^3 as my volume estimate.

Calculating Mass

I got the density of dolomite from Google. Converting 2.71 g/cm^3 to kg/m^3 gave 2710 kg/m^3.

I also found the density of limestone. I chose to use medium density as my base (since I do not know the density of Timp's limestone), and to use the middle of the medium density. The average of the min (2160 kg/m^3) and max (2560 kg/m^3) of medium density limestone was 2360 kg/m^3.

From there, I just assumed a 50/50 split between the two, yielding an average density of 2535 kg/m^3.

Then, multiplying that by the volume, I got 345,443,827,903,780 kg, which I shortened to 350 trillion in the video.

Hike

From the start, I had known that I would hike Timp and film from the top. And it almost happened.

First off, I made sure that I was prepared. I took cold weather clothing, as well as food and five liters of water. I also took a basic first aid kit and an extra pair of socks. I also had told my wife where I was going to be, and I told her to call the police and report me missing if I did not come home by a certain time.

When hiking alone, always make sure someone knows where you are.

I set out at 08:00 in the morning of the 16th of June. And early in the hike, I had enough energy to take pictures.

The first waterfall I came across.

The first waterfall I came across from a little higher.

Looking up into the area where Emerald Lake is.

Looking up at Robert's Horn.

One of my favorite waterfalls on the hike.

Selfie with one of my favority waterfalls on the hike.

Interesting vegetation.

By the time I reach Emerald Lake and the nearby shelter, I did not have much energy.

I ate my second lunch there, at about 13:00.

By this time, I had forded several streams (really just two streams several times), which I had not been warned about, even though I had done my research on the hike beforehand. My shoes were a little wet, but I was okay. But it would only get worse.

Shortly after I left the shelter, I ran into snow. I was not prepared for walking along a steep slope that was also slippery. It took me a good hour to go another mile.

It was around when I was 2.5 kilometers away from the summit, and about 1.5 kilometers from the top of the ridge that I looked back and saw a great view of the peak. At the time, I had gradually been going slower. I could tell that I was suffering from the onset of hypoxia, which explains my (almost) brain dead performance on the video.

Also, I had been told by other hikers that the wind at the top of the ridge was terrible, and it was calm where I was standing, which was important for getting good sound on a smartphone.

For my own health, I decided to not go to the summit, but instead to film right where I was and go back down.

In retrospect, the only thing I could have done better was to turn back earlier than I did.

I called my wife to update her on where I was, how I was doing, and what I was planning. Then I filmed, which took me several takes, mostly because the sun kept coming out from behind clouds, which made me squint, since the sun is brighter at 3200 meters elevation.

I finally got a take that I was satisfied with. It wasn't as good as I wanted; however, I was tired, and I knew that I had to get down.

I took another hour to make it back to the shelter, and each step on the snow was dangerous; I was in constant danger of making a mistake and sliding off the edge.

Also, while I was traversing the snow, something happened that made my situation a small crisis: I could no longer drink the water, nor eat the food, that I had brought. (Don't ask; it was not pretty.) I was five and a half hours from the end of the hike, and I was now without supplies, even though I had brought five liters of water and plenty of food.

I did see something cool though. I was almost to the end of the snow when I saw a mountain goat and her kid drop down from the cliff onto the snow where I was heading. The kid frolicked as the mother looked for a way down from where they were. It was the first time I had ever seen mountain goats up close.

When I got back to the shelter, there was a rough-looking cowboy and four hikers. The hikers were all together, but the cowboy was there on his own. He had brought in pack horses (who were a mile away), and he was offering watermelon to any passing folks.

I was grateful; that watermelon was the only food and water I got on my entire trip down, and it was the reason I made it back in one piece. It was a reminder to me that God's angels are sometimes mortal and sometimes rough.

I chatted a bit, but I had to get down before my time ran out.

The hike down was long and arduous. I called my wife twice when I had signal to let her know where I was, in case something happened. And there were plenty of people on the trail who helped.

But in the end, I had to make the hike myself. It took me until 20:20 to get down, and when I did, I had no reserves left.

I managed to drive home, and once there, my wife took care of me. I showered, ate the food she provided, and she even gave me a fresh squeezed lemonade she had bought earlier that day from the Provo Farmers Market.

I was getting chills, so she took my temperature. I had a elevated body temperature, I had at least three blisters, and I could barely walk.

It was one of the hardest things I have ever done.

Epilogue

What was the purpose of this post?

Well, since I did my own estimate of Timp's weight, I had to document how I did the process, and I knew that I also wanted to document the hike.

I know that I did not make it sound great, but it wasn't. I feel strongly that the world is saturated with fake content, especially on social media, and I did not want to add to it.

But I made it, and I made a video that I can be proud of.