Cardinal Peak Theodolite Survey

Cardinal Peak Theodolite Survey

June 22, 2023

22 miles (14 mtn biking, 8 hiking)

Results summary: South summit 7 inches taller than middle summit. South summit is true summit

I’ve recently started working on a project to accurately determine the true hundred highest peaks in Washington. There exist a handful of peaks that have yet to be surveyed accurately enough to determine yet if they make the list. Several peaks that are on the list have multiple summits and it is not known which is the true summit.

Last fall I discovered and surveyed that East Fury, previously unsurveyed, is in fact tall enough to qualify for the list. I also surveyed to determine that the SW summit of Buckner is the true highpoint and the NE summit is shorter, and the middle summit of Buck is the true summit, not the north peak. This June I discovered and surveyed that Big Kangaroo, previously unsurveyed, is tall enough to qualify for the list.

My main tool for making these measurements is a mechanical theodolite. This can measure angles with 20 arcsecond resolution, and is the tool used by the original surveyors. If I know inclination and declination angles and horizontal distances (ie from Google Earth) I can use trigonometry to calculate relative heights. This can determine which of two peaks is taller, and I can calculate height relative to a previously-surveyed location to determine absolute height.

I have a handful more peaks to measure that are close contenders for top 100 status but just need surveyed. The next one on my list was Cardinal Peak. Cardinal is tall enough and prominenent enough to be a top 100 peak, but it has multiple summits. The middle summit has been surveyed at 8,590ft according to the Pyramid Mountain O48120a5 1:24,000 quad. But the south summit, 480ft to the south, has never been accurately surveyed. By eye they appear to be of similar height. But the highest of these two points is the true summit, and thus the point climbers must reach if climbing the hundred highest peaks in Washington.

Traditionally most climbers just climb the middle summit. This is the surveyed point on the quad. But surveyed points are not necessarily the true summits. I discovered this on Buck Mountain and Buckner Mountain, both of which I surveyed. In each case the surveyed point on the quad is not the true summit. This is probably because a good point to survey is one that is visible from other surveyed points and/or one that it is easy to mount a theodolite on. A slightly taller point that is not easily visible from other surveyed locations and is tricky to mount a theodolite on would not necessarily be the surveyed point, even if it is the true summit.

On Cardinal the middle summit is much easier to mount a theodolite on and take measurements from. While the middle summit is broad and easily accessible by 3rd class scrambling, the south summit is a sharp rock spire requiring a short pitch of 5th class climbing to access.

As far as I’d researched, the only measurement taken of the south summit was by Don Duncan, who used a hand level to determine the south summit was slightly shorter. I don’t know any details about the measurement, but if I assume it was a 1x magnification hand level, then in my experience, at a distance of 480ft a height difference must be at least 1ft to be detectable with this device. If the height difference was less than 1 ft I don’t think a 1x hand level is accurate enough to measure that at that distance.

In the past few years several climbers have reported the GPS apps on their phones showing the south summit higher. Phones GPS units can have errors of 50ft or more vertical, so unfortunately these measurements are also not accurate enough to determine the true highpoint.

The Beckey guidebook says “The summit formation consists of three significant rock points: the wedge-shaped middle one is highest by a slight margin; 400ft SW is the jagged S summit, which may be equally high.” That sounds to me like it is unclear which is taller.

The area is covered by Lidar, the East Cascades North 2020 survey. I loaded the raw point cloud data in QGIS and found the highest measured points for each summit. This showed the south summit 8,595.9ft and the middle summit 8,595.8ft. Relative height is what matters in this case, though. So the south summit was measured as 0.1ft, or 1 inch, taller than the middle. That’s really close! The measured points near the summits were 0.5ft-3ft apart, meaning locations between these points were not measured. My friend who is a Lidar expert says as a rule of thumb each point can have measured vertical errors up to 2-4 inches. So even if the points hit the exact summits it would be too close to tell which point was highest.

But there’s also error in the unknown heights between points. The middle summit is broad, so it’s more likely the true summit was sampled. The south summit is sharp, so it’s more likely the true summit was not sampled, just a shorter point near the top. That means it’s more likely the south summit elevation is a slight underestimate. So my conclusion from the Lidar measurements was it’s too close to call, but likely the south summit is a little bit taller. But probably at most a foot or two, depending on how sharp the south summit was and where the points hit.

This led me to conclude that a more accurate survey was needed to definitely determine the true highpoint. My theodolite was accurate enough for such a survey. There are multiple ways to conduct such a survey, and I believe the most accurate I’ve found in a situation like this requires two people.

One person stands on one peak holding a meter stick vertically. The other stands on the second peak with the theodolite. The theodolite is set to be perfectly horizontal and pointed at the meter stick. By measuring where the cross hairs of the scope intersect the meter stick, and the height of the scope above the summit of the first peak, the height difference can be calculated. If the peaks are far away the two surveyors can communicate with radios. This is how I surveyed Buckner Mountain and how I intended to survey Cardinal. This situation was a bit more complicated since one of the peaks was technical.

Nick was free to join, and our plan was to mountain bike as far up the trail as possible to save time. It would be a cyclo-surv trip. Kind of like a biathalon requiring an athletic component and an accuracy/skill component.

I’d previously climbed Cardinal in 6.5 hours round trip by mountain biking up the entire trail section of the approach, about 9 miles. The trail is outside of wilderness, so biking is allowed. And this trail is well graded and frequently cleared by trail crews, so biking saves a lot of time. I’d also previously climbed Cardinal in winter (Feb 2020), though only the middle summit. So I was kind of hoping the middle was tallest so I wouldn’t have to go back in there again in winter for a true winter ascent of Cardinal.

Seeing 480ft between summits requires they not be obscured by clouds, and it looked like Thursday would be reasonable weather. It was supposed to be socked in in the morning, but gradually clearing, with only small chances of rain. Wednesday night we drove to the north fork entiat trailhead for the night. We were up and moving shortly after sunrise Thursday. We were loaded with 50lbs of surveying gear and a rope and rock rack. It was great to be able to split this among two people.

The trailhead register said the trail crew had gone through in early June, so we were optimistic about bikeability. But the trail goes through a recent burn zone, so stags fall pretty often. Indeed, there were about a dozen trees across the trail in the first three miles, but it still made sense to bike. After we cleared the burn zone it was mostly smooth sailing. We made good time until about mile 7, when we hit patchy snow. The drifts were too deep to bike through. Also we were within 0.5 miles of the start of the steep section, where I find the bike doesn’t necessarily save time.

So we ditched the bikes there and continued on foot. The snow patches soon cleared on the steep section. Then we turned left at the next intersection and encountered a few more patches. We soon left the trail and buwhacked up towards Cardinal. The woods were nice and open and progress was fast. We soon reached the edge of treeline and continued up on talus and patchy snow. Most of the snow was avoidable, but we needed to kick steps up a few sections.

Halfway up we saw the summit was still socked in the clouds, so we decided to rest there to give it time to clear. That would be more comfortable than resting on a cold and potentially windy summit. After a half hour we saw signs of clearing and continued up. We reached the saddle and saw clear skies to the northeast over Lake Chelan. The weather was interestingly coming from the northeast that day, so looked to be improving.

We scrambled up the north ridge, and then I decided to ditch my whippet. It seemed unlikely we’d need to cross any more snowfields. But, of course, 5 minutes up the ridge we encountered a mandatory steep exposed snowfield crossing on the east face. I went back down, got my whippet, and returned. I think I have a near-perfect track record of regretting ditching my ice ax on mountains.

We took advantage of fresh-looking tracks in the snow, likely by Kyle Fletcher from June 17. We managed across without putting on crampons, then made the final scramble to the summit.

I quickly laid down and whipped out my 5x sight level to get a preliminary sighting in case we got socked in the rest of the day. I mounted it on the highest piece of rock on the middle peak and sighted the highest visible rock on the south peak. It looked pretty clear that the south was a little higher, though I didn’t have the accuracy to measure how much higher.

Nick took the meter stick and a radio and headed over while I then mounted the theodolite and worked on leveling it. Nick had already previously climbed the south summit and was comfortable soloing the short 5.6 bit to get to the top. That would save a lot of time if I didn’t have to go over to belay then return to take a measurement.

I got the theodolite mounted exactly above the highest rock, as verified with my plum bob. I measured the height of the scope above the highest rock and recorded my measurements on paper. The highest rock was not attached to the mountain, so I also measured the vertical distance between the highest solid part of the mountain and the top of that rock. Nick soon radioed that he’d reached the summit. He held the meter stick vertically on top of the highest existing rock. I then tilted the scope so it was perfectly horizontal, with 0 degrees on both C and D dials. I then pointed it at the meter stick.

With my 30x magnification I could almost read the numbers but not quite. So I had Nick move his finger up until it lined up with the cross hairs. I then radioed him to stop and he read out the measurement. I would say this was accurate to +/-1/2 inch. I then rotated the theodolite 180 degrees horiztontally and flipped the scope over. I then tuned the scope back to 0 degrees and repeated the measurement. This is to account for slight leveling errors in the base of the theodolite. The final measurement is the average of these two.

If I take the difference between the scope’s height above the middle summit and the measured height that the cross hairs hit the meter stick that gives me the difference in height between the two summits. In theory this measurement should be sufficient to determine the height difference. But I’m always more confident in a result if multiple different measurements agree. In a situation like this the best second measurement is to repeat the whole process but Nick and I switch peaks. Thus I should bring the theodolite to the south summit, Nick stands with the meter stick on the middle summit, and we repeat. This creates what surveyors call a level loop.

Ideally the height differnece measurements agree. With the two measurements I can calculate closure error, and this gives an idea of the accuracy of the measurements. The problem here is that the south summit is 5th class and very small on top. That’s not great for hauling up 50 lbs of survey gear and setting up a tripod. But we thought it was important to get trustworthy results we could be confident in. So we planned to get that second measurement.

It would take too much time for both of us to be at the south summit doing traditional belayed climbing. So Nick just rapped down, left the rope there, and returned to the middle summit while I packed up and headed over to the south summit.

I needed to use the whippet on a few steep snow traverses, but otherwise it was third class to get to the base of the south summit. Nick had rappeled directly down from a rap anchor near the top. This was a steep aspect that was good for rappelling but trickier to climb than the 5.6 route up. I rigged up two prussiks and also a chest harness, just like climbing out of a crevasse. I didn’t want the big pack to flip me upside down. I started just climbing up the rock and shifting the prussik up as a safety backup. But when I got half way up I realized that was too sketchy to do with the huge pack and the tiny holds on the steep face. I was just in hiking boots so edging wasn’t great.

I downclimbed then tied the bottom of the rope to a rock to keep tension and continued up purely using the foot and waist prussiks. This was probably good refresher practice for crevasse self-rescue anyways. I eventually made it up, though getting over the lip was tough with the tensioned rope. I finally pulled myself over, then dropped the pack next to the anchor.

The summit area was small but luckily level enough and wide enough to mount the tripod. The top was a pile of rocks at the edge of the cliff, so I couldn’t mount the tripod exactly there. I had to mount it about 2ft back, but it was a stable location. I used my sight level and laser range-finder to measure the height of the scope above the rock pile, and also the height of the rock pile above the highest solid rock. I then leveled the theodolite, then pointed the scope to the middle summit and tuned it until it was perfectly horizontal.

I then radioed Nick I was ready. He held the meter stick on top of the highest rock on the middle summit, while I pointed the scope to it. He moved his finger until I told him to stop that it was level with the cross hairs, and he radioed me the measurement. As I was writing that measurement down a cloud rolled through and we lost visibility between peaks. Then it started hailing. The hail was small, but it was getting my paper wet and I was worried we’d have to quit without our last measurement.

We waited it out and after 20 minutes it let up and visibility improved. I radioed back to Nick and he got back to the summit. I rotated the horizontal dial, flipped the scope, and repeated to get the final measurement. I then wrote everything down and packed up.

I carefully rapped down the face, pulled the rope, and packed up. I then scrambled back to the middle summit and we redistruted gear and took a short food break. I had been slow with the measurements and we had been up there for several hours total. But I I felt confident that by being slow and careful I had trustworthy measurements in each direction.

We soon headed back down. After a steep snow traverse we scrambled back to the saddle, then scree surfed and boot glissaded back to the trees. The bushwhack and trail hike were quick, and we soon returned to the bikes. It was fun and fast mountain biking back down the trail, with only occasional delays to get over blowdowns. By 7:30pm we got back to the truck, and made it back to Seattle that night.

At home I analyzed the measurements. The first measurement (looking from middle to south) had the south summit 8.25 inches taller, and the second measurement (looking from south to middle) had the south summit 8.375 inches taller. So the measurements were consistent, and the average was the south summit is 8.3125 inches taller. I’d round that to 8 inches taller. The closure error is the difference between these, which is 0.125 inches. The rule of thumb is closure error should be less than level loop distance divided by 5000. In this case that is 2*480ft*12in/ft/5000 = 2.3 inches. So the closure error is within acceptable bounds.

This was using the heights to the highest existing rock on each summit. The highest existing rock on the south summit was a 2ft x 2ft x 3ft block that was not attached to the main bedrock. The highest rock on the middle summit was of similar size and also not attached to the main bedrock. In either case it was not really certain if those rocks were moved there by a person to be part of a cairn, or if they were natural.

If I subtract off the height of the loose rock I can find the height difference between the highest piece of non-loose rock that was definitely not moved by a human. After doing this I found the south summit is 7 inches taller than the middle summit.

Either way, comparing highest loose rock to highest loose rock or highest solid rock to highest solid rock, the south summit is taller. Loose rocks of that size could easily be moved by climbers in the future, so I would be most comfortable reporting the final result as the height difference between highest solid rocks. This result is that the south summit is 7 in taller than the middle summit, and thus the south summit is the true summit.

Here is a link to my raw measurements: https://docs.google.com/spreadsheets/d/1J6eLQ7d1l7UZB5_5TyKZF2fQF16XwzGR4WnhyXHCaeA/edit#gid=0

This brings up an interesting question for the Bulger list. Cardinal Peak is the peak on the Bulger list, and I would assume this means the true summit of Cardinal Peak is the one that needs to be climbed to claim climbing the Bulger peak. Some climbers go by a rule that if their head is above the summit height then they count it as climbed. That doesn’t seem too fair in this case, though, since that would mean you could skip out on the technical crux of the mountain and still claim an ascent. I always say I need to touch the true summit to claim the peak.

I’ll leave it to the official Bulger authorities to determine if the true summit needs to be climbed or if climbing the middle summit is acceptable in this case. Perhaps past ascents of the middle summit get grandfathered in but future ascents must go to the true summit.

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