Estimated Energy to hike Rabbit East Ridge Loop

I stumbled on an article at Outside Online about an equation developed by the Army for estimating the energy expended while walking on level ground, uphill, and downhill.

The equation takes into account the mass of the walker, the gradient (G), the speed (S), and converts that to an hourly energy expenditure (EE) in watts/kg. Notably, it takes into account downhill or negative gradients. Downhill walking requires less energy up to a -10% grade, then it starts taking more energy as you have to spend energy to control your descent. The somewhat complex formula is:

EE = 1.44 + 1.94*S^0.43 + 0.24*S^4 + 0.34*S*G*(1-1.05^(1-1.11^(G+32)))

This was a unique loop going up the Rabbit East Ridge, then down the trail toward Villager, then descending a wild ridge with no trails over 3 benchmarks, back to Barton Canyon and the start. I used three segments, Start to Rabbit summit, summit to descent ridge (800' gain), descent ridge to start.

I carried an average of 174 oz of water on the way up, 78 oz on the way to the descent ridge, and 32 oz on the descent ridge. I ran out of water on the way down.

Gradients were calculated using (rise/run)*100 to get a percentage. Downhill uses a negative gradient.

I converted everything from English units to metric, then converted the metric result, (watts/kg * mass), into calories (kilo-calories).

Here was the data:

Segment 1 (Start to Summit)

Speed (meters/sec)	0.4768426667
Gradient	13.24968434
EE (watts/kg)	5.002098962
Mass (body weight + pack + water)	77.5076
Watts/kg/hour (burn rate)	333.3644344
Calories burned	3000

Segment 2 (Summit to Descent Ridge)

Speed (meters/sec)	0.89408
Gradient	15.15151515
EE (watts/kg/hour)	8.04202677
Mass (body weight + pack + water)	74.78604
Watts/hour (burn rate)	517.140734
Calories burned	517

Segment 3 (Descent Ridge to start)

Speed (meters/sec)	0.54395076
Gradient	-11.83712121
EE (watts/kg/hour)	2.305600338
Mass (body weight + pack + water)	73.481965
Watts/hour (burn rate)	145.6758242
Calories burned	1748

Total Calories expended: 5265

The giant loop we did over Rabbit was one of the most physicaly difficult hikes I've ever done. The east ridge and the descent ridge were cross country, easy for the most part, but required attention to avoid cactus and agave. The first few hours and last few hours were all done in the dark across Barton Canyon. The canyon was filled with 20' ruts, boulders, and brush. It looks flat on the topo, but really isn't. So far, the Rabbit loop has the energy expenditure record, but I have a few more hikes to calculate.

Estimated Energy to hike Iron Mountain #1

I stumbled on an article at Outside Online about an equation developed by the Army for estimating the energy expended while walking on level ground, uphill, and downhill.

The equation takes into account the mass of the walker, the gradient (G), the speed (S), and converts that to an hourly energy expenditure (EE) in watts/kg. Notably, it takes into account downhill or negative gradients. Downhill walking requires less energy up to a -10% grade, then it starts taking more energy as you have to spend energy to control your descent. The somewhat complex formula is:

EE = 1.44 + 1.94*S^0.43 + 0.24*S^4 + 0.34*S*G*(1-1.05^(1-1.11^(G+32)))

I decided to test the equation against a solid benchmark hike, Iron Mountain #1 in the San Gabriel Mountains.

I broke the hike into 4 segments. Heaton to Allison Saddle, Allison to summit, summit to Allison, and Allison to Heaton.

For mass, I started with my body mass, then added 15 pounds for base pack weight, then added water based on my hike from 2012 when I consumed 224 oz. I took the average water mass at the midpoint of each segment, assuming I drank steadily down to 0 oz at the end. So, the average water mass for the segments was based on 196 oz for segment 1, 140 oz for segment 2, 84 oz for segment 3, and 28 oz for segment 4. I ignored food.

I calculated the speed for each segment using GPS data from that hike, obviously much slower going up. The speed includes all breaks along the way and rest time at the top. Including rest time should net out to zero for total energy because it results in a lower average speed, and lower calculated burn rate which is added back by the extra time.

Gradients were calculated using (rise/run)*100 to get a percentage. Downhill uses a negative gradient.

I converted everything from English units to metric, then converted the metric result, (watts/kg * mass), into calories (kilo-calories).

Here was the data:

Segment 1 (Heaton to Allison Saddle)

Speed (meters/sec)	0.7663542857
Gradient	21.77906029
EE (watts/kg/hour)	8.927773714
Mass (body weight + pack + water)	85.04857
Watts/hour (burn rate)	759.2943876
Calories burned	1523

Segment 2 (Allison Saddle to Summit)

Speed (meters/sec)	0.3988972308
Gradient	22.19794828
EE (watts/kg/hour)	5.763360009
Mass (body weight + pack + water)	83.34478
Watts/hour (burn rate)	480.3459721
Calories burned	1342

Segment 3 (Summit to Allison Saddle)

Speed (meters/sec)	0.5439507692
Gradient	-22.19794828
EE (watts/kg/hour)	2.612379286
Mass (body weight + pack + water)	81.75478
Watts/hour (burn rate)	213.5744938
Calories burned	437

Segment 4 (Allison Saddle to Heaton)

Speed (meters/sec)	0.7502769231
Gradient	-21.77906029
EE (watts/kg/hour)	2.737320404
Mass (body weight + pack + water)	80.16478
Watts/hour (burn rate)	219.436688
Calories burned	449

Total Calories expended: 3751

It was counter-intuitive that I spent more calories getting to Allison Saddle, that from Allison to the summit. However, I was carrying more water at the start over a longer distance. It was objectively much harder to go from Allison to the summit, but it took more time over a shorter distance. Plus, it was warmer which is something the equation does not take into account. It took less than half the energy to descend each segment, which seemed right, though my speed coming down to Allison was not very fast due to the gradient. I was also tired coming down. The total calories burned appeared reasonable, though my data was somewhat crude (for example, I used averages for water while it was actually a continuous curve. I suspect the Army's formula is a good enough estimate of the energy required for a hike. I am looking forward to additional calculations on some of my other "black pin" hikes.

Chaparrosa Peak Loop

HPS Star Emblem Peak
Hiked: 12/3/2021
Distance: 7.7 miles round trip on trail
Summit Elevation: 5541'
Elevation Gain: 1462'
Elevation Gain (in Empire State Buildings): 1.1
Round trip time: 3 hours 10 minutes
Recommended water: 40 oz.
Parking/Fees: Free at Pioneertown Mountains Preserve
Difficulty: Easy

Chaparrosa Peak is north of Joshua Tree in a transition zone between desert and the San Bernardino foothills. I got a late start arriving mid-morning. There are two trails to the summit. I decided to go up Pipes Canyon, the longer trail. There was a stream of water in the canyon that nourished enough small trees to create a good bit of shade. After wandering upstream a couple of miles, I reached the Owens ruins. Information on the cabin ruins were sparse. The trail cuts back to climb a gully, then rollercoasters over several bumps before reaching the intersection with the summit spur trail. Everything was signed and well maintained so there was little chance of getting lost. I was ready to be unimpressed, but the summit revealed wonderful views of granite towers, cliffs, and red lava rock. The only break I took was on the summit. I tried to push my pace on the way down, completing the loop in just over 3 hours. I made it more of a training hike than one ticking off an HPS peak. There was one other car in the visitors parking lot, but I didn't see anyone all day.

Owens ruins

Approaching the low prominence summit

Giant San Jacinto in the background

This area looks a lot like the San Ysidro mountains in Anza-Borrego

Thorn Point

HPS Star Emblem Peak
Hiked: 11/19/2021
Distance: 7.3 miles round trip on trail
Summit Elevation: 6920'
Prominence: 560'
Elevation Gain: 2002'
Elevation Gain (in Empire State Buildings): 1.6
Round trip time: 4 hours
Recommended water: 64 oz.
Parking/Fees: Free at Thorn Meadows Campground
Difficulty: Moderate

I got up at 3 AM to prep for a long day of driving to Los Padres, pretty standard. I always curse the drive, but never end up regretting it. The target was Thorn Point (HPS #25), home to an abandoned look out tower in the heart of the forest. The start was at Thorn Meadows campground, an 8 mile drive on a bumpy dirt road (7N03B) with one stream crossing. High clearance recommended. The top of the stream was frozen when I crossed and the temp at the trailhead was a shocking 27F. I got started with 3 layers and gloves and was cold for about 30 minutes before body heat and patches of sunlight warmed me up. The hike was beautiful from the start with a mix of large deciduous and evergreen trees. The first mile was fairly flat along a drainage, then gained a ridge. The slope was steady passing cliffs and randomly scattered boulders.

I was pretty close to the top before I spotted the tower. The trail took a somewhat indrect path with plenty of switchbacks to keep the gain in check. Scenery opened up behind as climb unfolded. Below the tower was the Sierra Club register in red cans, and a USFS register book that was in pieces. Next to the tower was a shack littered with debris. From what I gathered online, the tower has not been in use since the 1980s. The structure was made of steel girders while the tower was made up of decaying wood. It wasn't locked so I climbed up an poked around, carefully testing the floor as I went. The tower had a book with a story written by son of a ranger who used to man the tower in the 1950s. A few tools were lying around and a few people wrote about their interest in restoring the tower. The whole vibe was cool. I don't always agree with the Sierra Club, but Thorn Point deserves the emblem badge. After loitering for a while, I started down the trail, taking my time to soak in as much as possible. I had the entire mountain to myself. Nothing better to reboot the soul.

San Guillermo Mountain

Hiked: 11/19/2021
Distance: 2.5 miles round trip on use trail
Summit Elevation: 6606'
Prominence: 1086'
Elevation Gain: 884'
Elevation Gain (in Empire State Buildings): 0.6
Round trip time: 1 hours 30 minutes
Recommended water: 32 oz.
Parking/Fees: Adventure Pass
Difficulty: Easy

After hiking Thorn Point, I had some time and energy and wanted to increase my cardio and gain for the day. San Guillermo (HPS #146) was on the way back, a short hike starting at Pine Springs Campground. I parked near the restroom in the campground and wandered toward the start of the main ridge line. I didn't find the use trail until I was half way up the first rise. It was in decent shape and followed the main ridge south of the mountain, turning north to finish. The register cans were placed a little below the high point. Inside the cans was a 2-page print out of a hike from 2020 with signatures on the back of the pages. I put the pages in a plastic baggie, but a new register book is needed. I enjoyed the view north to Mount Pinos and Sawmill. Views were much nicer than I expected. Like Thorn Point, I had the entire mountain to myself.

Bobbie Benchmark and Peak 1704

Hiked: 11/5/2021
Distance: 5.5 miles round trip on trail and cross country
Summit Elevation: 2518' (Bobbie), 1704'
Prominence: 838' (Bobbie)
Elevation Gain: 1400'
Elevation Gain (in Empire State Buildings): 1.1
Round trip time: 2 hours 30 minutes
Recommended water: 40 oz.
Parking/Fees: $10 State Park Day Use Fee
Difficulty: Easy

With only a half day available to hike, I looked for something local and easy. I drove to Lake Perris State Park and paid the $10 day use fee, although I parked just outside the park and could have skipped payment. There are 8 peaks in the hills surrounding Lake Perris. I had climbed 7 of them on previous trips and aimed to get the last one, Bobbie Benchmark. There were only 3 ascents listed for Bobbie and no tracks. I parked on a small maintenance road just off Ramona Expressway directly south of the peak. There was no official trail so I decided to go directly up the south face, expecting light brush and knee high grass. I was pleasantly surprised to find a use trail going up from the end of the road. The use trail was in good shape on the lower half of the slope, then I lost it, then I found it again on the upper slope. It was scrambley and steep in a couple of spots, but not difficult. On top were great views of the lake and the nearby Bernasconi Hills high point.

Bobbie Benchmark

From the top, I looked at the gully between Bobbie and Bernasconi as a possible descent path. There is rock climbing wall at the bottom of the gully called Big Duck Rock and I estimated the odds of descending the gully without hitting a cliff. It was hard to tell. I started down, finding one class 3 move to reach the saddle. There was a trail heading into the gully so I followed it. It faded out not far from the top, but there were several animal trails continuing down. The animal trails were helpful, but twice I hit what I thought was a cliff, only to find a continuation by going up a little or to one side. I wasn't sure it was going to go until I had only a few hundred feet left. As I exited the gully, I saw two climbers just starting up a long wall on Big Duck Rock. The wall looked like it might be too long for a single rope and I didn't see any place they might belay, but that was not my concern.

Climbers on Big Duck Rock
I followed the base of Bobbie to the west side looking for a bonus. There were a three bumps southwest of the lake about a mile away. I headed toward the highest one, Peak 1704, not listed in Peakbagger. The legal status of this strip of land is unknown. It looks like it is outside the state park and between the park and the fairgrounds. I figured I would go unless someone stopped me. As I approached Peak 1704, I decided to go up the center gully, mostly class 2 with good rock. On top was a metal cylinder and a couple of small, unlabelled marks. There was also a swarm of bugs encouraging me to drop down the north side. I returned the way I came and continued to walk along the base of Bobbie back to the truck. All my trips around Lake Perris have been fun little adventures. Hunting is allowed in the park during the fall so wear bright colors.

Dept of water resources mark near the base of the gully, stamped PR103, unusual location

Looking back at Bobbie BM (right)