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