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.