Estimated Energy to hike Iron Mountain #1
Posted: Tue Dec 21, 2021 2:38 pm
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:
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).
Segment 1 (Heaton to Allison Saddle)
Segment 2 (Allison Saddle to Summit)
Segment 3 (Summit to Allison Saddle)
Segment 4 (Allison Saddle to Heaton)
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.
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:
Code: Select all
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 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).
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 |
| 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 |
| 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 |
| 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 |
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.