7. Februar 2024

# Back-of-the-envelope: energy expenditure in a multi-day footrace

How much energy do you spend on a multi-day foot race? I tried to estimate the expenditure first, using a back-of-the-envelope calculation before stumbling over a study researching exactly that. Fun with bananas.

It takes a lot of energy to cover the 360 km and the 25900 m elevation gain of the Swiss Peaks 360 footrace over 5.5 days. But how much did I spend? Loving to put numbers on things, I had to find out. As a caveat, I’m by no means an expert in this, but that doesn’t prevent me from giving it a shot.

A mass of 70 kg lifted up by 25900 m has the potential energy of around ~4.2k Calories (kcal). That’s the equivalent of 42 bananas, assuming a medium sized banana with 100 Calories. That clearly sets a *lower bound* for the amount of energy I must have spent on climbing. Just to get some reference.

Now, assume that I have a basal metabolic rate of ~1.8k Calories. That makes me spend ~10k Calories (=100 bananas) on essential body functions over the 5.5 days. On top of that, I assume it takes another ~5k Calories (=50 bananas) for other miscellaneous activity over the same period. That makes 15k Calories (=150 bananas), which still leaves the cost of running/walking over the distance and the elevation gain to be accounted for.

I looked up the cost of running/walking in a table from a paper on the subject (forgot where :-(, sorry), using the average slope of ~7%: this might be about 5 J / (m kg). So moving 70 kg over 360 km costs 30k Calories (=300 bananas).

Let’s add it up. This is 15k Calories (=150 bananas) for essential and non-essential body function, and 30k Calories (=300 bananas) for covering the distance and the elevation gain. A total of **45k Calories (=450 bananas)**, or 8.2k Calories (=82 bananas) per day. That is a lot of bananas!

Several weeks after I made the above back-of-the-envelope calculation, I discovered a paper titled *Total Energy Expenditure and Nutritional Intake in Continuous Multiday Ultramarathon Events* (International journal of sport nutrition and exercise metabolism, 1-7. 14 Sep. 2023, doi:10.1123/ijsnem.2023-0063), discussed in Jason Koop’s Research Essentials for Ultrarunners (issue #8). Over the Cocodona 250 (250 miles = 400 km) with 10000 m elevation gain, test subjects spent 9.3k Calories (=93 bananas) on average per day, finishing the course over an average of 3.4 days. Not so far away from my estimates.

What about the the fueling (intake) though? Who can eat 80-90 bananas a day? Unlikely! I lost about ~3 kg of body weight over the 5.5 days. Now, 3 kg of fat stores 21k Calories (=210 bananas), depending on which source on the Internet you trust. This would leave the energy-equivalent of 44 bananas to be consumed on each of the 5.5 days. That seems realistic.