So what ways are there of changing weight during exercise?
- Conversion of glucose to CO₂ (which is breathed out) and water (which we retain and ignore)
- Loss of water through the lungs
- Loss of water through sweating
Glycogen is the primary energy storage unit for muscles, and it is a complex of lots of glucose molecules. So muscles get their energy from the oxidation of glucose. If you trace through the glycolysis and pyruvate pathways and the Krebs cycle you see that each glucose (C₆H₁₂O₆) molecule + 3 O₂ ends up as 6 CO₂ and 12 H+. The CO₂ gets breathed out so counts as weight loss, the O₂ gets breathed in and counts as weight gain. My recollection is fuzzy, but I presume the lonely H+ will end up finding some oxygen to make water with, which will be retained; that’s another 3 O₂ of weight gain. So the combustion of a mole of glucose (= 180g) loses 6 moles of CO₂ (=6*44=264g), gains 6 moles of O₂ (6*32 = 192g) and retains 6 moles of water (6*18=108g). Or a net loss of 72g of carbon. In other words there is a net loss of 40% of original mass of glucose.
Now my handy-dandy heart rate monitor thinks I expended 2833 Calories to run my last marathon (bit more than 3 hours). And each gram of glucose produces about 4 Calories. So I lost .4 * 2833/4 grams = 283grams carbon. That’s about 5/8ths of a pound.
(The uncertainty here is whether the monitor correctly calculated calories burned (and I assume that includes a basal metabolic rate)).
Now when I take a breath, air enters my lungs at the outside temperature and humidity and leaves the lungs at body temperature and 100% humidity. So unless I’m running in 100% humidity at body temperature or above, I lose water with each breath. The question of “How much?” is going to depend on the initial amount of water in the air.
Last time I ran in Sacramento the temperature started out at 39, and probably climbed to 50 or so (I don’t know what it was at the end, but it still was chilly). I have no idea what the humidity was. As I write the humidity there is 50%. So let’s presume a humidity of 50% and an average temperature of 45.
Now Wikipedia tells me that the average tidal volume of the adult male or female is about 0.5liter. Now I bet that increases a bit in heavy exercise, but I don’t see any data on that, so assume 0.5liters. Now I take a breath each time my left foot strikes the ground, which happens about 85 times a minute when going at pace.
Now the amount of water the air can hold is determined by the temperature. At 37°C (body temperature), 100% humidity is about 40g/m³, while at 7°C (chilly Sacramento December morning air) it’s about 3.5g/m³. And there are 1000 liters in a m³. So every breath represents a loss of (40-4)g/m³ * .5l = 18 milli grams. Not much.
But we take lots of breaths. 85/minute * 3*60 (3 hours of minutes) = 15,300 breaths in a marathon. So that comes to about 275 grams of water lost (just from breathing) over a marathon. That’s a little less than 5/8ths of a pound.
(The uncertainties here are many. My tidal volume, whether that changes during heavy exercise, actual temperature, actual humidity).
And that leaves sweating. And I don’t have a good way to estimate this other than going out and measuring it. And I can’t measure it directly, but only my weight loss over the course of a run. I expect it’s going to depend hugely on factors like temperature, humidity, possibly wind, maybe even the phase of the moon.
(I must admit there is also a certain amount of mucus that runs out of my nose too. I shall call that sweat, and ignore it as a special case).
But the one test I have made so far says that running at roughly marathon pace on an indoor treadmill, I lose 3¼lbs an hour. Now if we assume I lose about a pound in 3 hours from metabolism and transipration, that still means I lost almost 3lb to sweat in an hour.
Sacramento will be cooler…