OK, it looks like it can be approximated fairly well this way.
Looking at web information on rebreathers, which seem like they might care a lot about how much O2 is actually metabolized vs. exhaled, I found
RB which includes this:
"In most circumstances, breathing rate, or respiratory minute volume (RMV), will be directly proportional to metabolic oxygen consumption rate. Thus, most passive-addition semi-closed rebreathers inject supply gas into the breathing loop at a rate determined by the diver's RMV"
Attempting to chase down the "In most circumstances", I found
Exercise Physiology and the Role of Physiological Testing :
Pulmonary ventilation [VE] is the amount of air moved in and out of the lungs per minute.
... The ventilatory equivalent ratio for oxygen [VE/V02] is equal to the pulmonary ventilation (VE) divided by oxygen consumption (VO2). ... Click here to see the response of the ventilatory equivalent ratios to exercise.
The link is to a graph
CYCLE VO2max PROJECT
that shows VE/VO2 as being about 21 at extreme rest, dropping to about 17 for moderate activity and past the anaerobic threshold, and then up to about 20 at peak limits. It seems reasonable to say that most recreational diving situations could use the value of 17 (or VO2/VE = 5.9%), but if you have a case of extreme underwater exercise, maybe a little higher, up to 20, would be appropriate. See the graph.
But ... The referenced discussion is for air (21% O2) at 1 atmosphere. As we all learned in OW training, we just waste the extra O2 we breath at higher pressures, at 33 FSW our VE doubles but our VO2 stays the same. Fortunately, this is accommodated by the way we compute SAC, which is normalized to equivalent gas consumption at 1 atmosphere.
The reference I cited in a previous post,
Calorie Burning , tells us that
"For pure carbohydrate and fat catabolism (breakdown), these caloric amounts are actually 5.05 and 4.73 Kcal/Liter O2, respectively"
Since there are 28.31 liters / cubic foot, that's 143 or 134 Kcal/ cubic foot O2, respectively. (The calories we talk about with respect to food and exercise are actually Kilocalories in scientific units.) If we approximate 50% of each in the absence of known CO2 expiration rates, we could use 148 Kcal / cubic foot O2 metabolized.
So if you know enough to calculate your SAC rate (average depth, dive time, delta-pressure, tank constant), you ought to be able to calculate how many calories you burned, with an uncertainty of
- As much as about 18% for activity level, which you can refine somewhat by using SAC rate information, or just using a higher [VE/VO2] for dives with extreme activity.
- About 7% for carbs vs. fat, which you'd need CO2 expiration rates to account for. Maybe use a mid-point assuming you'll burn some of each.
Let's try an example to see if the numbers make sense: Suppose you do a nice easy dive on air for 60 minutes and calculate an RMV of 0.5 cuft/min. Note I've slipped from the colloquial SAC to RMV, which is tank-independent, is expressed in volume/minute, and is what most divers usually mean when they say SAC.
So you breathed a 1 atmosphere equivalent of 0.5 * 60 = 30 cubic feet of air. Your SAC rate is nice and low, so use 5.9% VO2/VE, so you metabolized 1.77 cubic feet O2. At 148 cal / cubic foot, that means you've burned 262 calories. Doing a sanity check using some published values for the caloric expenditure of an hour of various exercises at
Exercise for weight loss: Calories burned in 1 hour - MayoClinic.com , this is about the same as a 200 lb person doing ballroom dancing, bowling, or (interpolating) walking at about 2.5 mph. For an RMV of 0.5 cuft/min, that sounds reasonable to me.
Note that the rate of caloric consumption is more or less linear with RMV (SAC rate). So if your dive was at an RMV of 0.7, you can expect to burn 262 * (0.7 / 0.5) = 367 calories per hour, about the same as bicycling < 10 mph (leisure) or playing volleyball. Or just (524 * RMV) calories per hour. This probably holds up to an RMV of about 1.0, at which point you need to use progressively lower values for VO2/VE, down to maybe 5% at peak output, or as little as (444 * RMV) calories / hour. RMV here is cubic feet / minute. Metric values use the same logic but need a different constant.
I'm also not sure about the effect of stress hyperventilation on VE/VO2, the reference was concerned with power output of exercise. So this might fail to hold for very high SAC rate dives for that reason, reducing the calories burned below the values shown above.
As others have pointed out, gearing up and down, entries and exits, etc, may be more strenuous, but we usually don't spend a lot of time at them relative to bottom time.
It's an interesting question I thought I'd look into - the fact that divers actually are instrumented for at least VE, and whether that's enough to estimate VO2 and therefore calories burned. I think the answer is yes, to a useable approximation.
I'll remind everyone that I'm not an exercise physiologist, I'm just playing one on the internet. To the extent that the cited web references are wrong, or I've misunderstood them, this analysis would be wrong. Anyone who can point out any errors or confusion, please do.
