I disagree with your numbers. We're already talking ppO2, so why are you dividing by atmospheric a second time? Also, you're talking about quantities of oxygen in the lungs, whereas this is talking about the quantity of O2 aready taken up by the alveoli. In other words, you're suggesting that the performance improvement is (1.3 / 2)/8 times smaller than I am reading it. It may be that the actual improvement won't be as big as eight percent, but that eight percent would take me from six to six and a half minutes in statics. Even half that would be worth considering.
Also, your assumption that that extra O2 storage 'replaces' CO2 is flawed. As you can read from my original post, this increase comes with little or no affect on CO2 stores. Unbound hemoglobin is where this O2 appears from, there is no replacement or displacement of CO2.
I am sorry, but you are wrong in all points. My calculation is correct. PAO2 is partial
alveolar oxygen pressure and represents the part of oxygen in the 760 mmHg of the total atmospheric pressure of the air inside the alveoli. That's unlike PaO2 (lowercase 'a'), which is partial
arterial oxygen pressure which then describes the pressure of oxygen in arteries leaving the alveoli. However, the values are very close to each other, so even if your values were for the PaO2 and not PAO2 as you previously quoted, the math would be the same.
In my calculation, the value is divided only once. It is a quite simple math - I compare normal resting pressure you mentioned (120 mmHg) with the one after hyperventilation (130 mmHg). It makes pressure difference of 10 mmHg of pure oxygen. The alveoli are not filled with pure oxygen though, and definitely not with any gas of pressure of 130 mmHg. They are filled with air (well, air + CO2 + water vapor) at the atmospheric pressure - hence with 760 mmHg of gas pressure. Please note, that I do not even assume any packing or forced inhalation. If your values were measured after packing or forced inhalation, I would then need to use significantly higher value than the normal atmospheric pressure of 760 mmHg, and that would reduce the result even much more!
So the result of 1.3% of difference (100% * 10 mmHg / 760 mmHg) is perfectly OK, and in fact even overestimated, because I am practically sure your data do not come from tidal inhalation, but from a forced or even packed inhalation. In such case the value could be even below 1%.
Furthermore your calculation assuming 6% to 8% performance increase from the 10 mmHg PAO2 difference, assuming it would make ~30s at 6 minutes is very wrong too even if it really were 6% - 8% (which is definitely not the case). You do not hold your breath (only) thanks to the air you have in your lungs. Primarily it is the oxygen that is already stocked in your blood that allows for it. So if you only manage to increase the O2 content in your lungs, you won't manage saturating your venous blood without a good level of hyperventialtion (which then has many more side effects limitating the O2 intake). So even if it were 6% - 8% of increase of O2 in lungs (which it is
not), it could make effect of only less than half of this value on the breath-hold length. However, as I wrote, the value is completely wrong anyway.
You are also absolutely wrong that the O2 does not replace any CO2. What else could it then replace if not CO2 in the alveoli??? The part of oxygen in air is 21% and constant. That represents 160 mmHg of PO2. In alveoli the 160 mmHg of PO2 are reduced by increased content of water vapor and especially by CO2, so normally it is just above ~100 mmHg.
So when you breathe air, you can only increase the PAO2 (and the content of oxygen in alveoli) by washing out the excess CO2. And that's indeed what happens with hyperventilation (or a purge breath) - in air there is 0.03% - 0.06% of CO2, in the normal alveolar air, there is around 5%-6%, so by increased ventilation you reduce the CO2 content and increase the partial pressure of oxygen (and the partial pressure of nitrogen, of course, too).
It means the 100 ml of difference in O2 and CO2 are perfectly correct. Additionally, as already mentioned, it assumes achieving the difference of 120 to 130 mmHg by only a single purge breath. You wrote about several hyperventilation breaths - that would wash out accordingly more CO2.
So, I am sorry to play a smart ass, but my calculation is all right, and the resulting difference of 5s to 12s is even highly overshot, because in reality the value would be even further lowered by several already mentioned but not calculated effects, and quite likely the result may be then negative.