In our club we have this 'toy', a 3 feet long plastic tube from an old aquarium, which we often play with when all that swimming becomes too much. There are liter measures on the thing and we fill it with water and go underneath it in the water with full breath (no packing) and empty as much of our lungs as possible.
From this thing, we can see a slow increase in lung volume as we train longer. Newcomers quickly rise in volume. My self I'm pretty steady on 5,3 liters, but others are much higher. Our club record is f.i. Lars Mou Andersen who blew almost 8 liters into the thing one night. I have also seen Bill Stromberg (Sweden) blow 10 liters (!) into a little hand-held machine (a spirometer?), and Hubert Maier (Germany) they say is up at 12 liters.
I believe the lung volume rises naturally from training, both fitness training (running, cycling, swimming) but also breathhold training (lung packing, etc.). Also the taller you are, the higher your volume is (Lars Mou is 6'4").
Of course lung volume is only one detail in being a good breathholder. There's also your fitness level, your techinique in the current discipline, fysiological adaptations (muscle types, etc.) and of course the 'trance' factor. The big lungs in freediving are like the height in basketball; it helps, but it's not a requirement.
Chris Engelbrecht, Copenhagen
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"Be like water, my friend." - Bruce Lee