pressure - Is there a depth at which a human body, with lungs full of air, will no longer float?

I was watching a special on divers who dove down hundreds of feet without tanks or gear. The show referred to a depth at which the diver was no longer buoyant and would actually sink, even with lungs full of air. Is there such a point and if so, why? What is happening there?

Answer

The diver would cease to be buoyant when the their average density matches that of the surrounding water; where density is weight (or mass) divided by volume. The density of the surrounding water is not going to change much with such depths as water is very hard to compress. However the diver's density will increase as the air in their lungs compresses; their weight remains the same but the volume displaced by their body reduces and thus the average density increases.

The human body's density is relatively close to that of water; a common figure is 985g/liter, vs 1000 g/liter for fresh water and 1020 g/liter for sea water. That's only 3.5% less dense than sea water, so if compressing air in their lungs can reduce the overall body volume by 3.5% they will achieve neutral density.

Imagine an 80 Kg adult male (176 pounds). At 985g/l, they would displace about 81.2 liters. 80 Kg of seawater would displace about 78.4 liters (at 1020g/l). If the diver's volume could be reduced by 2.8 liters, they would reach equivalent densities.

A typical adult male's lungs hold about 6 liters of air; if their lungs could be compressed by 50%, ie: down to 3 liters of volume, their body volume would drop to 78.2 liters, and they would be slightly denser than sea water. Air in a balloon would be reduced in volume by 50% at a depth of about 30 feet (each 30 feet of depth increases pressure by about 1 atmosphere) - but of course the ribs and lungs are not a simple balloon and the lungs would not compress that easily but they go much deeper.

Overall, these simple calculations suggest that free divers might approach or exceed neutral buoyancy due to lung compression; at the least, their buoyancy would be significantly reduced.

Complications: body densities vary; they start with full lungs which reduces their initial density (but there is more than enough pressure to compensate for that); good freedivers have larger lung capacity; any gear worn would have some effect on the calculations unless it was neutral buoyant itself, and fresh water would make neutral buoyancy much easier to achieve.

Nevertheless it's quite credible that deep freedivers would lose their buoyancy.