To elaborate on my previous brief posting, breathing in and out through the nose is always preferable, as the nose was specifically designed by either the grand designer or evolution for this purpose.
Land based species that do not possess noses tend to die out.
The nose acts as a filter and can reduce the inhalation of allergens and pollutants. It is also almost impossible to absorb a giant stinging hornet through your nose.
In "Body, Mind and Sport" John Douillard suggests that all training should be done at a level of intensity that allows you to breathe in and out through the nose using yogic breathing (pranayamadingdong(?)).
This is based upon Ayur Vedic principles and is a bit like an ultra-Maff (experienced runners will understand that).
However, as intensity increases there is a need to deliver more oxygen to the muscles than breathing through the nose can provide, so you are forced to breathe through the mouth (plus, in my case, my nose fills to the brim with yucky stuff and I can barely breathe through it anyway).
The way I learned to breathe more efficiently was to push out as more air as possible on each exhale, pushing from the pit of the stomach. The in-breath is automatic. My exhale tends to take about 5 steps, while my inhale takes about 3.
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