Actually normal rates are 12 to 16 breaths rating per minute
In a study of 19 healthy adults, the minute ventilation in REM sleep was 6.46 +/- 0.29(
SEM) liters/minute compared to 7.66 +/- 0.34 liters/minute when awake
during jumping increases from 2 to 3 times from normal rates
during playingYour heart speeds up to pump extra food and oxygen to the muscles.Breathing speeds up to get more oxygen and to get rid of more carbon dioxide. When a fit person, such as an athlete, exercises the pulse rate,breathing rate and lactic acid levels rise much less than they do in an unfit person.
during riding fastFor the type of effort you're describing, I think it would be easier to coordinate breathing with pedal strokes than breaths per minute.
At a good, hard effort that I can sustain for a long period of time (such as a long TT), I find that my breathing automatically falls on every other pedal stroke. For example, begin inhale on left led stroke and finish inhale during right leg stroke. Begin exhale on left led stroke and finish exhale on left right leg stroke.
For a really hard effort, such as intervals or hill climbing, I find that it's inhale left stroke, exhale right stroke. Basically doubling the breathing rate.
As for the "panting". That would be an effort where you are anaerobic and you're breathing is completely ragged. No pattern other than "as fast as possible.
during cycling increases from 5.5 to 6.0 percent
during skipping increases from 20 to 30 rates