Backstroke is one of the four competitive swimming strokes, performed on the back in a horizontal position.
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Breathing 3, 5, 7, 9, " br 3,5,7,9 on a set whiteboard" is to breathe every 3, then 5, then 7, then 9 strokes before returning back to 3 strokes before your next breath. If you can't get to 5, 7, or 9 strokes try adding 5 strokes to a breath once per lap. As you become more comfortable, you can add more strokes between breaths.
Increasing the duration between breaths is known as hypoxic training. Adding hypoxic training conditions the brain and body to become used to swimming with less oxygen. A common misconception is swimming hypoxic training is used to train a swimmer's lungs to increase in size or to extract more oxygen from each breath. The truth is hypoxic swimming training conditions the brain to become used to more time between breaths. Each swimmer has enough oxygen in one breath to sustain 30+ seconds before running into physiological trouble due to lack of oxygen. We breathe in and out regularly in our typical daily lives without extended gaps between breaths. Our brains become accustomed to this pattern, and when this regular pattern changes, the brain triggers the panicking urge to breathe as a safety mechanism to prevent oxygen deprivation to the brain. Hypoxic swimming training moves the brain's benchmark, so the safety mechanisms that encourage swimmers to take the next breath occur later.
Breathing 3,5,7,9, is to take a breath every 3, 5, 7, or 9 strokes. Increasing durations between breaths is known as hypoxic training, which is to training with less oxygen.
Adding increased breathing cycles to your swimming program complements your technique and conditioning. The urge to breathe can shorten the pulling phase and alter technique as the stroke compensates for less balance. This can cause the heart rate to spike as the stroke rate increases to compensate for the lack of pace. Becoming used to increased durations between breaths is to help prevent your stroke from deteriorating.
Your breathing cycle can be increased by three strokes upwards, e.g. breathing every 3, 4, 5, 6 strokes +. Never breathe every one or two strokes. Like a boxer, when you move your head, you move your body. If you breathe every two strokes, you condition your body to rotate further on one side and, due to the change in balance, decrease rotation on the non-breathing side. Breathing every three strokes or more ensures there are at least two strokes where your head does not influence the movement of your torso. Next time you go for a swim, watch for swimmers breathing every two strokes. Swimmers breathing every two strokes will have one form of technique on one side of their body and a different form of technique on the other. To breathe every two strokes is to lose balance and propulsion, negatively impacting your swimming conditioning.