Pedalling circles is a simple sounding technique to ensure that you are making the most of each part of the pedal stroke, rather than just pushing down when your foot is in the 2 o'clock to 5 o'clock positions and ignoring the rest of the pedal stroke.
Simple sounding, less straightforward in practice, but well worth getting used to because an efficient pedalling technique can significantly improve your speed and efficiency, and leave you feeling more in control.
We are all happy with pushing down on the pedals when they are at front, that's the 'easy' bit of cycling. Now think about the rest of the circle that your foot follows as you are cycling along and how each of the other parts of the circle could be improved.
- On reaching the bottom of the circle your foot moves backwards. The movement you should follow is often described as 'wiping your shoe'. Never felt much like wiping a shoe to me but the idea is simple - you push down a little while moving your foot backwards
- Next your foot will come up the back of the circle. Even with clipless pedals, actually pulling the pedal up with your foot is exceptionally difficult, but it is also unnecessary. Don't try pulling up, but instead focus on removing the weight from that pedal by very slightly lifting the leg as it moves upwards. Each time you push down with one foot you are physically lifting the other leg - say 10 kg weight, lifted 5000 times per hour! It is quite easy to adjust to this slight lifting of the rear, upward rising leg and makes an immediate and noticeable improvement
- Coming across the top. In principle you should be pushing your foot forwards slightly at the top, while the other is pushing backwards at the bottom.
All these techniques are very worth practicing, and when you 'pedal circles' you will find that your ride immediately feels smoother and faster...but it is hard work, and a bit of a challenge focussing on so many things at once!
Personally I focus most on the 'taking weight off the rear leg' aspect, and believe this has the greatest impact, but for you it may be different. But whichever aspects you prefer to focus on, you will certainly appreciate the new ride quality - perhaps above all over shorter distances where you can focus on your pedalling eg a sprint finish or short burst up a hill, but also simply because 'pedalling circles' feels more efficient and professional.