According to the Judas Priest song, Turning Circles is about examining our lives, about how choices made in the past have turned and affect us today. At least that is my interpretation of the lyrics. As far as I have been able to discern there is no relation between this and turning circles in the cycling world. Although if you hum the song while riding it may help you to turn circles.
In cycling, turning circles refers to an action, in this case a way of pedaling. When all is right in our own little cycling worlds, we are probably turning perfect circles. It is the action that we strive to attain whenever we ride, and generally results in the most efficient transfer of power from our legs to our bike drivetrain.
Some riders will turn circles without ever really realizing that they are doing so. It is their natural pedaling motion. It is the one thing that I have consistently been complimented on over the years - the fluidity of my pedaling motion and riding. I only wish that such ability was all that were required for success. Other riders may need to concentrate on turning circles, until it becomes second nature. You may be wondering just what game I am up to here, after all if the chainrings are round, how can you do anything other than turn circles? The key to understanding this is in the preceding paragraph - the efficient transfer of power. Yes cranks/pedals do spin in a circular motion, but in order to turn perfect circles you must equalize the transfer of power through the entire rotation. This is why, more than a few years ago, Shimano came out with an elliptical chainring known as biopace. Since they were not circular , you could not literally turn circles with them. What they supposedly did, was allow you to more evenly transfer power through an entire rotation. I had some on a bike once - for a very short period of time. They faded out of the cycling world fairly quickly.
Efficiency is also the reason you see and hear people who ride a lot clacking around your local coffee stop, buy expensive specialty shoes, why we put clipless pedals on our bikes. In earlier days toe clips and straps were used to perform the same function, and clips and straps are still commonly seen on fixed gear road bikes and track bikes today.
That sure connection between foot and pedal allows us to apply power throughout the rotation, on the downstroke, around the bottom, pulling up on the backstroke, and back over the top. The basic flat pedals you see on beach cruisers, townies, and what not, only allow you to transfer power on the downstroke - not very efficient, but perhaps all you really need for that type of bike.
The opposite of turning circles is, naturally, turning squares, the obvious connotation being that the motion is less fluid, and thus less efficient. If you closely study the pedaling motions of various riders, differences will become apparent; the two, circles and squares, are quite distinct. Another common term used to describe this is mashing - it even sounds bad. Mashing the pedals is not a worthy goal to attain towards. Interestingly you are more likely to hear the phrase mashing in conversation than you are to hear the phrase turning circles. I guess that when we have a bad day, mashing the pedals is a perfectly reasonable explanation. Good days, well, we don't really need a reason to have a good day, do we?
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