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This question establishes why velodromes all operate in an anticlockwise direction. Are velodromes designed this way, to make the left hand turn easier, or would it be just as easy to cycle clockwise around them?

Specifically: are there two lines of symmetry in the shape of the velodrome, one through the pursuit finish line in the middle of the straights and the other through the middle of the bend? Is this true for all velodromes?

Source: about 15 years ago I used to ride lots at Manchester velodrome, and I remember someone claiming this from around that time, and reporting that a novelty clockwise race had been really difficult.

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    It is not true that all velodromes are symmetrical -- it depends, in part, on whether the velodrome was converted from a previous use or purposefully-built and, if outdoors, on the terrain that was being used. In general, purpose-built velodromes are symmetric through the two main axes though there are oddities such as the Dick Lane Velodrome which is symmetric in two axes but, as an outdoor velodrome its terrain demanded that it be built with an "uphill" side and a "downhill" side. – R. Chung Mar 23 '17 at 16:25
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    Riding clockwise is difficult because no one does it. Ride clockwise regularly enough and it will begin to feel normal. As R. Chung says, most purpose built velodromes are symmetrical along the axes you mention and do not shape the transitions differently between end of straight leading into the turn and end of turn leading into the straight. There are however subtly different shapes used for the turns, with both the turn radius being variable and the average turn radius being different between tracks. Banking angles and angle transitions also vary. – alexsimmons Mar 23 '17 at 20:14
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UCI Regulations for Track cycling provide a very loose definition for velodromes (see page 75) even up to the Olympic level. The only strict requirements beyond track width and markings are that velodromes must be 133-500m long (250m exactly for Olympic events), the track shape should consist of two parallel straights connected by two bends and that there is a smooth transition between the straights and the bends. There is no requirement for a consistent radius or banking throughout each bend. There is no requirement that the straights should be the same length or relative elevation either.

Exact dimensions of various velodromes are difficult to find, however to give one example How the velodrome found its form features an interview with the engineers responsible for the velodrome used for the London 2012 games where they note:

The track in the London Velodrome doesn't have the usual reflection symmetry you find in buildings. "If you folded the track in half lengthwise, the two halves wouldn't match," says Weir. The track does have rotational symmetry, it looks the same if you spin it by a half-turn. But the slope of the track going into and out of the turns is not the same. "This is simply because you always cycle the same way around the track, and you go shallower into the turn and steeper out of it."

While it is likely that most velodromes feature rotational symmetry and many of those will also feature reflective symmetry this is not a requirement for a UCI homologated track.

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At my local velodrome (Derby, UK) cycling anti clockwise the corners have a much steeper gradient coming out of the corner to provide a speed boost as come out. The top of the track is also about 1.5 meters higher at the corner apex than at the top on the straights. It sounds as if all tracks might vary though

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