Tuesday, June 8, 2010

Analytical Cycling - Flying 200 Meter

A junior writes that he is going to do Canadian Nationals on the Bromonte track in Quebec and wants to know if an analysis based on the Flying 200 model can offer any advice.

He rode a 12.65s flying 200 at Bromonte last year. He said that when he rode his flying 200 last season, he was a meter from the rail when he started accelerating in turn 4, crossed the start line 1 meter from the measurement line, and stayed in the center of the sprinters lane for the distance. We looked up the temperature and barometric pressure for the date as well as the elevation of Quebec and then calculated air density, 1.151 kg/m^3, which was lower than standard conditions.


* Better Technique—This can improve the rider's time by 0.5s. This results from a longer acceleration before the dive and a better path. A better path will take some practice.
* More Power—(Always good) Ten percent more would improve this rider's time by 0.2s.

It's better to jump from as high as possible. It's better to stay close to the measurement line. It's better to have more power. These things are obvious. But where to jump is not as obvious. Should the rider cross wide at the start? This is not obvious either. Will doing all these things bring enough improvement to qualify? Running the flying 200 model can answer these questions.

Several of the plots at the end of this page show the elevation of the rider's center of mass. Remember that the center of mass goes down as a rider leans in a turn. Leans are dramatic on this track. Remember also that as a rider leans and the center of mass goes down, the rider's speed increases just like a roller coaster, slow at the top, fast at the bottom. This feature is often ignored in models, but it is included in this model since we are looking for very small changes........read more
The Lean:

Including lean in the analysis of a general model of a rider on a surface leads to several important conclusions:

* The faster the rider, the shorter the distance. As a rider leans in the turns, the rider's center of mass travels a shorter path than the rider's wheel.

* The taller a rider's center of mass, the shorter the distance. The length of the path of a rider's center of mass in a turn depends on the height of the rider's center of mass. The greater the height, the shorter the path in the turn.

* The shorter distance contributes significantly to faster times. It's not just that powerful riders go faster, they also travel a shorter distance through the turns.

* Times depend on the configuration of the velodrome. Velodromes with longer straights will have shorter distances in the turns (for a given length). This gives different radii and different speeds for nominally the same path.

* Speeds in the turns are faster because potential energy is converted to speed as the rider leans. This is offset by increased drag from the faster speed. The rider looses this speed when potential energy increases in the straights.

One sets up the model by first defining a velodrome. The velodrome can be any of several predefined velodromes or some custom configuration. Next one defines a path for study. This is the path on the surface of the velodrome which will be ridden by the rider. Next define the parameters that describe a rider such as weight, drag, and power. The model computes a time for the Flying 200m by writing the differential equations of motion for the rider and solving them based on the chosen path and velodrome configuration......read more

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