Cycling Modeling Breaks

How complicated are cycling models?

As complicated as cycling and cycles might seem, their modeling benefits from several important breaks which greatly simplify both the model and the analytics to gain insights.

For the most part, cyclists ride in straight lines

In Physics, things become messy when an object is moving in something other than a straight line. Here messy means we need to use the methods of Integral Calculus to add up the varying effects along the curve. When we are dealing with straight lines and constant forces, we only need to be able to multiply a few numbers together.

We will discuss stability and turning in their own section. Stability is extremely complicated to model, but why a cyclist can ride a cycle is less of interest than is how can we maximize our performance.

Cornering is important, and that turns out to be easy to understand once you recognize that the cycle wants to go in a straight line and you are trying to make it move like a satellite circling the earth.

Cycling Forces are largely constant in magnitude

Cycling is done dealing with three forces: Rolling Resistance, aerodynamic drag, and gravity. Of these, rolling resistance is in general constant in value, while gravitational effects can be described in similarly fashion for riding flats and doing ascent analytics.

Aerodynamic Drag is the more complicated force because it is dependent on the CyclistCycle speed. However, if you are asking how much pedaling you need to do to ride at a given velocity, it too becomes a constant value.

Riding Scenarios can be analyzed using simplified cycling models

Riding scenarios can be grouped into riding flats and riding hills. In either case, significant insights can be gained by eliminating road details. The result of these simplifications is that the analytics reduces to numerical multiplication exercises.

Gravity is a special type of force which simplifies modeling

Physics describes Gravity as a Conservative Force. The detailed explanation for this is not important, but its consequences are.

  • Work done against gravity such as during an ascent enables the CyclistCycle to reclaim that work during descents.
  • The amount of work required to make an ascent is easily computed as the combined weight of the CyclistCycle multiplied only by the elevation gain.
  • The amount of work required is NOT path dependent. A straight up path versus a serpentine route require the same amount of work.

We are more interested in Work and Power rather than velocity and position

This might seem a strange simplification if you are not a physicist. But in Physics, much effort goes into taking a force equation and determining the resulting object equations of motion.

In our case, we usually start off with a target velocity and ask what are the implications for the cyclist. Not having to compute these equations of motions means we do not need to use Differential and Integral Calculus to get at our results.

The Net Result is why physical cycling is understandable by non physicists

While you may not fully understand why these simplifications are important, here is the bottomline. Cycling Models are significantly simpler than even those used in Physics 101 textbooks.


Cycling as seen through the eyes of elite cyclists.