Friday, November 29, 2013

A minimal bike geometry

With this post I want to start a project that I've got in my mind for quite a long time. I've got a very busy year ahead so I don't know if I will be advancing as fast as I would like to.

As a first step, I want to define a minimal set of parameters that could determine completely the dynamic behaviour of a bike. Let's take a look to a typical bike geometry chart:

Specialized Venge 2014 geometry chart
As you can see, the number of parameters is very high and there isn't any explicit separation between parameters that affect fit (fit geometry) and parameters that affect handling (dynamic geometry). We can forget fit geometry if we consider that both stem and seatpost have infinite adjustment capability (with a Look Ergostem and a Titec El Norte seatpost for example) and, consequently, the position of the upper contact points can be set independently of the frame geometry. In short, fit is, in a strict sense, independent of frame geometry.

When talking about dynamic geometry, things are a little less obvious. Bike dynamic behaviour is affected by 3 parameters that have a relation with frame geometry: wheelbase, trail and bike+rider center of gravity position. Regarding the center of gravity, once we have defined the position of the upper contact points (stack and reach fit coordinates), the only intrinsic parameter of a frame that affects the COG position is the position of the BB with respect to the wheel axles. Consequently, a definition of bike geometry should take this into account.

The role of the wheelbase is obvious, it modifies weight balance. The last one, trail, is defined as the distance between the center of the contact patch and the intersection between the steering axis and the ground. I don't agree completely with this definition so I've defined a modified trail. In the following image you can see both definitions as a function of wheel, fork and frame parameters.

This way, the modified trail is the leverage of the steering moment generated by lateral forces in the contact patch. The following plot shows a comparison between both definitions.

The contour plot is the "traditional" trail. The surface plot is the modified one. The difference between them increases as head tube angles decrease
Taking all this into account, we can say that a minimal bike geometry from a dynamic POV can be defined with 4 parameters: wheelbase, trail, chainstay length (horizontal) and BB offset.

Next step is data gathering.

That's all for today. Thanks for reading!