Hello all, I was short of time these last weeks so I couldn't update the blog. The next few weeks I will have some free time to try to develop some topics that I have in mind.
This post is dedicated to lateral loads in the contact between the wheel and the road, as many of you know, this type of load has a strong relation with the riding style of the cyclist because it is generated by the lateral motion of the bicycle and the rider. I have searched for bibliography about this subject and I have noticed that it's a topic that has been almost forgotten. I have only found some papers, the very good "Bicycle Wheel" and a very old but very technical one, both are mainly dedicated to the behaviour of the wheels when they are loaded laterally but there isn't a method to quantify these loads. You can also read Cervélo's engineer Damon Rinard's thoughts about this topic here and here. I have also noticed that the EN testing protocol doesn't include any fatigue test for lateral loads for the frames.
I decided to study a little bit the subject after following a topic created in Weight Weenies about the big test of wheels that Roues Artisanales does from time to time. In the 2008 test you can find a drawing of the forces acting in the wheel-ground contact and a small experimental explanation given by a Mavic's engineer. After working a bit with this diagram I noticed that the lateral loads in the plane of the wheel were zero so something must be wrong, this and the lack of an analytical model make me try to develop a proper one.
First, to understand better the mechanics of standing pedalling we can watch this small video where we can see Cancellara's start of a Tour of California TT:
After watching the video we can conclude that:
1) The lateral movement of the bicycle and the rider is approximatedly a zigzag so I will consider that there is no moment in the vertical direction
2) The lean angle of the bicycle is zero when the crank arms are parallel to the ground and maximum when one of the legs is in its lowest position
The last conclusion is not always true but I will use it to simplify things:
3) The cyclist is always in vertical position so his lean angle is always zero
This last conclusion is generally true for standing pedalling in flat terrrain but it depends a lot on the cyclist. For example, Cancellara accelerates during climbing with his body perfectly vertical while Voeckler moves a lot his body even accelerating in flat terrain. Taking this into consideration I developed the following model:
The following graphics show the results obtained for different values of the parameters and also the normal and lateral forces decomposed in the coincident and normal to the bicycle planes. I have to point out that the time origin is set when the crank arms are parallel to the ground. The results obtained seem to agree with the minimal level of lateral stiffness to avoid pad rubbing recommended by some experimental studies.
As I have already commented the distribution of this force between the two wheels depends on the variable weight distribution of the system. After solving the in-plane loads model that I presented some time ago, I will be able to calculate the three components of force loading each wheel and, consequently, the frame.
That's all for today. Thanks for reading!
PD It's important to note that the lateral motion of the bicycle is more difficult to modelise, here I present a simplified model. It involves the lateral motion induced by the gravity during the first part of the movement and, when the lean angle approaches its maximum value, a progressive countersteering done by the cyclist to increase the height of the COG of the system and avoid falling. Due to the small sideslip angles involved, the difference between these forces and the real ones should be negligeable, specially for the rear wheel.