Tire dynamics and forces

Hi,
I'm doing a study about tire dynamics and have some question that I can't get answers to.
The first images shows the forces balances. Since we have no turqe the force has to balance ant the extensence of the T_r is obvious.

https://dl.dropboxusercontent.com/u/12866097/20160210_114226_resized.jpg [Broken]
However in the below picture when a Turqe is present we have a Driving resistence which I don't understand. You have the rolling resistance ofcourse but what is the driving resistance. The do not talk about aerodynamic force so it should not be it. and we see that T_d is to opposite direction of the movement. why is that? and how does it feel? it pushes the tire backwords? the presence of Driving force would explain it but what is it?
https://dl.dropboxusercontent.com/u/12866097/20160210_114210_resized.jpg [Broken]
On the brake phase you have the driving resistance backwords too and it make the T_b forwards. Please somebody explain it to me.
https://dl.dropboxusercontent.com/u/12866097/20160210_114217_resized.jpg [Broken]

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JBA
Gold Member
If you look at the solid profile lines vs the dashed line circle in each of the examples you will see that due the torque load of power being applied to the wheel the tire is distorted by being compressed in front of the contact patch and just the reverse occurs in the case of braking (which acts like a reverse torque being applied); and it is these distortions of the tire that create the added "driving resistance" in each case.

Randy Beikmann
rcgldr
Homework Helper
It would make more sense to explain that a driving torque shifts the contact patch forwards relative to the tire's axis, and a braking force shifts the contact patch backwards, due to the tire surface stretching in the direction of rotation. The effective radius of the tire is affected by this stretching, and the amount of stretching is quantified by the term slip ratio.

http://en.wikipedia.org/wiki/Slip_ratio

There's also rolling resistance due to hysteresis, the forces during recovery are less than the forces that occur during deformation, due to hysteresis, where some energy is converted into heat as a tire rolls.

http://en.wikipedia.org/wiki/Rolling_resistance

Randy Beikmann
Upon the figures and text I understand that T_d and T_b are respectively the reaction force on the wheel hub to driving force (mu_d-mu_r)*W and braking force (mu_b+mu_r)*W.

mu_r is a measure for the energy loss during rolling (rolling resistance) --> Rolling resistance force = mu_r*W