# Comparison of Achieved Rolling Resistance Values of Two Selected Tires on a Solid Surface
## 1 Introduction
Part of the rolling friction is also the partial slip of the tread figures in the contact surface and the losses associated with the adhesion and tearing of the tread figures from the road surface [8]. At very high speed, the rolling friction resistance is supplemented by the resistance associated with the formation of waves in the tire tread behind the contact surface [9]. The less resistant the tire is, the less rubber participates in the deformation of the tire. The roughness, respectively micro and macro-relief of the road surface on which the tire rolls often complicates the correct determination of the final value of the rolling resistance of the monitored tire [10; 11]. Due to the focus of the paper and the performed experiment, the following text is focused on the movement of a non-driven wheel rolling on a rigid (inelastic) pad. This means that during its rolling there is considered only the deformation of the tire. The force caused by the weight of the vehicle \(F_{n}\) and the pushing (sliding) force of the axle \(F_{s}\) act on the wheel axis (Figure 1). Adding both forces, there is an obtained result \(F\). The reaction of the substrate \(F_{nr}\) acts against this force. The reaction of the pad can be decomposed in a horizontal and vertical direction. This gives a horizontal reaction \(F_{v}\) rolling friction resistance and a vertical reaction \(F_{nr}\). The vertical reaction \(F_{nr}\) is shifted forward by a value with respect to the wheel axis. The causes of this phenomenon can be explained as follows [12]. When the tire is rolled, the tire is compressed in the front part of the contact surface and released in the rear part of the contact surface. At this place, the deformation work spent on deforming the tire in the front part of the contact surface is greater than the part of the work recovered in the rear part of the contact surface and behind it when the running surface springs into its original circular shape. The missing part of the work is used to overcome the internal friction of the tire and it is converted into heat manifested by the heating of the tire. It follows that greater vertical forces are required to deform the tire in front of the running surface, so that the running surface of the tire exerts a higher pressure on the pad. In contrast, in the rear part of the running surface, the tire exerts less pressure on the pad due to its imperfect flexibility (due to internal losses). Therefore, even elementary vertical reactions are larger in the front part of the contact surface than in its rear part. The resulting vertical reaction \(F_{nr}\) acting at the center of gravity of the elemental reaction pattern is therefore shifted by the value \"a\" in front of the wheel axis. The vertical reaction \(F_{nr}\), together with the wheel load \(F_{n}\), represent a pair of forces creating a moment of rolling friction resistance acting against the rotation of the wheel. \[M_{v}=F_{nr}\ \times a=F_{nr}\times r\times tg\varphi\left[N\times m\right] \tag{1}\]  
In order for the tire wheel to continue to move in a uniform motion, a pushing (sliding) force \(F_{s}\) must act on its axis. The compressive force of the axle \(F_{s}\), together with the horizontal reaction of the pad \(F_{v}\), gives a pair of forces acting against the moment of resistance of the rolling friction to the moment:  
\[M=F_{v}\ \times r\left[N\times m\right] \tag{2}\]  
The magnitude of the rolling resistance \(F_{v}\) is determined from the equilibrium condition of the above moments:  
\[F_{v}=\frac{a}{r}\times F_{nr}\left[N\right] \tag{3}\]  
The ratio \(\frac{a}{r}\) is the rolling resistance factor. Its geometric meaning is the tangent of the angle \(\varphi\). \[\frac{a}{r}=f=tg\varphi\left[-\right] \tag{4}\]  
Experimental device. The basis of our proposed test equipment is the soil channel of the cabinet construction (Figure 2, pos. 1). Its length is 6550 mm, width is 690 mm, and depth is 500 mm. Its working volume is 2.26 m\({}^{3}\). The construction is modular and it can be extended to the required length.