## 3 Results and Discussion
### Effect of Inflation Pressures and Rim Width
#### 3.3.2 Forces and Moments  
Figure 17 shows the stiffness coefficients for slip and camber forces as well as self-aligning and twisting torques versus inflation pressure.  
The upper left plot (Figure 17a) displays various trends in cornering stiffness coefficient. First, large differences were apparent between the different tire sizes bounded on the upper end by the  
Figure 17: Force and moment fitted stiffness coefficients versus inflation pressure for various bicycle tires with (**a**) cornering stiffness, (**b**) camber stiffness, (**c**) self-aligning stiffness and (**d**) twisting torque coefficients.  
\(26\times 4\)\" fat bike and \(29\times 2.3\)\" bald tires, with upper values in excess of 20 1/rad, and on the lower end by the \(29\times 2.3\)\" knobby tire, on either rim width, at around 10 1/rad. Aside from the \(26\times 4\)\" fat tire, the less-treaded tires had higher cornering stiffness above 20 psi (1.4 bar). Additionally, above this pressure, the cornering stiffness of the tires shown seemed to vary little with further increase in inflation pressure. Below this pressure, there were some nonlinear and disparate behaviors where cornering stiffness of the \(29\times 2.5\)\" file-tread increased rapidly with inflation pressure whereas that of the \(29\times 2.3\)\" knobby tire decreased gradually. Across the limited pressures measured, the \(27.5\times 2.8\)\" plus tire exhibited a different sensitivity (slope) than the other knobby tires.  
The plot of normalized camber stiffness, shown in the upper right (Figure 17b) showed similar overall groupings. The less-treaded variants exhibited higher camber stiffness coefficients, with a decreasing trend as inflation pressure increased, and the \(29\times 2.3\)\" bald tire topped the chart. Camber stiffness of the knobby tires fell off more quickly from 10 to 25 psi, whereas the \(29\times 2.3\)\" knobby tire on a 25 mm rim eventually achieved a slope similar to its less-treaded counterparts, albeit at a lower value (below 1.0 1/rad). Rim width had minimal effect.  
In the lower left plot (Figure 17c), the sign convention for the aligning torque should be kept in mind. Its value was negative because it acted to reduce the tire slip angle, and thus a larger stiffness magnitude resulted in a more negative value. Again, there was a grouping. Except for the \(26\times 4\)\" fat bike tire at 10 psi, the less treaded tires exhibited more self-aligning stiffness, with increased inflation pressure, albeit with diminishing magnitude. The \(29\times 2.3\)\" and \(27.5\times 2.8\)\" knobby tires grouped fairly close together with the lowest magnitudes of self-aligning stiffness. It should be noted that although the units of normalized self-aligning stiffness were in meters, this value was different from the pneumatic trail. As described earlier, the pneumatic trail can be derived by dividing the tire self-aligning moment by the lateral force due to slip (at zero camber).  
Normalized twisting torque stiffness, shown in the lower right plot (Figure 17d), showed a fairly rapid decrease with increasing inflation pressure up to about 30 psi (2.1 bar) for the measured tires. On the basis of the higher twisting torque stiffness magnitudes of the \(29\times 2.3\)\" bald and \(26\times 4\)\" tires, one would expect them to generate the most steering torque at low inflation pressures. For the \(26\times 4\)\", this was likely related to the difference in peripheral velocity across such a wide patch, and for the \(29\times 2.3\)\" bald tire it may have been related to the relatively small toroid radius and steep shoulder drop. Again, a minor change in rim width had minimal effect. Presumably, the steep slope of the \(27.5\times 2.8\)\" and \(29\times 3\)\" plus tires between 10 and 15 psi may have been related to the widely spaced shoulder knobs contacting at lower lean angles on the less inflated, softer, and more deformed tire.