## 3 Results and Discussion
### Effect of Inflation Pressures and Rim Width
#### 3.3.1 Footprints  
Figures 15 and 16 illustrate the effect of varying inflation pressure on the tire footprints for the \(29\times 2.3\"\) knobby tire on 25 mm rim. The images show that as inflation pressure increased from left to right, the contact patch length and width became smaller and thus contact patch area was reduced. Interestingly, for the \(29\times 2.3\"\) knobby tire at 10 psi, in the leftmost plot, the tire deformed enough for the shoulder knobs to contact the ground (even at zero camber), and thus the shape of the patch became significantly wider. As inflation pressure increased, fewer and fewer individual knobs remained in the contact patch. Figure 16 shows contact patch characteristics as functions of inflation pressure. The \(29\times 2.3\"\) knobby, \(29\times 2.3\"\) bald, \(29\times 2.5\"\) file-tread, and \(29\times 2.5\"\) bald tires were measured at eight pressure increments. This gave added resolution to various trends. The other three knobby tires in \(27.5\times 2.8\"\), \(29\times 3\"\), and \(26\times 4\"\) are also shown, but with inflation pressure at just two levels, 10 psi (potential use case for lightweight riders or usage on soft or loose terrain), and the \"nominal\" pressure considered in previous sections. Finally, two additional datapoints of the \(29\times 2.3\"\) knobby and \(29\times 2.5\"\) file-tread tire on slightly narrower, 22 mm internal rim widths are shown to begin to explore those effects. Figure 15: Footprints for \(29\times 2.3\"\) knobby tire at inflation pressures of 10, 20, 30, 40, and 50 psi (0.7, 1.4, 2.1, 2.8, and 3.4 bar) from left to right on 25 mm inner width rim. The upper left plot (Figure 16a) suggests the ranking of tires in terms of contact patch area varied somewhat with inflation pressure, but in general the contact patch area decreased in a seemingly nonlinear fashion with increasing inflation pressure. Here, the 26x4\" fat bike tire remained near the largest, whereas the \(29\times 2.3\)\" knobby surpassed the plus tires between 10 and 20 psi. The contact patch area of the less-treated tires in the form of the \(29\times 2.5\)\" file-tread on the 25 mm rim, \(29\times 2.3\)\" bald, and \(29\times 2.5\)\" bald tire seemed slightly more sensitive in the lower pressure regime (from 10 to 15 psi), whereas as pressure was increased (beyond 20 psi), the curvature stabilized. The \(29\times 2.3\)\" knobby on 22 mm rim and \(29\times 2.5\)\" file-tread tire on 22 mm rims showed a small decrement in contact patch area with respect to their 25 mm rim variants. The upper right plot (Figure 16b) depicts how the tread void ratio within the contact patch area varied between tires and with inflation pressure. It is quite clear that the knobby tires had higher void ratios than the \(29\times 2.5\)\" file-tread on 25 mm rim at all but the lowest inflation pressure. The \(26\times 4\)\" fat bike tire and \(29\times 2.3\)\" knobby tire were both around 80% void ratio at low pressures, which for the \(29\times 2.3\)\" knobby tire on 25 mm rim fell to 74% at 50 psi. Seemingly, scaling the knob size up for the \(27.5\times 2.8\)\" and \(29\times 3\)\" plus tires caused a small reduction in their void ratio with respect to the \(29\times 2.3\)\" knobby tire on the 25 mm rim. The void ratio of the \(29\times 2.5\)\" bald tire, which contained only  
Figure 16: Tire footprint parameters versus inflation pressure for various bicycle tires with (**a**) contact patch area, (**b**) void ratio, (**c**) contact patch length and (**d**) contact patch width. the negative grooves, reduced from 20% to 10% with increasing inflation pressure, whereas the nearly slick \(29\times 2.3\)\" bald tire hovered at a void ratio less than 5%. The lower two plots show the contact patch length (Figure 16c) and width (Figure 16d) versus inflation pressure. Here, the length was generally at least twice the width or more.