# Characterization and Modelling of Various Sized Mountain Bike Tires and the Effects of Tire Tread Knobs and Inflation Pressure

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## Abstract

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## 1. Introduction

## 2. Materials and Methods

#### 2.1. Measurement

#### 2.1.1. Tire Inflated Radius

#### 2.1.2. Tire Profile

#### 2.1.3. Footprints

#### 2.1.4. Force and Moment

#### 2.1.5. Static Lateral and Radial Stiffness

#### 2.2. Fitting the Data

- $Y$: output variable. In this case, either lateral force, ${F}_{y}$, or self-aligning moment, ${M}_{{Z}_{SA}}$;
- $X$: input variable; here, either slip or camber angle in radians;and
- $B$: stiffness factor, which determined the slope at the origin;
- $C$: shape factor, which controlled the limits of the range of the sine function;
- $D$: peak value (when C was constrained as specified);
- $E$: curvature factor for the peak, controlling its horizontal position;
- ${S}_{H}$: horizontal shift;
- ${S}_{V}$: vertical shift.

- ${M}_{{Z}_{TW}}$: twisting torque due to camber, which was then normalized by
- $N$: the tire normal load in Newtons;and
- $\phi $: camber angle in radians;
- ${m}_{r}$: linear twisting torque coefficient;
- ${t}_{w}$: non-linear twisting torque coefficient.

## 3. Results and Discussion

#### 3.1. Various Sizes of Mountain Bike Tires

#### 3.1.1. Cross-Sectional Profiles

#### 3.1.2. Footprints

#### 3.1.3. Forces and Moments

#### 3.1.4. Static Lateral and Radial Stiffness

#### 3.2. Effect of Tread Knobs

#### 3.2.1. Cross-Sectional Profiles

#### 3.2.2. Footprints

#### 3.2.3. Forces and Moments

#### 3.2.4. Static Lateral Stiffness

#### 3.3. Effect of Inflation Pressures and Rim Width

#### 3.3.1. Footprints

#### 3.3.2. Forces and Moments

#### 3.3.3. Static Lateral Stiffness

## 4. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 3.**Force and moment raw data, smoothed lines, and fit curves for 29 × 2.3” knobby on 25 mm rim at 25 psi (1.7 bar) with (

**a**) normalized lateral force vs. slip angle, (

**b**) normalized lateral force vs. camber angle, (

**c**) normalized self-aligning moment vs. slip angle and (

**d**) normalized twisting torque vs. camber angle.

**Figure 4.**Cross sectional profiles for 29 × 2.3”, 27.5 × 2.8”, 29 × 3”, and 26 × 4” knobby tires, respectively.

**Figure 6.**Force and moment fitted curves for 29 × 2.3”, 27.5 × 2.8”, 29 × 3”, and 26 × 4” knobby tires with (

**a**) normalized lateral force vs. slip angle, (

**b**) normalized lateral force vs. camber angle, (

**c**) normalized self-aligning moment vs. slip angle and (

**d**) normalized twisting torque vs. camber angle.

**Figure 8.**(

**a**) Static lateral and (

**b**) radial stiffness of 29 × 2.3”, 27.5 × 2.8”, 29 × 3”, and 26 × 4” knobby bicycle tires.

**Figure 9.**Images of (

**a**) original treaded 29 × 2.3” knobby and its bald tire counterpart and (

**b**) the 29 × 2.5” file-tread tire with its bald tire counterpart.

**Figure 10.**Cross sectional profiles of 29 × 2.3” knobby tire (solid) overlaid with its bald variant (dashed), on the left, and 29 × 2.5” file-tread tire (solid) overlaid with its bald variant (dashed), on the right.

**Figure 11.**Footprints for 29 × 2.3” knobby, 29 × 2.3” bald, 29 × 2.5” file-tread, and 29 × 2.5” bald tires at 25 psi (1.7 bar) on 25 mm inner width rim.

**Figure 12.**Force and moment fitted curves for 29 × 2.3” knobby, 29 × 2.3” bald, 29 × 2.5” file-tread, and 29 × 2.5” bald tires at 25 psi (1.7 bar) on 25 mm inner width rim with (

**a**) normalized lateral force vs. slip angle, (

**b**) normalized lateral force vs. camber angle, (

**c**) normalized self-aligning moment vs. slip angle and (

**d**) normalized twisting torque vs. camber angle.

**Figure 13.**Schematic illustrating non-destructive measurement of lateral shear stiffness of tire tread knobs via loads applied to unmounted tire squeezed between appropriately sized aluminum plates.

**Figure 14.**Bar chart of knob, tread, bald carcass, measured, and calculated total tire stiffness for 29 × 2.3” knobby tire comparing relative stiffness magnitudes at 25 psi (1.7 bar).

**Figure 15.**Footprints for 29 × 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.

**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.

**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.

**Figure 18.**Knob, tread, bald carcass, measured, and calculated total tire stiffness, and knob count for 29 × 2.3” knobby tire comparing stiffness magnitudes across inflation pressures.

**Table 1.**Imperial-based marketing size versus European Tyre and Rim Technical Organisation (ETRTO) designation.

Tire Size (in) | ETRTO (mm) |
---|---|

29 × 2.3” | 58–622 |

29 × 2.5” | 63–622 |

29 × 3.0” | 76–622 |

27.5 × 2.8” | 71–584 |

26 × 4.0” | 102–559 |

© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

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**MDPI and ACS Style**

Dressel, A.; Sadauckas, J.
Characterization and Modelling of Various Sized Mountain Bike Tires and the Effects of Tire Tread Knobs and Inflation Pressure. *Appl. Sci.* **2020**, *10*, 3156.
https://doi.org/10.3390/app10093156

**AMA Style**

Dressel A, Sadauckas J.
Characterization and Modelling of Various Sized Mountain Bike Tires and the Effects of Tire Tread Knobs and Inflation Pressure. *Applied Sciences*. 2020; 10(9):3156.
https://doi.org/10.3390/app10093156

**Chicago/Turabian Style**

Dressel, Andrew, and James Sadauckas.
2020. "Characterization and Modelling of Various Sized Mountain Bike Tires and the Effects of Tire Tread Knobs and Inflation Pressure" *Applied Sciences* 10, no. 9: 3156.
https://doi.org/10.3390/app10093156