MTB Tire Dynamics Simulator - [Pacejka & FastBike Model]
MTB Tire Dynamics Simulator
Pacejka Magic Tire Formula · FastBike Twisting Torque Polynomial
Dressel, A.; Sadauckas, J.
RESEARCH INTERACTIVE
Every option is a tire, rim and pressure the paper actually tested
Paper’s tires The paper’s four knobby tires at their nominal pressure. A chip fills the selected slot (A or B).
A → — B → —
Fy/° — — mr —
Lateral force Fy vs slip angle α
Cornering stiffness — slope at the origin, measured range only
The steeper the line, the less steering angle the tire needs to make the same cornering force.
FIG. 6a
Lateral force Fy vs camber angle φ
Camber stiffness — force from leaning alone
The dotted line is the tangent rule: the force a tire would need to make from a lean alone. A line above it makes more than that.
FIG. 6b
Self-aligning moment Mz vs slip angle α
Negative = the moment that turns the wheel back toward straight
More negative means a stronger pull back toward straight. The paper could only measure the first couple of degrees of slip.
FIG. 6c
Twisting torque vs camber angle φ
FastBike polynomial: MZTW = mr·φ·N·(1 + tw·φ²)
The torque a leaned tire puts on the steering. A bigger value means more steering effort, which the paper links to the “autosteer” feel of fat bikes.
FIG. 6d
Contact patch footprint
The paper’s fitted ellipse, drawn to scale at zero camber
Mostly air: the void ratio is the share of the ellipse not touching the ground. Lower pressure makes it longer and wider.
FIG. 5, 16
Side by side Overlaid 0%
Cornering versus inflation pressure
Every tire the paper tested is drawn; yours is highlighted
Pick a quantity below. Tires with only two points were measured at just two pressures.
FIG. 16, 17
Tire cross-section
Outline of the tire on its rim, traced from the paper’s photographs
Crowns are lined up and one scale is shared, so widths and knob heights compare directly. The grey bar is the rim’s inner width.
FIG. 4, 10
Knobs as springs
Stiffness of the 29″ × 2.3″ knobby on a 25 mm rim, in N/m
Knobs push in parallel (they add up), but the whole tread sits in series with the carcass (the weaker one dominates). Fewer knobs touch the ground as pressure rises.
FIG. 14, 18
Static stiffness
Pushed sideways and straight down, not rolling (N/m)
Lateral = sideways give of the tire on its rim. Radial = vertical. The tires you have selected are highlighted.
FIG. 8
This redfoxrun | post millennium renaissance project is based on the 2020 paper. 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 · The paper is © 2020 its authors, licensed CC BY 4.0. Changes: values shown here are printed in the paper or read from its figures (±3–5 %) and re-plotted. Not endorsed by the authors or MDPI.