Simulation
MTB Suspension Load Simulation
A forward-dynamic 9-DOF mountain bike model with unilateral tyre contact and circle-to-curve contact detection, built to determine realistic design loads on components like the rear hub across technical trail terrain.
Links & Resources
The Engineering Question
How do you determine realistic design loads for a component as stressed as a mountain bike rear hub? Lab testing and field measurements remain the primary tools, but numerical simulation plays a complementary role: it allows rapid exploration of terrain types, rider weights, and suspension configurations that would be impractical to test experimentally.
Model
The simulation extends the classical 4-DOF half-car model with several MTB-specific features. Tyre contact is unilateral: the wheels can leave the ground, allowing the bicycle to become airborne over obstacles. Rather than prescribing a road profile as a function of time, the model introduces an additional degree of freedom for position along the course and runs as a forward dynamic simulation with terrain contact detection.
High pitch angles on steep terrain mean that tyre-road interactions can occur anywhere around the tyre's circumference, not only at the bottom. Contact detection is therefore circle-to-curve rather than point-to-curve. Both the front and rear suspension forces are two-dimensional because the front fork is inclined relative to the chassis and the rear suspension uses a pivoting linkage.
The bicycle is treated as three rigid bodies connected by a revolute joint at the rear suspension pivot and a telescopic slider at the front fork: 9 generalized coordinates, 4 constraint equations, yielding a system of 13 differential-algebraic equations integrated forward in time.
Implementation
Despite the multi-body formulation, the full model is implementable in approximately 100 lines of code. A simplified version is available on GitHub for those who want to experiment with suspension parameter variations — stiffness, damping, geometry — and observe their effect on comfort, dynamic load factors, and airborne phases.
Outputs
The primary output is the time history of forces at key attachment points, including the rear axle and suspension linkage. These forces feed directly into component fatigue and durability assessments. Secondary outputs include suspension travel history, wheel-lift events, and chassis pitch dynamics — all relevant to both component design and ride quality optimization.