Bekker–Reece Empirical Model Excel Solver Template

The Bekker–Reece model extends Bekker’s original pressure–sinkage relationship by incorporating soil shear strength parameters—specifically cohesion (c), internal friction angle (φ), and soil density—to describe how normal pressure varies radially across the tire–soil contact patch. Unlike purely geometric or linear approximations, this empirical framework treats the contact area as an elliptical or circular footprint where pressure decays from a maximum under the axle toward zero at the leading and trailing edges, governed by soil rheology and tire geometry. The Excel Solver Template automates the nonlinear parameter estimation process: users input experimental data (e.g., total normal force, sinkage, tire radius, width) and initial guesses for soil constants; Solver then minimizes the residual error between predicted and observed pressure integrals (i.e., total load) or average pressure using constrained nonlinear optimization. This template is particularly valuable in early-stage vehicle design, agricultural machinery development, and planetary rover mobility studies—where high-fidelity FEM simulations are impractical—enabling engineers to rapidly assess trade-offs between tire inflation pressure, tread geometry, and terrain adaptability. Its transparency, auditability, and low computational overhead make it a preferred pedagogical and field-deployable resource in terramechanics education and applied off-road vehicle research.