Agricultural Engineering / Bekker Terramechanics Sinkage
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LABORATORY 37 · AGRICULTURAL ENGINEERING

Bekker Theory of Off-Road Terramechanics & Rigid Wheel Sinkage

Evaluate pressure-sinkage behavior of agricultural soil under plate loading to determine Bekker terramechanic sinkage exponent and cohesive/frictional moduli. Explore interactive farm machinery simulation, irrigation hydraulics, and agricultural engineering telemetry.

FARM MACHINERY · SOIL & WATER · POST-HARVEST · STRUCTURES

Your virtual agricultural engineering laboratory.

SOIL NORMAL PRESSURE P—
FIELD & TEST CELL TELEMETRY

Ready to sample with Sinkage z_s = 3.0 cm.

3.0 cm
Test soil: Tilled agricultural silt loam

Adjust Sinkage z_s, then execute agricultural trial.

Agricultural engineering telemetry and biosystems states are evaluated rigorously using 64-bit IEEE 754 precision. Residuals reflect ordinary least-squares regression across successive observations. Continuous data structures support high-fidelity agricultural and environmental modeling.

Agricultural assumptions and boundary condition limits

The power-law relationship applies to vertical sinkage up to 6.0 cm; at extreme sinkage, lateral soil flow causes blowout. Evaluated on tilled agricultural loam soil using a circular bevameter flat plate of diameter 10.0 cm (b = 5.0 cm). Data transformed into natural logarithmic coordinates ln(z_s) and ln(p) to extract sinkage exponent n and combined modulus k.

Agricultural apparatus & field instrumentation sensors.

Agricultural Bevameter Test Rig

Applies controlled hydraulic vertical loads to soil penetration plates while logging displacement.

Interchangeable Circular Bevameter Plates

Provides hardened steel plates of 50 mm, 100 mm, and 150 mm diameters for Bekker modulus separation.

High-Precision Hydraulic Pressure Transducer

Measures hydraulic actuator pressure to compute plate normal contact force with 0.05 kN precision.

Linear Potentiometer Sinkage Sensor

Monitors plate vertical penetration into the soil surface with 0.1 mm measurement accuracy.

Digital Strain-Gauge Telemetry Console

Logs simultaneous force-displacement signals at 50 Hz during continuous plate depression.

Core Soil Sampler & Bulk Density Ring

Extracts undisturbed 100 cm³ soil cores to establish pre-test bulk density and moisture content.

FOLLOW THE METHOD

A reason behind every step.

Evaluate pressure-sinkage behavior of agricultural soil under plate loading to determine Bekker terramechanic sinkage exponent and cohesive/frictional moduli. Standardized parameter settings: 1.0, 2.0, 3.0, 4.0, 5.0, 6.0 cm.

01

Soil Surface Preparation and Bevameter Setup

Level the tilled field test patch, remove loose surface crop residue, and anchor the bevameter reaction truck firmly over the site.

02

Plate Mounting and Zero Contact Referencing

Attach the 100 mm diameter circular test plate, lower it until light initial contact (0.5 kPa) occurs, and zero the displacement sensor.

03

Constant-Velocity Hydraulic Loading

Advance the hydraulic actuator downward at a controlled rate of 10 mm/s, driving the plate into the soil up to 6.0 cm sinkage.

04

Continuous Force-Sinkage Telemetry Logging

Record instantaneous sinkage depth z_s and vertical contact force continuously throughout the penetration stroke.

05

Discrete Pressure-Sinkage Extraction

Extract normal contact pressure p = F / A_p at discrete sinkage depths of 1.0, 2.0, 3.0, 4.0, 5.0, and 6.0 cm.

06

Logarithmic Transformation and Regression

Compute natural logarithms ln(z_s) and ln(p), plotting the linearized curve and determining the Bekker sinkage exponent n from the slope.

YOUR NOTEBOOK · 0 OBSERVATIONS

Turn measurements into agricultural engineering insight.

See a complete example report ↗

Points are your recorded observations. The solid regression line validates Bekker Terramechanics Sinkage mathematical scaling.

LINEAR REGRESSION FIT · y = mx + b
ln(p) = n · ln(z_s) + ln(k) = 0.8500 · ln(z_s) + 2.1000
#Plate Sinkage z_s (cm)Soil Normal Pressure p (kPa)ln(Sinkage z_s) (ln[cm])ln(Normal pressure p) (ln[kPa])Remove

No readings yet. Execute an agricultural trial and record it.

Calculate it yourself.

CHECK YOUR UNDERSTANDING

Explain what the agricultural metrics mean.

In Bekker's classical terramechanic equation p = (k_c/b + k_phi) · z^n, what does n represent?

For most tilled agricultural loams, the Bekker sinkage exponent n typically falls in what range?

If ln(p) = 0.8500 · ln(z_s) + 2.1000, what is the fitted Bekker sinkage exponent n?

What terramechanical instrument measures soil pressure-sinkage and shear strength in the field?