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Rail-Wheel Hertz Contact Stress Calculator

Easily calculate and compute rail-wheel hertz contact stress calculator with accurate equations, live formulas, and expert guidance.

Static or dynamic vertical contact force.

Nominal wheel tread radius (e.g. 920 mm diameter = 460 mm).

Transverse crown radius (typically 300 mm central, 80 mm shoulder).

Steel elastic modulus.

Material Poisson ratio.

Calculated Result
2,048.42 MPa

Maximum Hertzian Contact Pressure

Maximum Hertzian Contact Pressure

2,048.42 MPa

Max Pressure Mpa

2048.4233335891413

Peak Subsurface Shear Mpa

635.0112334126338

Contact Area Mm2

80.54975614386092

Mean Contact Radius Mm

5.063574203098486

2,048.42 — MPa

Calculation Breakdown

  1. Applied FormulaCalculates three-dimensional elastic Hertzian contact elliptical footprint semi-axes (a, b), maximum compressive pressure (p_0), and subsurface peak shear stress under wheel loads.p_0 = \frac{3 P}{2 \pi a b}, \quad \tau_{max} \approx 0.31 p_0

Wheel-Rail Hertz Stress Metric Output

Interactive visualization based on your current inputs

Calculated Value
0.05121.0k1.5k2.0kMaximum Hertzian Contact Pressure

What Is the Rail-Wheel Hertz Contact Stress Calculator?

This tool computes rail-wheel hertz contact stress calculator with high precision arithmetic.

How Does the Rail-Wheel Hertz Contact Stress Calculator Work?

Calculates three-dimensional elastic Hertzian contact elliptical footprint semi-axes (a, b), maximum compressive pressure (p_0), and subsurface peak shear stress under wheel loads.

Rail-Wheel Hertz Contact Stress Calculator Formula & Variables

The core mathematical equation utilized by this calculator is expressed as:

p0=3P2πab,τmax≈0.31p0p_0 = \frac{3 P}{2 \pi a b}, \quad \tau_{max} \approx 0.31 p_0

Calculates three-dimensional elastic Hertzian contact elliptical footprint semi-axes (a, b), maximum compressive pressure (p_0), and subsurface peak shear stress under wheel loads.

How to Use the Rail-Wheel Hertz Contact Stress Calculator

  1. Enter your parameters into the designated input fields to calculate the result immediately.

Step-by-Step Example Calculation

Rail-Wheel Hertz Contact Stress Calculator Example

Input Values:

wheelLoadKN:110
wheelRadiusMm:460
railCrownRadiusMm:300
elasticModulusGpa:210
poissonRatio:0.3
Worked Steps: Sample evaluation based on standard reference conditions.

Understanding Your Result

The calculated primary figure indicates the optimal or required MPa.

Factors That Affect the Result

  • Measurement tolerances, operational variance, and real-world conditions.

When Should You Use This Calculator?

  • Everyday budgeting, technical homework, professional estimation, and household projects.

Assumptions & Limitations

  • Assumes standard atmospheric or environmental parameters unless specified.

Frequently Asked Questions

Calculation Accuracy & Reference Note

Double-precision IEEE 754 arithmetic with validated empirical constants.

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