CALCULATORS / MATERIAL RESPONSE AND SELECTION

Hertzian contact screening calculator

Hertz sphere on plane with supplied effective elastic modulus; elastic frictionless contact.

materials-contact-stress.napkin / editable

SCENARIO COMPARISON

Compare the numbers.

This source describes an analytical model. Its quantities and checks are the view.

Scenario	contactRadiusmm	peakMPa
	0.195743	1246.14
	0.181712	1156.81

All calculated quantities are listed with the inputs. Switch to Source to inspect the equations.

SCENARIOS / CALCULATED VALUESSAME SOURCE

Change an input to see the consequences.

contact pressure budget1246.14 MPa✓ passes

BASELINE INPUTS

load100 Nradius10 mmeffectiveModulus100 GPa

CALCULATED

contactRadius0.19574 mm

peak1246.1 MPa

Edits change the baseline source.

THE SOURCE

Edits below update the same model.

# Hertzian contact screening
# Scope: Hertz sphere on plane with supplied effective elastic modulus; elastic frictionless contact.
# Status: illustrative worked example; engineering review pending.
# Inputs are example values. Checks are editable example requirements, not standards.

load = 100 N
radius = 10 mm
effectiveModulus = 100 GPa

contactRadius := (3*load*radius/(4*effectiveModulus))^(1/3) [mm]
peak := 3*load/(2*pi*contactRadius^2) [MPa]

check contact pressure budget: peak <= 2000 MPa

scenario alternative: load = 80 N

Calculated from your source · not saved

Baseline · Baseline

contact pressure budget1246.14 MPa ✓ passes

alternative · alternative

contact pressure budget1156.81 MPa ✓ passes

Illustrative first-order example. Checks are editable requirements, not design standards. The broader topic may require additional equations, data, and validation.

Formula and units

This example uses the following equations. Input names and units match the editable source above.

contact radius: contactRadius = (3*load*radius/(4*effectiveModulus))^(1/3) [mm]
peak: peak = 3*load/(2*pi*contactRadius^2) [MPa]

Original worked example

These are the baseline values in the downloadable source. Edits above let you test your own values.

Given

load: 100 N
radius: 10 mm
effective modulus: 100 GPa

Calculated

contact radius: 0.195743 mm
peak: 1246.14 MPa

Assumptions and limits

Hertz sphere on plane with supplied effective elastic modulus; elastic frictionless contact.

The requirement checks use the limits written in this example. Passing a check does not establish that the model covers every load, material behavior, or operating condition in a real design.

Download this .napkin example ↓

Take it further with your agent

Napkin keeps the inputs, equations, checks and assumptions together in one study. Your agent sets it up; you change the numbers.

Try with Claude ↗

codex 'Use Napkin (https://napkin.engineering/mcp, or the local Napkin plugin) to build a study: Hertzian contact screening. Inputs: contact shapes; load; elastic properties. Outputs: contact patch; peak pressure. Model scope: Screening with user-supplied or cited material properties. Read napkin_capabilities and the current snapshot. Ask me for the values that matter, label assumptions with units, author .napkin source, validate it and apply it with napkin_source using the current revision, then open the study. Add checks for the limits I supply. Keep unsupported analyses explicit.'

Claude needs the Napkin connector; Codex needs the Napkin plugin. Set up your agent ↗

The broader study

The topic brief below describes the broader scope. The worked example above states the particular calculation it implements.

Inputs: contact shapes, load, elastic properties
Outputs: contact patch, peak pressure
Modes: calculate, compare, sweep
Drawing: Material tradeoff plot

EXECUTABLE WORKED EXAMPLE · FIRST-ORDER MODEL · CHECK THE SCOPE & ASSUMPTIONS