Hairspring Concentric Breathing Change Calculator
Calculate the diameter envelope of a modeled concentric breathing hairspring excursion without inferring spring geometry from a terminal-curve name.
Description
A concentric-breathing model summarizes a supplied diameter and excursion.
A concentric-breathing model summarizes a supplied diameter and excursion. The returned envelope follows the implementation’s chosen convention.1
Calculate the diameter envelope of a modeled concentric breathing hairspring excursion without inferring spring geometry from a terminal-curve name.
When to use Hairspring Concentric Breathing Change Calculator
Use this tool to calculate the diameter envelope of a modeled concentric breathing hairspring excursion without inferring spring geometry from a terminal-curve name.
Choose a supported reference focus or prepare the watch measurements, evidence and explicit limits requested. Confirm units and date conventions before running.
How to use Hairspring Concentric Breathing Change Calculator and understand its results
- Choose a supported reference focus or prepare the watch measurements, evidence and explicit limits requested. Confirm units and date conventions before running.
- Enter meanDiameterMillimeters, radialExcursionMillimeters using the field table and calculation rules, then run the tool.
- Read diameterExcursionMillimeters, excursionRatio, maximumDiameterMillimeters, minimumDiameterMillimeters. The explanation below defines the units, signs, ordering and any flags or placeholder values.
- If the tool reports an input issue, correct the values and run it again. Apply the stated assumptions when interpreting a successfully returned result.
| Input field | Meaning | Value type; see rules below | Requirement |
|---|---|---|---|
| meanDiameterMillimeters | Mean breathing diameter (mm) | number; minimum: 0 | Required |
| radialExcursionMillimeters | Radial excursion (mm) | number; minimum: 0 | Required |
Enter positive mean diameter and nonnegative excursion with 2excursion<mean. Return excursion, ratio and the stated bounds in mm.
diameterExcursion=2radialExcursion; ratio=2excursion/mean; bounds=mean±excursion Units, indexing, boundary conditions and exceptional cases are defined in the calculation rules above.
| Output field | Meaning | Value type |
|---|---|---|
| diameterExcursionMillimeters | Diameter excursion (mm) | number; minimum: 0 |
| excursionRatio | Diameter excursion ratio | number; minimum: 0 |
| maximumDiameterMillimeters | Maximum diameter (mm) | number; minimum: 0 |
| minimumDiameterMillimeters | Minimum diameter (mm) | number; minimum: 0 |
{
"input": {
"meanDiameterMillimeters": 10,
"radialExcursionMillimeters": 0.2
},
"output": {
"diameterExcursionMillimeters": 0.4,
"excursionRatio": 0.04,
"maximumDiameterMillimeters": 10.2,
"minimumDiameterMillimeters": 9.8
}
}Limitations and assumptions
The bounds use ±excursion directly; the tool does not derive terminal geometry, actual coil motion or rate behavior.
Numeric inputs, where present, must be finite. Follow the calculation-specific rules for overflow, underflow and exceptional cases. Missing required fields, extra fields, wrong value types and violations of the calculation rules are input errors.
Alternative or Complementary methods
Use Breguet Overcoil Terminal Curve Lookup: Return the documented geometry, date, purpose, breathing intent, or limitation of a Breguet overcoil terminal curve. For a complementary task, use Isochronism Amplitude Rate Slope Calculator: Measure the endpoint rate change and slope between two caller-supplied amplitude observations; this does not turn a two-point slope into a complete isochronism curve.
References
Similar or alternative tools
- Breguet Overcoil Terminal Curve Lookup
Return the documented geometry, date, purpose, breathing intent, or limitation of a Breguet overcoil terminal curve.
- Isochronism Amplitude Rate Slope Calculator
Measure the endpoint rate change and slope between two caller-supplied amplitude observations; this does not turn a two-point slope into a complete isochronism curve.