Balance–Spring Temperature Rate Change
Estimate relative period and rate change from T proportional to the square root of balance inertia divided by hairspring stiffness, using caller-supplied first-order coefficients.
Description
Small temperature changes in oscillator inertia and spring stiffness produce a first-order period change.
Small temperature changes in oscillator inertia and spring stiffness produce a first-order period change. Rate change has the opposite sign to period change.1
Estimate relative period and rate change from T proportional to the square root of balance inertia divided by hairspring stiffness, using caller-supplied first-order coefficients.
When to use Balance–Spring Temperature Rate Change
Use this tool to estimate relative period and rate change from T proportional to the square root of balance inertia divided by hairspring stiffness, using caller-supplied first-order coefficients.
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 Balance–Spring Temperature Rate Change 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 balanceInertiaCoefficientPerCelsius, hairspringStiffnessCoefficientPerCelsius, temperatureChangeCelsius using the field table and calculation rules, then run the tool.
- Read relativePeriodChange, relativePeriodChangePercent, relativeRateChangeApproximation. 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 |
|---|---|---|---|
| balanceInertiaCoefficientPerCelsius | Balance inertia coefficient (1/degC) | number | Required |
| hairspringStiffnessCoefficientPerCelsius | Hairspring stiffness coefficient (1/degC) | number | Required |
| temperatureChangeCelsius | Temperature change (degC) | number | Required |
Enter finite signed coefficients per °C and temperature change. Return relative period change, percentage and its negative as approximate rate change.
relativePeriod=0.5(inertiaCoefficient−stiffnessCoefficient)×temperatureChange Units, indexing, boundary conditions and exceptional cases are defined in the calculation rules above.
| Output field | Meaning | Value type |
|---|---|---|
| relativePeriodChange | First-order relative period change | number |
| relativePeriodChangePercent | First-order relative period change (%) | number |
| relativeRateChangeApproximation | First-order relative rate-change approximation | number |
{
"input": {
"balanceInertiaCoefficientPerCelsius": 0.00002,
"hairspringStiffnessCoefficientPerCelsius": -0.00004,
"temperatureChangeCelsius": 10
},
"output": {
"relativePeriodChange": 0.00030000000000000003,
"relativePeriodChangePercent": 0.030000000000000002,
"relativeRateChangeApproximation": -0.00030000000000000003
}
}Limitations and assumptions
No nonlinear temperature curve, material coefficient or seconds/day rate is fitted.
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 Middle Temperature Rate Error Calculator: Calculate the middle-temperature departure from the straight line between caller-supplied low- and high-temperature daily rates. For a complementary task, use Balance Rim Thermal Expansion Change Calculator: Calculate linear thermal expansion of a balance rim from its diameter, material coefficient, and signed temperature change.
References
-
Balance–Spring Temperature Rate Change — tool.io
Similar or alternative tools
- Middle Temperature Rate Error Calculator
Calculate the middle-temperature departure from the straight line between caller-supplied low- and high-temperature daily rates.
- Balance Rim Thermal Expansion Change Calculator
Calculate linear thermal expansion of a balance rim from its diameter, material coefficient, and signed temperature change.