Middle Temperature Rate Error Calculator
Calculate the middle-temperature departure from the straight line between caller-supplied low- and high-temperature daily rates.
Description
Middle-temperature error is the observed rate’s departure from interpolation between two endpoint rates.
Middle-temperature error is the observed rate’s departure from interpolation between two endpoint rates. It quantifies curvature at one supplied intermediate temperature.1
Calculate the middle-temperature departure from the straight line between caller-supplied low- and high-temperature daily rates.
When to use Middle Temperature Rate Error Calculator
Use this tool to calculate the middle-temperature departure from the straight line between caller-supplied low- and high-temperature daily rates.
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 Middle Temperature Rate Error 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 highRateSecondsPerDay, highTemperatureCelsius, lowRateSecondsPerDay, lowTemperatureCelsius, middleRateSecondsPerDay, middleTemperatureCelsius using the field table and calculation rules, then run the tool.
- Read linearMiddleRateSecondsPerDay, middleTemperatureErrorSecondsPerDay, observedMiddleRateSecondsPerDay, profile, rateChangeHighToMiddleSecondsPerDay, rateChangeLowToMiddleSecondsPerDay. 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 |
|---|---|---|---|
| highRateSecondsPerDay | High-temperature daily rate (s/day) | number | Required |
| highTemperatureCelsius | High temperature (degC) | number | Required |
| lowRateSecondsPerDay | Low-temperature daily rate (s/day) | number | Required |
| lowTemperatureCelsius | Low temperature (degC) | number | Required |
| middleRateSecondsPerDay | Middle-temperature daily rate (s/day) | number | Required |
| middleTemperatureCelsius | Middle temperature (degC) | number | Required |
Enter finite rates and temperatures with low<middle<high. Return interpolated/observed rates, signed error, sign-based profile, middle−low rate and high−middle rate differences.
error=middleRate−[lowRate+(middleT−lowT)/(highT−lowT)×(highRate−lowRate)] Units, indexing, boundary conditions and exceptional cases are defined in the calculation rules above.
| Output field | Meaning | Value type |
|---|---|---|
| linearMiddleRateSecondsPerDay | Linearly interpolated middle rate (s/day) | number |
| middleTemperatureErrorSecondsPerDay | Middle-temperature error (s/day) | number |
| observedMiddleRateSecondsPerDay | Observed middle rate (s/day) | number |
| profile | Middle-temperature profile | string; one of "gainAtMiddle", "lossAtMiddle", "zeroMiddleError" |
| rateChangeHighToMiddleSecondsPerDay | High-to-middle rate change (s/day) | number |
| rateChangeLowToMiddleSecondsPerDay | Low-to-middle rate change (s/day) | number |
{
"input": {
"highRateSecondsPerDay": 0,
"highTemperatureCelsius": 38,
"lowRateSecondsPerDay": 0,
"lowTemperatureCelsius": 8,
"middleRateSecondsPerDay": 2,
"middleTemperatureCelsius": 23
},
"output": {
"linearMiddleRateSecondsPerDay": 0,
"middleTemperatureErrorSecondsPerDay": 2,
"observedMiddleRateSecondsPerDay": 2,
"profile": "gainAtMiddle",
"rateChangeHighToMiddleSecondsPerDay": -2,
"rateChangeLowToMiddleSecondsPerDay": 2
}
}Limitations and assumptions
No thermal curve fit, uncertainty or compensation mechanism is derived.
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 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. 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
-
Middle Temperature Rate Error Calculator — tool.io
Similar or alternative tools
- 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.
- 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.