Raup Coil Log-Spiral W-D Parameters Solver

Fit logarithmic whorl radial expansion per full turn and report Raup-style D under explicit inner/outer radius convention; only W/D are estimated, not generating shape, axial translation or 3D reconstruction.

Description

Logarithmic coiling expresses multiplicative radial expansion per turn.

Logarithmic coiling expresses multiplicative radial expansion per turn. The chosen inner/outer radius convention defines the distance parameter.

When to use Raup Coil Log-Spiral W-D Parameters Solver

Use this tool to fit logarithmic whorl radial expansion per full turn and report Raup-style D under explicit inner/outer radius convention; only W/D are estimated, not generating shape, axial translation or 3D reconstruction.

Prepare the fossil measurements or occurrence records and the chosen calibration parameters. Retain the stated coordinate, age and measurement conventions.

How to use Raup Coil Log-Spiral W-D Parameters Solver and understand its results

Prepare the fossil measurements or occurrence records and the chosen calibration parameters. Retain the stated coordinate, age and measurement conventions.
Enter cumulativeTurns, outerWhorlRadiiMm, innerWhorlRadiiMm using the field table and calculation rules, then run the tool.
Read fittedWhorlExpansionW, meanInnerOuterDistanceD, logRadiusFitRSquared. 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
cumulativeTurns	Cumulative turns	list of number	Required
outerWhorlRadiiMm	Outer whorl radii mm	list of number	Required
innerWhorlRadiiMm	Inner whorl radii mm	list of number	Required

Align increasing cumulative turns with positive outer and nonnegative inner radii no greater than outer. Fit log radius, require positive slope and return W, mean D and R².^[1]

Paired lists must be nonempty and have equal lengths. Each sequence checked for increasing order must contain at least two strictly increasing values. The least-squares fit needs at least two aligned observations and a varying independent variable; a constant dependent variable has reported R² of 1.

W = exp(slope of ln(outer radius) versus turns); D = mean(inner/outer)

Units, indexing, boundary conditions and exceptional cases are defined in the calculation rules above.

Output field	Meaning	Value type
fittedWhorlExpansionW	Fitted whorl expansion w	number
meanInnerOuterDistanceD	Mean inner outer distance d	number
logRadiusFitRSquared	Log radius fit r squared	number

json

{
  "input": {
    "cumulativeTurns": [
      0,
      1,
      2
    ],
    "outerWhorlRadiiMm": [
      10,
      20,
      40
    ],
    "innerWhorlRadiiMm": [
      5,
      10,
      20
    ]
  },
  "output": {
    "fittedWhorlExpansionW": 1.9999999999999998,
    "meanInnerOuterDistanceD": 0.5,
    "logRadiusFitRSquared": 1
  }
}

Limitations and assumptions

Only W and D are estimated; no axial translation, generating shape or 3D reconstruction.

Numbers and computed results must be finite; overflow produces an error. Numeric lists are limited to 100,000 entries; the rules above may require smaller limits. Missing required fields, extra fields, wrong value types and violations of the calculation rules are input errors.

Alternative or Complementary methods

Use Foraminifera Test Coiling Ratio Percent: Report observed foraminiferal coiling proportions with ambiguous tests retained on the full denominator; chirality alone does not infer temperature or a species identity. For a complementary task, use Body Size Frequency Log-Normal Fit Check: Summarize empirical population moments in log body-size space with a caller skewness screen; not a formal distribution goodness-of-fit test or proof of lognormality.

References

Raup Coil Log-Spiral W-D Parameters Solver — tool.io

Similar or alternative tools

Foraminifera Test Coiling Ratio Percent
Report observed foraminiferal coiling proportions with ambiguous tests retained on the full denominator; chirality alone does not infer temperature or a species identity.
Body Size Frequency Log-Normal Fit Check
Summarize empirical population moments in log body-size space with a caller skewness screen; not a formal distribution goodness-of-fit test or proof of lognormality.