New formula to calculate the skin effect in isolated tubular conductors at low frequencies
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Bibliographic record
Abstract
The exact solution of the AC/DC resistance ratio of an isolated tubular conductor involves the calculation of values from 12 Kelvin functions. Previous approximate solutions are complicated, and graphical solutions require interpolation from sets of curves. A simplified solution, based on a new formula, is presented. The values of the resistance ratio derived from this formula are within ±1% of those derived from the exact solution in the practical ranges 0.05 ≤ (thickness/diameter) ≤ 0.40 and 0 < √(frequency/DC resistance) ≤ 3000, except for t/D2 = 0.40 and √(f/Rdc) > 2000. For practical tubular conductors, the formula can be used for frequencies up to about 10 kHz, depending on the thickness t and the outer diameter D2. The application of the skin effect formula to a steel-cored conductor can result in significant error.
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.002 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it