New formula to calculate the skin effect in isolated tubular conductors at low frequencies
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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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.003 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.004 | 0.002 |
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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".