Binary Flutter as an Oscillating Windmill — Scaling & Linear Analysis
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Bibliographic record
Abstract
Alternating pitch and heave of a foil can tap light wind or slow free water flow, as the design flow speed for an oscillating blade in any fluid is shown to be limited by its material's ratio of endurance stress to density. The free amplitude of flutter instability is inherently suited to reciprocating a pump whose stroke needs to vary to efficiently capture the changeable wind. Whereas the useful pumping work of multiblade rotary windpumps with their fixed stroke is only 10% of the ideal annual wind energy capture. Stability algebra of a foil free in pitch and elastic in heave is analytically solved for the first time to prove the stability contours of all Theodorsen frequencies radiate from the same super node of total imbalance and pitch inertia the same as for a virtual mass confined to the 3/4 chord point. The flutter frequency only involves these totals and the trail of the center of pressure behind the pitch axis. Oscillation is damped in the low ratios of total to virtual typical of hydrofoils in water but heavier- than-air wings can be unstable. High intrinsic pitch inertia ratio and trail decrease the tailheavy imbalance ratio needed to force pitch by heave. Perturbing the equations for heave varying as semi-rotary roll, an unswept wing of low enough dynamic imbalance ratio can start to flutter in light wind but stop and feather in storms. The dynamic imbalance can be reduced at large scale and low design windspeed where the gravity effect of static imbalance more safely forces pitch. Between starting and stopping, the amplitude ratio of pitch to roll drops, containing the rise with windspeed of the bending moment amplitude.
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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 | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.001 | 0.001 |
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