Sensitivity Analysis of a Supersonic Airfoil’s Optimal Design Using Taylor Series
Bibliographic record
Abstract
In this study, we conducted a sensitivity analysis to determine the optimal design of a supersonic airfoil. The design includes four independent variables: angle of attack, thickness of the upper surface, and the locations of the upper and lower surfaces' maximum thicknesses. The output is the maximum lift-to-wave drag ratio. First, we used a first-order Taylor approximation to analyze the impact of each design variable on the output. The first three variables have similar effects, while the fourth has less influence. Next, we applied a second-order Taylor approximation to further explore how each variable affects the output and the response function near the optimal design point. The results show that small variations in the design variables lead to minor changes in airfoil performance. We also identified the variable ranges around this point that satisfy the constraints through numerical calculations. Finally, we compared our approach with factorial design, a common sensitivity analysis method, and found that Taylor approximations offer a more detailed theoretical explanation of the results.
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How this classification was reachedexpand
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 | 0.001 | 0.002 |
| 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) | 0.000 | 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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, 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".