Optimizing Candle Shapes for Maximum Flame Luminosity and Minimal Wax Residue
Bibliographic record
Abstract
Combustion processes are among the most widely used energy conversion methods, with candles as a small-scale example. As with similar processes, energy efficiency in candles is often sought. While previous studies have independently investigated the behavior of candle flames, burning wax, and air flows, an optimized relationship between all three remains underexplored. This study aims to investigate candle shapes that maximize flame luminosity and to explore the shapes resulting in minimal wax residue. To investigate the former, the relationship between luminosity and wax pool radius will be explored through both theory and experimentation. Then, for the latter, the growth rate of the wax pool as a function of time will be theoretically and experimentally studied. Candle shapes will be predicted based on the previous results and fluid dynamics theory. They will then be tested and compared. Preliminary results show that an inverted paraboloid-shaped candle produces the most luminous flame, and thin cylindrical candles (radius ~1cm or less) limit wax residue the most, but more trials will be recorded to ensure accuracy of these results and explore more shapes. This study’s limitations include measurement precision affected by environmental factors like natural air currents, even in a controlled setting, and the limited number of candle shapes that can be tested, which might not fully capture the most optimal geometries. Regardless of the specific findings, this study will contribute to a better understanding of small-scale combustion processes, with potential applications in energy efficiency, more sustainable candle designs, and fluid dynamics research.
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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 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.003 | 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 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".