Formulas for the fuel of climbing propeller driven airplanes
Why this work is in the frame
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Bibliographic record
Abstract
Purpose The purpose of this paper is to derive and solve equations for the fuel required by internal combustion engine airplanes on trajectories with a constant rate of climb or descent. Three modes of flight are considered: constant angle of attack, constant speed, and constant Mach number. Design/methodology/approach Newton's second law of motion is used to derive the equations. These are Riccati equations or reduced to such equations after neglecting a small term. A change of variable transforms them into second order linear differential equations that are solved exactly. Findings Formulas are found for the weight of fuel, speed, altitude, horizontal distance, time to climb, and power required. Practical implications The formulas obtained have direct applications for the analysis of aircraft performances and mission planning. Originality/value The formulas obtained are new and fundamental for the analysis of aircraft dynamics.
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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 | 0.000 | 0.000 |
| 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 it