Method to Calculate Aircraft VNAV Trajectory Cost Using a Performance Database
Bibliographic record
Abstract
Vertical Navigation (VNAV) trajectory optimization has been identified as a means to reduce fuel consumption. Due to the computing power limitations of devices such as Flight Management Systems (FMSs), it is very desirable to implement a fast method for calculating trajectory cost using optimization algorithms. Conventional trajectory optimization methods solve a set of differential equations called the aircraft equations of motions to find the optimal flight profile. Many FMSs do not use these equations, but rather a set of lookup tables with experimental, or pre-calculated data, called a Performance Database (PDB). This paper proposes a method to calculate a full trajectory flight cost using a PDB. The trajectory to be calculated is composed of climb, acceleration, cruise, descent and deceleration flight phases. The influence of the crossover altitude during climb and step climbs in cruise were considered for these calculations. Since the PDB is a set of discrete data, Lagrange linear interpolations were performed within the PDB to calculate the required values. Given a takeoff weight, the initial and final coordinates and the desired flight plan, the trajectory model provides the Top of Climb coordinates, the Top of Descent coordinates, the fuel burned and the flight time needed to follow the given flight plan. The accuracy of the trajectory costs calculated with the proposed method was validated for two aircraft; one with an aerodynamic model in FlightSIM, software developed by Presagis, and the other using the trajectory generated by the reference FMS.
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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 | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.005 | 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".