This paper presents an Improved Range Equation (IRE) for fully fueled aircraft that incorporates climb, cruise, and descent phases within a single analytical framework. Unlike the classical Bréguet equation, which assumes steady cruise and neglects non-cruise segments, the proposed formulation introduces phase-dependent fuel fractions to account for mission-wide fuel consumption. The model is validated against (i) a forward–backward iterative numerical method based on BADA data and (ii) real flight trajectories obtained via waypoint reconstruction (which is also the ground truth). Three aircraft types—ATR72-600, B737-800, and B777-300—were analyzed across nine routes ranging from 155 km to 7538 km. Results show that the IRE reduces the relative error compared to measured waypoint distance/s by approximately 26–77% compared with the classical Bréguet equation, depending on aircraft class. Here, the reported percentages represent the reduction in percentage error relative to the Bréguet-based estimates using waypoint-reconstructed trajectories as ground truth. For short-haul flights (ATR72-600),, improvements of nearly 60–73% were observed, while for medium- and long-haul aircraft, improvements of 26–77% were observed. The proposed model also closely matches the numerical method, with differences typically below 70–80 km from the original value, again depending on aircraft class. These results demonstrate that incorporating climb and descent phases significantly improves range prediction accuracy, particularly for short-haul missions where non-cruise segments represent a substantial portion of total flight distance. The IRE retains the analytical simplicity of the Bréguet formulation while achieving accuracy comparable to computationally intensive numerical methods.
Batra et al. (Sun,) studied this question.