Aircraft Trajectory Optimization and Contrails Avoidance in the Presence of Winds

Abstract

There are indications that persistent contrails can lead to adverse climate change, although the complete effect on climate forcing is still uncertain. A flight trajectory optimization algorithm with fuel and contrails models, which develops alternative flight paths, provides policy makers the necessary data to make tradeoffs between persistent contrails mitigation and aircraft fuel consumption. This study develops an algorithm that calculates wind-optimal trajectories for cruising aircraft while avoiding the regions of airspace prone to persistent contrails formation. The optimal trajectories are developed by solving a non-linear optimal control problem with path constraints. The regions of airspace favorable to persistent contrails formation are modeled as penalty areas that aircraft should avoid and are adjustable. The tradeoff between persistent contrails formation and additional fuel consumption is investigated, with and without altitude optimization, for 12 city-pairs in the continental United States. Without altitude optimization, the reduction in contrail travel times is gradual with increase in total fuel consumption. When altitude is optimized, a two percent increase in total fuel consumption can reduce the total travel times through contrail regions by more than six times. Allowing further increase in fuel consumption does not seem to result in proportionate decrease in contrail travel times.

Aircraft Input Prediction in the Presence of Spatially Varying Wind Field

“…The wind derivatives are not approximated as they are assumed to be calculated by Eq. (2). Replacing all the other derivative terms with their approximations and rearranging the equations such that they are in form of f(x) = 0 yields the following algebraic equations.…”

“…For example, wind can be utilized to fly through optimal trajectories to save time or/and fuel. 2 Wind is also used for soaring by extracting energy in the form of airspeed or altitude gain. 3 Thus, whether detrimental or beneficial, information about the wind aircraft is exposed to is important to know.…”

Wind Field Estimation and Its Utilization in Trajectory Prediction

“…Assign as t b Recalculate the input/control variables based-on intent information Propagate the states from t b − 1 → ∆tLH Store the result from t k → t k + ∆tLH Go to next step [2] No : Go to next step 3: End Prediction.…”

“…, q, which indicates the number of the aircraft in the vicinity. [2] Read current aircraft position : x k j , y k j [3] Read ownership aircraft flight data : x k , y k , V k , µ k 2: Estimation.…”

“…For example, wind can be utilized to fly through optimal trajectories to save time or/and fuel. 2 Wind is also used for soaring by extracting energy in the form of airspeed or altitude gain. 3 Thus, whether detrimental or beneficial, information about the wind aircraft is exposed to is important to know.…”