An Optimal Strategy for Persistent Contrail Avoidance

Persistent contrails have been recognized as a potential threat to the global climate. This paper presents a methodology to optimally reroute aircraft trajectories to avoid the formation of persistent contrails with the use of mixed integer programming (MIP). The main contributions of this paper are the introduction of a more realistic fuel burn model, and the implementation of a quadratic cost function. Existing MIP path planning literature has used a 1-norm approximation of the vehicle acceleration for fuel burn. The fuel burn model created for this paper is based on aircraft data and engine performance software, and the fuel burn cost was approximated with piecewise linear, and quadratic functions for implementation into the MIP. Fuel optimal trajectories for contrail avoidance were created for each cost function and the results were compared. In addition, differences between the linear and quadratic cost were investigated with a pathological obstacle field, and the sensitivity of the trajectory to changes in the planning horizon length and time step size are presented. For a specific scenario, it was found that persistent contrails could be avoided with a 2.76% increase in fuel burn.

[1]  Yoshiaki Kuwata,et al.  Trajectory planning for unmanned vehicles using robust receding horizon control , 2007 .

[2]  Jonathan P. How,et al.  Receding horizon control of autonomous aerial vehicles , 2002, Proceedings of the 2002 American Control Conference (IEEE Cat. No.CH37301).

[3]  Robert Sausen,et al.  The impact of cruise altitude on contrails and related radiative forcing , 2005 .

[4]  C.S. Ma,et al.  Mixed Integer Linear Programming Trajectory Generation for Autonomous Nap-of-the-Earth Flight in a Threat Environment , 2005, 2005 IEEE Aerospace Conference.

[5]  John David Anderson,et al.  Aircraft performance and design , 1998 .

[6]  Klaus Gierens,et al.  A note on how to avoid contrail cirrus , 2005 .

[7]  B. Moor,et al.  Mixed integer programming for multi-vehicle path planning , 2001, 2001 European Control Conference (ECC).

[8]  Barry E. Schwartz,et al.  An Hourly Assimilation–Forecast Cycle: The RUC , 2004 .

[9]  Jan Roskam,et al.  Preliminary calculation of aerodynamic, thrust and power characteristics , 1987 .

[10]  Robert B. Noland,et al.  Variability of Contrail Formation Conditions and the Implications for Policies to Reduce the Climate Impacts of Aviation , 2005 .

[11]  Andrew M. Carleton,et al.  Climatology: Contrails reduce daily temperature range , 2002, Nature.

[12]  Matt R. Jardin.  Ideal free flight through multiple aircraft neighboring optimal control , 2000, Proceedings of the 2000 American Control Conference. ACC (IEEE Cat. No.00CH36334).

[13]  Tim Yoder,et al.  Development of aircraft fuel burn modeling techniques with applications to global emissions modeling and assessment of the benefits of reduced vertical separation minimums , 2007 .

[14]  Add Picture,et al.  Workshop on the Impacts of Aviation on Climate Change: A Report of Findings and Recommendations , 2006 .

[15]  R. D'Andrea,et al.  Low observability path planning for an unmanned air vehicle using mixed integer linear programming , 2004, 2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601).

[16]  E. Feron,et al.  Robust hybrid control for autonomous vehicle motion planning , 2000, Proceedings of the 39th IEEE Conference on Decision and Control (Cat. No.00CH37187).

[17]  Yoshiaki Kuwata,et al.  Three Dimensional Receding Horizon Control for UAVs , 2004 .

[18]  Mark B. Milam,et al.  Real-Time Optimal Trajectory Generation for Constrained Dynamical Systems , 2003 .

[19]  Kelly Klima,et al.  Assessment of a global contrail modeling method and operational strategies for contrail mitigation , 2005 .