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TOHP - Trajectory Optimization of Hypersonic Planes

Project Leader: Prof. Dr. Kurt Chudej
Contact: Prof. Dr. Kurt Chudej

Project start: 2016 Project end: 2017

Project team:

  • Prof. Dr. Kurt Chudej

External partners:

  • Dr.rer.nat. Armin Rund, Institut für Mathematik und Wissenschaftliches Rechnen, Karl-Franzens-Universität Graz, Austria
  • Dr.-Ing. Markus Wächter, German Institute of Science and Technology, TUM Asia Pte Ltd., Singapore, Singapore

Project description:


The design of new hypersonic airplanes is a difficult task. Flying in the hypersonic flight regime yields considerable aerothermic loads. Therefore innovative lightweight materials and a sophisticated thermal protection system are mandatory for the airplane. Budget and weight restrictions are directly connected with the design of the thermal protection system.This yields a coupled ode-pde optimal control problem consisting of a standard trajectory optimization problem coupled with an instationary nonlinear heat equation. Moreover the coupling includes the bow shock and a boundary layer aroud the airplane.


Several competences from engineering and mathematics have to be combined for the successful numerical solution of this challenging mathematical optimal control problem.


Numerical results for this challenging mathematical optimal control problem have been computed. Moreover for the first time an index analysis of the semidiscretized model variant was done, revealing a high index which explains the observed numerical difficulties.


Chudej, Kurt; Rund, Armin; Wächter, Markus: Trajectory optimization of a hypersonic plane s.t. heat limits. In: Tikhomirov, Dmitrij; Mammen, Heinz-Theo; Pawletta, Thorsten (Hrsg.): ASIM-Treffen STS/GMMS 2016 - Workshop der ASIM/GI Fachgruppen STS und GMMS: Tagungsband: am 10.- 11. 3. 2016 an der Hochschule Hamm-Lippstadt. - Wien, Österreich: ARGESIM Verlag Wien, 2016. - S. 101-108. - (ARGESIM Report; 51)

Board of Directors: Prof. Dr. Jörg Rambau, Prof. Dr. Lars Grüne and Prof. Dr. Vadym Aizinger

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