Master of Science Thesis A Mission Planning Tool Design for Re-Entry Stefan van Doorn September 21, 2010 ii Preface The Aerospace Engineering Masters at the Delft University of Technology is concluded with an individual research. The research is documented in a thesis work. This report presents the thesis work of the author. In addition to the thesis work, a presentation on the research is given which is open to the public. Finally, the student will defend the thesis work in private with a graduation committee. The research presented in this thesis work has been carried out at the chair of Astrodynamics and Space Missions at the aforementioned faculty. The time spent on the research is equal to 42 ECTS or 7 months. Formally, the thesis work is known under the code AE5-006. This report is intended for two types of readers. First, it is intended for the graduation committee who grades the student. Second, it is intended for people who are interested in mission planning for atmospheric entry. It can serve as a means to broaden ones knowledge on the subject or as a start for further research. In order to fully understand the contents of this thesis work, it would certainly be helpful if the reader has a Bachelor's degree in Aerospace Engineering. In specific, the reader should have some background knowledge on flight mechanics, control theory and numerical methods. The background theory for angle of attack and bank angle planning is given in chapters2 and3. The design of a generic flight simulator can be found in chapter5. If the reader is interested in angle-of-attack or bank angle planning, he/she should take a look at chapter 6 or7, respectively. The testing of guidance systems, employing the bank angle planner, can be found in chapter8. For the derivation of the first and second derivative of drag with respect to energy, the reader is referred to appendixD. The author would like to thank his thesis supervisor Dr.ir.Erwin Mooij in specific for his guidance during the research. One of his key qualities during a progress meeting is to give the student extra work. Of course, this is only because the student has gained new insights into the problem. Another quality of his is that he can speak very en- thusiastically about atmospheric entry and related areas. Finally, it is worthnoty to mention that during the progress meetings there was always time for a joke. Without the support of my girlfriend Marlot Jansen and parents Evelyne and Bart van Doorn this thesis work would not have been possible. PhD student ir.Jeroen Melman is thanked for his contribution of programming code and the discussions about step-size control for numerical integration. Mirjam Boere and I have worked together on the development of a generic flight simulator. She is, therefore, thanked for her contribution. Finally, a iii special word of appreciation goes out to the students from the 9th floor for keeping the author company during this work. Specifically, in random order, Tom de Groot, Mir- jam Boere, Vivek Vittaldev, Valentino Zuccarelli, Antonio Pagano, Nicoletta Silvestri, Dominic Dirkx, Hessel Gorter and Willem van der Weg. The company of Elgar van Veggel and Arthur Tindemans, both Aerospace Engineering students, was also highly appreciated during coffee and lunch breaks. This thesis work is dedicated to my grandfather, who taught me my first English words. Stefan van Doorn September 21, 2010 The picture on the front page illustrates: a) the ballistic entry, b) the glide entry b and c) skipping entry [Loh, 1968]. iv Summary A transition through the Earth's atmosphere is inevitable if it is desired to bring or return something useful from space. Mostly, these are astronauts or samples from a celestial object. The transition is also known as the atmospheric entry. The entry is characterised by a vehicle that has a high energy. This energy needs is reduced by drag upon transition through the atmosphere. Three types of entry can be distinguished: ballistic, glide and skip entry. A typical glide entry flight has three phases: the hypersonic transition, the Terminal Area Energy Management (TAEM) phase and the actual landing. In the hypersonic transition phase, there are various threats that can pose a risk to the vehicle. The heating and structural loading can become severe enough to damage the vehicle and/or the crew. In the hypersonic transition phase, the attitude of the vehicle has to be controlled such that the vehicle safely ends up at the TAEM interface. The process of determining the attitude throughout entry is called mission planning. For on-board mission planning, simplifications need to be made on the vehicle, its environment and the flight dynam- ics to achieve an acceptable computation speed. As a consequence, the real trajectory will deviate from the planned trajectory. The trajectory tracker has the task to steer the vehicle towards the planned trajectory. The combination of a planning and tracking algo- rithm forms a guidance algorithm. The main question of this thesis work is formulated as: Is it possible to design an on-board executable guidance algorithm, for the hypersonic transition phase, that safely targets the TAEM interface? A simulator has been built to serve as a test bed for the guidance algorithm. A systems-based approach is taken in the modelling of the vehicle and environment. The advantage is that the software has a clear modular structure and it becomes easy to extend the simulator with new capabilities. The trajectory propagation operates on the integration of the equations of motion expressed in Cartesian components with respect to an inertial reference frame. This allows for a stable integration and an easy inclusion of complex environment models. The performance and validity of a guidance algorithm can only be assessed if tested with a validated simulator. Therefore, a validation has been carried out using the already validated software called Simulation Tool for Atmospheric Re-entry Trajectories. The design of a trajectory planner has been decomposed into an angle of attack and bank angle planner. The angle of attack planner operates on the assumption of an v equilibrium-glide trajectory. First, a trajectory is designed in the height-velocity space. Second, this trajectory is converted to an angle-of-attack profile. The method can take path constraints and performance parameters into account. The performance parameters are the flight range, heat flux and integrated heat load. The bank angle planning algorithm is centered around an iterative search for a drag profile that corresponds to the required trajectory length. The drag profile is a lin- ear spline consisting of three segments. From this drag profile, a bank angle profile is deduced. One bank reversal is planned. The point of initiation is determined by the minimisation of the cross-range error. The required trajectory length is updated and the drag profile search is repeated as part of the iteration. By incorporating the bank angle planning and tracking algorithms in one guidance algorithm, the main question is answered positively. The algorithm executes fast enough for an on-board implementation. Furthermore, the interface is successfully targeted under the assumption that the constraint on the final heading can be taken care off. The first recommendation is to include the meeting of the final heading constraint in the planning algorithm. Another recommendation concerns the breakpoints of the linear spline, which give rise to tracking problems. In addition, planning a linear spline does not allow for a flexible profile, while the mission definition might demand it. It is recommended to tackle these two problems by planning a smooth profile. The algo- rithm requires a trial-and-error process to obtain the angle of attack profile and tracking algorithm gains to ensure mission success. This limits the flexibility of the planner for on-board execution. Future work should integrate the angle of attack planning as well. A more advanced guidance algorithm has to be developed to solve the problem of manual gain selection. vi Nomenclature Symbols b Characteristic length [m] C Direction cosine matrix [ ] − C Geopotential coefficient [ ] − C Aerodynamic coefficient [ ] − C Constant in the heat flux model [] c Characteristic length [m] D Drag force/acceleration [N] E Energy [J] e Ellipticity [ ] − F Force vector [N] G Universal Gravitational Constant [m3=(kg s2)] · g Gravitational acceleration vector [m=s2] h Height [m] I Moment of inertia [kg m2] · i Unit vector [ ] − J Harmonic coefficient [ ] − k Gain [ ] − L Lift force [N] M Mach [ ] − M Pitch moment [N m] · m Mass [kg] m Order [ ] − n g-load [ ] − n Degree [ ] − P Legendre polynomial [] Q Integrated heat load [J] q Pressure [N=m2] q_ Heat flux [W=m2] R Radius [m] R Specific gas constant [J=(kg mol)] · r Radial distance [m] vii S Geopotential coefficient [ ] − S Side force [N] S Surface [m2] S Trajectory length [m] s Distance mass element to vehicle [m] T Temperature [K] t Time [sec] U Gravitational potential [m2=s2] u Input [ ] − V Velocity [m=s2] w Weight [ ] − x Cartesian position coordinate [m] y Cartesian position coordinate [m] z Cartesian position coordinate [m] α Angle of attack [rad] β Side-slip angle [rad] β Inverse of scale height [m−1] γ Flight-path angle [rad] γ Ratio of specific heats [ ] − δ Latitude [rad] δ Control surface deflection [rad] δ Kronecker delta [ ] − δ Step-size scaling parameter [ ] − θ Angular displacement [rad] ρ Density [kg=m3] σ Bank angle [rad] τ Longitude [rad] χ Heading angle [rad] ! Planet rotational velocity [rad=s] ζ Damping [ ] − Index (if other than above) 0 At seal-level A Aerodynamic A Airspeed AA Aerodynamic reference frame w.r.t. airspeed variables AG Aerodynamic reference frame w.r.t.