Abstract
The development of fully reusable launch systems has been the topic of many studies since the 1960s. Over the years, several aspects of both so-called single- and two-stage-to-orbit space planes have provided many interesting research topics. Amongst others, the constrained trajectory optimisation has proven to be a challenging subject. In this chapter, an inverse-dynamics approach is combined with trajectory optimisation and analysis, by discretising a representative (vertical-plane) ascent trajectory into a number of flight segments, and by parametrising the guidance in terms of flight-path angle as a function of altitude. When the individual guidance parameters are varied, the effect on performance indices payload mass and integrated heat load can be analysed. This can subsequently lead to a refinement of the trajectory. To do so with limited effort, design-of-experiment techniques are used. It is shown that with this relatively simple simulation scheme, combined with variance analysis and response-surface methodology, the insight in the trajectory dynamics can be increased. Alternatively, this method can be used as refinement to an otherwise (local) optimum trajectory. It is stressed, though, that the application of design of experiments to the ascent-trajectory problem cannot replace numerical optimisation. Finally, the impact of using thrust-vector control as a means to (partially) trim the vehicle shows significant fuel savings and should therefore be included in the optimisation process.
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Notes
- 1.
De Selding, P.B., “SpaceX to launch SES-10 on previously flown Falcon 9 this year”, Spacenews, August 30, 2016. http://spacenews.com/spacex-to-launch-ses-10-satellite-on-reused-falcon-9-by-years-end/. Accessed October 5, 2017.
- 2.
Various alternatives to design of experiments exist, e.g., Latin hypercube sampling [18] or optimised hypercube sampling [19]. Even though potentially efficient methods, it was decided to use a fully deterministic approach that is simple to implement and allows for a structured variance analysis of the results.
- 3.
Variation of k parameters with two (three) possible values, also called levels, results in a total of 2k (3k) combinations.
- 4.
Two design points are said to collapse when one of the design parameters has (almost) no influence on the function value and the two designs differ only in this parameter. As a consequence this means that effectively the same point is evaluated twice, and for deterministic simulation models this is not a desirable situation.
- 5.
The simulation stops after 3000 s, which is about 700 s more than the flight duration of the reference trajectory, so not reaching h = 120 km after this time indicates a vehicle “crash”.
- 6.
Only two factors determine 90% of the variation in integrated heat load, i.e., parameters that determine the shape of the second part of the trajectory where thermal loading is larger.
- 7.
A response surface with only linear terms assumes no interactions or higher-order effects in the response. This may not be true for all ranges of factor variation, but to do so allows for a comparison with the results of ANOVA. Also, the linear factor variation (minimum and maximum values only) allows for a fast analysis during conceptual trajectory design.
- 8.
A batch with factor variations over three levels, allowing to include quadratic effects, has been executed using the L 81 orthogonal array. This array requires 81 simulations for a maximum of 40 independent factors. With the same column assignment as for the L 32-batch, the response surface gives a maximum payload mass of 7895 kg when both linear and quadratic terms are included, and 7899 kg with only linear terms. This analysis confirms the consistency of the approach and shows indeed that quadratic terms have a marginal effect for fitting the surface through the data points.
- 9.
The use of TVC interacted with the flight-path angle steering loop, Equation (5), and some high-frequency, small-amplitude oscillations were induced in the commanded angle of attack. This led to oscillations in the thrust-elevation angle. Without doing a redesign, the gains were set to K γp = 2.0, K γi = 1.8 and K γd = 0 for the complete trajectory, which solved the problem. However, it was observed that changing the gains has a noticeable effect on the fuel mass, so in a future design the gains should be optimised.
References
Dinardi, A., Capozzoli, P., Shotwell, G.: Low-cost launch opportunities provided by the falcon family of launch vehicles. In: The Fourth Asian Space Conference. Taipei (2008)
Cribbs, D.: Performance uncertainty analysis for NASP. In: 2nd International Aerospace Planes Conference. Orlando (1990)
Lovell, C.K., Schmidt, P.: Mission performance of hypersonic vehicles. In: AIAA Guidance Navigation and Control Conference. Baltimore (1995)
Schmidt, D.K., Lovell, T.A.: Mission performance and design sensitivities for hypersonic airbreathing vehicles. J. Spacecr. Rocket. 34(2), 158–164 (1997)
Wagner, A., Thevenot, R.: STS 2000: a reference air-breathing SSTO. In: AIAA 3rd International Aerospace Planes Conference. Orlando (1991)
Calise, A.J., Flandro, G.A., Corban, J.E.: Trajectory Optimization and Guidance Law Development for National Aerospace Plane Applications. NASA CR-182994. NASA, Washington DC (1988)
Corban, J.E., Calise, A.J., Flandro, G.A.: Rapid near-optimal aerospace plane trajectory generation and guidance. J. Guid. Control. Dyn. 14(6), 1181–1190 (1991)
Van Buren, M.A., Mease, K.D.: Aerospace plane guidance using time-scale decomposition and feedback linearisation. J. Guid. Control. Dyn. 14(6), 1166–1174 (1992)
Lu, P.: Entry guidance: a unified method. J. Guid. Control. Dyn. 37(3), 713–728, (2014)
Lu, P.: Inverse dynamics approach to trajectory optimization for an aerospace plane. J. Guid. Control. Dyn. 16(4), 726–732 (1995)
Hess, R.A., Gao, C., Wang, S.H.: Generalized technique for inverse simulation applied to aircraft maneuvers. J. Guid. Control. Dyn. 14(5), 920–926 (1991)
Morio, V., Cazaurang, F., Vernis, P.: Flatness-based hypersonic reentry guidance of a lifting-body vehicle. Control. Eng. Pract. 17(5), 588–596 (2009)
Shaughnessy, J.D., Zane Pinckney, S., McMinn, J.D., Cruz, C.I., Kelley, M.L.: Hypersonic vehicle simulation model: Winged-Cone configuration. NASA Technical Memorandum 102610, Langley Research Center, Hampton, 1990
Hattis, P.D., Malchow, H.D.: Evaluation of some significant issues affecting trajectory and control management for air-breathing hypersonic vehicles. In: AIAA Fourth International Aerospace Planes Conference. Orlando (1992)
Powell, R.W., Shaugnessy, J.D., Cruz, C.I., Naftel, J.C.: Ascent performance of an air-breathing horizontal-takeoff launch vehicle. J. Guid. Control. Dyn. 14(4), 834–839 (1991)
Gregory, I.M., Chowdhry, R.S., McMinn, J.D., Shaughnessy, J.D.: Hypersonic vehicle model control law development using H ∞ and μ-synthesis. NASA Langley Research Center, Hampton (1994)
Vinh, N.X.: Optimal Trajectories in Atmospheric Flight. Elsevier, Amsterdam (1981)
Iman, R.L.: Latin hypercube sampling. In: Encyclopedia of quantitative risk analysis and assessment. Wiley, New York (2008)
Park, J.S.: Optimal Latin-hypercube designs for computer experiments. J. Statist. Plann. Inference 39(1), 95–111 (1994)
Mooij, E.: Re-entry test vehicle configuration selection and analysis. In: Fasano, G., Pintr, J.D. (eds.) Space Engineering. Modeling and Optimization with Case Studies, pp. 199–235. Springer, Berlin (2016)
Taguchi, G.: System of Experimental Design. Engineering Methods to Optimise Quality and Minimise Costs, 2nd edn, vol. 1. UNIPUB/Kraus International Publications, White Plains (1988)
Phadke, M.S.: Quality Engineering Using Robust Design. Prentice-Hall, Englewood Cliffs (1989)
Marée, A.G.M., Mooij, E., Zandbergen, B.T.C.: Space-plane analysis: the generation of a reference trajectory. Report LR-749, Delft University of Technology, Faculty of Aerospace Engineering, 1994
Hattis, P., Malchow, H., Shaughnessy, J., Chowdry, R.: Integrated trajectory and control analysis for generic hypersonic vehicles. In: 3rd International Aerospace Planes Conference, AIAA-1991-5052 (1991)
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Mooij, E. (2019). Single-Stage-to-Orbit Space-Plane Trajectory Performance Analysis. In: Fasano, G., Pintér, J. (eds) Modeling and Optimization in Space Engineering . Springer Optimization and Its Applications, vol 144. Springer, Cham. https://doi.org/10.1007/978-3-030-10501-3_12
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