# Finding the optimal shape of the leading-and-trailing car of a high-speed train using design-by-morphing

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## Abstract

We present a new, general design method, called *design-by-morphing* for an object whose performance is determined by its shape due to hydrodynamic, aerodynamic, structural, or thermal requirements. To illustrate the method, we design a new leading-and-trailing car of a train by morphing existing, baseline leading-and-trailing cars to minimize the drag. In design-by-morphing, the morphing is done by representing the shapes with polygonal meshes and spectrally with a truncated series of spherical harmonics. The optimal design is found by computing the optimal weights of each of the baseline shapes so that the morphed shape has minimum drag. As a result of optimization, we found that with only two baseline trains that mimic current high-speed trains with low drag that the drag of the optimal train is reduced by \(8.04\%\) with respect to the baseline train with the smaller drag. When we repeat the optimization by adding a third baseline train that under-performs compared to the other baseline train, the drag of the new optimal train is reduced by \(13.46\%\). This finding shows that bad examples of design are as useful as good examples in determining an optimal design. We show that *design-by-morphing* can be extended to many engineering problems in which the performance of an object depends on its shape.

## Keywords

Design-by-morphing Train head Optimization Genetic algorithm Artificial neural network Drag reduction## Notes

### Acknowledgements

We thank Alain Demeulenaere and David Gutzwiller for valuable contributions to the science and engineering results and to NUMECA, USA, Inc. for software and computational support. Partial support was supplied by NSF Grants AST-1009907 and AST-1510703 and by NASA PATM Grants NNX10AB93G and NNX13AG56G. Partial support for computational work was provided by NSF XSEDE (NSF OCI-1053575) and NASA-HEC.

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