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This paper presents the results of a numerical algorithm development to optimize the engine strokes in a linear engine incorporating combustion and kickback. Due to the free piston reciprocal movement occurring in linear engines, the stroke of linear engines cannot be determined by using of fixed position. The reciprocating motion is namely the result of pressure acting on the piston and kickback. Kickback bore size is the main parameter that can influence the velocity of the motion. A numerical algorithm of a variational principle has been developed to optimize the kickback bore size. The resulting function of velocity is important to control the compression ratio and improve of engine thermal efficiency.
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