## 1 Introduction  
Spark ignition engines, which have been used in motor vehicles for over 140 years, still have a relatively low effective efficiency of conversion of fuel combustion energy into mechanical energy of rotation, despite significant developments. The best spark ignition engines used in motor vehicles currently obtain a peak effective efficiency of about 40% [1], what means that in the best case scenario, 60% of the energy delivered with the fuel is lost. In the case of low engine load, the loss of energy may exceed 80% of the value resulting from fuel combustion. To solve this and other problems, the European Commission has initiatives aimed at obtaining automotive engines with significantly increased efficiency. A peak thermal conversion efficiency of more than 50% is expected for engines developed in the Horizon 2020 Program [2]. However, at the moment this is only one of the targets for R&D projects which will be finished in the years 2020 to 2021, so an implementation of the developed engines for mass production will undoubtedly take place in the next few years. There are many different methods to improve this situation. It is worth mentioning here the most important methods, such as direct injection, thermal insulation of the combustion chamber, turbocharging, downsizing, downspeeding, the implementation of exhaust energy recovery using thermoelectric generators [3], or the advanced mechatronic systems, such as variable valve timing or continuously variable valve lift. Among the ways to improve the effective efficiency (fuel conversion efficiency) of an internal combustion engine, an interesting method is to increase the expansion ratio to be significantly higher than the compression ratio of the engine. This leads to a significant increase in the thermal efficiency of the theoretical comparative cycle of the engine [4], but also gives tangible benefits in the effective efficiency of the engine performing such a cycle [5]. Figure 1 presents the concept of using an increased expansion ratio to improve the efficiency of an internal combustion engine. In a particular case, the working medium pressure can be decreased to match the ambient pressure. Differentiation of the compression and expansion ratios of the engine may be accomplished in several ways. The first well-known solution was developed by the English engineer [PERSON] in the second half of the nineteenth century [6]. The engine concept by [PERSON] was characterized by shorter intake and compression strokes than the power and exhaust strokes. This solution, however, was a significant disadvantage due to the sophisticated crank mechanism with respect to classical four-stroke engine. The increased interest in construction solutions of engines with increased expansion occurred in the second half of the twentieth century, when the concept by [PERSON] [7] was developed. This concept was based on the classic four-stroke engine, but with suitably modified valve timing so as to get a reduced effective length of the compression stroke--Late Intake Valve Closing--or by reducing the degree of filling of the cylinder in a supercharged engine with an additional charge cooling by expansion in the intake stroke as a result of an Early Intake Valve Closing strategy. Engines performing an Atkinson/Miller cycle, but based on the classic four-stroke engine, have been used in motor vehicles since the mid-1990s [8]. Due to the specific characteristics of this type of solution, they often occur in vehicles with hybrid drive systems, diesel locomotives, and in industrial applications [9], where the engine operates with an average high load. The Atkinson cycle is also used in modern engines for conventional propulsion systems in order to reduce pumping losses in the low load region [10]. Research and development of engines performing Atkinson/Miller cycles are also carried out in Poland at several universities [11; 12].