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Engine cycles in which the effective compression ratio is smaller than the effective expansion ratio (see compression ratio discussion under Engine Fundamentals) can be referred to as over-expanded cycles. In modern practice, over-expanded cycles are implemented with either early (EIVC) or late (LIVC) intake valve closing. The primary effect of EIVC and LIVC is a reduction in temperature at the end of the compression stroke. The lower temperature enables the use of higher geometric compression ratios that yield a longer expansion ratio and an efficiency benefit.
Over-expanded cycles are commonly referred to as Miller or Atkinson cycles; referring to the inventors Ralph Miller and James Atkinson. The use of these terms in the literature is not consistent.
Ralph Miller did not conceive of the idea of using valve timing to control effective compression ratio. This is evidenced by the fact that it was discussed in a 1927 report as an option to limit knock in aviation engines when using low octane fuels .
Miller was primarily interested in using intake valve closing timing to limit TDC temperatures. In two of his patents, he described variable intake valve timing mechanisms that allowed IVC to vary with engine load in order to control the in-cylinder temperature at the end of the compression stroke. He claimed his ideas for naturally aspirated and forced induction diesel and spark ignition . Miller’s motivation was to increase power density. In the 1954 patent, the end-of-compression temperature was to decrease as load increased so that the engine could burn more fuel at full load while staying within the limits of the material properties. It was specifically targeted to boosted/inter-cooled engines. The 1956 patent was targeted specifically to SI engines and was intended to avoid pre-ignition and allow a richer fuel/air ratio at full load while maintaining a high geometric compression ratio.
While Miller mentions both early and late intake valve closings, he seemed to prefer closing the intake valve early while the cylinder volume was still increasing because additional expansion after intake valve closing could further cool the intake charge. He referred to this as “internal cooling” . Figure 1 illustrates Miller’s EIVC strategy for a boosted diesel engine from the 1954 patent. Note that variable intake valve closing timing was required between 50-100% load. Modern engine design approaches referred to as using the Miller cycle are typically boosted and include both early  and late intake valve closings .
Occasionally, engines with late intake valve closings are referred to as Atkinson cycle engines. Some prefer to restrict reference to Atkinson cycle engines as those that are naturally aspirated and have a late intake valve closing. However, the original patents by James Atkinson do not refer to valve closing timing but to an engine in which one engine cycle is completed in a single revolution of the crankshaft and with a crankshaft mechanism that allowed a higher expansion ratio than compression ratio. The management of intake valve closing timing to achieve this effect is not mentioned .
While Atkinson deserves credit for perhaps being the first to recognize the benefits of having different compression and expansion ratios, Miller should be credited for devising a recipe for achieving a set of objectives that remains relevant even to modern internal combustion engines. Thus it would be justifiable to refer to manifestations of over-expanded cycles that rely on variable intake valve closing timing for their implementation as Miller cycle engines—whether they use forced induction or not and regardless of whether they are compression ignition or spark ignition. Miller’s ideas have been successfully applied commercially while it is unknown if Atkinson’s mechanism was ever done so.
However, ignorance of the historical context is widespread and both Atkinson and Miller are often credited with the modern implementation of over-expanded cycles using IVC timing. Labeling some of these as “Atkinson” cycle engines is completely arbitrary. An example of such arbitrary approach is the terminology used by the US EPA, who considers the Atkinson cycle to be an over-expanded cycle applied to naturally aspirated engines with either EIVC or LIVC and the Miller cycle to be an Atkinson cycle (i.e., EIVC or LIVC) boosted with a turbocharger or supercharger .