Which concept has the best working cycle?
This study is available here in English as a PDF file..
5stroke engine 
Naturally aspirated Ottocycle engine 
Turbocharged Ottocycle engine 

Intake  
Optimal filling with forced charging (at a charging pressure of several bars). 
Optimal filling of the cylinder is not possible under suction (filling at a reduced pressure of less than 1 bar). 
Optimal filling of the cylinder with forced charging (filling at positive pressure). 
Optimal filling with forced charging (at a charging pressure of several bars). 

Compression  
As a result of the low compression ratio compression is noncritical over the whole working range, with no risk of knock. 
...


Power  
The complete power stroke is made up from the power strokes in the 4stroke highpressure cylinders, with a moderate energy yield, and a subsequent power stroke in the lowpressure cylinder (the additional stroke). The end result is an expansion ratio of about 1:14 over the whole working range and thus a high efficiency. 
An expansion ratio of the order of 1:11 does not produce a particularly good efficiency. 
A low expansion ratio results in a poor efficiency. 
... High efficiency at low loads (expansion ratio 1:16), but poor efficiency at high power outputs (expansion ratio 1:6). 

Exhaust  
The exhaust stroke in the 4stroke highpressure cylinder corresponds to the power stroke in the lowpressure cylinder (the additional stroke in the lowpressure cylinder delivers work to the crankshaft). With no exhaust manifold, the exhaust stroke from the lowpressure cylinder impinges directly onto the turbine of the turbocharger. Here a proportion of the residual energy is utilised to compress the induced air. 
The high level of residual energy in the exhaust gas is not used. 
The very high level of residual energy in the exhaust gas is only utilised in the turbocharger to a small extent to compress the induced air. Here, however, no work is transmitted to the crankshaft. 
Only with high compression and expansion ratios, with utilisation of a proportion of the residual energy in the turbocharger to compress the induced air, is a good energy yield obtained. Here, however, no work is transmitted to the crankshaft. 
5stroke engine 
Naturally aspirated 
Turbocharged 

Summary  
High power density with a high efficiency over the whole working range. 
Average power density with average efficiency. 
High power density with poor efficiency. 
High power density, but efficiency varies from very good to
very poor (depending on the compression and expansion ratios). 
The 5stroke engine combines all the advantages of the other engine concepts, but
without their disadvantages. As a result of the twostage expansion in the 5stroke
cycle the overall expansion ratio is independent of the compression ratio  that is
the key to success for the 5stroke engine. The 5stroke concept provides the developer
with additional degrees of freedom in the engine design and enables both the
compression ratio and the overall expansion ratio to be independently and optimally determined. 
The 5stroke engine improves efficiency over the whole working range, at both part load and full load. In the 4stroke cycle the compression and expansion ratios are identical, as dictated by the principle of the cycle. Since the compression ratio is limited as a result of combustion constraints, the expansion ratio and thus the efficiency are likewise limited. The design of a 4stroke engine with a comparable high efficiency is physically impossible. 
Miller and Atkinson cycles
The Miller and Atkinson cycles also aim to break away from the condition that the compression
and expansion ratios must be equal. Here the effective compression is reduced relative to the
geometrical compression by very late closure of the inlet valves. In fact some people,
not entirely without justification, consider the Miller and Atkinson cycles to be 5stroke
cycles, and the compression stroke is indeed divided into two strokes, i.e. backwashing and
compression. In principle, these two cycles offer advantages relative to the classic Otto
cycle that can be compared with those of the Schmitz fivestroke cycle presented here.
The flow losses resulting from the late closure of the inlet valves in the Miller and Atkinson
cycles can be compared with the flow transfer losses in the fivestroke cycle and as a result,
or so one could believe, the 5stroke concept has no essential advantages compared with the Miller and Atkinson cycles.
However, this is only true at first glance. On the one hand, the flow losses in the Miller and Atkinson cycles are inextricably connected with an unavoidable rise in entropy involving heavy losses, since the backwashed fresh mixture must be "pushed" through a valve clearance that is closing by a piston that is moving upwards and thus generating pressure. 
In the case of the 5stroke cycle this generation of entropy can be almost entirely
avoided by clever valve control. On the other hand, the 5stroke cycle has a decisive
advantage compared with the Miller and Atkinson cycles thanks to the twostage expansion,
and the low expansion ratio that is possible in the highpressure combustion cylinders as
a result. This low expansion ratio leads to a slow variation of combustion volume during
combustion, so that the overall effective expansion ratio deviates far less from the geometric
expansion ratio, in particular at high rpms. Moreover, the Miller and Atkinson cycles can
only be optimised for one particular rpm, unless one resorts to a complex form of variable
inlet valve control.
A further advantage of the 5stroke cycle consists in the fact that the exhaust gases exit from only one cylinder, and thus the exhaust manifold can be dispensed with, which on the one hand helps to save cost and space, and on the other hand enables a more efficient process of impulse charging. One could, so to speak, consider the flow transfer from the highpressure cylinders to the lowpressure expander not simply as "unnecessary" flow losses, but rather as a useful guiding of the exhaust gases towards the entry to the turbine, coupled with a serial extended expansion. In contrast, the backflow in the case of the Miller and Atkinson cycles cannot demonstrate such "usefulness". 
And in comparison to the car diesel engine?
The 5stroke engine achieves the level of consumption of a modern car diesel engine.  But for the same power output and consumption the 5stroke engine is cheaper, lighter, quieter, and more environmentally friendly. 
Are there still good reasons for building car engines in the form of 4stroke engines? NO.Do you have a different opinion? Have a discussion with the inventor, Gerhard Schmitz, on the public blog. 
^{1)} 
VCR = Variable Compression Ratio.
Internal combustion engines with a mechanically variable compression ratio. You can find an example of a current design of VCR engine at www.mce5.fr Comment: The VCR engine allows the compression ratio to be optimally adjusted at each operating point. Since the VCR engine is also based on the 4stroke cycle, compression and expansion ratios are also identical here. The VCR engine has a high efficiency at low loads and achieves good CO2 emissions and consumption in the New European Driving Cycle (NEDC). At all operating points with a low compression ratio the VCR engine has a poor efficiency. This applies in particular to operation at average and high loads. As a result of the independent determination of compression and expansion ratios in the design of the 5stroke concept the need for a mechanical adjustment of the compression ratio no longer exists. 