The texte below is a clarification about the
WANKEL THEORITICAL SWEPT VOLUME DEFICIENCY
which has been added to the page
Meilleures salutations, Gilles
WANKEL THEORITICAL SWEPT VOLUME DEFICIENCY
For the piston, it is obvious that the relaxation volume is generated
by the movement of the piston surface (because it is a one dimensional
engine : piston axis only),
which guaranty that the effect of applied pressure
opens an extra volume rigorously equal to the gas expansion volume.
However, this is not generally the case with other engines, and specially
(which are 2 dimensional engines : radially and tangentially, where it is
needed to defined 2 different volumes :
– one being the volume generated by the movement of the pushing tangential
– the other being the total observed volume.
Those two volumes are not generally equal.
For this reason, the Wankel total engine displacement volume does not give
the whole story about the engine.
WANKEL ANALOGIE 1 –
A PISTON WITH CYLINDER LATERAL CAVITIES
Lets imagine building a piston engine, and making thousands of deep cavities
every where in the cylinder wall,
such that the total volume of all cavities be twice the volume of the
This engine will run, but as the piston falls, hot gas will go into the
and there will be more and more cavities accessible as the piston gets near
bottom dead centre.
The final volume will be 3 times the cylinder volume (2 will be the cavities
volume, 1 will be the cylinder itself).
Of course, the pressure during relaxation will fall due to this excess
and the efficiency will not be good. That exactly what append in a Wankel !
This is not about chamber surface here, it is about an excess of volume.
The real volume measured at the end of the relaxation ìs three times the
generated by the movement of the tangential surface of push !
It is like if the total piston volume at the end of relaxation
would be 3 time greater than the actual cylinder volume !
WANKEL ANALOGIE 2 –
A PISTON WITH CYLINDER HEAD MOVING UP !
Let looks at the Wankel excess swept volume intuitively.
Consider just one of the Walkel rotor surface, horizontal when at TDC and
vertical when at BTC.
By analogy to a piston, measured the distance (radius) from the engine
to this rotor surface when horizontally (TDC) and then when vertically
The difference correspond to the crankshaft drop (stroke) of the "piston
in relation to the engine center.
In piston engine, the "cylinder head" is fix and does not move during the
Now, observe the distance from the engine center
to the contour wall vertically and horizontally just over those rotor
The "cylinder head equivalent" is closer inward when at TDC and further
outward when at BDC ?
During the 90 rotation, not only the "piston equivalent surface" of the
rotor has moved inward,
but the "cylinder head equivalent" contour wall has moved outward.
Worse, the cylinder head did move twice as much outward
compared to the rotor surface inward displacement !
It is also important to notice that the "piston equivalent surface"
component dropping (stroke) inward in the direction of the engine center
is at no time producing any contribution to the rotational force,
which lead to the conclusion that the crankshaft pure radial stroke
component is useless in the process,
even detrimental in making excess swept volume.
(the Quasitubine has no crankshaft and no inward net displacement).
WHAT DOES THAT MEANS ?
These two very simple intuitive look at the Wankel helps understanding and
the fact that there are 2 swept volumes,
one inward (making useful work on the crankshaft) and a larger one outward
not only unproductive,
but destroying the efficiency by reducing the internal pressure.
In the Wankel, the useful swept volume is not the actual chamber volume,
which make the Pressure-Volume P-V Diagram complex to use correctly !
Where does the lost of energy go ?
As explained in detail at http://quasiturbine.promci.qc.ca/QTpasWankel.html
compressing a gas increases its temperature, and allowing it to relax
(either by allowing the piston to move, or by allowing new cavities in the
or by creating a geometric excess swept volume), the gas will cool down…
That is exactly what is happening in the Wankel,
where the excess swept volume lead to an excess cooling, and a poor cold
In the Quasiturbine, there is no crankshaft,
and therefore no radial drop (stroke) of the equivalent ‘piston surface’,
and the radial distances of those blade surfaces to the centre are kept
unchanged from TDC and BDC.
The "cylinder head equivalent" moves outward by the exact amount of
"tangential surface of push" swept volume, which guaranty the Quasiturbine
is as efficient as the piston…
The Quasiturbine is very different from the Wankel !
HOW TO FIX THE WANKEL ?
Impossible, except by moving to the Quasiturbine concept, where this excess
swept volume is none.
The Quasiturbine does in fact correct the Wankel theoretical swept volume
and consequently, does not have its limitations…
SHOW ME THE WANKEL TANGENTIAL PUSHING SURFACE
The rotational force does not come from the volume but from the pressure
acting on the tangential surface.
Consider one pressurized Wankel chamber and find out the force generating
the rotation ?
This force is equal to the (pressure) time the (difference in radius of the
two contour seals contact),
time the (thickness of the rotor).
Draw the Wankel contour on a board, and cut the triangular rotor,
turn it slowly by pointing on the contour the difference between two
successive seal radius
(this is proportional to the tangential surface of push).
Plot this difference of radius of the seals for different angle from TDC to
(ideally plot them on the radius, inward starting from the contour,
and at the chamber front seal for each rotor position).
These differential radius are proportional to the surfaces on which
the pressure is exercising useful work at each instant, and the movement of
this surface is
equivalent to the surface movement of the piston, so it does generate a
You find that the tangential surface evolution define a volume which is 1/3
of the total volume…
There is the internal lost in pressure in this two dimensional engine !
WHAT ABOUT THE ACTUAL ROTOR SURFACE SWEPT VOLUME ?
Are you more comfortable considering the rotor surface and the total off
center load on that rotor surface ?
You can precede that way as well.
In rotary engine there are generally 2 surfaces sweeping volume,
one is the rotor surface projected in the radial direction (unproductive
and the other is the tangential surface of push (the only useful tangential
Failure to distinguish both component of the generating swept surfaces is a
but propagate miss-comprehension of the Wankel.
Knowing at each time where the rotor surface is permit to calculate the
of the surface swept volumes angular (radial and tangential) component for
each Wankel angle position,
and then make the total integration (addition).
Results are the same as the tangential surface of push radial method.
WANKEL ROTOR SWEPT VOLUME RESULTS
Starting with the same chamber maximum volume and with the same amount of
turning slowly both engine will show that the amount of work done
is much more with the piston and less with the Wankel.
This is due to the fact that the piston is a one dimensional engine (only
the piston axis affect the volume)
while the Walkel is a two dimensional engine (radius and tangential
coordinates both affect de volume)
that does not meet the Pressure-Volume P-V Diagram.
The Quasiturbine researchers did the calculation including the
correct Wankel swept volume integration and the results are shown in the
first graph at
The result show that the useful Wankel surface sweep volume
is only one third of the actual total chamber volume :
an extra geometric swept volume is not generating any power, but
catastrophically lowering the pressure…
which alone explain the poor efficiency of the Wankel !
No argument related to the shape of the combustion chamber explain correctly
the Wankel inefficiency,
but excess volume does… PV diagram correctly describes only engine
with no such excess volume, like the piston engines.
All Wankel PV diagram analysis are wrong… and high efficiency will never
This should help understand why in rotary engine, sweep volume are
generally different from the actual chamber volume. Sweeping volume need to
be adequately defined.
Better than showing the maths, we give 2 calculation methods for the swept
Consequently, to properly analyze the Wankel,
it is important not to assume that its sweep volume is the actual internal
COMPARING ENGINES CONCEPTS
The useful Wankel surface sweep volume is only one third of the actual total
Redoing the same calculation with the Quasiturbine show that the QT swept
exactly equal to the actual chamber volume, because it has been a contour
Piston show no excess swept volume either, which simply explain their
Almost every one does assume the energy is coming from the swept volume,
which is correct for the piston and the Quasiturbine engine, but not for the
Consequently, only "engine types" without any relaxation excess volume
can be successfully compared and match in results on the basis of
displacement volume and efficiency,
which means that piston and Wankel will not match, while piston and
(both have zero excess relaxation volume).
The shaft RPM is the most interesting comparison basis
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