Editing Wankel engine (section)

===Chamber volume===
In a Wankel rotary engine, the chamber volume <math>V_k</math> is equivalent to the product of the rotor surface <math>A_k</math> and the rotor path <math>s</math>. The rotor surface <math>A_k</math> is given by the rotor tips' path across the rotor housing and determined by the generating radius <math>R</math>, the rotor width <math>B</math>, and the parallel transfers of the rotor and the inner housing <math>a</math>. Since the rotor has a trochoid ("triangular") shape, the sine of 60 degrees describes the interval at which the rotors get closest to the rotor housing. Therefore,

:<math>A_k=2 \cdot B \cdot (R+a) \cdot \sin (60^\circ) = \sqrt 3 \cdot B \cdot (R+a)</math><ref name="Bensinger 1973 p. 64">{{cite book |last1=Bensinger |first1=Wolf-Dieter |title=Rotationskolben-Verbrennungsmotoren |place=Berlin, Heidelberg, New York |date=1973 |isbn=978-3-540-05886-1 |oclc=251737493 |language=de |page=64}}</ref>

The rotor path <math>s</math> may be integrated via the eccentricity <math>e</math> as follows:

:<math>\sum \, ds= \int_{\alpha= 0^{\circ}}^{\alpha=270^{\circ}} e \cdot \sin \frac {2} 3 \alpha \, d \alpha = 3e</math>

Therefore,

:<math>V_k= A_k \cdot s = \sqrt 3 \cdot B \cdot (R+a) \cdot 3e</math><ref name="Bensinger 1973 p. 65"/>

For convenience, <math>a</math> may be omitted because it is difficult to determine and small:<ref name="Yamamoto 1981 p. 15"/>

:<math>V_k= \sqrt 3 \cdot B \cdot R \cdot 3e</math><ref name="Yamamoto 1981 p. 15"/><ref name="Corbat Pawlowski 1973 p. 8">{{cite book |last1=Corbat |first1=Jean Pierre |last2=Pawlowski |first2=Uwe L. |title=Kreiskolbenmotoren des Systems NSU-Wankel ihre Berechnung und Auslegung |place=Basel |date=1973 |isbn=978-3-0348-5974-5 |oclc=913700185 |language=de-CH |page=8 |quote=Formula 56 with k=R/e}}</ref><ref name="Bender Göhlich Springer-Verlag GmbH 2019 p. 126">{{cite book |last1=Bender |first1=Beate |last2=Göhlich |first2=Dietmar |publisher=Springer-Verlag |title=Dubbel Taschenbuch für den Maschinenbau Band 3. |place=Berlin |date=2019 |isbn=978-3-662-59714-9 |oclc=1105131471 |language=de |page=126}}</ref><ref name="Ansdale Keller 1971 p. 79">{{cite book |last1=Ansdale |first1=R.F. |last2=Keller |first2=H. |title=Der Wankelmotor: Konstruktion und Wirkungsweise |place=Stuttgart| publisher=Motorbuch-Verlag |year=1971 |language=de |page=79 formula 6.13}}</ref><ref name="v Manteuffel 1971 pp. 74">{{cite book |last1=v Manteuffel |first1=P. |title=Mechanical Prime Movers |chapter=Rotary Piston Engines |publisher=Macmillan |place=London |year=1971 |isbn=978-1-349-01184-1 |doi=10.1007/978-1-349-01182-7_6 |pages=74}}</ref>

A different approach to this is introducing <math>a'</math> as the farthest, and <math>a</math> as the shortest parallel transfer of the rotor and the inner housing and assuming that <math>R_1=R+a</math> and <math>R_2=R+a'</math>. Then,

:<math>V_k= \sqrt 3 \cdot B \cdot (2 \cdot R_1+R_2) \cdot e</math>

Including the parallel transfers of the rotor and the inner housing provides sufficient accuracy for determining chamber volume.<ref name="Yamamoto 1981 p. 15">{{cite book |last1=Yamamoto |first1=K. |title=Rotary Engine |publisher=Sankaido |year=1981 |isbn=978-99973-41-17-4 |page=15 |quote=Formula 2.27 and 2.30; Yamamoto uses V<sub>h</sub> for V<sub>k</sub>. In this article, V<sub>k</sub> is used for convenience}}</ref><ref name="Bensinger 1973 p. 65"/>