Mathematics of the Wankel Engine shapes

Peter Dow

Peter Dow

@peter-dow-2pfGj0 • Oct 27, 2024
Regarding the mathematics of the unusual shape and profile of the Wankel engine triangular rotor and combustion chamber housing, I'm reviewing a mathematics demonstration I have just come across but which has been on the internet for a few years but, like me, you may not have come across it before now.


"Wankel Rotary Engine: Epitrochoidal Envelopes" by Tony Kelman on the Wolfram Demonstrations Project.



<a href="https://www.youtube.com/watch?v=lBzmtXxlLEw" target="_blank" rel="nofollow noopener noreferrer">Wankel Rotary Engine: Epitrochoidal Envelopes - YouTube</a>
#-Link-Snipped-#

This Demonstration gives an animation of an epitrochoid and associated planetary-motion envelope curve. The configuration shown has applications in the internal combustion engines invented by Felix Wankel and popularized by Mazda in RX-7 and RX-8 cars

Review by Peter Dow

If you think this video looks interesting, I highly recommend that you download the Wolfram CDF player software so that you can experiment with the features of Tony Kelman's demonstration. To quote Tony

"The "eccentricity ratio" changes the shapes of the curves. The "reference frame" determines what is held stationary in the animation: either the epitrochoid (blue), the envelope curve (purple), or the centers of rotation of both curves. The "inner" envelope is the triangular rotor shape used in place of a piston in a Wankel rotary engine, whereas the "outer" envelope is the continuation of the envelope curve along the opposite extreme of motion."
So selecting reference frame = epitrochoid allows the display of the familiar KKM Wankel engine and selecting reference frame = fixed centers shows Wankel's original DKM engine with rotating housing.

You can slow the rotation animation down as well..

Looking at eccentricity ratios widely different from what we see in real Wankel engines is quite a revelation too.

As if all that wasn't enough, you also get to download and look at Tony's open source code and in particular the maths equations he uses to generate the curves.

Tony suggests some extensions to his demonstration. Well I have ideas of my own - I'd like to see computations of the areas between the curves representing the combustion chambers and a calculation of compression ratios for example.

Unfortunately, I don't have the Mathematica developers software package which, unlike the free player I got to view the demo, you have to pay - A LOT - for.

Excellent demonstration! Can't praise it highly enough!
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  • Ramani Aswath

    Ramani Aswath

    @ramani-VR4O43 • May 28, 2014

    #-Link-Snipped-# said: Excellent demonstration! Can't praise it highly enough!

    Agreed.

    I also use Wolfram Alfa quite a bit for routine calculations. Their search engine is also amazing.

    Wankel Engine was a rage when we were students. In my opinion it suffered a premature retirement because of poor emission and fuel economy. Deserves another look.
  • Peter Dow

    Peter Dow

    @peter-dow-2pfGj0 • Jun 12, 2014

    I also use Wolfram Alfa quite a bit for routine calculations. Their search engine is also amazing.
    Well the Wolfram Mathematica package looks even more amazing but as I understand it, the free one-month trial version doesn't allow import / export and since I know I can't afford the to pay for the full version, I think trying the trial version would be a frustrating exercise so I've been looking for free alternatives to build on.

    After I started this topic, I have since found another trochoids interactive demonstration webpage, this time by Christopher J. Henrich. His code is in Javascript which means it is pretty much open source, can run on most modern web browsers and therefore is ideal for me to modify.

    So I've made a start and I'm publishing a webpage today which partially performs some of what Tony Kelman's demonstration does. I've a lot more to do yet but if you want to see how far I've got and monitor my progress, then click to my webpage using the following link.

    My page includes links back to Christopher J. Henrich's original webpage and he is OK with me publishing this link. Anyway see for yourself.

    #-Link-Snipped-#

    Wankel Engine was a rage when we were students. In my opinion it suffered a premature retirement because of poor emission and fuel economy. Deserves another look.
    The Wankel rotary-engine hasn't been retired altogether but has taken up niche applications where the lightness, simplicity, ease of starting and high power to weight ratio offer a good solution. Things like hand-power tools - chainsaws, strimmers and what have you.

    Also I believe Mazda are using a Wankel rotary-engine as a "range extender" in a hybrid vehicle to recharge the batteries.

    Maybe though with our modern CAD tools if we look we will find something to improve the Wankel rotary-engine or variants therefore for more general applications?
  • Sarathkumar Chandrasekaran

    Sarathkumar Chandrasekaran

    @sarathkumar-FEGRPw • Jun 12, 2014

    Peter Dow
    Well the Wolfram Mathematica package looks even more amazing but as I understand it, the free one-month trial version doesn't allow import / export and since I know I can't afford the to pay for the full version, I think trying the trial version would be a frustrating exercise so I've been looking for free alternatives to build on.

    After I started this topic, I have since found another trochoids interactive demonstration webpage, this time by Christopher J. Henrich. His code is in Javascript which means it is pretty much open source, can run on most modern web browsers and therefore is ideal for me to modify.

    So I've made a start and I'm publishing a webpage today which partially performs some of what Tony Kelman's demonstration does. I've a lot more to do yet but if you want to see how far I've got and monitor my progress, then click to my webpage using the following link.

    My page includes links back to Christopher J. Henrich's original webpage and he is OK with me publishing this link. Anyway see for yourself.

    #-Link-Snipped-#



    The Wankel rotary-engine hasn't been retired altogether but has taken up niche applications where the lightness, simplicity, ease of starting and high power to weight ratio offer a good solution. Things like hand-power tools - chainsaws, strimmers and what have you.

    Also I believe Mazda are using a Wankel rotary-engine as a "range extender" in a hybrid vehicle to recharge the batteries.

    Maybe though with our modern CAD tools if we look we will find something to improve the Wankel rotary-engine or variants therefore for more general applications?
    great work sir. Hats off to your hard work.