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Author Topic: Interested in the mathematics of the Wankel Engine shapes?  (Read 3521 times)

Peter Dow

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Interested in the mathematics of the Wankel Engine shapes?
« on: 29/05/2014 15:58:17 »
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.

Wankel Rotary Engine: Epitrochoidal Envelopes" by Tony Kelman on the Wolfram Demonstrations Project [nofollow]

Quote
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

Quote
"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!

CliffordK

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Re: Interested in the mathematics of the Wankel Engine shapes?
« Reply #1 on: 29/05/2014 18:41:02 »
I had seen a design for a "wankle" engine a while ago with a square piston and hinged corners that made a most interesting compression sequence.  I think the advantage was that one could do essentially 2 complete 4-stroke sequences per revolution.  Somewhere I had made an Excel spreadsheet to demonstrate the movement, but it has since perished.  Perhaps I could recreate it again, not that I was ever convinced that the engine itself could be made to be durable enough for practical use.

Peter Dow

• Jr. Member
• Posts: 42
Mathematics of the Wankel rotary-engine shapes webpage by Peter Dow
« Reply #2 on: 12/06/2014 20:34:32 »
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.

Mathematics of the Wankel rotary-engine shapes Webpage by Peter Dow [nofollow]

I had seen a design for a "wankle" engine a while ago with a square piston and hinged corners that made a most interesting compression sequence.  I think the advantage was that one could do essentially 2 complete 4-stroke sequences per revolution.  Somewhere I had made an Excel spreadsheet to demonstrate the movement, but it has since perished.  Perhaps I could recreate it again, not that I was ever convinced that the engine itself could be made to be durable enough for practical use.
A square rotary piston, with 4 apexes, forming 4 engine chambers? That's only 1 more apex and chamber than the Wankel's 3 so I don't see how that can double up the number of chambers you'd need to do 2 complete 4-stroke sequences per revolution?

I would have thought that in order to do 2 complete 4-stroke sequences per revolution you'd need to double up on the chambers, so that would be a hexagonal rotary piston with 6 apexes and 6 chambers, no?

Somewhere I had made an Excel spreadsheet to demonstrate the movement, but it has since perished.  Perhaps I could recreate it again, not that I was ever convinced that the engine itself could be made to be durable enough for practical use.

I didn't know you could do animation with a spreadsheet. I thought it was all boxes and equations between boxes, no?

Well anyway, check out my new webpage [nofollow], published today and see if that can help revive your memory.

I suggest values to try would be

Sign = +, D=3, N=M=4 - your 4-apex rotary piston

and

Sign = +, D=5, N=M=6 - a 6-apex rotary piston

and you can adjust the rho slider to modify the engine housing shape.

If you find anything of interest you could capture the screen image and post it here. Or if you can't get the interactive display to work at all, let me know and I will see if I can help.

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Mathematics of the Wankel rotary-engine shapes webpage by Peter Dow
« Reply #2 on: 12/06/2014 20:34:32 »