Trochoid Math
01-25-2009, 07:35 PM
#1
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So this is some pretty heady stuff, but I'm pretty good with math and am looking for a challenge: reinventing the shape OF the rotary engine. I'm trying to see if I can come up with something with more working chamber volume, less SA. Anyways, I've found a couple of useful links but what I've found is a bit confusing. The cocoon shape of a housing is a simple epitrochoid (http://www.mekanizmalar.com/epitrochoid.swf, where outer disk radius is half the inner disk's and distance of the green dot is half the radius of inner disk. ie. 200-100-50 and you'll see the familiar shape). Yet the eccentric shaft creates this motion in the rotors with lobes that, if you look head-on, are obviously a circle around another circle (a hypocycloid, http://www.mekanizmalar.com/hypocycloid.swf). If someone could suggest some reading, or perhaps just explain the connection between the two very different types of trochoids, it would be much appreciated.
01-25-2009, 08:35 PM
#3
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Sorry for the triple post but this is a bit of a revelation.
Another, perhaps simpler question has turned up while I've looked this over: if you play with the epitrochoid link above, and rather than having the "green point" (the line that the apex seals draw around the chamber) being half the radius of the outer circle, make it nearly the same size as the radius. Like 200-100-80, then the shape becomes much more extreme but the rotors still retain their motion and the working chambers become WAY bigger. I can imagine that setup making **** loads of torque although the lateral acceleration of the rotors would also be more significant so I imagine you couldn't make it rev quite so high. But the compression would be so great you would probably have to reduce how far out the rotors curve. Maybe there would be no need for a dish in the rotor, since it would give the flame far more space to propogate and greatly up the volume/surface area ratio. Honestly, this seems infinitely simpler than what Mazda currently produces and would solve all their problems. So, anyone know why they haven't done this?
Another, perhaps simpler question has turned up while I've looked this over: if you play with the epitrochoid link above, and rather than having the "green point" (the line that the apex seals draw around the chamber) being half the radius of the outer circle, make it nearly the same size as the radius. Like 200-100-80, then the shape becomes much more extreme but the rotors still retain their motion and the working chambers become WAY bigger. I can imagine that setup making **** loads of torque although the lateral acceleration of the rotors would also be more significant so I imagine you couldn't make it rev quite so high. But the compression would be so great you would probably have to reduce how far out the rotors curve. Maybe there would be no need for a dish in the rotor, since it would give the flame far more space to propogate and greatly up the volume/surface area ratio. Honestly, this seems infinitely simpler than what Mazda currently produces and would solve all their problems. So, anyone know why they haven't done this?
Old rotary
New rotary
01-25-2009, 10:27 PM
#6
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Originally Posted by mazdaspeed7' post='915309' date='Jan 25 2009, 07:43 PM
What do you plan to do about the 2 distinct chambers at TDC? Not to mention making a poor combustion chamber shape even worse...
I'm leaning towards a flatter rotor face with a slight dish (rather than a much bigger dish), given the whole 2 chambers problem. Combined with turbo-charging , I would imagine the application could be scaled very easily to make a torquey, compact package or a larger more high-performance model with relatively small dimensions. Of course the idea is nothing without serious flow testing, but I don't see a serious problem with it. That's what other people's criticism is for
However, it is promising that the 16x will involve greater eccentricity. I believe Mazda is thinking on the same lines I am currently...
01-26-2009, 02:24 PM
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Originally Posted by ColinRX7' post='915312' date='Jan 25 2009, 09:14 PM
If you had a TEAM of engineers, production models, a manufacturing division, a testing facility.. You could beat Mazda to the punch and then everyone will know that it really WAS your idea!
Well, given I came up with the idea after Mazda has already been developing it for a few years, I don't think it was my idea in any way. But it is interesting to come to the same conclusion based on simple observations of an epitrochoid shape.
I have more interesting ideas to come though. Looking at seeing if I can make a five, six or seven sided rotor which will mimic the Rolls Royce/Moller idea of having two rotors in series...but without the huge drawback of being heavy (since there would only be one somewhat heavier rotor compared to a regular wankel) while burning much more efficiently.
01-28-2009, 09:40 PM
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Originally Posted by j9fd3s' post='915369' date='Jan 26 2009, 06:00 PM
have you read the book "rotary engne" by kenichi yamamoto? a quick google search finds it. its got all the calculations, PLUS it explains WHY they picked the dimensions they did
You can download that book and more from Paul Lamars web site.
http://www.rotaryeng.net/index.html
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