All of the MATH for a 13B you could ever ask for
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From: NYC
All of the MATH for a 13B you could ever ask for
So I'll preface this by saying that I'm still in high school, meaning a lot of what I'm about to share is too complicated for me to actually explain why it's true. However, I worked on making a 13B in CAD for awhile and really spent way longer than I would've liked on that. So I wanted to compile all of the math and dimensions I had to whip up. I'll include links and a Desmos graph of the more visual stuff and update this thread as I get time.
For starters:
Here's a graph of the compression ratio of a 13B (or any rotary with the same housing shape).
It also includes the parametric equation to create the rotor housings, based on eccentricity (E, 1.5cm) and the rotor's center to tip distance (r, 10.5cm)
https://www.desmos.com/calculator/lcsdre0mys
Try messing around with some of the sliders if you're curious to see how it comes together. I also added the displacement of each rotor and the total displacement of a 2 rotor.
These equations all work for the 12A and renesis, however I'm not sure what their e/r ratios are, but I know they're similar to the 13B's anyways.
The resources I used to put this together:
Rotary Parametrics
Four Rotor (super interesting entry paper for the 787B by Mazda, worth a read IMO)
Mazda 13B Rotary CAD Someone else's CAD of the 13B. Don't agree with some of the dimensions on the interior but the exterior appears good, not that I've measured it.
I also have a few CAD files around if anyone's interested. Willing to CAD a few accessible parts on my S4 GTU if anyone wants to see something in particular. Other than that, I'll try to keep it focused on the math and technical data needed to really get into the depths of how the rotary engine works. Hope you guys enjoy this!
- Joe
For starters:
Here's a graph of the compression ratio of a 13B (or any rotary with the same housing shape).
It also includes the parametric equation to create the rotor housings, based on eccentricity (E, 1.5cm) and the rotor's center to tip distance (r, 10.5cm)
https://www.desmos.com/calculator/lcsdre0mys
Try messing around with some of the sliders if you're curious to see how it comes together. I also added the displacement of each rotor and the total displacement of a 2 rotor.
These equations all work for the 12A and renesis, however I'm not sure what their e/r ratios are, but I know they're similar to the 13B's anyways.
The resources I used to put this together:
Rotary Parametrics
Four Rotor (super interesting entry paper for the 787B by Mazda, worth a read IMO)
Mazda 13B Rotary CAD Someone else's CAD of the 13B. Don't agree with some of the dimensions on the interior but the exterior appears good, not that I've measured it.
I also have a few CAD files around if anyone's interested. Willing to CAD a few accessible parts on my S4 GTU if anyone wants to see something in particular. Other than that, I'll try to keep it focused on the math and technical data needed to really get into the depths of how the rotary engine works. Hope you guys enjoy this!
- Joe
Hope you are getting some extra credit for this.
IRT displacement, it's really more effective displacement or how often it fires. "While a four-stroke piston engine completes one combustion stroke per cylinder for every two rotations of the crankshaft (that is, one-half power stroke per crankshaft rotation per cylinder), each combustion chamber in the Wankel generates one combustion stroke per driveshaft rotation, i.e. one power stroke per rotor orbital revolution and three power strokes per rotor rotation." https://en.wikipedia.org/wiki/Wankel_engine
IRT displacement, it's really more effective displacement or how often it fires. "While a four-stroke piston engine completes one combustion stroke per cylinder for every two rotations of the crankshaft (that is, one-half power stroke per crankshaft rotation per cylinder), each combustion chamber in the Wankel generates one combustion stroke per driveshaft rotation, i.e. one power stroke per rotor orbital revolution and three power strokes per rotor rotation." https://en.wikipedia.org/wiki/Wankel_engine
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