[math-fun] Unsymmetrical Wankel engine
What keeps diesels from starting backwards--valving? What about external combustion (jet) engines? An engine with perhaps similar problems can be made from http://toobnix.org/?p=741 http://vimeo.com/38945542 generating compression from increasing the twist (decreasing the pitch) along the length. Further along, the rotors can continuously deform to circularity to accommodate porting. --rwg "Minnesota: Come for the culture. Stay, because your car won't start." It just took me a minute to get the ps on my original mention of the toobnix: No manual entry for man overboard wds> two-stroke engine symmetrical and can get deranged on start and then run backwards The Wankel engine also is symmetrical, as least as depicted here: http://en.wikipedia.org/wiki/File:Wankel_Cycle_anim_en.gif Can one devise an unsymmetrical Wankelian engine with a preferred direction of time? To do so, it seems we want to replace the Reuleaux triangle with a chiral, but still constant-width, shape. http://en.wikipedia.org/wiki/Reuleaux_triangle The Reuleaux triangle is the curve of constant width=1 with least area (the circle has the greatest area). But consulting http://en.wikipedia.org/wiki/Curve_of_constant_width we see that any triangle ABC, including a general and hence chiral triangle, can be converted into a curve of constant width as explained in this picture: http://en.wikipedia.org/wiki/File:How_to_make_mathematical_roller_curve_base... (The width is 2x+2y-a-b-c.) I believe this allows us to construct a Wankelian engine from any such arising from a triangle is sufficiently close to equilateral. Specifically, imagine the const-width thing (call it "CW") rolling around inside the "stadium" (outer boundary of the Wankel combustion compartment). As it does so, inside CW some small fixed circular ink-pad inks out a black shape inside CW. Cut that shape out of CW's inside, leaving a hole. As CW rolls round the stadium the hole will roll round the fixed circle. It thus can be used to transmit torque to a rotating rod with fixed axis. -- Warren D. Smith
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Bill Gosper