No one seems to agree on how to measure the displacement of a rotary engine, here’s why – Jalopnik

Language is an imperfect medium, but it’s what we have, so let’s get on with it. Determining the volume of inventor Felix Wankel’s rotary engine can generate more arguments than claiming what a GT car should be these days, and a lot of that has to do with the way we use the word “displacement.” Rotary engines are weird because instead of neat, clean, easily measurable cylinders we get this alien three-lobed tortilla chip thing that rotates in a strange figure-of-eight pattern around an eccentric axis. The axis is not called “eccentric” because it likes to put ketchup on ice, but because it is offset from the center of rotation.

Figuring out how much space is available for air in the chamber created by the engine’s spherical triangle should be a relatively simple piece of math, right? After all, that’s what we usually mean by “displacement.” Let’s calculate it using the formula from Mazda’s book “Rotary Engine”, written by Kenichi Yamamoto, also known as the father of the Mazda rotary engine. That formula is 3√3eRb, or three times the square root of three times “e” times “R” times “b.”

Here’s what these letters mean: Distance from rotor center to tip (R); eccentricity (e), or the offset between the center of the lobe in the rotor and the center of the crankshaft; and the width of the rotor housing (b). In a Mazda 13B engine, R equals 105 mm, e equals 15 mm and b equals 80 mm, giving us a volume of 654.7 cubic centimeters per rotor and a total of 1.3 liters (1,309 cc) between the two rotors.

So we’re done here, right? Rotational displacement fixed!

Not quite. The problem is that this formula only calculates the volume for a single chamber, while each rotor actually creates three.

Then why doesn’t the formula calculate the volume for all three rooms at the same time? Mazda may only want to actively measure chambers during their combustion cycles (the volume formula in “Rotary Engine” is for the “working chamber”), but we count cylinder volume in reciprocating engines regardless of which stroke they are working on. This is the point being made Hemmings in a quote from G. Fred Leydorf, an advanced engine engineer for American Motors, who once considered creating a rotary engine for his Ramblers. In 1973, Leydorf said, “With the Wankel… all three chambers of each rotor complete the four-stroke cycle – so they must be counted in its displacement.”

That Hemmings article also mentions NSU, the German company that was one of the early adopters of Felix Wankel’s revolutionary rotary engine, and why the company adopted the single-rotor displacement engine. Max Bentele, an engineer at Curtiss-Wright, visited NSU in 1958 and told the company that it could avoid being overtaxed in Europe for its engine size if it reported only single-chamber engine displacement, a practice that Mazda adopted and continued.

So we can count the rotating displacement with a single chamber per rotor (also called ‘geometric displacement’) or we can count all the chambers, also called ‘thermodynamic displacement’. And that’s it, that’s how we can determine the rotational displacement, right? Right?

The problem here is that we don’t double the displacement of two-stroke engines, so why would we do that for rotary engines? It is because the “equivalent engine displacement” method is useful for race classification to ensure that rotary engine cars do not fall into small engine categories and take the podium. It is a pragmatic approach, just as Formula 1 used to have different rules for displacement of naturally aspirated and forced induction engines, to level the playing field. Rotary engines may have some potentially crippling drawbacks, such as oil consumption, poor fuel economy and apex seals that wear out quickly, but power-to-displacement isn’t one of them.

But if we want to take “equivalent displacement” and “thermodynamic displacement” to their logical conclusions, why not double the three-chamber displacement, as some people do with the one-chamber displacement? Can we honestly say that the Mazda 13B is not a 7.9-liter (7,854 cc) engine? We’ll call it ‘hyperbolic displacement’.