The Rotary Wankel Engine

The Wankel engine is a type of internal combustion engine which uses a rotary design to convert pressure into a rotating motion instead of using reciprocating pistons. Its four-stroke cycle is generally generated in a space between the inside of an oval-like epitrochoid-shaped housing and a roughly triangular rotor. This design delivers smooth high-rpm power from a compact, lightweight engine.
The engine was invented by engineer Felix Wankel. He began its development in the early 1950s at NSU Motorenwerke AG (NSU) before completing a working, running prototype in 1957. NSU then subsequently licenced the concept to other companies across the globe, who added more efforts and improvements in the 1950s and 1960s.
Because of their compact, lightweight design, Wankel rotary engines have been installed in a variety of vehicles and devices such as automobiles and racing cars, aircraft, go-karts, personal water craft, and auxiliary power units.

Design
In the Wankel engine, the four strokes of a typical Otto cycle occur in the space between a three-sided symmetric rotor and the inside of a housing. In the basic single-rotor Wankel engine, the oval-like epitrochoid-shaped housing surrounds a rotor which is similar to a Reuleaux triangle, a three-pointed curve of constant width, but with the bulge in the middle of each side a bit more flattened. From a theoretical perspective, the chosen shape of the rotor between the fixed apexes is basically the result of a minimization of the volume of the geometric combustion chamber and a maximization of the compression ratio, respectively. Thus, the symmetric curve connecting two arbitrary apexes of the rotor is maximized in the direction of the inner housing shape with the constraint not to touch the housing at any angle of rotation (an arc is not a solution of this optimization problem).
The central drive shaft, also called an eccentric shaft or E-shaft, passes through the center of the rotor and is supported by bearings. The rotor both rotates around an offset lobe (crank) on the E-shaft and makes orbital revolutions around the central shaft. Seals at the corners of the rotor seal against the periphery of the housing, dividing it into three moving combustion chambers. Fixed gears mounted on each side of the housing engage with ring gears attached to the rotor to ensure the proper orientation as the rotor moves.
The best way to visualize the action of the engine in the animation at left is to look not at the rotor itself, but the cavity created between it and the housing. The Wankel engine is actually a variable-volume progressing-cavity system. Thus there are 3 cavities per housing, all repeating the same cycle. Note as well that points A and B on the rotor and e-shaft turn at different speed, point B moves 3 times faster than point A, so that one full orbit of the rotor equates to 3 turns of the e-shaft.
As the rotor rotates and orbitally revolves, each side of the rotor gets closer and farther from the wall of the housing, compressing and expanding the combustion chamber similarly to the strokes of a piston in a reciprocating engine. The power vector of the combustion stage goes through the center of the offset lobe.
While a four-stroke piston engine makes 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 each driveshaft rotation, i.e. one power stroke per rotor orbital revolution and three power strokes per rotor rotation. Thus, power output of a Wankel engine is generally higher than that of a four-stroke piston engine of similar engine displacement in a similar state of tune; and higher than that of a four-stroke piston engine of similar physical dimensions and weight.
Wankel engines also generally have a much higher redline than a reciprocating engine of similar power output, mostly because of the gearing from the rotor to the e-shaft; and also because the smoothness inherent in the circular motion, which eliminates dangerous vibration that can occur in reciprocating engines due to the nature of their operation.
National agencies that tax automobiles according to displacement and regulatory bodies in automobile racing variously consider the Wankel engine to be equivalent to a four-stroke engine of 1.5 to 2 times the displacement; some racing sanctioning bodies ban it altogether.

Differences and Challenges
There are several defining characteristics that differentiate a rotary engine from a typical piston engine.

Fewer Moving Parts
The rotary engine has far fewer moving parts than a comparable four-stroke piston engine. A two-rotor rotary engine has three main moving parts: the two rotors and the output shaft. Even the simplest four-cylinder piston engine has at least 40 moving parts, including pistons, connecting rods, camshaft, valves, valve springs, rockers, timing belt, timing gears and crankshaft.
This minimization of moving parts can translate into better reliability from a rotary engine. This is why some aircraft manufacturers (including the maker of Skycar) prefer rotary engines to piston engines.

Smoother
All the parts in a rotary engine spin continuously in one direction, rather than violently changing directions like the pistons in a conventional engine do. Rotary engines are internally balanced with spinning counterweights that are phased to cancel out any vibrations.
The power delivery in a rotary engine is also smoother. Because each combustion event lasts through 90 degrees of the rotor's rotation, and the output shaft spins three revolutions for each revolution of the rotor, each combustion event lasts through 270 degrees of the output shaft's rotation. This means that a single-rotor engine delivers power for three-quarters of each revolution of the output shaft. Compare this to a single-cylinder piston engine, in which combustion occurs during 180 degrees out of every two revolutions, or only a quarter of each revolution of the crankshaft (the output shaft of a piston engine).

Slower
Since the rotors spin at one-third the speed of the output shaft, the main moving parts of the engine move slower than the parts in a piston engine. This also helps with reliability.

Challenges
There are some challenges in designing a rotary engine: Typically, it is more difficult (but not impossible) to make a rotary engine meet U.S. emissions regulations.
The manufacturing costs can be higher, mostly because the number of these engines produced is not as high as the number of piston engines.
They typically consume more fuel than a piston engine because the thermodynamic efficiency of the engine is reduced by the long combustion-chamber shape and low compression ratio.

Fuel consumption and emissions
Just as the shape of the Wankel combustion chamber prevents preignition, it also leads to incomplete combustion of the air-fuel charge, with the remaining unburned hydrocarbons released into the exhaust. While manufacturers of piston-engine cars were turning to expensive catalytic converters to completely oxidize the unburned hydrocarbons, Mazda was able to avoid this cost by enriching the air/fuel mixture and increasing the amount of unburned hydrocarbons in the exhaust to actually support complete combustion in a 'thermal reactor' (an enlarged open chamber in the exhaust manifold) without the need for a catalytic converter, thereby producing a clean exhaust at the cost of some extra fuel consumption. World gasoline prices rose sharply at the time Mazda introduced their Wankel engine, making the cleaner exhaust/increased fuel consumption tradeoff an unwelcome one for consumers.
In Mazda's RX-8 with the Renesis engine, fuel consumption is now within normal limits while passing California State emissions requirements. The exhaust ports, which in earlier Mazda rotaries were located in the rotor housings, were moved to the sides of the combustion chamber. This approach allowed Mazda to eliminate overlap between intake and exhaust port openings, while simultaneously increasing exhaust port area. The Renesis engine even meets California's Low Emissions Vehicle or LEV standards.