The rotary engine was a type of aircraft engine that was used for a short period of time, between about 1909 and 1918. At the time they had some of the best performance figures for the middle-horsepower class, around 100hp, but limitations in the design meant they had little room for growth. When even small engines started moving into the 100hp area, the rotary fell from use.
The rotary was a traditional Otto cycle engine with the cylinders arranged pointed outwards from a single crankshaft, similar to the radial engine. In the case of a rotary, the crankshaft was fixed solidly to the aircraft frame, and the cylinders spun round, attached to the propeller.
The first effective rotaries were built by Stephen Balzer, who was interested in the design primarily for two reasons. One was that at the low RPM engines of the day ran at, the force of any one explosion needed to generate 100hp was quite large. In order to damp out these pulses, engines needed to mount a large flywheel, which was basically dead weight. In the rotary design the engine itself doubled as its flywheel, so rotaries were automatically lighter than similarly sized engines. Another advantage to the rotary was that the cylinders had good airflow over them even when sitting still, which was an important concern given the alloys they had to work with. Balzer's early engines didn't even use cooling-fins, a feature of every other air-cooled design, one that is complex to manufacture. Another advantage, not realized at first, is that the pistons do not actually reciprocate, they orbit a common center. This leads to smoother running. Balzer's first designs were ready for use in 1899, at which time they were the most advanced in the world. Other aircraft engines would not catch up in performance for a decade. He then became involved in Langley's Aerodrome attempts, which banrupted him while he tried to make much larger versions.
The next major advance in the design was Lauren Seguin's Gnome from 1908. Originally a 5-cylinder 50hp engine, the production versions were scaled up to an 50hp 7-cylinder design, which soon reached 80hp, and then 110. The engine was at this later standard when WWI started, and the Gnome quickly found itself being used in a tremendous number of aircraft designs. It was so good that it was licensed by a number of companies, include the German Oberursel firm, later purchased by Fokker. It was not at all uncommon for French Gnomes to meet German versions in combat.
The Gnome (and its copies) had a number of features that made it unique, even among the rotaries. Notably, the fuel was mixed and sprayed into the center of the engine through a hollow crankshaft, and then into the cylinders through the piston itself, a single valve on the top of the piston let the mixture in when opened. The valves were counter balanced so than only a small force was needed to open them, and releasing the force closed them without any springs. The center of the engine is normally where the oil would be, and the fuel would wash it away. To fix this the oil was mixed in liberal quantities with the fuel, and the engine spewed smoke from the burning oil. Finally, the Gnome had no throttle or carburetor, with the fuel being sprayed into the spinning engine, the motion alone was enough to mix the fuel fairly well. Of course with no throttle, the engine was either on or off, so something as simple as reducing power for landing required the pilot to cut the ignition, "blipping" the engine on and off.
Throughout the early period of the war, the power-to-weight ratio of the rotaries remained ahead of that of their competition. They were used almost universally in fighter aircraft, while traditional water cooled designs were used on larger aircraft. The engines had a number of disadvantages, notably terrible fuel consumption because the engine was always "full throttle". In combat the huge "flywheel" the rotary had originally been designed to create turned out to result in tricky handling due to gyroscope effects as well. But they maintained their edge through a series of small upgrades, and many newer designs continued to use them.
In 1918 saw the introduction of the inline powered Fokker D.VII. Through superb design the D-VII was able to dogfight with the rotaries, and outclimb and outrun them with ease due to its 185hp engine. Aircraft had evolved so that speed had become the most important aspect of ability, and speed can only be provided through increased power. Larger rotaries were attempted, but the gyroscopic effects were overwhelming and they proved to be largely unworkable. Inline engines were able to increase power through increased RPM, another trick the rotary couldn't match. By the end of the year only a single new rotary was designed, Fokker's own D-VIII, designed solely to provide some use for their Oberursel factory. When the war ended, the rotary disappeared almost instantly, with WWI engines being used for training for a short time until their poor fuel economy drove the users to newer engines.
The two original benefits were now no longer valid at the end of the war. Air cooling proved to be entirely "doable" as production techniques improved to the point where finning was no longer an issue. In addition as the size of the engines grew, the propellers themselves became large enough to act as the flywheel. Faster RPM also dramatically reduced the need for a flywheel at all. This left the rotary with high fuel and oil consumption compared to other designs, and not much else.
Perhaps more seriously, having such a large weight spinning in an aircraft produces significant gyroscopic effects. Maneuvering an aircraft with this kind of engine required a lot of skill since it didn't always respond to controls as expected. It is said that the rotary powered Sopwith Camel could execute a turn to the right at double the speed to the left, by manuvering the plane around the massive gyroscopic momentum of the engine. With even larger rotaries, the planes proved almost unflyable.