Why don't piston engine airplanes have mufflers?

It helps increase power output fairly simply. When the engine's exhaust value opens, exhaust starts to flow out of the exhaust port (being pushed fairly quickly by the piston). That means we a have a stream of fairly dense exhaust moving away from the exhaust port at fairly high speed. read more

Most all engines have a muffler or baffle of some sort. The reason is to keep cold air from shock cooling the engine valves once the engine is turned off. Consider that the exhaust manifold and subsequent pipe used for routing the exhaust reach temperature of over 1000 degrees f., and in fact can glow cherry red. read more

However, given the low RPM speeds of our old-fashioned aviation piston engines, those mufflers need to be large and the equally old airframe designs have no space for them. So in aviation the mufflers are still causing a power loss. read more

They do have small mufflers and it does help, but the 5.7 liter engines on Cessna 172's have very short exhaust pipes and they aren't going to be quiet at full power with any amount of muffling. Even a car with that size engine and a lot more pipe and muffling is very loud at high power. read more