Most aircraft piston engines fall into two general categories:1
- Radial engines (radials for short2) have their cylinders radiate out from the crankshaft in a star pattern; they tend to have a blunt, cylindrical nose shape, and are generally air-cooled.
- Inline engines (inlines) have their cylinders all in a line along the crankshaft from front to back; they tend to adopt a more streamlined style of nose, and are almost always liquid-cooled.
As coolant, piping for same, and radiators tend to have positive mass, and aircraft are typically operated in a positive gravity field, the liquid-cooling system needed by most inlines imposes an unavoidable weight penalty; additionally, it makes these engines comparatively fragile compared to air-cooled radials of similar size, as the whole engine can easily be disabled by a leaky coolant line.3
However, even though the radiator, by its very nature, has to stick out into the airstream in order to lose heat to said ambient airstream, it does not (necessarily) impose a drag penalty; in the process of being cooled by the ambient air, it transfers thermal energy to said air, and some clever mad scientists figured out how to use this to generate thrust, essentially turning the radiator into a primitive jet engine. The thrust generated by this process (known as the Meredith effect) can easily exceed the drag produced by the radiator, turning the radiator into a net thrust producer; back when fighter aircraft still used pistons and props, this gave inline-powered fighters a performance advantage over their radial-powered counterparts, which is why most of the really successful piston fighters of World War II used liquid-cooled inline engines. (Today’s inline-powered aircraft, which generally do not have a need to outrun pursuing fighters, make do with simple non-thrust-producing radiators.)
There doesn’t seem to be any reason why a properly-designed radial couldn’t benefit from the Meredith effect as well; indeed, it should work somewhat better with an air-cooled radial, since the thrust-producing air is being heated by the cylinders directly, cutting out the liquid middleman and one of the two efficiency-robbing energy transfers necessary in a liquid-cooled system. Yet, despite this, and the fact that these big radials were used to power heavy aircraft that needed every bit of thrust they could possibly get, and the fact that the wide, flat, blunt nose of a radial engine makes the drag problem especially acute (and, thus, any possible way of reducing drag all the more desirable), none of the big radials ever was designed to take advantage of the Meredith effect.4
1: In practice, so as to pack lots of cylinders into the smallest possible space, the larger engines from both groups tend to fall closer towards the middle; all but the smallest post-World-War-I radials have at least two to four rows of cylinders, stacked one in front of another, while most midsize-and-larger inlines have multiple parallel cylinder banks (again, usually from two to four).
2: No relation to the kind of radials you navigate with, except insofar as they both pertain to aviation.
3: This is one of the big reasons why all the really big World-War-II-and-later aircraft piston engines (the ones powering the big bombers of the war and the big propliners of the decade following it) were radials. Big piston engines are unreliable enough on their own; trying to keep a really big liquid-cooled inline running would be an absolute nightmare.
4: You sometimes hear that the NACA cowling design used on essentially all post-mid-1930s radials was designed to produce extra thrust from the heated cooling air. This is a misconception. Although the NACA cowling did indeed reduce (and quite dramatically, too) the drag penalty of a radial engine, it did this solely by smoothing the rough aerodynamic lines of the uncowled radial; no Meredith-effect wizardry was involved.
Note: Not a duplicate of this other question. That one asks whether radials used the Meredith effect; this one asks why they didn't.