Three Cylinder Radial For ICE In Prius?
 

I've read that a radial engine (Radial, not rotary) is lighter and more powerful than an inline engine of the same cylinder number and displacement.What are the objections to a horizontally mounted three cylinder radial engine in place of the inline four the Prius comes with? Any idea of the fuel efficiency comparisons? All I can find is Hours per gallon numbers.

It wouldn't fit is the first thing that came to mind.
Radial engines have more power because they were air craft engines. Piston air craft engines were designed around being ran at 1/3 to 1/2 power for best economy.
The fuel economy would likely be pretty terrible on account of typical car and truck engines are built around best fuel economy at 10 to 20% power.

Then, would a smaller radial engine at 33%-50% power compare in fuel economy to the 1.8 four in the Prius?

Well the prius would probably be doing around 80 mph at 30% engine load.
So not much of a comparison could be made.
It's just the wrong application.
Really about the only thing that could be done to improve fuel economy on a prius engine by a noticeable amount would be to rip out the gas motor and drop in a turbo diesel.

Then, I'd need an even smaller radial engine that will give the needed HP at 30.
A flat head engine, or disk valves would reduce the physical size.

The only 3-cyl radial I can remind by now is the proposed Zoche ZO 03A which was meant as a 2-stroke Diesel design but IIRC it didn't reach production scale.

But anyway, the problem with radials is their frontal area, plus they would be more suitable to longitudinal applications.

Where would you find a 3-cylinder radial? I don't think I've ever seen a radial engine that wasn't for aircraft use, and AFAIK the main benefit of the radial layout is that you got all the cylinders out in the airflow for cooling*. The few liquid-cooled ones I could find https://en.wikipedia.org/wiki/Catego...radial_engines were either pre-1920s, or experimental WWII designs. (Except for one Soviet one.)

*Which of course means that, for automotive use, you have to supply the airflow somehow.

The closest to "automotive" use I found some examples of radial air-cooled engines were small battle tanks such as the Stuart. In my country, there were some which had their radial engines replaced with water-cooled Scania V8 engines.

I'm thinking, now, of the Revetec cam lobe engine.Similar to the following, but with another parallel to the first so that there wouldn't be the "bang, bang, nothing, nothing" of the two piston version.

https://www.youtube.com/watch?v=zI3lac7ll6s

Frontal Area wouldn't matter inside the hood, and I had envisioned the engine laid forward horizontally, feeding a 90 deg case.