You can cut a fairly tight radius with a 7 1/4" blade with the right teqnique. I used to cut fireplace mantle arches out of full 1 1 /4" thick pine fairly often on the job site.
The procedure went something like this:
1) Do a radius arc line on the workpiece, either by bending a thin fillet to arc specs, or with a trammel.
2) Make the 1st cut about 1/2" deep, but keep the cut about 1/8" on the offall side of arc.
3) Repeat step 2 untill you end up with a 3/8" or so trough behind the finish arc line.
4) Once you have room for the backside (rear of saw blade) the blade will not bind in the cut, leaving you to only be concerend with placement of the leading edge of the blade. That way you can make a clean accurate finish curve cut.
5) Grind out bad bumps, followed up with a belt sander, followed by an offall arch sanding block maybe 10" long, followed by loose sandpaper by hand.
I could do a 5' or so arc like this in about 20-30 minutes or so, ready to stain. It does take some skill to guide a saw that acurately free hand, but after 20 years of framing, I found it fairly easy. Most of my guys could do it, but the results were mixed.
The trick is to keep a minimal amount of the blade in the cut, along with making room for the back side of the blade.
Joe