Hand Tools Archive
Patternmakers use planes like you describe. They are equipped with a set of blades and matching detachable curved bottom plates in a series of radii.
f course it is a lot simpler to start with one round plane of the minimum radius and just take several passes until you have matched your radius. The radius is going to vary along the length of the plank anyway, so a single radius blade isn't going to be effective. You do have a set of radius gauges, so you know when you've hit your target curve, don't you?
An alternative to round planes or backing out planes is a set of shaves: