Traditional woodworkers use a scorp for roughing out concave shapes like bowls, spoons, and chair seats. Pfeil makes this 7″ long scorp with a contoured ash handle and a thick steel shank to reduce chatter as you pull the 1-1/4″ blade toward you. Less chatter = smoother curves.
Woodcraft sells it for $30. Note: this scorp requires honing before use. But if your honing skills leave something to be desired, Woodcraft will hone it for $5 extra.