What's the noun for planings? Here's the word you're looking for.
plane
A level or flat surface.
(geometry) A flat surface extending infinitely in all directions (e.g. horizontal or vertical plane).
A level of existence or development. (eg, astral plane)
A roughly flat, thin, often moveable structure used to create lateral force by the flow of air or water over its surface, found on aircraft, submarines, etc.
“Suddenly, I heard a plane fly overhead. It was low in the sky, slow, and noisy.”
“Yet, not to do so is to remove historical events from the plane of analysis and to place it at the level of religious remembrance.”
“The distance between images taken along the optical z-axis and the number of images projected into a single plane is indicated.”
planer
A woodworking tool which smooths a surface or makes one surface of a workpiece parallel to the tool's bed.
A large machine tool in which the workpiece is traversed linearly (by means of a reciprocating bed) beneath a single-point cutting tool. (Analogous to a shaper but larger and with the workpiece moving instead of the tool.) Planers can generate various shapes, but were most especially used to generate large, accurate flat surfaces. The planer is nowadays obsolescent, having been mostly superseded by large milling machines.
(archaic, printing) A wooden block used for forcing down the type in a form, and making the surface even.
“If the surface isn't smooth use your planer or belt sander.”
planisphere
Any representation of part of a sphere on a plane surface
(astronomy) Any of several charts of the celestial sphere having an overlay or window that may be adjusted to show the stars visible at a particular time, or from a particular place
