Basically cross sanding flattens the floor fast by cutting and tearing across the grain where the timber is weakest thus levelling the floor out quickly and easily.
Most floors are already flat so do not require a harsh cross sanding, but if there’s slight cupping, crowning or the floor is uneven, which is usually the case with reclaimed installations, the quickest and most effective way to level the area is to cross sand.
Once you have cross sanded the area and all is flat you will need to use the same grit sandpaper to sand with the grain before you progress onto finer grits, this is what removes the horrible cross grain scratches that the Internet tells you ruin your floor.
I better add this so as not to confuse you, cross grain sanding should be done at either 45 or 33 degree angles, only on severe cupping or protruding repairs would you ever cut straight across the grain, but if you do find yourself in this scenario and doing this, make sure once finished you use the same grit sandpaper to do another pass at 45 degrees and again with the grain.
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