Fill the bottom of the box with 3 inches of sawdust. Put your first layer of root vegetables on top of the sawdust, leaving 1/2 inch spaces between the vegetables. Leave 3 inches of space between the vegetables and each side of the box.
Cover the first layer of vegetables with 1/4 inch sawdust. Put the second layer of vegetables over this, with the same spacing as the first layer of vegetables.
Repeat this layering of 1/4 inch sawdust with vegetables until you get to within 3 inches of the top of the box. Fill the box the rest of the way with sawdust. Store the box in your root cellar or basement.