The preliminary question is, how much will the plywood sag under the weight? I should think that it would depend on (a) how thick the sheet is and (b) how heavy the weight is. (Also possibly relevant might be the area occupied by the weight; would a 100-lb weight on a 36 sq. in. base cause more sag than the same weight distributed over, say, 324 sq. in.?)
My real question is this: is there a formula or rule of thumb to calculate how thick the plywood sheet needs to be to support a given weight without sagging beyond a certain limit?
I know I could prevent sagging altogether by putting a fifth leg in the center, but the space beneath the table needs to be completely open.
Thanks in advance for any insights you might have.