Yes, the math is probably somewhat similar to what carpenters use to determine if a tabletop will sag as a function of its length: https://woodbin.com/calcs/sag

Yes, the math is probably somewhat similar to what carpenters use to determine if a tabletop will sag as a function of its length: https://woodbin.com/calcs/sagulator/ https://woodbin.com/calcs/sagulator/ Obviously not the same because the force isn't being applied perpendicular to the edges, but still, almost certainly will be not nearly linear.