Mattress Firmness as a Pressure Problem: Peak Interface Pressure Across Body Masses, and the Mass Above Which No Uniform Surface Stays Below the Capillary Threshold

Mattresses are sold in firmness grades with no numbers attached, yet the quantity a sleeper's circulation experiences is interface pressure. This paper models a bony region of the body as a cylinder sinking into a linear spring layer, balances the load over the curved contact patch, and computes peak pressure at the hip and shoulder for body masses of 55, 75, and 95 kg across mattress stiffness from 40 to 220 kPa per metre. Peak pressure rises steadily with stiffness — at 75 kg, from 3.97 kPa on the softest layer to 6.38 kPa on the firmest — while sink depth falls. Scoring both failures against a capillary threshold of 4.27 kPa and a 110 mm support limit, a stiffness window exists for the 55 kg sleeper (40, 60, 80, 100 kPa per metre) and a narrow one for the 75 kg sleeper (40), but none at all for the 95 kg sleeper, whose best achievable peak is 4.8 kPa even before the support limit is applied. A uniform surface, the arithmetic shows, cannot serve the heaviest sleepers below the threshold; zoned construction is a necessity for them, not a luxury. This study is simulated, not measured.