A Pillow-Loft Rule from Neck Geometry: Compressed Loft as a Function of Shoulder Width, Head Mass, and Fill Stiffness for Side and Back Sleeping

Pillows are sold by fill and by adjectives, but the quantity the neck experiences is the compressed loft under the head at three in the morning. This paper derives the loft requirement from shoulder geometry: for side sleeping the support gap that a pillow must fill is half the shoulder breadth minus 4 cm, which for a 44 cm shoulder breadth is 18.0 cm, and because fill materials compress by stated fractions of 0.28 to 0.55 under the head, the uncompressed loft that must be bought differs sharply by fill — 25.0 cm in solid latex against 40.0 cm in down for the same neck. A standard 15 cm down pillow leaves that sleeper's neck tilted 28.0 degrees from neutral. The deliverable is a two-measurement rule — shoulder breadth and fill compression — that replaces firmness adjectives with arithmetic. This study is simulated, not measured.