How Far a Toss Travels: Motion Transfer Across a Shared Mattress as a Function of Distance, and the Separation at Which a Partner's Turn Falls Below Perception

Manufacturers advertise motion isolation in units of wine glasses balanced on mattresses, but the quantity a sleeping partner experiences is an amplitude at a distance, and it obeys a decay law. This paper models a turn-over event as a stated 10 mm displacement decaying exponentially across the mattress, with stated decay lengths of 0.55 m for continuous-coil construction, 0.28 m for pocket springs, and 0.16 m for foam. Against a stated perception threshold of 0.8 mm, the disturbance stays perceptible for 1.39 m across a coil mattress, 0.71 m across pocket springs, and 0.4 m across foam. At the 0.85 m centre separation of a queen bed, the coil mattress still delivers 2.13 mm to the partner while foam delivers 0.05 mm. Bed width and mattress construction are shown to be substitutes with an exact exchange rate, and the width at which even the most coupled mattress falls silent is computed. This study is simulated, not measured.