Fall-Impact Flooring Priced by Impact Physics: How Much Compliance a Floor Needs to Keep a Hip Below the Fracture Threshold

Hip fracture after a sideways fall is one of the most consequential injuries of old age, and impact-absorbing flooring is widely sold as a partial answer, usually as a thin underlay a few millimetres thick. This paper prices that claim against a physical bound. A sideways fall from standing is modelled with an effective mass at the hip, a greater-trochanter drop height set by stature, and the soft tissue over the trochanter and the floor treated as two springs in series (SIMULATED, NOT MEASURED). The fracture-force range for older femora under sideways loading is taken as a stated input of 2,500-4,500 N, with the design target at its lower end. For a reference body of 70 kg and 1.70 m, the model gives an impact velocity of 4.16 m/s, an impact energy of 212.5 J, and a peak force on a rigid floor of 5,645 N. Nominal thin products change this very little: 12 mm cork gives 5,637 N, 15 mm rubber crumb 5,619 N, and 10 mm foam underlay 5,264 N (a 6.7% reduction). A 50 mm foam pad gives 4,267 N and a nominal sprung timber floor 3,184 N, still above the 2,500 N target. Meeting the target requires a floor stiffness of no more than 18,296 N/m deflecting 136.6 mm at peak force: 273.3 mm of foam (estimated $3,260 per 20 m2 room, a 283.3 mm raised floor needing a 3.4 m ramp, and a 4.78-fold wheelchair push-force penalty) or a sprung platform with 136.6 mm of travel (estimated $3,786 per room) with far smaller mobility penalties. Cork would need to be 16.40 m thick and rubber crumb 6.56 m thick to supply the required stiffness. The paper states in full what flooring cannot do: head impacts, wrist fractures, and falls onto furniture-height edges are outside this design entirely.