A Hip Protector Sized by the Energy It Must Actually Absorb, and the Fall-Energy Window in Which Passive Protection Works

Hip fracture after a sideways fall is an energy problem with a narrow solution space. This paper computes, from a stated fall model, the impact energy delivered to the greater trochanter, the energy the body can absorb before a stated femoral fracture-force threshold is reached, and the excess a wearable pad must absorb at its design point. With an effective mass fraction of 0.30, a body-and-floor stiffness of 60,000 N/m, and a central fracture-force threshold of 3,000 N (input range 2,000-4,500 N), the body alone tolerates 75.0 J. A 70 kg standing fall delivers 123.6 J, an excess of 48.6 J. A foam-plus-shell pad of area 0.036 m2, plateau stress 100,000 Pa and usable strain 0.65 absorbs 65,000 J/m3, so absorbing the excess requires 20.8 mm of foam, 168.7 g per pad (337.3 g per pair), at a manufacturing cost of $17.68 per pair. The pad caps the trochanter force at 2,520 N at its plateau. The protection window at the central threshold is 75.0-201.7 J: below it a pad is unnecessary, inside it the sized pad brings the peak trochanter force below 3,000 N, and above it the pad bottoms out and the force rises above the threshold again. Standing falls for 50, 70 and 90 kg bodies fall inside the window; falls down steps at 206.0 J (70 kg) and falls from height at 294.3-529.7 J fall above it. SIMULATED, NOT MEASURED.