== A. Slab impact velocity, v = sqrt(2 g s (sin a - tan(phi_bed) cos a)) == alpha=21 phi_bed=22.0: v(s=1 m)=0.00 v(2 m)=0.00 v(5 m)=0.00 m/s alpha=21 phi_bed=17.0: v(s=1 m)=1.20 v(2 m)=1.69 v(5 m)=2.68 m/s alpha=23 phi_bed=22.0: v(s=1 m)=0.61 v(2 m)=0.86 v(5 m)=1.36 m/s alpha=23 phi_bed=17.0: v(s=1 m)=1.46 v(2 m)=2.07 v(5 m)=3.27 m/s alpha=25 phi_bed=22.0: v(s=1 m)=1.05 v(2 m)=1.49 v(5 m)=2.35 m/s alpha=25 phi_bed=17.0: v(s=1 m)=1.69 v(2 m)=2.39 v(5 m)=3.78 m/s alpha=28 phi_bed=22.0: v(s=1 m)=1.49 v(2 m)=2.10 v(5 m)=3.33 m/s alpha=28 phi_bed=17.0: v(s=1 m)=1.98 v(2 m)=2.80 v(5 m)=4.42 m/s alpha=30 phi_bed=22.0: v(s=1 m)=1.72 v(2 m)=2.43 v(5 m)=3.84 m/s alpha=30 phi_bed=17.0: v(s=1 m)=2.15 v(2 m)=3.04 v(5 m)=4.80 m/s == B. Thorax impact (fixed back), lumped model calibrated to the paper's 10 kg @ 7 m/s -> C = 0.49 == calibrated k1 = 15761 N/m (c1 = 300.0 Ns/m, k3 = 1.0e+06 N/m^3): 10 kg @ 7 m/s -> C = 0.490, peak force 10.70 kN NOTE: the paper (Methods, 'Impact simulations') calibrates its body modulus so that a 10 kg rigid block at 7 m/s gives C = 0.49 'in line with' Kroell et al. 1974. The Kroell fixed-back series used 19.5-23.1 kg pendulums at 4.9-7.2 m/s (secondary sources; the SAE report itself is paywalled and was not read), i.e. 2-2.5 x more energy. With the paper's calibration point those real Kroell energies over-compress the model thorax: rigid 23.1 kg @ 7.2 m/s -> C = 0.70, F = 14.3 kN, AIS~6.0 rigid 19.5 kg @ 4.9 m/s -> C = 0.53, F = 7.6 kN, AIS~6.0 rigid 23.1 kg @ 4.9 m/s -> C = 0.58, F = 7.6 kN, AIS~6.0 rigid 1.6 kg @ 14.0 m/s -> C = 0.25, F = 19.1 kN, AIS~1.0 ALTERNATIVE calibration 23.1 kg @ 7.2 m/s -> C = 0.49: k1 = 84156 N/m (check C = 0.490, F = 11.2 kN); 10 kg @ 7 m/s then gives C = 0.29 Snow blocks against the chest (contact area 0.12 m^2). F_cap = sigma_c * A: volume rho v sigma_c | C AIS Fpeak crushed E_kin E_crush | C with the stiffer (23.1 kg) calibration 0.125 400 2.0 30 | 0.41 4.1 3.1 0.0cm 100J 0J | C_alt = 0.21 0.125 400 3.0 30 | 0.57 6.0 3.6 0.0cm 225J 1J | C_alt = 0.21 0.250 400 2.0 30 | 0.57 6.0 3.3 0.0cm 200J 0J | C_alt = 0.21 0.250 400 3.0 30 | 0.60 6.0 3.6 5.3cm 450J 192J | C_alt = 0.21 0.500 400 1.0 30 | 0.45 4.9 2.1 0.0cm 100J 0J | C_alt = 0.21 0.500 400 2.0 30 | 0.60 6.0 3.6 4.8cm 400J 172J | C_alt = 0.21 0.500 400 3.0 30 | 0.60 6.0 3.6 16.7cm 900J 601J | C_alt = 0.21 0.500 400 4.0 30 | 0.60 6.0 3.6 30.2cm 1600J 1087J | C_alt = 0.21 1.000 400 2.0 30 | 0.60 6.0 3.6 11.2cm 800J 402J | C_alt = 0.21 1.000 400 3.0 30 | 0.60 6.0 3.6 24.8cm 1800J 892J | C_alt = 0.21 0.125 400 2.0 100 | 0.41 4.1 3.1 0.0cm 100J 0J | C_alt = 0.22 0.125 400 3.0 100 | 0.57 6.0 4.7 0.0cm 225J 0J | C_alt = 0.32 0.250 400 2.0 100 | 0.57 6.0 3.3 0.0cm 200J 0J | C_alt = 0.31 0.250 400 3.0 100 | 0.68 6.0 12.0 0.4cm 450J 52J | C_alt = 0.46 0.500 400 1.0 100 | 0.45 4.9 2.1 0.0cm 100J 0J | C_alt = 0.23 0.500 400 2.0 100 | 0.68 6.0 12.0 0.3cm 400J 36J | C_alt = 0.45 0.500 400 3.0 100 | 0.68 6.0 12.0 4.1cm 900J 492J | C_alt = 0.60 0.500 400 4.0 100 | 0.68 6.0 12.0 9.6cm 1600J 1148J | C_alt = 0.61 1.000 400 2.0 100 | 0.68 6.0 12.0 3.6cm 800J 429J | C_alt = 0.60 1.000 400 3.0 100 | 0.68 6.0 12.0 11.6cm 1800J 1387J | C_alt = 0.61 0.125 400 2.0 300 | 0.41 4.1 3.1 0.0cm 100J 0J | C_alt = 0.22 0.125 400 3.0 300 | 0.57 6.0 4.7 0.0cm 225J 0J | C_alt = 0.32 0.250 400 2.0 300 | 0.57 6.0 3.3 0.0cm 200J 0J | C_alt = 0.31 0.250 400 3.0 300 | 0.69 6.0 14.0 0.0cm 450J 0J | C_alt = 0.46 0.500 400 1.0 300 | 0.45 4.9 2.1 0.0cm 100J 0J | C_alt = 0.23 0.500 400 2.0 300 | 0.69 6.0 13.4 0.0cm 400J 0J | C_alt = 0.45 0.500 400 3.0 300 | 0.79 6.0 25.4 0.0cm 900J 0J | C_alt = 0.64 0.500 400 4.0 300 | 0.88 6.0 36.0 0.1cm 1600J 36J | C_alt = 0.76 1.000 400 2.0 300 | 0.78 6.0 24.2 0.0cm 800J 0J | C_alt = 0.62 1.000 400 3.0 300 | 0.88 6.0 36.0 0.8cm 1800J 275J | C_alt = 0.79 0.125 400 2.0 inf | 0.41 4.1 3.1 0.0cm 100J 0J | C_alt = 0.22 0.125 400 3.0 inf | 0.57 6.0 4.7 0.0cm 225J 0J | C_alt = 0.32 0.250 400 2.0 inf | 0.57 6.0 3.3 0.0cm 200J 0J | C_alt = 0.31 0.250 400 3.0 inf | 0.69 6.0 14.0 0.0cm 450J 0J | C_alt = 0.46 0.500 400 1.0 inf | 0.45 4.9 2.1 0.0cm 100J 0J | C_alt = 0.23 0.500 400 2.0 inf | 0.69 6.0 13.4 0.0cm 400J 0J | C_alt = 0.45 0.500 400 3.0 inf | 0.79 6.0 25.4 0.0cm 900J 0J | C_alt = 0.64 0.500 400 4.0 inf | 0.88 6.0 36.4 0.0cm 1600J 0J | C_alt = 0.76 1.000 400 2.0 inf | 0.78 6.0 24.2 0.0cm 800J 0J | C_alt = 0.62 1.000 400 3.0 inf | 0.91 6.0 39.9 0.0cm 1800J 0J | C_alt = 0.79 Threshold velocities for a 0.125 m^3, 400 kg/m^3 block (50 kg), paper calibration 10 kg@7 m/s: sigma_c= 30 kPa: C>=0.2: 1.0 m/s; C>=0.3: 1.5 m/s; C>=0.34: 1.7 m/s; C>=0.4: 2.0 m/s; C>=0.49: 2.5 m/s sigma_c= 100 kPa: C>=0.2: 1.0 m/s; C>=0.3: 1.5 m/s; C>=0.34: 1.7 m/s; C>=0.4: 2.0 m/s; C>=0.49: 2.5 m/s sigma_c= 300 kPa: C>=0.2: 1.0 m/s; C>=0.3: 1.5 m/s; C>=0.34: 1.7 m/s; C>=0.4: 2.0 m/s; C>=0.49: 2.5 m/s sigma_c= inf kPa: C>=0.2: 1.0 m/s; C>=0.3: 1.5 m/s; C>=0.34: 1.7 m/s; C>=0.4: 2.0 m/s; C>=0.49: 2.5 m/s Threshold velocities for a 0.125 m^3, 400 kg/m^3 block (50 kg), stiffer calibration 23.1 kg@7.2 m/s: sigma_c= 30 kPa: C>=0.2: 1.9 m/s; C>=0.3: never (<8 m/s); C>=0.34: never (<8 m/s); C>=0.4: never (<8 m/s); C>=0.49: never (<8 m/s) sigma_c= 100 kPa: C>=0.2: 1.9 m/s; C>=0.3: 2.9 m/s; C>=0.34: 3.2 m/s; C>=0.4: 3.8 m/s; C>=0.49: 4.7 m/s sigma_c= 300 kPa: C>=0.2: 1.9 m/s; C>=0.3: 2.9 m/s; C>=0.34: 3.2 m/s; C>=0.4: 3.8 m/s; C>=0.49: 4.7 m/s sigma_c= inf kPa: C>=0.2: 1.9 m/s; C>=0.3: 2.9 m/s; C>=0.34: 3.2 m/s; C>=0.4: 3.8 m/s; C>=0.49: 4.7 m/s Threshold velocities for a 0.5 m^3, 400 kg/m^3 block (200 kg), paper calibration 10 kg@7 m/s: sigma_c= 30 kPa: C>=0.2: 0.5 m/s; C>=0.3: 0.7 m/s; C>=0.34: 0.8 m/s; C>=0.4: 0.9 m/s; C>=0.49: 1.2 m/s sigma_c= 100 kPa: C>=0.2: 0.5 m/s; C>=0.3: 0.7 m/s; C>=0.34: 0.8 m/s; C>=0.4: 0.9 m/s; C>=0.49: 1.2 m/s sigma_c= 300 kPa: C>=0.2: 0.5 m/s; C>=0.3: 0.7 m/s; C>=0.34: 0.8 m/s; C>=0.4: 0.9 m/s; C>=0.49: 1.2 m/s sigma_c= inf kPa: C>=0.2: 0.5 m/s; C>=0.3: 0.7 m/s; C>=0.34: 0.8 m/s; C>=0.4: 0.9 m/s; C>=0.49: 1.2 m/s Threshold velocities for a 0.5 m^3, 400 kg/m^3 block (200 kg), stiffer calibration 23.1 kg@7.2 m/s: sigma_c= 30 kPa: C>=0.2: 0.9 m/s; C>=0.3: never (<8 m/s); C>=0.34: never (<8 m/s); C>=0.4: never (<8 m/s); C>=0.49: never (<8 m/s) sigma_c= 100 kPa: C>=0.2: 0.9 m/s; C>=0.3: 1.4 m/s; C>=0.34: 1.6 m/s; C>=0.4: 1.8 m/s; C>=0.49: 2.3 m/s sigma_c= 300 kPa: C>=0.2: 0.9 m/s; C>=0.3: 1.4 m/s; C>=0.34: 1.6 m/s; C>=0.4: 1.8 m/s; C>=0.49: 2.3 m/s sigma_c= inf kPa: C>=0.2: 0.9 m/s; C>=0.3: 1.4 m/s; C>=0.34: 1.6 m/s; C>=0.4: 1.8 m/s; C>=0.49: 2.3 m/s Contact pressure at the chest = F / A_contact: a 3-6 kN chest force spread over 0.12 m^2 is 25-50 kPa, i.e. of the order of the snow's own crushing strength and two to three orders of magnitude below skin-laceration pressures -- the classic 'fractures without external wounds' signature of a broad, soft, heavy impactor. == C. Quasi-static burial: chest load under H m of snow == H(m) rho pressure(kPa) force on 0.12 m^2 (kN) static C (paper calib.) static C (stiffer calib.) 1.0 300 2.9 0.35 0.11 0.02 1.0 400 3.9 0.47 0.14 0.03 1.0 500 4.9 0.59 0.17 0.03 2.0 300 5.9 0.71 0.20 0.04 2.0 400 7.8 0.94 0.26 0.06 2.0 500 9.8 1.18 0.30 0.07 3.0 300 8.8 1.06 0.28 0.06 3.0 400 11.8 1.41 0.34 0.08 3.0 500 14.7 1.77 0.40 0.10 4.0 300 11.8 1.41 0.34 0.08 4.0 400 15.7 1.88 0.42 0.11 4.0 500 19.6 2.35 0.47 0.14 Quasi-static chest stiffness in vivo is ~5-25 kN/m at 3-6 cm compression (CPR studies: ~400-500 N for 5 cm), and 5-6 cm CPR compressions fracture ribs in roughly a third of (mostly elderly) patients; young adults tolerate more. 3-4 m of 400 kg/m3 snow gives ~1.4-1.9 kN on a 0.12 m^2 chest: enough for 20-40 % quasi-static compression on the soft (paper) calibration, only ~10 % on the stiff one -- so a static burial of that depth can, but need not, break ribs, and does so more easily if the load is concentrated (rock or ledge under the back). == D. Skull: force available from a snow block vs. fracture tolerance == Temporo-parietal fracture forces (Allsop et al. 1991, flat 5x10 cm plate / 2.54 cm disc, 10.6-12 kg drop): 2.5-10 kN, mean 5.2 kN; Yoganandan et al. 2004 review: 5.6-9.9 kN, mean 7.7 kN. crushing 30 kPa over 20 cm^2 -> max force 0.06 kN crushing 30 kPa over 50 cm^2 -> max force 0.15 kN crushing 30 kPa over 100 cm^2 -> max force 0.30 kN crushing 100 kPa over 20 cm^2 -> max force 0.20 kN crushing 100 kPa over 50 cm^2 -> max force 0.50 kN crushing 100 kPa over 100 cm^2 -> max force 1.00 kN crushing 300 kPa over 20 cm^2 -> max force 0.60 kN crushing 300 kPa over 50 cm^2 -> max force 1.50 kN crushing 300 kPa over 100 cm^2 -> max force 3.00 kN A snow block cannot transmit more than sigma_c * A_contact; to reach 2.5-5 kN on a temporal bone the load must be concentrated (head on a hard object, e.g. a camera used as a pillow as Buyanov suggests) or the snow must be very hard.