Scientific Approach to Ski Safety

SCIENTIFIC CORRESPONDENCE world record in 1976 using his old equip the following simulation. The jump length Scientific approach ment and flight style were less than 60% l obtained this way is 186.6 m, the flight of the results obtained with athletes of time t1 = 6.59 s, the landing velocity v1 = to ski safety today. 31.4 m s-1, and the equivalent landing The figure ~a) shows the profile of the height h1 = 0.89 m (at v 0 = 28.6 m s-', vpo SIR - During the 1994 Ski Flying World jumping hill in Planica and the trajectory = 2.24 m s-1, m = 70 kg). Starting out from Championships in Planica, Slovenia, y = y(x) of this reference jump. The this simulation, an increase of vpo to 3.0 m 1 1 athletes performed jumps of more than approach velocity v0 was set to 28.6 m s- s- (variation A), corresponding to an 4 200 m for the first time, the present (mean of the officially measured values). excellent take-off jump of the athlete , record being 209 m. Despite the fact that The jump length of l = 186.7 m to be increases the jump length to 195 m (t1 = millions of spectators witnessed these obtained (mean jump length from the 6.92 s, v1 = 31.52 m, h1 = 1.59 m). The jumps, distances of more than 191m have field) was found at a take-off velocity same jump length can be obtained using 1 been ignored by the International Ski component due to the athlete's jumping an approach velocity v0 of 28.98 m s- (B). Federation (FIS) in an attempt to reduce force (perpendicular to the ramp) of A wind blowing up the hill (130°, mea 1 the jump lengths; this procedure obviously Vpo = 2.24 m s- . The flight path deviates sured from a horizontal line) with a con does not reduce the hazards of this remarkably from the parabolic trajectory. stant speed of 1.4 m s-1 also results in l = dangerous sport. Scientific studies are The actual angle of the tangent to the 195 m (C). We also considered variations urgently needed to provide a reliable basis of the L and D values in functions corre on which safety enhancement strategies sponding to different flight styles, athletes can be based. 0 or equipment. Increasing all L and D We have performed wind-tunnel mea values in these functions by 11% (case D) surements with world class athletes in I -5o or just L by 2.3% (E) also leads to a 195-m various flight positions, undertaken field "' jump. A reduction of the mass (athlete measurements during the world champi with equipment) to 63 kg also results in onships in ski flying 1994, and have -100 l = 195m (F). Finally, a shallow ramp mapped ski jumping to a computable angle of -9.7° (compared with -11.6°) -:<P ! simulation model. Our results explain the b) yields l = 195m again (G). In sim effects of equipment, flight style changes, 31 40 :~!/ ---- ~ -- ; ulations C, D, E and F the equivalent land the reason for the high tumbling risk and ing height is reduced to 1.37 m, compared i ! / / v !. sensitivity to gusts observed. This informa .§. 29 . 20 ; / : with A (1.59), B (1.49) or G (1.62 m). tion is of use for making changes to the In the real world, the change of one 27 v ! FIS regulations. .: .: parameter will influence the others; We measured the high torque of the athletes have to solve extremely difficult skis in the airstream and the FIS fol Cj optimization problems in real time. The lowed our suggestion to limit the per ~400 longest jump performed so far led to 209 centage of front ski to total ski length ., m, which results from a simulation using before the 1994-95 winter (to 57%). As a ll. 300 v = 28.44 m s-1 (measured in the field), Lt 0 1 consequence the pitching moment 200 Vpo = 3.0 m s- (assumption of an excellent 4 balance has been eased and only one take-off jump ) , and L increased by 5.6%. tumbling accident occurred during the 100~--~----~---.----r-- This increase in L is realistically imagin 1994-95 World Cup, compared with 10 in 0 50 100 150 able for this world-record jump. The 1993-94. Another urgent problem is the x(m ) landing velocity obtained is 31.44 m s-1 anorexia deliberately induced by the and h = 2.43 m. Using an appropriate Results with the reference jump. a, Profile of 1 athletes (low weight increases the jump the jumping hill in Planica and the trajectory parameter protocol to simulate the 196-m length). We suggest a regulation relating )1x), with the flight position angles found in jump from 1995 at the Oberstdorf ski length to body weight (a self-regulat the field (means of 15 jumps) sketched jumping hill results in h1 = 2.62 m. The ing approach). above. b, Velocity 1-(x) and angle of the athlete could not stand this jump in the Simulations can predict the trajectory flight path tp(x). c, Lift force ~ and drag force competition. during the flight phase and investigate the Fd. L and D values used for this reference Wolfram Muller 2 effects of parameter and initial value vari jump (in m ): 0.2 and 0.4 (at t = 0 s), 0.65 Dieter Platzer ations1-4. We developed a highly reliable and 0.60 (0.2 s), 0.68 and 0.58 (0.4 s). 0.77 Bernhard Schmolzer mapping of ski jumping to a computable and 0.64 (2.3 s), 0.79 and 0.73 (4.0s), 0.78 /nstitut fur Medizinische Physik und and 0.79 (5.0 s) and 0.79 and 0.86 from Biophysik, simulation model, which contains the 6.0 s onwards. Linear interpolation was used 3 Harrachgasse 21, dependencies of the lift and drag forces between. The air density was 1.15 kg m- ; to the flight position. A representative set the mass m of the athlete with equipment 8010 Graz, Austria of data, obtained with the 1994-95 World was 70 kg. 1. Koenig, H. in Uhrentechnische Forschung- Skiflug Cup winner (who was the first to fly more 235-253 (Steinkopf, Stuttgart, 1952). than 200m) in a 5 x 5m2 wind tunnel, was path cp = cp (x), and the velocity v = v(x) 2. Remizov, P.R. J. Biomech. 17(3), 167-171 (1984). 3. Denoth, J., Luethi, S. M. & Gasser, H. Int. J. Sport used to determine a reference jump. The are shown in b. The plot in c of the lift Biomech. 3, 404-418 (1987). values for the lift area L and the drag force F1 (acting perpendicularly to the 4. Hubbard, M., Hibbard, R. L., Yeadon, M. R. & Komar, A. Int. J. Sport Biomech. 5, 258-27 4 (1989). area D from the series of wind tunnel actual tangent to the path) and the drag 5. Tani, l. & Juchl, M. in Scientific Study of Skiing in Japan measurements were chosen according to force Fd shows that the velocity com (ed. Kinoshita, K.) 35-53 (Hitachi, Tokyo, 1971). the mean position angles measured for 15 ponent perpendicular to the hill at land 1 excellent jumps during the world champi ing (4.18 m s- ) corresponds to that of a Scientific Correspondence onships in ski flying, Planica, Slovenia, jump onto a horizontal plane from h1 = 1994. 0.89 m height (equivalent landing Scientific Correspondence is intended to provide a forum in which readers may L and D values have increased marked height). 5 raise points of a scientific character. ly during the past two decades due to How do the initial values and para Priority will be given to letters of fewer changes in equipment and flight style. L meters influence the flight? We kept L and than 500 words and five references. and D measured with the holder of the D values constant from t = 5 s onwards in NATURE · VOL 375 · 8 JUNE 1995 455 .

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