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°) -:

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