Closer Look At The Shape Of The High Jump Run-up
By Jesus Dapena, Indiana University, U.S.A. Michiyoshi Ae, University of Tsukuba, Japan; Akira Iiboshi, Kagoshima University, Japan Thanks to some video analysis done by Iiboshi and his team, new information can now be plugged into the method for drawing the path of the high jumper's footprints on the ground. The original article by Dapena on this subject was in issue #131 of Track Coach. From this I gather elite jumpers have an unusual sense of finding the right spot to jump from. No matter what the differences are ... they get the runup to work. It is similar to Finnish javelin throwers, who may differ in the first part of the run, but who all seem to know what to do in the last two steps. The path of the footprints in a high jump runup can be idealized as a straight line perpendicular to the bar, followed by a circular arc which ends at the takeoff (Figure I). Such a path is de fined by the position of the takeoff foot (its x and y coordinates), the angle between the bar and the final direction of the footprints' path (f), and the radius of the curve (r).

A method for drawing the path of the footprints on the ground was described in previous papers. (See Dapena, et aI., 1993; Dapena, 1995a.) However, the numerical values needed for the implementation of this method were based on limited information. Recent work by Iiboshi, et al. (1994) provides data that can help us to improve the design of the runup. They used a special video analysis technique to measure the footprint locations of the top eight men and seven of the top eight women in the high jump finals of the 1991 World Championships. The last successful jump was analyzed for each athlete, with the exception of Heike Henkel, who had to be studied in a successful jump in which the bar was set 5cm below her winning height. The Japanese research team also collected other data, such as the final speed of the runup (v) and the final direction of motion of the center of gravity (e.g.) at the end of the runup. FITTING A CURVE TO THE FOOTPRINTS (NOTE: This paper will refer to athletes that take off from the left foot; to make the text applicable to athletes who take off from the right foot, the words "right" and "left" should be interchanged.) We used a computer program to fit an arc of a circle to the footprint locations reported by Iiboshi, et al. (1994). There are many ways to fit a circle to the footprints of a high jump curve; we decided to use the circle that passed through the takeoff foot print and made the best possible fit with the second, third and fourth foot prints before the takeoff. Notice that we ignored the next to last footprint (i.e., we used footprints 0, 2, 3 and 4, skipping footprint 1). The reason for this was that many jumpers seem to plant the right foot in the next-tolast support outside the general curve, and therefore the inclusion of this footprint would have a misleading effect on the shape of the fitted curve. Figure 2 shows the footprints of the 15 athletes analyzed at the 1991 World Championships and the circular arc that we fitted to the curve of each runup. The arc was continued backward up to the point where it was perpendicular to the bar; from there, the path was extended backward along a straight line. The drawings show that all the jumpers in the sample followed very closely the modeled circular path in the last steps of the runup (although, as expected, in several jumps the next-to-last footprint was clearly outside the general curve). About half of the jumpers (e.g., Austin, Kovacs) used a strict "straight line plus circular arc" approach, and their footprints followed very closely not only the curved section, but also the straight section of the path modeled by the computer. The remaining jumpers (e.g., Drake, Henkel) started the straight section of the runup somewhat farther outward than predicted by the computer model, and later converged into the final circular path. In some jumpers (e.g., Drake, Kostadinova) the second type of runup may have served to produce a more gradual transition from the straight section of the runup to the final part of the curve, which should make the transition more comfortable. The disadvantage is that this runup is obviously more complicated than the first type, and may therefore lead to more inconsistency. In other jumpers (e.g., Grant, Kemp) the second type of runup seemed to be the result of the opposite reason: a sudden change in the direction of running at the start of the curve (essentially, a kink in the path at footprint 5) before settling into the final curvature of the runup. This does not seem advisable, because the sudden change in

direction may interfere with the runup speed; it may also lead to inconsistency. The fitted curves allowed us to calculate the radius (r) and the final direction (f) of the curve for each jumper. These values are shown in Figure 2.

RELATIONSHIP BETWEEN THE RUNNING SPEED AND THE RADIUS OF THE CURVE The proportion between the square of the running speed and the radius of the curve used by an athlete determines how much the athlete will lean. This can be expressed by the formula q=v2/r; the larger the value of q, the greater the lean. This means that an increase in v while keeping the radius constant will increase q, and the athlete will lean more; an increase in r while keeping the running speed constant will decrease q, and the athlete will lean less. If an athlete wants to achieve a given amount of lean, the ratio q between v2 and r needs to have some particular value which will be different for each amount of lean. If we knew the typical value of q for high jumpers, we would be able to use the running speed of any jumper to estimate the appropriate radius for the footprints of that jumper, using the equation r=v2/q. To check the value of q for each high jumper in the sample, we would need to divide the square of the average running speed of the athlete in the entire curve by the radius of the curve. Iiboshi, et al. (1994) did not measure the average running speed during the entire curve for the athletes shown in Figure 2, but they did report the final speed at the end of the runup. We used the value of this reported speed to make a rough estimate of q for each jumper, using the formula q=v2/r. The value of q was 6.8 ± 0.8 m/s2 for the men, and 4.8 ± 1.0 m/s2 for the women. These results indicated that the men tended to lean more than the women. A greater lean requires the athlete to make larger horizontal forces on the ground during the curve. It is possible that the greater strength of the men allowed them to run with a greater lean without excessive dis comfort to interfere with the runup speed. We can use the final runup speed of a high jumper and the average value of q to estimate an appropriate radius for the jumper's runup curve. This will not necessarily be the optimum radius for that individual, but it is useful as a rough guideline. For the men, the prediction equation is r=v2/6.8; for the women, r=v2/4.8. (These equations replace the one given in the previous papers, which was based on data from a single jumper.) RELATIONSHIP BETWEEN THE FINAL DIRECTIONS OF THE PATHS OF THE C.G. AND OF THE FOOTPRINTS The sketch in Figure 1 shows that the e.g. travels directly over the footprints during the straight part of the runup. However, in the transition to the curve the body tilts toward the left. The tilt is maintained during the curve, and the e.g. follows a path that is somewhat closer to the center of the curve than the footprints. At the end of the curve, the paths of the e.g. and of the footprints converge, and this puts the e.g. more or less directly above the left foot by the end of the takeoff. A consequence of the convergence of the two curves is that the final angle of the e.g. path (p) is always larger than the corresponding angle of the footprints' path (t). Iiboshi, et al. (1994) reported the value of angle p for each of the jumpers shown in Figure 2. Using the values of f which we computed from the fitted curves, we were able to calculate the difference between angles p and f: 15 ± 5°. In the previous papers (Dapena, et aI., 1993; Dapena, 1995a) the difference between angles p and f was used to produce a table that showed for several values of the final direction of the runup (angle p, which indicates the final path of the e.g.) a distance called "j". This distance is necessary for the calculation of the direction of the center of the curve relative to the takeoff point (see Figure 3), and therefore it is

ultimately needed for drawing the path of the footprints on the ground. The newly calculated difference between angles p and f leads to a modified table for the calculation of j (Table 1).

PRACTICAL IMPLICATIONS To draw the path of the footprints on the ground, we strongly advise the reader to follow the detailed instructions given in the previous paper (Dapena, 1995a), but

using the new formulas to estimate the radius of the curve (r=v2/6.8 for the men; r=v2/4.8 for the women), and the new table to estimate the value of distance j.

THE FOLLOWING IS FROM "THE PREVIOUS PAPER" Dapena, 1995a ACTUAL DRAWING OF THE RUN-UP
Materials needed: a measuring tape (10-20m long), a piece of chalk, and white adhesive tape. Tell the athlete to make a few jumps at a challenging height, using his/her present run-up. Using adhesive tape, make a cross on the ground to mark the position of the takeoff point (point A in Figure 1).

Put one end of the measuring tape at point A, and measure a distance j parallel to the bar .The value of j depends on the desired final direction of the run-up: FINAL DIRECTION OF RUNUP 25 degrees 30 degrees 35 degrees 40 degrees 45 degrees 50 degrees VALUE OF J 0.50m 1.40m 2.30m 3.25m 4.25m 5.30m

(General guidelines for the optimum value of the final direction of the run-up were given previously. If you want to try an angle intermediate between the ones given in this table, you can use a value of j intermediate between the ones given in the table.) Mark the new point (B) with chalk. Put one end of the measuring tape at point B, and measure a distance k=10 meters in the direction perpendicular to the bar. Mark the new point (C) with chalk. The line joining point A and point C indicates the direction of the center of the curve relative to the takeoff point. To find the center of the curve (point D), put one end of the tape at point A, and make the tape pass over point C. The center of the curve will be aligned with points A and C, and it will be at a distance r from point A. (General guidelines for the optimum value of r were given previously .) Mark point D with chalk. With center in D and radius r, draw an arc from point A to point E. (Point E has to be at the same distance from the plane of the bar as point D.) Arc A-E is the run-up curve. Mark it with strips of adhesive tape. Put a transverse piece of tape at point E to mark the start of the curve. Starting at point E, draw a straight line perpendicular to the bar (E-F), and mark it with strips of adhesive tape. Set the bar at a challenging height, and have the jumper take a few jumps. By trial and error, find the optimum position for the start of the runup (point G), and mark it with a transverse piece of adhesive tape. The run-up is now ready. The set-up just described can be left in place for training, and it will contribute to drill into the athlete the pattern that the run- up should follow. Items to remember: • Point E indicates the place where the curve should start, but the athlete does not necessarily have to step on this point. • Some jumpers may find it difficult to follow exactly the path marked by the adhesive tape in the transition from the straight to the curved part of the run-up. This should not be a problem: It is acceptable to deviate some- what from the path marked by the adhesive tape in the area around point E, as long as the athlete deviates consistently in the same way in every jump. • It is important to follow the tape very precisely in the middle and final parts of the curve. As mentioned, the set-up described above can be left in place for training. However, one or two marks will have to suffice for competitions. Distances a, b, c and d should be measured in the training set-up (see Figure 2). In the competition, distance a will be used to reconstruct the position of point H. Distances b and c will then be used to reconstruct the triangle formed by the standard and points a and H. This will allow the athlete to locate the start of the run-up (point g). Distance d can be used to find the position of point E if the rules of the competition allow for a mark to be placed at that point.

END OF "PREVIOUS PAPER"
OTHER CONSIDERATIONS The jumps shown in Figure 2 used a wide range of values for the radius of the curve (between 6.71 m and 13.32 m). If the path of the foot prints had had the same final direction (angle f) in all these jumps, the distance between the right standard and the straight part of the runup (measured outward from the standard) would have needed to have a variability of about 4 meters. This is demonstrated by the

hypothetical run ups shown in Figure 4a. However, Figure 2 shows that the distance from the right standard to the straight part of the runup was actually constrained between approximately 4 and 6 meters for all the jumps, a variability range of only 2 meters.

The small variability in the position of the straight part of the runup in spite of the large variability in the radius of the curve implied that the athletes in the sample tended to make systematic changes in the final angle of the footprints as they made changes in the radius. This can be understood better with the help of Figure 4b. The straight parts of the three hypothetical run-ups shown in this drawing were all at the same distance from the right standard (5 meters). Each runup used a different radius, but still they all ended up at the same takeoff point. The differences between the three run-ups started with differences in the starting point of the curve. By traveling deeper to ward the plane of the standards before starting the curve, the athlete can use a smaller radius, and still reach the same takeoff point. However, the final angle of the footprints' curve will also be smaller (i.e., the final path of the footprints will be more parallel to the bar). The high jumpers in the sample did not follow exactly the pattern of variation shown in Figure 4b, because the distance between the right standard and the straight part of the runup did fluctuate in the sample (see Figure 2). However, this fluctuation was rather small (about I meter in either direction around the 5meter point), and therefore the basic relationships of the hypothetical jumps of Figure 4b were present in the jumps of Figure 2: the athletes who used a large radius (e.g., Henkel, Kostadinova) tended to have large values of f, while the athletes who used a small radius (e.g., Conway, Babakova) tended to have small values of f. In theory, a high jumper should be able to try any combination of radius (r) and final angle of the footprints' path (f): for any given value of f, the jumper should be

able to try a wide variety of values of r, as shown in Figure 4a; and for any given value of r, the jumper should be able to try a wide variety of values of f, as shown in Figure 4c. However, to a great extent this did not happen; the jumpers in the sample tended to follow a pattern similar to the one shown in Figure 4b, in which there was a positive correlation between the values of rand f. It is not clear why the jumpers linked the values of rand f in this way, but we have come up with two possible theories: The first theory is based on the relationship between the radius of the curve and the need for the generation of angular momentum. During the bar clearance, a high jumper needs angular momentum in order to make the appropriate rotations over the bar. This rotation can be broken down into a twist rotation and a somersault rotation (Dapena, 1995b). The twist rotation serves to turn the back of the athlete toward the bar; the somersault rotation makes the shoulders go down and the knees go up during the bar clearance. Taking into account the final direction of the runup, the somersault rotation can be broken down into a forward somersaulting component and a lateral somersaulting component. One of the main purposes of the curved runup is to favor the production of the lateral somersaulting component of the angular momentum. (The other one is to lower the e.g. in the last steps of the runup.). The high jumpers who are traveling more parallel to the bar at the end of the runup will tend to need a smaller amount of forward somersaulting angular momentum and a larger amount of lateral somersaulting angular momentum in order to produce a total somersault rotation that makes the longitudinal axis of the athlete be perpendicular to the bar at the peak of the jump. This means that, to some extent, we should expect athletes who are traveling more parallel to the bar at the end of the runup to use tighter curves (smaller radius) in order to facilitate the generation of a larger amount of lateral somersaulting angular momentum during the takeoff. This may be part of the reason why the athletes who used smaller radius values tended to be those who were traveling more parallel to the bar at the end of the runup (Figures 2 and 4b). The second theory is that the high jumpers in the sample may not have fully explored all the possible options for the distance between the right standard and the straight part of the runup. They may all be starting within the narrow range between 4 and 6 meters simply because the other high jumpers also start there. If this is the case, the jumpers are unnecessarily restricting the combinations of rand f that they can use. For instance, let us assume that a jumper who is using the combination r=9 m and f=23° with the straight part of the runup 5 meters out from the right standard (i.e., the middle path in Figure 4b) wishes to try a runup with a 7 meter radius, but maintaining fat 23°. If this jumper keeps the straight part of the runup at the 5 meter distance, it will be impossible to combine the 7 meter radius with a final angle of 23°; the athlete will have to change the final angle to 12° (see Figure 4b). However, if the jumper brought the straight part of the runup to a distance of less than 4 meters from the right standard, the combination of a 7meter radius with a final angle of 23° would be possible (Figure 4a). If the second theory is correct, the next question would be, what drives the athletes' decisions within Figure 4b (or within Figure 2)? Do they decide to use a certain radius, and are then forced into a final angle that mayor may not be desirable? Or do they decide to use a certain final angle, and are then forced into a radius that mayor may not be desirable? At this time, we do not know for certain the reasons for the linkage found between

the radius of the curve and the final direction of the foot prints in the finalists from the 1991 World Championships. However, we believe that coaches should feel free to experiment with a variety of combinations of rand f, even if some of those combinations take the straight part of the runup out of the 46 meter range currently used by most high Jumpers.

FROM: TRACK COACH 138