Once initial velocity was calculated by each of the previous methods, the following formula was used to obtain displacement (y):
Jump and Reach
Reach height was determined using either a one- or overlapped two-hand reach, with or without plantar flexion (Figure 1). Subjects were required to perform a maximum vertical jump, and touch the Vertec™ at the highest point of the jump. Displacement for each Vertec™ method was calculated by subtracting the reach height obtained for that method from the jump-and-reach height. All jumps were performed in duplicate, and the best jump based on Vertec™ displacement was used for analysis.
To determine whether significant differences existed between the different methods for determining displacement or reach height, 3 separate (1 for each type of jump) 1-way repeated measures analysis of variance (RMANOVA) were run using a statistical software (SPSS, v17.0). These were followed by Bonferroni post hoc tests to determine which methods differed. Cohen's d effect sizes were also calculated using an online calculator (4). Pearson r was used to determine correlation between methods for determining displacement. Statistical significance was set a priori at p ≤ 0.05.
Averages for the 3 types of jumps in each of the 6 displacement determination methods are presented in Table 2. All jump displacements were significantly intercorrelated (p ≤ 0.01) with a minimum r-value of 0.94 for the CMJs, 0.84 for the RCMJs, and 0.95 for the SVJ.
Repeated measures of analysis of variance indicated there were differences between displacement determination methods for CMJs, F(1,14) = 190.526, RCMJs, F(1,14) = 231.556, and SVJ. F(1,14) = 186.171. Bonferroni post hoc tests indicated that for each of the 3 types of jumps investigated in this study, impulse vs. flight time was the only pairwise comparison in which no significant difference was noted (p > 0.05). Additionally, all jump-and-reach methods significantly overestimated jump displacement compared with force plate measurements. Table 3 shows the difference between methods for jump height determination expressed in Cohen's d effect sizes. The 1-hand reach with plantar flexion was the method of reach that was closest to the impulse and flight-time methods.
Because of its importance in sport, vertical jump has been used as a performance variable by a number of studies. These studies have investigated variables that can predict vertical displacement (8,12-14,19,20), used vertical jump as an independent variable (2,3,5,7,14,18), or tested training methods that can possibly improve vertical jump performance (6,9,11). Consequently, comparison between different populations or training methods should be relatively straightforward. However, a problem arises with such comparisons, as these studies have used different methods for determining vertical jump height. The purpose of the current investigation was to examine potential differences between some of these different types of jump displacement determination. Our investigation notes significant differences between jumps using different reach height methods and between force plate and Vertec™ methods, with some of these differences being larger than 1.5 SDs.
Previously, Aragón-Vargas (1) reported that estimating vertical displacement based on flight time was a stable, consistent measure of the actual vertical displacement of the center of mass when compared with video analysis. Therefore, it is recommended that future studies involving vertical jump as a dependent or independent measure use flight time to determine displacement when video analysis is not possible. According to the present results, the impulse-momentum method could also be used, as the results of this method were similar to those obtained by flight time.
However, in many situations, a switch mat or force plate is not available, for example, in nonlaboratory settings, and jump-and-reach tests are simple and convenient to use. In these scenarios, it is important to minimize the difference between the estimated and actual displacements, especially when the investigation is interested in the displacement of the center of mass or the estimation of power. Based on our results, it seems that the reach method has significant effects on the determined displacement from the Vertec™. Although all methods based on the Vertec™ overestimated displacement, the 1-hand reach with plantar flexion had the smallest differences compared with values obtained from both the impulse momentum and the flight-time methods for all 3 types of jumps investigated.
Figure 3 shows a frame of a subject performing a vertical jump and the force curve for that jump. The bold vertical line indicates the exact moment of the frame, and a bold horizontal line indicates the baseline force (the subject's body weight). At the moment of the image, although the subject's heels are off the ground, the amount of force applied to the ground is still greater than that necessary to support their body weight. Therefore, at that moment, the subject is still applying force that will contribute to vertical COM displacement. For that reason, estimating jump displacement via jump-and-reach tests, and considering reach height when the subject is flat footed, will result in overestimation of vertical displacement when compared with the impulse-momentum method.
When using the flight-time method, the force plate or a switch mat assumes flight only after the feet have left the ground. Consequently, measuring reach height for jump-and-reach with the subject plantar-flexed adds the time during which the plantar flexion occurs to the flight time if one compares these 2 methods. In this case, this displacement during plantar flexion is considered part of the jump displacement. Davis et al. (8) investigated the relationship between body segment length and vertical jump displacement. Foot length was the only segment that was significantly related to displacement, although this correlation was modest. However, vertical jump was determined via a jump-and-reach test, and reach height was determined with the subjects flat footed. Based on our results, it seems that this correlation could be in part because of the method used for determining displacement (along with changes in the moment arm for the propulsive torque at the ankle). If the same study were performed with the use of a force plate, a switch mat, or video analysis, the relationship between foot length and vertical displacement may not be significant. Therefore, the method used for determining displacement possibly induced an erroneous result, which could be avoided if reach height were determined with the subjects reaching with plantar flexion.
The difference between measuring reach height with 1 or 2 hands is also noteworthy. When performing a jump-and-reach test, the thoracic area is laterally rotated so that 1 shoulder dips as the other is raised. If initial reach height is measured with the subjects overlapping both hands, this difference in shoulder height will not be present. When compared with one of the methods that estimates displacement of the center of mass, the overlapping of hands to determine initial reach should result in an additional overestimation of displacement, because of the rotation increases reach, but the center of mass theoretically remains the same (as one side rises, the opposite is lowered). Therefore, it is not surprising that the 1-hand reach with plantar flexion method yielded the closest results to both force plate methods.
To our knowledge, this is the first study to investigate the outcomes of different methods for determining reach height for jump-and-reach tests. It is interesting to note that all 4 methods using Vertec™ overestimated displacement compared with force plate methods. There seems to be a difference between the displacement of the center of mass, foot, and hand. Future studies could further investigate this difference.
Finally, it is important to note that, although vertical COM displacement has been the primary focus of a large number of studies, in some sports-such as basketball or volleyball-the final reach height is what matters the most. In these cases, the primary focus of investigation could be on hand displacement rather than on center of mass displacement, for which jump-and-reach tests could be used with different methods for determining reach height.
When comparing groups of individuals from different data sets, one must consider both the method of reach height (if performed) and jump displacement to make valid comparisons. If plantar flexion is not performed during reach measurement for jump-and-reach tests, jump displacement will be erroneously high. Ideally, vertical jump studies should use video analysis, flight-time, or impulse-momentum methods. However, if none of these approaches are available, then jump-and-reach tests could be alternatively used, and the inherent overestimation of displacement may be attenuated by having subjects initially maximally plantar flex while reaching with one hand.
This investigation was supported in part by a grant from the Fed Ex Institute of Technology. The authors wish to thank Michael Falvo and Christopher Moore for their help in data collection.
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Keywords:Copyright © 2010 by the National Strength & Conditioning Association.
vertical jump; standing reach; impulse momentum; flight time