本研究的目的為應用曲率理論探討助跑對單腳與雙腳垂直跳躍的影響，實驗受試者為高中男子排球隊與女子排球隊各12名，(其中男選手的平均年齡、身高與體重分別為17.6±0.63歲、186.5±2.06公分以及79.04±5.32公斤；而女選手的平均年齡、身高與體重分別為17.8±0.73、169.8±3.24公分以及64.3±7.46公斤)，每位選手需分別以雙腳與單腳等不同方式進行三種垂直跳，包括原地垂直跳、第一距離的助跑垂直跳與第二距離的助跑垂直跳，其中過程中以高速攝影機(Redlake, 250 Hz)進行矢狀面(sagittal plane)2D拍攝以取得相關運動學資料，並以Kistler Quattro Jump 測力板，取得垂直方向的跳躍時著地期的單維力量。
透過運動學的分析與人體勁度的運算，以及由曲率理論算出的衝量所推估出的提昇高度HCurvature與實驗的提昇高度HCMJ-APJ (助跑跳的高度與原地跳高度之差)作相關分析後，主要研究結果為：(一)相對於原地垂直跳，助跑垂直跳所能提昇的高度的比值RAp，單腳助跑跳躍(RAp值男選手0.84±0.18與女選手0.70±0.38)顯著高於雙腳的助跑跳躍的值(0.48±0.16與0.32±0.18)；(二) 單腳助跑跳躍有較小的徑向位移，但有較大類人體勁度(stiffness)的趨勢，但不達顯著差異(p<.05)；(三) 助跑提昇高度HCMJ-APJ與曲率理論推估高度HCurvature的相關方面，單腳跳躍與雙腳跳躍的相關係數R值分別為0.55與0.70，以上相關值屬於中相關以上，尤其以單腳跳躍的型態，因此，根據以上結果，曲率理論推估的提昇高度對於助跑效益而言，為有效的量化評估方法。

The purpose of this study was to investigate the effects of the approach on one–foot and two–foot vertical jumps by curvature theory. The subjects participated in this study were the senior high school volleyball players with age 17.6±0.63 years, height 186.5±2.06 cm and weight 79.04±5.32 kg in boys and age 17.8±0.73 years, height 169.8±3.24 cm and weight 64.3±7.46 kg in twelve girls. Each subject performed three varied vertical jumps (without approach, approach with shorter distance and approach with longer distance) by both one-foot and two-foot. Redlake high-speed camera (250 Hz) was used to 2D cinematograph analysis at sagittal plane, and the vertical component of ground reaction force recorded by force plate (Quattro Jump, 500 Hz) during takeoff phase.
By processing the analysis of kinematics, the calculation of human stiffness, and the correlation analysis between the estimated lift height HCurvature, which was determined by the impulse from curvature theory, and experimental lift height HCMJ-APJ, the results could be summarized as following: 1. for the ratio of approach lift-height RAp, the one-foot jump(male: 0.84±0.18, female: 0.70±0.38) significantly greater than two-foot jump(male:0.48±0.16, female: 0.32±0.18); 2. one-foot jump have smaller radial displacement, and with trends of greater human stiffness (but without significant difference, p<.05); 3. for the correlation analysis of HCurvature and HCMJ-APJ, the correlation coefficient R of one-foot and two-foot vertical jump are 0.55 and 0.70, respectively. Which are belonging to middle and higher level of correlation, especially in one-foot vertical jump. And based on the results, for the efficiency of horizontal approach, the estimated lift-height from curvature theory is the valid and quantitative parameter to estimate the effects of approach on vertical jumps

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