Backward Double Integration is a Valid Method to Calculate Maximal and Sub-Maximal Jump Height

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The backward double integration method uses one force plate and could calculate jump height for countermovement jumping, squat jumping and drop jumping by analysing the landing phase instead of the push-off phase. This study compared the accuracy and variability of the forward double integration (FDI), backwards double integration (BDI) and Flight Time + Constant (FT+C) methods, against the marker-based rigid-body modelling method. It was hypothesised that the jump height calculated using the BDI method would be equivalent to the FDI method, while the FT+C method would have reduced accuracy and increased variability during sub-maximal jumping compared to maximal jumping. Twenty-four volunteers performed five maximal and five sub-maximal countermovement jumps, while force plate and motion capture data were collected. The BDI method calculated equivalent mean jump heights compared to the FDI method, with only slightly higher variability (2–3 mm), and therefore can be used in situations where FDI cannot be employed. The FT+C method was able to account for reduced heel-lift distance, despite employing an anthropometrically scaled heel-lift constant. However, across both sub-maximal and maximal jumping, it had increased variability (1.1 cm) compared to FDI and BDI and should not be used when alternate methods are available.

Original languageEnglish
Pages (from-to)1191-1197
Number of pages7
JournalJournal of Sports Sciences
Issue number10
Early online date31 Mar 2022
Publication statusPublished - 31 Dec 2022

Bibliographical note

Funding Information:
This investigation was funded by CAMERA, the RCUK Centre for the Analysis of Motion, Entertainment Research and Applications, EP/M023281/1


  • Countermovement jump
  • squat jump
  • drop jump
  • force plate
  • vertical jump
  • flight time


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