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A novel mathematical modeling has been proposed to generate synthetic vertical force signal induced by a single person jumping. This model can replicate much of the temporal and spectral features of the real jumping loading more reliably than the existing half-sine models coupled with Fourier series analysis. This includes lack of symmetry of individual jumping pulses and near-periodic nature of consecutive pulses. The model therefore offers way forward as to the development of a new generation of synthetic narrow-band jumping loads. In these, the shape and frequency content of the jumping force can be changed easily on a jump-by-jump basis, which simulates better on what is happening in reality during human jumping. The synthetic jumping loading can be used in assessing vibration serviceability of civil engineering structures for which such dynamic excitation is relevant, such as assembly structures and concert venues. DOI: 10.1061/(ASCE)EM.1943-7889.0000044 CE Database subject headings: Vibration; Excitation; Mathematical models; Dynamic models; Dynamic loads; Vertical loads.

Because of inherent variability in all human cyclical movements, such as walking, running and jumping, data collected across a single cycle might be atypical and potentially unable to represent an individual's generalized performance. The study described here was designed to determine the number of successive cycles due to continuous, repetitive countermovement jumping which a test subject should perform in a single experimental session to achieve stability of the mean of the corresponding continuously measured ground reaction force (GRF) variables. Seven vertical GRF variables (period of jumping cycle, duration of contact phase, peak force amplitude and its timing, average rate of force development, average rate of force relaxation and impulse) were extracted on the cycle-by-cycle basis from vertical jumping force time histories generated by twelve participants who were jumping in response to regular electronic metronome beats in the range 2-2.8 Hz. Stability of the selected GRF variables across successive jumping cycles was examined for three jumping rates (2, 2.4 and 2.8 Hz) using two statistical methods: intra-class correlation (ICC) analysis and segmental averaging technique (SAT). Results of the ICC analysis indicated that an average of four successive cycles (mean 4.5 ± 2.7 for 2 Hz; 3.9 ± 2.6 for 2.4 Hz; 3.3 ± 2.7 for 2.8 Hz) were necessary to achieve maximum ICC values. Except for jumping period, maximum ICC values took values from 0.592 to 0.991 and all were significantly (p ≤ 0.05) different from zero. Results of the SAT revealed that an average of ten successive cycles (mean 10.5 ± 3.5 for 2 Hz; 9.2 ± 3.8 for 2.4 Hz; 9.0 ± 3.9 for 2.8 Hz) were necessary to achieve stability of the selected parameters using criteria previously reported in the literature. Using 10 reference trials, the SAT required standard deviation criterion values of 0.49, 0.41 and 0.55 for 2 Hz, 2.4 Hz and 2.8 Hz jumping rates, respectively, in order to approximate the ICC results. The results of the study suggest that the ICC might be a less conservative but more objective method to evaluate stability of the data. Based on these considerations, it can be recommended that a force time history due to continuous, repetitive countermovement jumping should include minimum of four (the average from the ICC analysis) and possibly as many as nine successive jumping cycles (the upper limit of the ICC analysis) to establish stable mean values of the selected GRF data. This information is important for both experimental measurements and analytical studies of GRF signals due to continuous, repetitive countermovement jumping. Key pointsThe number of successive jumping cycles due to continuous, repetitive countermovement jumping obtained from a test subject during in a single testing session influences the stability of the corresponding ground reaction force variables on a cycle-by-cycle basis.Researchers have used different criteria and methods for determining stability of ground reaction force data for a variety of activities, making comparisons among studies and activities difficult.In the present study, segmental averaging technique indicated that an average of ten successive jumping cycles were necessary to achieve stability of the selected force parameters using criteria previously reported in the literature, while less conservative test-retest intra-class correlation (ICC) analysis showed that an average of four successive jumping cycles were necessary for stability.Based on these considerations, it can be recommended that a force time history due to continuous, repetitive countermovement jumping should include minimum of four (the average from the ICC analysis) and possibly as many as nine successive jumping cycles (the upper limit of the ICC analysis) to achieve stability of jumping force data on a cycle-by-cycle basis.Knowledge about the stability of jumping force data is an important to maximize reliability of their experimental and analytical characterizations.