The interpretation of relative momentum data to assess the contribution of the free limbs to the generation of vertical velocity in sports activities

The contribution that the free limbs (the arms and lead leg) make to vertical velocity at take-off during jumping activities was determined by using a relative momentum approach. This requires the momentum of each free limb to be quantified relative to the joint at which the limb is attached to the body between the touchdown (or start of movement) and the take-off. The contribution that each makes to the vertical velocity at take-off requires interpretation of the momentum data. It has been shown that two interpretations cited in the literature pose difficulties, and a third is offered. This interpretation is that: (1) the contribution of a single limb to vertical velocity at take-off is determined by the increase in the positive relative momentum value between the beginning (touchdown) and end (take-off) of the action; (2) when considering a single limb, the negative relative momentum can be ignored as it makes no direct contribution to upward movement; and (3) the contribution of relative momentum for a number of limbs together is the increase in the positive value of the sum of the relative momentum for all limbs between the start and end of the action. This interpretation was applied to a counter-movement vertical jump and a running stride. In the countermovement jump, the arms were found to produce a relative momentum of 30.9 N s, which was 12.7% of the peak total body vertical momentum. In running, the arms produced a relative momentum of 3.75 N s, which corresponded to 6.4% of the peak total body vertical momentum, while the arms and lead leg combined produced a peak value of 2.45 Ns, which corresponds to a contribution of 4.2%. We conclude that the proposed interpretation enabled sensible estimations to be made of the contribution of the arms to jumping performance.