This study aimed to determine the critical speed (CS) and the work above CS (D`) from three mathematical models of para-athletes during a treadmill handcycling exercise. Nine hand-cyclists with spinal cord injuries performed a maximal incremental handcycling test and three tests to exhaustion at a constant speed to determine the speed-time relationship. The three tests to exhaustion were performed at intensities between 90% and 105% of peak speed derived from the incremental test. Then, the determination of CS and D` was modelled by linear and hyperbolic models. CS and D` did not present any significant differences among the three mathematical models. Low values in the standard error of estimate for CS were found for the three models (Linear: Distance-time: 1.7±0.5%; Linear: Speed-1/time: 3.0±1.9% and Hyperbolic: 1.2±0.6%). Based on the simplicity to calculate, the CS modelled by linear-distance-time can be a practical method for handcyclist coaches.
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