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Critical speed and finite distance capacity: norms for athletic and non-athletic groups

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Two parameters in particular span both health and performance; critical speed (CS) and finite distance capacity (D′). The purpose of the present study was to: (1) classify performance norms, (2) distinguish athletic from non-athletic individuals using the 3-min all-out test (3MT) for running, and (3) introduce a deterministic model highlighting the relationship between variables of the 3MT.


Athletic (n = 43) and non-athletic (n = 25) individuals participated in the study. All participants completed a treadmill graded exercise test (GXT) with verification bout and a 3MT on an outdoor sprinting track.


Meaningful differences between non-athletic and athletic individuals (denoted by mean difference scores, p value and Cohen’s d with 95% confidence intervals) were evident for CS (− 0.74 m s−1, p < 0.001, d = − 1.41 [1.97, − 0.87]), exponential growth time constant (\(\tau_{{\text{g}}}\); 2.75 s, p < 0.001, d = − 1.29 [− 1.45, − 0.42]), time to maximal speed (\(t_{\max }\); − 2.80 s, p < 0.001, d = − 0.98 [− 1.51, − 0.47]), maximal speed (\(S_{\max }\); − 1.36 m s−1, p < 0.001, d = − 1.56 [− 2.13, − 1.01]), gas exchange threshold (GET; − 5.62 ml kg−1 min−1, p < 0.001, d = − 0.97 [− 1.50, − 0.45]), distance covered in the first minute (1st min; − 81.69 m, p < 0.001, d = − 1.91 [− 2.52, − 1.33]), distance covered in the second minute (2nd min; − 52.02 m, p < 0.001, d = − 1.71 [− 2.30, − 1.15]) and maximal distance (− 153.78 m, p < 0.001, d = − 1.27 [− 1.82, − 0.74]). The correlation coefficient between key physiological and performance variables are shown in the form of a deterministic model created from the data derived from the 3MT.


Coaches and clinicians may benefit from the use of normative data to potentially identify exceptional or irregular occurrences in 3MT performances.

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\(1{\text{st}} \min\) :

Distance covered in the 1st minute of the 3MT (m)

\(2{\text{nd}} \min\) :

Distance covered in the 2nd minute of the 3MT (m)

\(3{\text{rd}} \min\) :

Distance covered in the 3rd minute of the 3MT (m)

\({\text{3MT}}\) :

3-Minute all-out test

\(A_{{\text{g}}}\) :

Exponential growth amplitude (m s1)

\(A_{{\text{d}}}\) :

Exponential decay amplitude (m s1)

\({\text{CS}}\) :

Critical speed (m s1)


Critical power (W)


Finite distance achievable at speeds exceeding CS (m)

e :

Euler’s constant (i.e., a mathematical constant ~ 2.718)


Gas exchange threshold (ml kg1 min1)


High-intensity interval training


Moderate-intensity continuous training


Instantaneous speed at any time t during the 3MT (m s1)


Speed evoking GET (m s1)

\(S_{\max }\) :

Maximal speed attained during the 3MT

\(\tau_{{\text{g}}}\) :

Exponential growth time constant (s)

\(\tau_{{\text{d}}}\) :

Exponential decay time constant (s)

\(t_{{{\text{LIM}}}}\) :

Time limit to exhaustion (s)

\(t_{\max }\) :

Time to achieve \(S_{max}\) during the 3MT (s)

\(\dot{V}{\text{O}}_{{{\text{2max}}}}\) :

Maximal oxygen uptake rate (ml kg1 min1)

\({\text{s}}\dot{V}{\text{O}}_{{{\text{2max}}}}\) :

Speed evoking \(\dot{V}{\text{O}}_{{{\text{2max}}}}\) (m s1)


Finite energy expendable at power outputs exceeding CP (J)


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We would like to that all participants, athletic and non-athletic alike, for their willingness and whole-hearted efforts to participate all-out in this study. We would also like to thank Grant Gait-Smith for his hard work and effort during the data collection process.


No financial support was received.

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Correspondence to Mark Kramer.

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Communicated by Anni Vanhatalo.

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Kramer, M., Thomas, E.J. & Pettitt, R.W. Critical speed and finite distance capacity: norms for athletic and non-athletic groups. Eur J Appl Physiol 120, 861–872 (2020).

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