Table 2.
Testing protocol characteristics and modelling methods of studies investigating critical speed (CS) and D′ measurement
| Study | Alternative test protocol | Fixed effort distance | Fixed effort duration | Fixed effort intensity | linear (distance time) | linear (inverse time) | 2-parameter hyperbolic | 3-parameter hyperbolic | Exponential | Other models | Measurement or modelling assessment |
|---|---|---|---|---|---|---|---|---|---|---|---|
| Ari and Deliceoglu [15] | – | 2 trials; 800 and 2400 m | – | – | x | x | x | – | – | – | Comparison of models for determining CS and D′ values |
| Ari et al. [21] | – | – | 3 trials; 6, 9, 12 min | – | x | x | – | – | – | – | Comparison of models for determining CS and D′ values; comparing two different COD test protocols on CS and D′ |
| Beck et al. [22] | – | – | – | 4 trials; 1–12 min | x | x | x | – | – | – | Comparison of models for determining D′ values |
| Berthoin et al. [76] | – | – | – | 3 continuous trials at 90, 100, 110% MAV. 3 intermittent trials (15:15 s) at 120, 130, 140% MAV with passive recovery | x | – | – | – | – | – | A comparison between continuous and intermittent CS and D′ |
| Billat et al. [23] | – | – | – | 4 trials; 90, 100, 120, 140% vO2max | – | – | x | x | – | – | Comparison of models for determining CS and D′ values; comparison of models for predicting performance |
| Bosquet et al. [24] | – | – | – | 5 trials; 95, 100, 105, 110, 120% PTV | x | x | x | x | x | – | Comparison of models for determining CS and D′ values; comparison of models for predicting performance |
| Broxterman et al. [73] | 3MT | – | – | 3 trials; 90, 100, 120% Speak | – | x | – | – | – | – | Comparison between multi-trial testing and 3MT for determining CS and D′ values |
| Buchheit et al. [56] | – | – | – | 3 intermittent trials (at 15:15 and 30:30 s each) at 90, 95, 100% VIFT | x | – | – | – | – | – | Comparison of testing protocols for determining intermittent CS and D′ values |
| Busso and Chatagnon [41] | – | 8 distancesa; 800, 1000, 1500, 1600, 2000, 3000, 5000, 10,000 m | – | – | – | – | x | – | – | – | Comparison of distances used within the model for determining CS and D′ values. Comparison between predicted and actual performance |
| Busso et al. [42] | 3MT | 2 trials; 1200, 3600 m | – | – | x | – | – | – | – | – | Comparison between multi-trial testing and 3MT for determining CS and D′ values. Reliability of 3MT. Performance prediction based on CS and D′ estimates |
| Çabuk et al. [25] | – | 3 trialsa; 1500, 3000, 5000 m | – | – | x | x | x | – | – | – | Comparison of models for determining CS and D′ values; comparison of models for predicting performance |
| Carter and Dekerle [57] | – | – | – | 4 trials; 80% difference of LT and O2max, 100, 110 and 120% O2max | – | x | – | – | – | – | A comparison of CS and D′ determined under different test conditions (flat vs. gradient) |
| de Aguiar et al. [26] | 3MT | 3 trials; 800, 1600, 2400 m | – | – | x | x | – | – | – | – | Comparison between models, and 3MT for determining CS and D′ values. Reliability of 3MT |
| Fukuda et al. [78] | – | – | – | 3 intermittent trials (10:10 s) at 110, 120, 130% PV | x | – | – | – | – | – | Reliability assessment. Parameter assessment (critical rest interval) |
| Fukuda et al. [77] | – | – | – | 3 intermittent trials (15:15 s) at 110, 120, 130% PV | x | – | – | – | – | – | Parameter assessment (critical rest interval) |
| Galbraith et al. [81] | – | 3 trials; 1200, 2400, 3600 m | – | – | x | – | – | – | – | – | Reliability assessment |
| Galbraith et al. [58] | – | 3 trials; 1200, 2400, 3600 m | – | 3 trials; 100, 105, 110% vO2max | x | – | – | – | – | – | A comparison of protocols for determining CS and D′ values (same-day track TTs [different recovery periods] vs. multi-visit treadmill TTEs) |
| Gama et al. [27] | 3MT | – | – | 4 trials; varying resistances by elastic cords | x | x | x | – | – | – | Comparison between models, and 3MT for determining CS and D′ values |
| Gama et al. [82] | 3MT | – | – | – | – | – | – | – | – | – | Reliability assessment |
| Gamelin et al. [43] | – | – | 3 trials; 6, 9, 12 min | – | x | x | x | x | x | – | Comparison of models for predicting performance |
| Gifford and Collins [59] | – | 3 trialsa; 800, 1500, 3000 m | – | – | x | – | – | – | – | – | Comparison of number of trials (2 vs. 3) for determining CS and D′ values |
| Girardi et al. [28] | – | 3000, 5000, 10,000 m, half- and full-marathona | – | – | x | – | x | – | – | – | Comparison of distances used within the model for determining CS and D′ values; comparison of models for determining CS and D′ values; comparison of models for predicting performance |
| Hill et al. [29] | – | – | – | 5–7 trials; ~ 3 to ~ 10 min | x | x | x | x | x | – | Comparison of models for determining CS and D′ values |
| Hill et al. [30] | – | – | – | 5 trials; ~ 2.5 to 16 min | x | x | x | – | – | – | Comparison of models for determining CS and D′ values |
| Hinckson and Hopkins [44] | – | – | – | 3 trials; ~ 2, 4 and 8 min | x | – | – | – | – | – | Reliability of testing results. Performance prediction based on modelling |
| Housh et al. [31] | – | – | – | 4 trials; ~ 2–12 min | x | x | x | x | x | – | Comparison of models for determining CS and D′ values |
| Hughson et al. [45] | – | – | – | 6 trials; 19.2–22.4 km/h (~ 2–12 min) | – | x | – | – | – | – | Performance prediction |
| Hunter et al. [60] | 3MT | – | 3 trials; 3, 7, 12 min | – | x | x | x | – | – | – | Comparison of CS and D′ derived from training, TTs and a 3MT. Measurement reliability |
| Jaén-Carrillo et al. [72] | – | – | 2 trials; 3 and 9 min | – | – | x | – | – | – | – | Comparison of surface (track, road and, gravel) on CS and D′ estimation |
| Kachouri et al. [79] | – | – | – | 2 continuous trials at 95 and 105% vMTT. 2 intermittent trials at 95 and 105% vMTT (1:1 @ half of Tlim (continuous) of the respective intensity. Jog recovery) | x | – | – | – | – | – | Comparison of continuous and intermittent CS and D′ |
| Kalva-Filho et al. [83] | 3MT (20 m shuttle) | – | – | – | – | – | – | – | – | – | Reliability assessment |
| Kordi et al. [61] | – | 3 trials; 1200, 2400, 3600 m | – | – | x | – | – | – | – | – | Comparison of the number of trials used (2 vs. 3) for determining CS and D′ values |
| Kramer et al. [62] | 3MT (traditional, and 50 and 25 m shuttle) | – | – | – | – | – | – | – | – | – | Comparison of linear and shuttle 3MT CS and D′ values |
| Kramer et al. [63] | 3MT (traditional, and 50 and 25 m shuttle) | – | – | – | – | – | – | – | – | Bi-exponential modelling | Comparison of linear and shuttle 3MT CS and D′ values. Comparison of values using typical method and modelling |
| Kramer et al. [64] | 3MT (traditional, and 50 and 25 m shuttle) | – | – | – | – | – | – | – | – | – | Comparison of linear and shuttle 3MT CS and D′ values |
| Kuo et al. [84] | 3MT | – | – | – | – | – | – | – | – | – | Reliability assessment |
| Lanzarini et al. [40] | 1 | 3 trials; 800, 1500, 3000 m | – | – | x | x | x | x | – | – | Comparison of models for determining CS and D′ values |
| Leslie et al. [65] | – | – | – | 4 trials; ~ 2–15 min | – | x | – | – | – | – | Comparison of CS and D′ values under different environmental conditions |
| Liu et al. [119] | 3MT (30 m shuttle) | – | – | – | – | – | – | – | – | Bi-exponential modelling | A comparison of CS and D′ values from typical 3MT interpretation vs. bi-exponential modelling |
| Loures et al. [32] | – | – | – | 100, 110 and 120% vO2max | x | x | – | – | – | – | Comparison of models on D′ value |
| Manuel and Lance [46] | – | 100 m, 200 m, 400 m, 800 m, 1000 m, 1500 m, 1609 m (1 mile), 2000 m, 3000 m, 5 km (all surfaces), 10 km (all surfaces), 1-h run, 21.1 km (half-marathon), 42.2 km (marathon)a | – | – | x | – | – | – | – | – | Performance prediction |
| Massini et al. [66] | – | 3 trials; 900, 2100, 3300 m | – | 3 trials; 90, 95, 115% vO2max | x | x | – | – | – | – | Comparison of trial surface, and TT vs. TTE tasks on CS and D′ values |
| Mizelman et al. [33] | – | – | – | – | – | x | – | x | x | Omni-domain model | Comparison of CS and D′ between different models |
| Morton and Billat [80] | – | 3000, 5000, 10,000 ma | – | 3 intermittent trials; 60:60 s @ 120:50% CS; 180:180 s @ 110:60% CS; 30:60 s @ 135:65% CS | x | – | – | – | – | – | Comparison of continuous and intermittent CS and D′ values |
| Nimmerichter et al. [34] | – | – | – | 3 trials; 70% of the difference between VT and MAS, 98, 110% MAS | x | x | x | – | – | – | A comparison of models for CS and D′ estimation. Comparison of models for performance prediction |
| Nimmerichter et al. [85] | – | 3 trials; 500, 1200, 2000 m | – | – | – | x | – | – | – | – | Reliability assessment |
| Patoz et al. [35] | – | – | – | 4 trials; 90, 100, 110, 120% peak speed | – | x | x | x | x | – | Comparison of models on CS and D′ values |
| Patoz et al. (2021) [36] | – | – | – | 4 trials; 90, 100, 110, 120% peak speed | x | x | x | – | – | – | Comparison of models on CS and D′ values |
| Pepper et al. [47] | – | – | – | 4 trials; 12.88–21.74 km/h | x | – | x | – | – | – | Performance prediction |
| Perez et al. [48] | 3MT | – | – | – | – | – | – | – | – | – | Performance prediction |
| Pettitt et al. [49] | 3MT | – | – | – | – | – | – | – | – | – | Performance prediction |
| Ruiz-Alias et al. [50] | – | – | 4 trials; 3, 5, 10, 20 min | – | – | x | – | – | – | – | Comparison of predicted and actual performance. Variability of estimates |
| Ruiz-Alias et al. [86] | – | – | 2 trials; 3, 9 min | – | – | x | – | – | – | – | Reliability assessment |
| Ruiz-Alias et al. [67] | – | – | 2 trials; 3, 9 min | – | – | x | – | – | – | – | Effect of different surfaces, trial order (long-short or short-long), and same-day vs. multi-visit testing on CP and W′ |
| Ruiz-Alias et al. [13] | – | – | 4 trials; 3, 5, 10, 20 min | – | x | x | – | x | – | Stryd and Golden cheetah | Comparison of models for determining CS and D′ values; comparison of models for predicting performance |
| Ruiz-Alias et al. [37] | – | – | 6 trials; 3, 4, 5, 10, 20, 30 min | – | x | x | x | x | – | Stryd and Golden cheetah | Comparison of models for determining CS and D′ values; comparison of models for predicting performance |
| Ruiz-Alias et al. [38] | – | – | 6 trials; 3, 4, 5, 10, 20, 30 min | – | x | x | x | x | – | Stryd and Golden cheetah | Comparison of models, task lengths used, and number of trials used on CP and W′. Performance prediction |
| Ruiz-Alias et al. [51] | – | – | 5 trials; 3, 4, 5, 10, 20 min | – | – | x | – | – | – | – | Performance prediction based on CP vs. CS modelling |
| Saari et al. [14] | 3MT (30 m shuttle) | 3 trials; 600, 810, 1020 m | – | – | x | x | – | – | – | – | Comparison of multi-trial testing to 3MT shuttle on CS and D′ values |
| Smith et al. [68] | – | – | – | 4 trials; 90, 100, 105, 110% PV | x | – | – | – | – | – | Comparison of number of trials required, and the lengths of the trials used on CS and D′ values |
| Smyth et al. [52] | – | – | – | – | x | – | – | – | – | – | Performance prediction (from training data) |
| Smyth and Muniz-Pumares [53] | – | – | – | – | x | – | – | – | – | – | Comparison of different distances modelled on CS and D′ values. Performance prediction |
| Solomonson et al. [69] | 3MT | – | – | – | – | – | – | – | – | – | Effect of external loading on CS and D′ values |
| Sousa et al. [74] | 3MT | – | – | 3 trials; 2–10 min | x | x | – | – | – | – | Comparison of 3MT and multi-trial testing on CS and D′ values |
| Triska et al. [70] | – | – | 2, 5, 10 and 3, 7, 12 min | – | – | x | – | – | – | – | Comparison of task lengths tested on CS and D′ values |
| Triska et al. [71] | – | – | Duration matched to treadmill trials | 75% difference of VT and MAS, 98%, 108% MAS | – | x | – | – | – | – | Influence of surface type, and TT vs. TTE on CS and D′ values |
| Vandewalle [54] | – | 1500, 3000, 5000, 10,000 ma | – | – | – | – | x | x | x | – | Comparison of distances modelled on CS and D′ values. Performance prediction of models |
| Vassallo et al. [75] | 3MT | – | – | 70% of the difference between GET and vO2max, 80% of the difference between GET and vO2max, 100, 110% vO2max | x | – | – | – | – | – | Multi-visit testing vs. 3MT for CS and D′ values. Reliability assessment |
| Zagatto et al. [39] | – | – | – | 3 trials; 100, 110, 120% vO2max | x | x | x | – | – | – | Comparison of models on CS and D′ values |
| Zinoubi et al. [55] | – | 1500, 3000, 5000, 10,000 ma | – | 3 trials; 90, 100 and 110% sMTT | x | – | – | – | – | – | Comparison of trial lengths on CS and D′ values. Performance prediction |
CP critical power, CS critical speed, CVST critical velocity shuttle test, GET gas exchange threshold, LT lactate threshold, MAS maximal aerobic speed, MAV maximal aerobic velocity, PTV peak treadmill velocity, PV peak velocity, sMTT speed of Montreal track test, Speak peak speed, TT time trial, TTE time to exhaustion, VIFT variable intermittent fitness test, vMTT velocity of Montreal track test, VT ventilatory threshold, vO2max velocity of O2max, – no data to report, x the model used
aRace data