# Relationship between Cyclic and Non-Cyclic Force-Velocity Characteristics in BMX Cyclists

^{1}

^{2}

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Study Participants

#### 2.2. Design

#### 2.2.1. Force–Velocity (Fv) Jump Test

#### 2.2.2. Torque–Cadence (Tc) Cycling Tests

#### 2.3. Data Processing

^{2}values, the characteristic variables ($To{r}_{0}$, $Ca{d}_{0}$, ${S}_{Tc}$, and ${P}_{max}$) were extracted and averaged for further analysis.

#### 2.4. Statistical Analyses

## 3. Results

^{−1}(2.3–5.1%), respectively. The typical errors of Tc characteristics are displayed along with the descriptive data (Table 3).

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**Example profiles from one participant. (

**a**) force–velocity (Fv) profile from the vertical jump test, (

**b**) torque–cadence (Tc) profile from a ramp start, (

**c**) Tc profile from a flat-ground sprint. Filled points indicate the axis intercept values of linear regression models.

**Figure 2.**Correlation coefficients between force-velocity characteristics (${F}_{0}$, ${v}_{0}$ ,${S}_{Fv}$ , and ${P}_{max}$ ) from a vertical jumping test and torque–cadence characteristics ($To{r}_{0}$, $Ca{d}_{0}$, ${S}_{Tc}$, and ${P}_{max}$ ) from BMX ramp starts (circles) and flat-ground sprints (triangles) on a BMX bike. Error bars represent 95% confidence intervals of the correlation coefficients.

**Figure 3.**Comparison of dichotomous classifications for force–velocity (Fv) characteristics from the vertical jumping test and torque–cadence (Tc) characteristics from the ramp starts, placing each participant (points) in one of four quadrants. Right side quadrants of

**a**–

**d**: Fv characteristic greater than the group median. Upper two quadrants of

**a–d**: Tc characteristic greater than group median. Numbers on data points represent participants’ intra-group rankings in terms of ramp start performance (mean velocity).

**Table 1.**Parameters describing the construction of force–velocity (Fv) and torque–cadence (Tc) profiles.

Descriptive Parameter | Value | Fv | Tc Start | Tc Sprint |
---|---|---|---|---|

number of data points (loading conditions or pedal strokes) | mean ± s.d. | 4.8 ± 0.6 | 6.3 ± 1.0 | 15.8 ± 3.0 |

minimum | 3 | 4 | 10 | |

maximum | 5 | 7 | 20 | |

r^{2} of regression | mean ± s.d. | 0.92 ± 0.08 | 0.91 ± 0.04 | 0.95 ± 0.03 |

minimum | 0.72 | 0.87 | 0.86 | |

maximum | 1.00 | 0.97 | 0.98 |

**Table 2.**Measurement and extrapolation ranges of the force–velocity (Fv) and torque–cadence (Tc) profiles

Variable | Value | Unit | Fv | Tc Start | Tc Sprint |
---|---|---|---|---|---|

v or Cad | minimal measured value | (% v_{0} or Cad_{0}) | 35 ± 5 | 29 ± 2 | 24 ± 1 |

maximal measured value | (% v_{0} or Cad_{0}) | 49 ± 5 | 73 ± 5 | 78 ± 4 | |

measurement range width | (m·s^{−1} or rev·min^{−1}) | 0.37 ± 0.07 | 99 ± 13 | 118 ± 16 | |

extrapolation range width | (m·s^{−1} or rev·min^{−1}) | 1.28 ± 0.35 | 60 ± 18 | 47 ± 11 | |

extrapolation ratio | (extrap. range width: meas. range width) | 3.4 ± 0.5 | 0.6 ± 0.2 | 0.4 ± 0.1 | |

F or Tor | minimal measured value | (% F_{0} or T_{0}) | 49 ± 5 | 28 ± 3 | 24 ± 2 |

maximal measured value | (% F_{0} or T_{0}) | 65 ± 6 | 77 ± 3 | 85 ± 3 | |

measurement range width | (N or N·m) | 466 ± 74 | 152 ± 41 | 176 ± 33 | |

extrapolation range width | (N or N·m) | 1081 ± 311 | 69 ± 9 | 42 ± 14 | |

extrapolation ratio | (extrap. range width: meas. range width) | 2.3 ± 0.6 | 0.5 ± 0.1 | 0.2 ± 0.1 |

_{0}, v

_{0}: force (F) and velocity (v) axis intercepts, respectively, of the linear force–velocity (Fv) model. Tor

_{0}, Cad

_{0}: torque (Tor) and cadence (Cad) axis intercepts and slope, respectively, of the linear torque–cadence (Tc) model.

Parameter | Mean ± s.d. | Minimum | Maximum | Typical Error | Percentage of Typical Error (%) |
---|---|---|---|---|---|

jump test, n = 12 | |||||

F_{0} (N) | 3067 ± 538 | 2137 | 3938 | - | - |

v_{0} (m·s^{−1}) | 2.5 ± 0.4 | 1.7 | 3.2 | - | - |

S_{Fv} (N·s·m^{−1}) | −1255 ± 323 | −1953 | −826 | - | - |

P_{max jump} (W) | 1935 ± 519 | 1365 | 2815 | - | - |

ramp start, n = 11 | |||||

Tor_{0 start} (N·m) | 307 ± 54 | 238 | 394 | 21 | 7.1% |

Cad_{0 start} (rev·min^{−1}) | 226 ± 25 | 185 | 276 | 19 | 8.6% |

S_{Tc start} (N·m·min·rev^{−1}) | −1.37 ± 0.24 | −1.71 | −0.86 | 0.16 | 12% |

P_{max start} (W) | 1817 ± 383 | 1159 | 2376 | 67 | 3.7% |

sprint n = 11 | |||||

Tor_{0 sprint} (N·m) | 290 ± 51 | 221 | 365 | 14 | 4.8% |

Cad_{0 sprint} (rev·min^{−1}) | 218 ± 12 | 199 | 239 | 11 | 5.1% |

S_{Tc sprint} (N·m·min·rev^{−1}) | −1.32 ± 0.18 | −1.55 | −1.09 | 0.11 | 8.2% |

P_{max sprint} (W) | 1662 ± 365 | 1149 | 2285 | 43 | 2.6% |

_{0}, v

_{0}, S

_{Fv}: force (F) and velocity (v) axis intercepts and slope, respectively, of the linear force–velocity (Fv) models based on concentric F and v during vertical squat jumps under various loading conditions. P

_{max jump}: theoretical maximal jumping power (defined as ½F

_{0}× ½v

_{0}). Tor

_{0}, Cad

_{0}, S

_{Tc}: torque (Tor) and cadence (Cad) axis intercepts and slope, respectively, of the linear torque–cadence (Tc) models based pedal strokes during ramp starts and flat-ground sprints. P

_{max start}, P

_{max sprint}: theoretical maximal cycling power (defined as power at ½Tor

_{0}and ½Cad

_{0}).

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**MDPI and ACS Style**

Gross, M.; Gross, T.
Relationship between Cyclic and Non-Cyclic Force-Velocity Characteristics in BMX Cyclists. *Sports* **2019**, *7*, 232.
https://doi.org/10.3390/sports7110232

**AMA Style**

Gross M, Gross T.
Relationship between Cyclic and Non-Cyclic Force-Velocity Characteristics in BMX Cyclists. *Sports*. 2019; 7(11):232.
https://doi.org/10.3390/sports7110232

**Chicago/Turabian Style**

Gross, Micah, and Thomy Gross.
2019. "Relationship between Cyclic and Non-Cyclic Force-Velocity Characteristics in BMX Cyclists" *Sports* 7, no. 11: 232.
https://doi.org/10.3390/sports7110232