# SOLIDWORKS Flow Simulation – Ski Jumping

Let’s find out the optimal forward lean angle for a Ski jumper in SOLIDWORKS Flow Simulation to help him get the longest jump in his life!

In this article we will try to determine the value of a lift force as a function of a forward lean angle (FLA) of Ski jumper. To find this characteristic, we tested four different body position. The body position in our studies are shown in the figures below:

Fig. 1a. Body position at forward lean angle equal to 20° | Fig. 1b. Body position at forward lean angle equal to 30° |

Fig. 1c. Body position at forward lean angle equal to 40° | Fig. 1d. Body position at forward lean angle equal to 60° |

# Definition of case study

In the first step we will try to estimate the real velocity of ski jumper which depends on the forward lean angle. The most important is to find the drag force for each case. To do this, we define two goals: drag force and lift force on surface of a ski jumper’s body.

For all cases, we assume that horizontal velocity component of a Ski jumper is equal to 100 km/h.

After doing the necessary calculations, we know the value of Drag force for velocity of 100 km/h for each FLA. By including decreased velocity and increasing Drag force, the following equation will determine real velocity for Ski jumper:

Table 1. Estimated real velocity for Ski jumper assuming influence of a drag force
| |||

FLA [°] | Velocity [km/h] | Drag force [N] | Real velocity [km/h] |

20 | 100 | 61.86 | 100.00 |

30 | 100 | 85.98 | 71.95 |

40 | 100 | 126.23 | 49.00 |

60 | 100 | 257.76 | 24.00 |

# Results

Below we can observe the distribution of aerodynamic drag coefficient as a function of FLA:

Fig. 2a. Distribution of aerodynamic drag coefficient(FLA of 20°) | Fig. 2b. Distribution of aerodynamic drag coefficient(FLA of 30°) |

Fig. 2c. Distribution of aerodynamic drag coefficient(FLA of 40°) | Fig. 2d. Distribution of aerodynamic drag coefficient(FLA of 60°) |

In the first case, the biggest aerodynamic resistance appears on surface of head (fig. 2a). This resistance increases together with the increase of FLA and moves towards chest and shoulders (fig. 2b), forearms and abdomen (fig. 2c), to finally cover all front area of a ski jumper’s body (fig. 2d).

Figures 3. show the streamlines that are passing the ski jumper. For a low value of forward lean angle, we can observe a laminar flow. For a high value of forward lean angle, the airflow is separating.

Fig. 3a. Streamline flow passing a ski jumper(FLA of 20°) | Fig. 3b. Streamline flow passing a ski jumper(FLA of 30°) |

Fig. 3c. Streamline flow passing a ski jumper(FLA of 40°) | Fig. 3d. Streamline flow passing a ski jumper(FLA of 60°) |

Based on the simulation results, we can draw a graph that represents the lift force as a function of forward lean angle:

*Fig. 4. Lift force as a function of forward lean angle*

# Conclusions

SOLIDWORKS Flow Simulation is very useful in getting the optimal parameters of body position to achieve better results in Ski jumping. It surely can be used as a supporting tool for athletes.

###### Author:

###### Mateusz SZTANGRET

SOLIDWORKS and SOLIDWORKS Simulation Specialist at SOLIDEXPERT

- Mateusz Sztangret