Relative Velocity

Figure 1: Rugby Tackle x4 Image Sequence

Relative velocity of the rugby tackle was calculated from frame 17. A single point digitisation model was created using the hips of the players as a reference point. The players were digitised through until frame 50, where contact has just been made.

Table 1: Velocity and Relative Velocity of rugby tackle

Graph 1 and 2: Relative Velocity of players (VLR & VRL)

Graph 1 and 2 shows the calculated relative velocity of left player as observed by the right player (VLR) and right player as observed by the left player (VRL) respectively. The black vertical lines in the graphs represent the point of contact at frame 38, after 0.76sec. Graph 2 is a mirror image of Graph 1, as the players moving towards each other and the right player is the one travelling in a negative direction, this results in VRL to have negative values.

Relative velocity is continuously altering going from a max value of (-)4.77ms‾¹ at the start of the move down to (-)2.75 ms‾¹ just before the point of contact. This decrease is a result of both players reducing their velocity in preparation for contact. For the last few frames before contact  the relative velocity slightly increases to (-)3.40ms‾¹, as both players push their bodies forward. After contact has been made, relative velocity decreases to (-)2.46 ms‾¹.

Figure 2 shows the frames approaching the point of contact, frames 26-35. The blue and red lines represent the distance travelled throughout these frames only by both players. During these ten frames, there is very little movement from either player as both are preparing for the point of contact. Velocity decreases as a result of this thus causing the decrease in relative velocity als

Figure 3 : Rugby Tackle x4 Image Sequence

Figure 3 shows the immediate frames before contact, as well as the frame of actual contact, where relative velocity increases as both players are stepping into the tackle. During these frames the feet  of both players remain in somewhat the same position but as the hips are moving forward, this causes the increase in relative velocity  to (-)3.40ms‾¹.  Once contact has been made, the relative velocity decreases and it would be expected that eventually the relative velocity would return t o zero as both bodies would be moving in the same direction at the same speed

Graph 3: Horizontal Velocity

Graph 3 shows the horizontal velocity of both players. The vertical black line in the graph represents the point of contact of the players at frame 38. Graph 3 shows a similar trend to the relative velocity graph. The horizontal velocity of the left player increases initially but decreases as the player nears the point of contact. Just before the point of contact, the horizontal velocity of the left player increases as he pushes his body forward, moving into the tackle. A similar trend can be seen for the right player also. As the right player is travelling in a negative direction, his velocity is constantly negative. To begin with, horizontal velocity is increasing but closer to the point of contact horizontal velocity decreases and continues to decrease after contact is made. After contact, velocity of the left player decreases while horizontal velocity of the right player decreases momentarily but then increases and towards the end becomes relatively constant.

Graph 4: Linear Velocity

Graph 4 shows the linear velocity of both players. This graph has similar trends as the other graphs, velocity decreases nearing the point of contact, but in the final couple of frames before contact, velocity of left player increases while the velocity of the right player levels off with only minor increases. After contact, velocity of the left player immediately decreases while the velocity of the right player slowly begins to increase. Towards the end of the tackle, both players are nearing the same velocity value, which would result in zero relative velocity once both bodies are moving in the same direction

Conclusion:
Relative velocity of two bodies refers to the velocity of body A in accordance with body B or vice versa. Relative velocity can also be used to calculate the velocity of an object through a fluid i.e. swimming, rowing. In these cases, the velocity would be calculated of the swimmer relative to the velocity of the water, or the velocity of the oar relative to the water. Relative velocity can also be calculated with reference to air when the wind speed and direction is known. This can be used in outdoor sports such as javelin throw or shot put by measuring the relative velocity of the javelin or shot put with reference to the wind.