The data is in the process of analysis. Conclusions are pending the completion of the data analysis.
Data and Results
| Eric Gibble | Cristobal Palmer | ||||||||||
| 13-Mar-01 | |||||||||||
| Properties of the soccer kick | |||||||||||
| Scale Factor for photo (in pixels) | Using the diameter of the ball | ||||||||||
| File | horizontal | veritcal | diameter | ||||||||
| 124-75-10.psd | vertical | 0 | 89 | 89 | |||||||
| horizontal | 87 | 0 | 87 | ||||||||
| slant 1 | 65 | 62 | 89.82761268 | ||||||||
| slant 2 | -65 | 59 | 87.78382539 | ||||||||
| Average: | 88.40285952 | ||||||||||
| File | horizontal | vertical | diameter | ||||||||
| 113-75-10.psd | vertical | 0 | 89 | 89 | |||||||
| horizontal | 88 | 0 | 88 | ||||||||
| slant 1 | 60 | 66 | 89.19641248 | ||||||||
| slant 2 | -67 | 55 | 86.68333173 | ||||||||
| Average: | 88.21993605 | ||||||||||
| File | horizontal | vertical | diameter | ||||||||
| 101-75-10 | vertical | 0 | 87 | 87 | |||||||
| horizontal | 85 | 0 | 85 | ||||||||
| slant 1 | -65 | 60 | 88.45903006 | ||||||||
| slant 2 | 71 | 55 | 89.81091248 | ||||||||
| Average: | 87.56748564 | ||||||||||
| Actual Diameter of Soccer Ball (in meters) | |||||||||||
| diameter 1 | 0.21 | ||||||||||
| diameter 2 | 0.211 | ||||||||||
| Average: | 0.2105 | ||||||||||
| Scale Factor: | Avg. dia.(pixels) | Actual(m)/Image(pix) | |||||||||
| File | |||||||||||
| 213-70-10W | 100.205 | 0.002100694 | |||||||||
| 162-75-10S | 86.59 | 0.002430997 | |||||||||
| CH12-70-10W | 98.85 | 0.002129489 | |||||||||
| CH31-70-10S | 86.09 | 0.002445116 | |||||||||
| mass of ball (kg) | |||||||||||
| 0.429 | |||||||||||
| File | Time (s) | H(pix) | V(pix) | D(pix) | D(real) | Velocity(m/s) | momentum (kg*m/s) | mass of leg | |||
| Wide Stance | if momentum is conserved | ||||||||||
| 213-70-10W | 0.02 | 68 | 111 | 130.17 | 0.273447283 | 13.67236415 | |||||
| 0.01 | 37 | 55 | 66.29 | 0.139254977 | 13.92549773 | ||||||
| 13.79893094 | ball | 5.919741374 | |||||||||
| 0.01 | 62.43 | 0.1311463 | 13.11463001 | leg after collision | 6.109471545 | ||||||
| this value is closer to the "truth" | |||||||||||
| 0.02 | 129 | 4 | 129.06 | 0.271115513 | 13.55577566 | ||||||
| 0.02 | 136 | 13 | 136.62 | 0.286996757 | 14.34983783 | ||||||
| 0.02 | 135 | 7 | 135.18 | 0.283971758 | 14.19858789 | ||||||
| 0.01 | 67 | 10 | 67.74 | 0.142300983 | 14.2300983 | ||||||
| 14.08357492 | leg before collision | 0.420329455 | |||||||||
| Shooters' Stance | |||||||||||
| 162-75-10S | 0.02 | 118 | 67 | 135.69 | 0.329861936 | 16.49309678 | the value to the left is wrong because it | ||||
| 0.01 | 58 | 34 | 67.23 | 0.163435905 | 16.34359048 | assumes that P of ball after collision=P of leg | |||||
| 16.41834363 | ball | 7.043469418 | before collision but this ignores P | ||||||||
| of leg after collision. | |||||||||||
| 0.02 | 113 | 57 | 126.56 | 0.307666936 | 15.38334681 | ||||||
| 0.02 | 124 | 45 | 131.91 | 0.320672768 | 16.03363841 | ||||||
| 0.02 | 125 | 44 | 132.52 | 0.322155676 | 16.10778381 | ||||||
| 15.84158968 | leg before collision | 0.444618852 | |||||||||
| 0.01 | 54 | 32 | 62.77 | 0.15259366 | 15.25936598 | ||||||
| 0.01 | 57 | 32 | 65.37 | 0.158914251 | 15.89142511 | ||||||
| 15.57539554 | leg after collision | 26.45989726 | |||||||||
| Palmer | |||||||||||
| Wide Stance | |||||||||||
| CH12-70-10W | 0.02 | 178 | 28 | 180.19 | 0.383712645 | 19.18563227 | |||||
| 0.02 | 180 | 24 | 181.59 | 0.38669393 | 19.33469651 | ||||||
| 0.03 | 259 | 43 | 262.54 | 0.559076075 | 18.63586916 | ||||||
| 0.03 | 259 | 48 | 263.41 | 0.56092873 | 18.69762435 | ||||||
| 18.96345557 | ball | 8.135322441 | |||||||||
| 0.03 | 189.53 | 0.403602074 | 13.45340246 | leg after collision | 5.004781441 | ||||||
| 0.01 | 47 | 35 | 58.6 | 0.124788063 | 12.47880627 | This makes sense | |||||
| 0.01 | 57 | 40 | 69.63 | 0.148276328 | 14.82763278 | considering my leg would | |||||
| 0.01 | 49 | 37 | 61.4 | 0.130750632 | 13.07506323 | have less mass than Eric's | |||||
| 0.01 | 79 | 16 | 80.6 | 0.171636823 | 17.16368235 | ||||||
| 0.01 | 80 | 25 | 83.82 | 0.178493778 | 17.84937785 | ||||||
| 15.07891249 | leg before collision | ||||||||||
| Shooters' Stance | 0.02 | 133 | 28 | 135.92 | 0.332340109 | 16.61700546 | |||||
| CH31-70-10S | 0.02 | 138 | 34 | 142.13 | 0.347524277 | 17.37621385 | |||||
| 0.02 | 137 | 31 | 140.46 | 0.343440934 | 17.1720467 | ||||||
| 17.05508867 | ball | 7.316633038 | |||||||||
| 0.01 | 41 | 31 | 51.4 | 0.125678941 | 12.56789406 | ||||||
| 0.01 | 43 | 26 | 50.25 | 0.122867058 | 12.28670577 | ||||||
| 12.42729992 | leg after collision | 2.083806755 | |||||||||
| 0.02 | 126 | 45 | 133.79 | 0.327132013 | 16.35660065 | ||||||
| 0.02 | 114 | 54 | 126.14 | 0.308426879 | 15.42134394 | ||||||
| 0.02 | 120 | 53 | 131.18 | 0.320750261 | 16.03751307 | ||||||
| 15.93848589 | leg before collision | ||||||||||
Analysis and Discussion
When we began this investigation, we hoped to find clearly that one kicking position allowed the shooter to kick the ball harder. That is, we thought that a "Shooters’ Stance" would make the ball go faster after being kicked. At first we did find this to be the case. When Eric kicked the ball, it went faster when it was placed closer to his plant foot (Shooters’ Stance), but with Cristóbal we found that he could make the ball go faster if we placed the ball further from his plant foot (Wide Stance).
We had to determine the scale factor of the actual ball to the ball in the picture in order to find the velocity values. We did this by measuring the diameter of the ball and then finding the average diameter of the ball (in pixels) in each picture. We then measured how much the ball had moved (in pixels) from one flash to the next, and since the flashes were at regular time intervals, we were able to use this data to determine the actual velocity of the ball.
We then found the mass of the ball using a balance scale, and we used this mass value to calculate the momentum of the ball after being kicked in each of the four photographs we analyzed. Since the mass of the ball never changed, the faster-moving shots had more momentum.
Assuming that momentum is conserved in the collision of the leg and the ball, the following must be true:
Piball + Pileg = Pfball + Pfleg
Since the ball was stationary before the collision, Piball is zero, so the equation simplifies to:
Pileg = Pfball + Pfleg
Pileg - Pfleg = Pfball
Mleg = Pfball / (Vileg – Vfleg)
In this way we calculated the mass of the leg involved in the collision. By looking at the equation we can come to two conclusions: the more mass involved, 1. the greater the momentum imparted into the ball and 2. the less the velocity of the leg changes from before to after the ball is kicked.
This equation also provided us with a convenient reality check, since Cristóbal’s leg is less massive than Eric’s. We did find that the data reflected this, but the masses given by the equation varied considerably, especially in the case of Eric’s Shooters’ Stance kick. We had been getting leg mass values of two, five and six kilograms, but that picture resulted in a value of 26 kilograms for the mass of Eric’s leg. Oddly enough, this was not the picture that gave us the fastest final velocity for the ball.
This inconsistency either indicates that our method lacked precision, or that the relationship between the stance taken and the momentum transferred to the ball is not what we thought at all.
There were several factors that we were not able to consider. Two major ones were the fact that the path of the leg is an arc and not a line, and the fact that the ball is spinning after it is kicked. We know, for example, that some of the momentum of the foot went into making the ball spin, so the equations we used above are flawed. Also, what part of the leg should be tracked when finding velocity? Since the path is an arc, the outermost part (the toe) will be going fastest, but the toe is not representative of the part of the leg that is taking part in the collision.
| Introduction/Goals | ||
| Pictures | Capture and Analysis | Discussion and Results |
| Conclusion | Home | To NCSSM HSI Website |