Kobe - Fake Jump or Real
23/06/08 08:26 Filed in: Physics
We have all seen the Kobe Bryant video of him jumping
over an Aston Martin - this keeps coming up on the
Internet. There has been vast discussions of whether
this is real or fake. I will do my best to examine
the evidence. In short (in case you don’t want to
read the whole thing) Kobe can most likely really
jump that high, it is possible that there was some
perspective trickery involved. Here is the video in
case you are brand new to the WWW:
First, let me give a personal note to Kobe and his
friends:
Ok, now on to the analysis. Question: was the jump fake? Well, one way to answer this is to look at his acceleration in the air. This is somewhat problematic because he is not a rigid object while in the air. To compensate for this, I will mark the location of his important body parts and plot the motion of his center of mass. Again, I use Tracker Video Analysis to get x,y positions of each part in each frame. I tracked the motion of his calf, thigh, trunk, arms and head. To find the y-value of the center of mass, I used:
I used this table (http://oregonstate.edu/instruct/exss323/CM_Lab/bsp_deleva.htm) to get the percentage values of a typical person’s body parts (that way I did not need the total mass). Doing so, I obtain the following plot:
Where I have fit a quadratic function to the center of mass plot. Relating this fit to the kinematics equation:
so, the A value in the fit is 1/2
times the acceleration. This means that the
acceleration (in the y-direction) is twice the A
value for an acceleration of -11.6
m/s2. Yes, I know this is not what
would be expected (the expected value of -9.8
m/s2), but I think it is ok.
Also, I looked at his horizontal positions (and did the same thing as above)
Here you can see that his horizontal motion is fairly constant (for his center of mass). This is what you would expect for a jump. There is no force in the horizontal direction (while in the air) so there should be no horizontal acceleration. Notice that the motions of the body parts CAN have acceleration, but as a whole, non.
As a comparison, I did another analysis of a jumper - but this jumper used a trampoline. This is video of some world-record trampoline dunk.
Notice that this quality is even worse than the Kobe video (but they do give a nice sideways view - thank you Japanese show people. Here is the data for the horizontal and vertical motions:
First, note that this analysis shows a vertical acceleration of -6.76 m/s2 with a much higher RMSE (and with much poorer quality video). The horizontal motion shows constant velocity (as expected).
Conclusion: The jump seems real. He is a professional basketball player, so one would expect that he can jump. I am sure I have seen some other video of a person jumping over a moving car, so not an impossible stunt (though still impressive).
Next, was some there some sort of trickery involved? First, let me look at the car. Doing an analysis for the motion of the car (just in the horizontal direction although it is clear it is going down hill).
Here is the plot of the position of the car. You can see that it is moving at a fairly constant velocity (9.79 m/s or about 22 mph). The question I originally thought of “was it turning around him or something”. This doesn’t say for sure, but I would think it would have a non-constant velocity in this case.
Did the camera play some type of perspective trick? Here is an image of two frames overlapping:
This shows Kobe and where he was standing and how that compares to the position of the car at a later time. From this it looks like he was standing very near to the front right tire of the car (clearly not in the middle). This suggests that perhaps there was trickery involved. It really would be foolish of him to jump over a car without trickery. What if he missed by just a little and injured himself - that would not be good for his basketball career, would it?
Conclusion: In my opinion (for what its worth), Kobe has the ability to jump over a moving car. It am not sure if trickery was involved.
Next: I had planned to include an analysis of a jump that was fake, but apparently these are difficult to find. When I find one, I will post that.
- When making a video, please do not wear dark colors. Also, it would help if your outfit had distinguishing patterns on it. This video is very difficult to analyze because it is hard to see where you are (legs and arms and stuff). It would help if you wore a bright red cap or something.
- Your other video (of you jumping over a pool of snakes) was much easier to analyze because you didn’t change your body position. Whenever possible, please do that again.
- I must give bonus points to your film crew. Thank you very much for not moving the camera while he is jumping and for having a nice perpendicular shot that does not need perspective correction (I still haven’t figure out how to do that).
- Finally, I know these jumps may be fun, but please be careful. Oh, the quality of videos on youtube pretty much sucks. I found one somewhere else that looked much better but it had repeating frames.
- Oh, one more. The next time you do a jump, send me a note and I will analyze it as soon as possible.
Ok, now on to the analysis. Question: was the jump fake? Well, one way to answer this is to look at his acceleration in the air. This is somewhat problematic because he is not a rigid object while in the air. To compensate for this, I will mark the location of his important body parts and plot the motion of his center of mass. Again, I use Tracker Video Analysis to get x,y positions of each part in each frame. I tracked the motion of his calf, thigh, trunk, arms and head. To find the y-value of the center of mass, I used:
I used this table (http://oregonstate.edu/instruct/exss323/CM_Lab/bsp_deleva.htm) to get the percentage values of a typical person’s body parts (that way I did not need the total mass). Doing so, I obtain the following plot:
Where I have fit a quadratic function to the center of mass plot. Relating this fit to the kinematics equation:
so, the A value in the fit is 1/2
times the acceleration. This means that the
acceleration (in the y-direction) is twice the A
value for an acceleration of -11.6
m/s2. Yes, I know this is not what
would be expected (the expected value of -9.8
m/s2), but I think it is ok.
- First, you will see that the data fits a parabola very well (the listed RMSE of 0.015 - this is root mean square error - 0 would be a perfect fit).
- Next, why would this be off? I calibrated my data from the poor quality video using the height of Kobe Bryant as 1.98 meters (as listed on wikipedia). He was never standing up nice and straight except when his arms were over his head (making it difficult to see his head). So, this could be a cause for the different acceleration.
- Lastly, I really guessed about the location and percentage of mass for Kobe’s body parts.
Also, I looked at his horizontal positions (and did the same thing as above)
Here you can see that his horizontal motion is fairly constant (for his center of mass). This is what you would expect for a jump. There is no force in the horizontal direction (while in the air) so there should be no horizontal acceleration. Notice that the motions of the body parts CAN have acceleration, but as a whole, non.
As a comparison, I did another analysis of a jumper - but this jumper used a trampoline. This is video of some world-record trampoline dunk.
Notice that this quality is even worse than the Kobe video (but they do give a nice sideways view - thank you Japanese show people. Here is the data for the horizontal and vertical motions:
First, note that this analysis shows a vertical acceleration of -6.76 m/s2 with a much higher RMSE (and with much poorer quality video). The horizontal motion shows constant velocity (as expected).
Conclusion: The jump seems real. He is a professional basketball player, so one would expect that he can jump. I am sure I have seen some other video of a person jumping over a moving car, so not an impossible stunt (though still impressive).
Next, was some there some sort of trickery involved? First, let me look at the car. Doing an analysis for the motion of the car (just in the horizontal direction although it is clear it is going down hill).
Here is the plot of the position of the car. You can see that it is moving at a fairly constant velocity (9.79 m/s or about 22 mph). The question I originally thought of “was it turning around him or something”. This doesn’t say for sure, but I would think it would have a non-constant velocity in this case.
Did the camera play some type of perspective trick? Here is an image of two frames overlapping:
This shows Kobe and where he was standing and how that compares to the position of the car at a later time. From this it looks like he was standing very near to the front right tire of the car (clearly not in the middle). This suggests that perhaps there was trickery involved. It really would be foolish of him to jump over a car without trickery. What if he missed by just a little and injured himself - that would not be good for his basketball career, would it?
Conclusion: In my opinion (for what its worth), Kobe has the ability to jump over a moving car. It am not sure if trickery was involved.
Next: I had planned to include an analysis of a jump that was fake, but apparently these are difficult to find. When I find one, I will post that.
