Yes, everyone was predicting that undefeated MMA fighter Ronda Rousey would beat Holly Holm last weekend—but that's not what happened. Instead Holm won the match with a well-placed kick to the head. Boom, Ronda was out. If you really knew who would win these matches ahead of time, why fight?
From a physics perspective, what can we figure out from this final kick to the head? Can we estimate the impact force from this hit? Well, yes—we can always estimate something, even if it requires some wild guesses. That's never stopped me before; why should it stop me now?
Let me start with some video analysis. If you search for a while, you can find a shot of "the kick" seem from above. This view is nice, since you can see the whole horizontal motion of the kick as Holly whacks Ronda in the face. It's not a perfect video (some frame rate issues), but it will do. Scaling the video based on the length of Holly's leg, I get the following trajectory for her foot.
In case you missed the fight (or haven't seen one of the billion GIFs online), the blue data shows the foot moving from upper right down to the left. The head recoils going up and to the right. But how fast was the foot? Using the 3 data points that are clear right before the hit, I can get an average foot speed of 6.3 m/s (14 mph) with a velocity vector of (-5.85,2.39,0) m/s—this will be important later. Also, the foot has a recoil velocity of (-1.26,-1.04,0) m/s. Notice that this analysis doesn't include the motion of the foot in the vertical direction (since I can't see that).
But what about the force? First, let's think about the Momentum Principle. This says that the net force on an object is equal to it's rate of change in momentum, which I can write as:
I know the change in velocity for this foot—so if I can get values for the time of impact and the mass of the foot, then I will get a value for the force the head exerts on the foot (which is the same magnitude that the foot exerts on the head). Now for my first wild estimate—the mass of the foot is about 1.2 kg based on Holly's weight of 134 pounds and this paper on mass distributions of the human body. Yes, it's actually more than just her foot that hits Rousey. How about I use an adjusted foot mass of 2.5 kg (just a guess) to take into account the mass of the rest of her leg?
Now for the impact time. I can switch to a better quality video (but not viewed from the top) to estimate that. It looks like the foot was in contact with the face for about 2 frames. With a frame time of 0.033 seconds, this gives an impact time of about 0.066 seconds.
Putting this all together, I get an average force during the impact with a value of (173.9, -130.3, 0) Newtons and a magnitude of 217 N (48.7 pounds). Maybe that doesn't seem like much, but just consider the following points:
- This is the AVERAGE force. At some point during this interaction, the peak force could be significantly higher.
- Think of 50 pounds. Think of a 50 pound dog. Think of that 50 pound dog sitting on your head. Yes, that's not so fun.
Remember, this is just a rough approximation of this impact force. Needless to say, the force was clearly enough to accelerate Rousey's head in a way to knock her out. Oh, but don't worry—I still think Rousey is an impressive fighter, too.
