# Fight Science = Bad Science

Fight Science is an entertaining show. Great graphics. The basic idea is to look at the science in different fighting styles. They had a clip-style commercial on it during a MythBusters episode I was watching. And from that, I can say that the kicking looked cool, but the science needs some work.

### The Setup

The basic idea is that they wanted to compare kicks from different fighting styles. From what I can gather, they collected data by having some dudes kick this “kicking bag”. During the kick, they measured the force exerted on the bag and they had a sensor on the kicker’s leg – I assume to measure the kinematics of the kick (position, speed, acceleration). I didn’t get (nor could I find online) a good picture of this setup, so I will use my uber-drawing skills instead.

Here is the problem. How do you physics-ly determine which fighting style has the most awesome kick? I can think of a couple of things, but Fight Science focuses on speed (or acceleration – you can judge) and force. I tried to get a basic transcript of the important part. Here it is (paraphrased since I couldn’t clearly hear the names of the kickers). I think I got the important things they said. (I used letters to represent the different kickers)

Which kick was the most powerful? C’s strike produced the highest ration of force to velocity. It was the most effective technique, but why? The answer: physics. The force of the kick relies on both mass and acceleration. C wasn’t the fastest, only 99 mph to Taekwondo’s 136. But, Capoeira delivers the highest ratio of mass to acceleration in a single strike. From there, it is simple mathematics. And the numbers never lie

I am not making this stuff up. That is just about exactly what was said. There are a couple of huge errors here – and that is what I will focus on.

### Ratio Error

Suppose I wanted to compare boxes of cereal – you know, just because. To make this comparison, I measure the volume of the box and the mass. I do this because clearly those are both important things. What to do now? I have two variables for each box. How do I compare them? Oh wait. I know, I will divide the mass by the volume. So, here are the results.

I left off the units because I just made this stuff up anyway. The best cereal is box C. Although Box A has the biggest mass, its ratio of mass to volume is smaller making Box C clearly the best.

Why are they dividing force by velocity? I don’t get it. Oh, wait, it’s physics. Here is the data they presented.

### Acceleration and Velocity

I hate to sound so attacky, but I just don’t get it. At one part they say velocity. On the graph, they present the speed in miles per hour. And then they try to relate this to acceleration – you know because of Newton’s second law. Acceleration and velocity are not the same thing. Velocity is the time-rate at which something’s position changes. Over some time interval interval, the average velocity is:

Acceleration is the time-rate at which the velocity changes. Over some time interval, the acceleration is:

Not the same. For the same motion, one can be zero, and the other can be non-zero.

### Newton’s Second Law

I don’t know where they (Fight Science) was trying to go, but it seems like they are talking about force, mass and acceleration. They probably wanted to quantify the kick in terms of Newton’s second law, which is commonly written as:

So, if I am correct that they are using velocity as acceleration, what does their ratio of mass to acceleration mean? Maybe they meant to say something else. I am having trouble grokking this whole thing. Maybe they are also confusing force and mass. They didn’t measure the mass, so how could they find the ratio of mass over acceleration?

### The Real Problem

The mistakes aren’t the problem. The problem is the goal. It seems that they are trying to use this kicking exercise as an example to talk about physics. They have fallen in the classic trap of throwing out cool physics diagrams and terms that most people would interpret as physics. Fight Science is not alone in this error, lots of other shows do it also (see Ruff Ruffman). I see two better options:

• Option A: Redo the physics and explanations so that they are consistent with scientists’ ideas and they make sense. I know that sometimes this really isn’t feasible to explain complex ideas in a short time frame. If you want to follow this option, feel free to call me. I would love to help.
• Option B: Forget the physics. Just look at the cool kicking stuff.

Note: ScienceBlogs is now a partner with National Geographic. I don’t think I should let that stop me from doing what I normally do though – right?

Note 2: I still think National Geographic is a great channel. In fact, since we are sort of related to them, I should offer my services. I have tons of National Geographic-type skills. (cave diving)

1. #1 caleb
December 19, 2009

f = ma

f = m * ( dv / dt )
f / dv = m / dt

clearly mass divided by time is the important calculation they were going for. i mean, thats how i always compare kicks.

2. #2 caleb
December 19, 2009

“Sometimes he takes things apart and can’t put them back together.”

Also, it’s called “re-engineering”. i can’t tell you how many things I have made more efficient by taking apart, and putting back together with far less screws than the OEM thought necessary..

3. #3 Jaime
December 19, 2009

Not that they managed to show that they knew what they were doing, but there really is some sense ion what they did…

The speed of the leg is also a measure of momentum generated by the kicker. Momentum that you then want converted into force in your opponents face. The technique that has the highest momentum-to-force ratio is the one that more effectively converts available movement of the foot into broken bones. So if all your kickers are of the same size, and so you can suppose that equal velocities means equal momenta, the ratio is proportional to the inverse of the stopping time of the leg after it comes in contact with its target.

So yes, they may be alternative measures which are better, and they definitely could explain the logic of their choices better. But there’s a chance that they did think about the whole thing in a not-so-bad-science-way.

4. #4 ijc
December 20, 2009

The efficacy of a strike is reasonably given by the component of the impulse that is normal to the surface being struck.

This component is given by force*(duration of the collision). Since the duration maybe difficult to measure precisely without a high speed camera, we can constrain the displacement which occurs in the collision to be some constant L, and then say that the impulse is force*L/velocity. If L is the same for all kicks then it cancels out of the ratio, and this is why the are comparing force and velocity.

Sure, it’s easy to object to the analysis above by quibbling about the distance L. But I will attest that kick efficacy = force/velocity is the kind of calculation that theoretical physicists do all the time, the commonality being that we have isolated the relevant variables and are not concerned with second order effects.

5. #5 Anonymous Coward
December 21, 2009

It’s a hard problem, and it’s not obvious to me if there’s a single parameter for characterizing the “best kick”: Force is obviously important, but if the force lasts for an extremely brief duration it won’t cause much damage. Impulse is obviously important, but if it’s imparted over a large surface area and over a long time period, it won’t cause much damage.

Calculating the ratio of force to velocity is a way of characterizing the mass of the striking object and its rigidity, both of which are important elements of a “good” kick. While this ratio is absolutely not the be-all end-all of what makes a “powerful” kick, it’s not obvious to me that it’s that much less meaningful than the other numbers discussed.

Re: the original post
> How do you physics-ly determine which fighting style has the most awesome kick? I can think of a couple of things

Such as?

It’s not a trivial problem, and the “best kick” for one task may not be the “best kick” for another.

6. #6 PJ Grant
February 4, 2010

Sorry, Rhett, but your point is lost amid your incredible inability to string together more than one semi-coherent sentence at a time. For a critique to be truly effective, you must make sure your grammar parses, your sentence structure flows, and that the lay person has the faintest clue what you are talking about.

It would also help for you to have seen the show you are dissing, rather than just an ad for it. As a mathematician, I had several problems with the show, but still, I found your argument to be ill thought out, ill executed, and (by and large) beside the point. Good luck in future, but I shall not be reading your blog again.

7. #7 Zoe
May 20, 2010

Fight Science is more Show Fight Science.
I watched this whole episode and I laughed at the Physics too. Hey, I really enjoyed the cool kicking and the muscular, lithe agility of the fighters, and that’s really what I wanted to watch. I’m a female physicist from UC Berkeley who’s learnt jujitsu, by the way.
Actually I thought the whole scene was executed really well. You have to give them credit for delivering such entertainment in a reasonably science-y package.
What I would’ve done?
1) I would’ve divided the force by the fighter’s muscle mass. That’s the REAL meaningful ratio – power per size of the fighter – how much bang for the buck they’d deliver.

2) The capoiera explanation was a bit screwed up. I’d have used a better analogy to explain it – a spinning top for example!

8. #8 Dude
May 28, 2010

well. i’m a martial artist and i’ve seen this episode. i personally think that it was a good test, i remembered that they measured the force with some device that was inside the bag. but you now, it’s a show that is supposed to entertain people.

9. #9 Zach
January 7, 2012

Necro.

My question is if the qualitative information is decent. My math is poor at best, so I don’t pay so much attention to the numbers–though it is good to know that they aren’t necessarily accurate–what I’m more interested in is if conclusions like “This can kill a man” are valid.

I watch the show because I want to know if the human body is actually capable of such “superhero” feats, in other words.

Sometimes I also wonder about the historical accuracy, particularly when it comes to ninjutsu.