I need some barefoot math help

Hi everyone. I am in a weird progressive math class in college and we are figuring out how math is involved in our everyday lives. We are doing a project and are allowed to pick something that we do in our everyday lives and then we need to explain the math that is involved with it. I picked barefoot running and am trying to figure out loading rates, impact rates, etc... Does anyone know this type of math or where I may find it so I can do this paper? I know it involves kinematics, but this math I think is way above my head. I don't have to understand it, just have to be able to show it's there. Thanks!
 
Oh and I looked in the

Oh and I looked in the library here and couldn't find much. I did find some of the math on the 2010 Lieberman et al paper, but I can't explain it. Thanks again!
 
Oh, man. I'd totally go easy

Oh, man. I'd totally go easy way out, lol. Pace goals, total time spent broken down into rates of speed, etc. But that's because I'm simpleton when it comes to math and have to doublecheck myself when helping my daughter on her 4th grade math homework...



Good luck, and hopefully someone smarter will offer an idea.
 
Lol! Lomad I was thinking the

Lol! Lomad I was thinking the same thing but unfortunately the math my teacher requires is at least 100 level math. I was thinking originally along the lines of cadence of 180 = 3 steps per second kind of thing. Too simple I was told. Right now I have this long complex problem that I hope he can explain to me because I don't understand it in the least. I guess that's why I'm not a mathmatician or anything.
 
Have you looked at

Have you looked at Liebermann's videos on his Harvard site? They show pretty clearly how the loading rates work. With that, you might be able to figure out the paper well enough to explain it.



Best of luck

Paleo
 
The base equation you need to

The base equation you need to know is Force=(mass)(acceleration), simply put F=ma. where a= dv/dt so F=m(dv/dt) acceleration is the derivative of velocity which is the derivative of position, dv/dt means the change in velocity with respect to time. you can use that equation to model impact force. realize that your acceleration term should be pos. before the foot hits the ground lets call it time t1. the acceleration is in respect to the up/down motion of the foot.

now that you have it to find total force integrate from 1 to delta t to get the total force. that's a simplified calculus and dynamics explanation to the forces involved. there is also a natural damping factor (c) and oscillation about the ankle that you can model, as well as a natural frequency at a constant cyclical force function (i.e. F(t)=Fsine(theta)) assuming no acceleration (constant velocity). to model the cyclical motion of the foot treat it like a rotating sphere in 2D space with an observer at arbitrary point b who is moving at your velocity. you might want to double check this equation but i believe you can use position: R(b)=R(a)+R(b/a), velocity: V(b)=V(a)+omegaXR(b/a)+V(b/a)xyz, we will assume constant speed so the acceleration term is 0.

loading rates and impact rates will either involve derivative calculus and/or mechanics of solids. for instance once you find the total force that is the loading you need to find out how long it takes the foot to make full impact. then simply divide. ie F/t=how much force per unit time. For more info check out stress, strain, and shearing forces on google under mechanics of solids (also called mechanics of materials).

I hope this helps.
 
I kind of understand what you

I kind of understand what you said Kean. Tonight was my math class and we had to explain what our papers are about to the classroom. At first when I said I was a barefoot runner and was interested in looking at the differences in collision forces of the foot to the ground between shod running and barefoot running, everyone looked at me like I was stupid. After 5 minutes of me explaining how we barefooters run with a different form and siting some of Dr Liebermans study, I had the class eating out of my palm and asking lots of questions. It made it easier that Dr Liebermans paper has graphs which the lay person can understand. I don't know if I converted anyone, but everyone sure got into the discussion and was genuinely curious. My teacher had a hard time understanding the math Lieberman uses. He told me that one of his equations was similar to Einsteins theory of something, relativity maybe? I forget what he said exactly, but it was very interesting to learn about this a little and to be able to share it with my classmates. Can't wait till I finish the paper and can do my actual presentation in front of the class.
 
If you video tape it, please

If you video tape it, please be sure to share it with us, Mr. Ambassador!
 
Lol! I'm only an ambassador

Lol! I'm only an ambassador because I truly believe in barefoot running and how good it can be for ones health. If you'd have asked me about barefoot running a year ago I'd have laughed at you. Amazing how things change.
 
wow, who are you taking and

wow, who are you taking and what math? i had some projects in math but never that involved.i had a teacher at sylvania i really liked. i'm having trouble remembering his name though. i do know his first name is Scott and if i remember his last name i'll tel you.



Mike
 
This is mth 105 Mike.  His

This is mth 105 Mike. His name is Ross something. It's a weird class. This is the first term of this class actually being taught the way the class was origionally designed, so you could say we are an experimental class. I think my teacher thinks of himself somewhat like this 80's movie where the teacher goes to ghetto neighborhood where the students are all failing school and he turns them around. I can't remember the name of the movie.

The class is not normal, we don't just learn formulas. We do a lot of hands on things, usually in groups during class. We started with codes, upc numbers, frieze patterns. While working in groups we as a group figure out how to do complex problems with no instruction and we make sure our group mates understand how to solve the problem.

The class may be weird, but it is a really interesting class that's designed to help the students realize math is used in everything. The math involved in my project for example, is way beyond my knowledge (250-300 level), but by attempting to understand myself I actually learn a bit more than just memorizing a formula. I guarantee you with just memorizing a formula, at the end of term, I would have what I jokingly call a memory dump and it would be gone. I would forget it because it was a formula I never cared about and I know I will never use. By being involved and invested in my project, a project that I actually am interested in and care about, I will learn more and it will be something I may use in real life, even if it's just me trying to sound smart and prove points to my wife.
 
i don't think we ever sound

i don't think we ever sound smart to women.
 
Actually, my wife says that

Actually, my wife says that is something that irritates the crap out of her about me. I won't argue something unless I have facts and stats and so when I do that, she has nothing to stand on. A lot of people will argue something, even if they are completely wrong and have no proof. My wife is one of those people sometimes. Lol!
 
The math and physics you want

The math and physics you want is the impulse force.

Impulse Force

(average force)*(time the force is applied) = (mass)*(change in velocity)

Essentially this equation is telling us that it takes more force to stop a moving object quicker.

Looking at the right hand side of this equation. The mass would be the mass of your body. The velocity would be the speed at which you are falling toward the ground. Whether you are wearing shoes or not, the right hand side of this equation will be approximately constant.

The time the force is applied is the time it takes for your body's vertical motion to come to a complete stop. The average force is the force your body must absorb during the given time interval. The right hand side of this equation will remain constant approximately. Therefore, if the time the force is applied is increased, then the average force will decrease, and vice versa.

So, when someone heel strikes, their body's vertical motion comes to a stop very very quickly. However, when midfoot striking, the time for the body's vertical motion to come to a rest increases because the heel has to come down, the arch of the foot does its job, generally the knees bend, etc. While all of this may only add fractions of a second to the time it takes for the body's vertical motion to come to a stop, it can cut the force applied to the body in half or more. The best way to quantify this is to look at some video taken with a high speed camera of people running both with shoes and barefoot, and watching how long it takes for their body to come to rest in both situations. Perhaps Dr. Lieberman has such a video that you can use.
 
Thank you Vendoskt and yes he

Thank you Vendoskt and yes he does have videos and graphs. He also has the math for this as well, like the actual equation. It's way above my head but I understand the concept of it and the graphs, even if I don't understand the actual math of it.
 
Nick:Don Goss (ArmyPTUNC

Nick:

Don Goss (ArmyPTUNC here on the site) is an Army Doctor doing a sojourn at UNC Chapel Hill, during which he is also conducting a joint loading/impact study in which I have served as a participant. He could probably help you out a good bit. There's also the mathematics to figure out a cadence and stride length required to maintain a particular pace. It's very straightforward, but also tricky. Here's my long-past post describing how I worked it out for myself.

" I was (and frankly, still am a bit) dismayed at the loss of speed and at the potential prospects for regaining any speed at all, much less back to my 6:15/mile traditional, shod running pace.

I ran with LTC Rex Hall to have him watch my form in person and help me improve it. While running, I asked him how one might go about increasing one's BFR speed.

A quick check of the math works out like this: in traditional heel-striking form, I was making 54-inch (4.5-foot) strides at a cadence of 188 steps/minute, or 1,173 steps per mile, resulting in a 6:15/mile pace. The BF math is as follows: 32-inch (2.67-foot) strides at a cadence of 233 steps per minute, or 1,977 steps per mile, resulting in a 8:30/mile pace.

So by decreasing my stride length by almost half and increasing my cadence by 24%, I've been able to add 2:15/mile to my pace with no difficulty at all. Not what I was hoping for, but being older, I'll live with it.

The problem is that I'm pretty much maxed out at that cadence, and my soles are pretty much maxed out at that pace (unless I'm on dirt or grass that don't abrade like concrete does, giving me some room to allow more friction as I speed up).

Rex Hall's theory was that to increase speed BF, rather than significantly lengthening your stride by extending the angle between each leg and your hip joint forward and backward, which will increase the friction your feet experience due to push-off and braking effects, you should simply hold your feet up in the air for a longer time. This sounds like what Master Abide is advocating from a different angle now that I've read what he says above about " high knees and butt kickers."

But my experience is that to get any significant increase and still keep my feet landing under my center of gravity, I've got to lean forward more with my hips at the same time to provide the forward motion without the push-off and braking effects coming into play. The biggest downside to this is that while holding your feet up for a longer time before setting them down, you get more impact on each foot plant due to gravity's pull effectively increasing as you increase the time above dirt. This is a recipe for stress fractures if you don't gradually work up to it. Since my initial stress fracture 7 months ago, I've not even begun to attempt this again yet, and probably won't until this summer (and then, only on dirt, and VERY SLOWLY). "

I have attempted it many times in recent months, and found that the softer the surface, the easier it is on the body to raise higher and then hold your feet up for a longer time.

But this is about math. Just an idea. I'm a hard-core NON-mathematician who is married to a college math and physics major who teaches high school math now. I only use math when I have to in order to get an answer I simply must have. It makes my brain overheat and smoke come out my ears.

Hope this helps. Particularly look up Don Goss. Good luck!
 
I'm no math whiz either Phil

I'm no math whiz either Phil and when I do math out in "the real world" I never use any of this advanced stuff. It's too easy to mess up. I always break things down to the most basic math I can. Thanks for the advice and I will look into it. Are you in the military yourself?