Author Topic: Rolling or Cat-Hang to Drop?  (Read 4244 times)

Offline Roberto Espinoza Jr.

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Rolling or Cat-Hang to Drop?
« on: June 15, 2012, 10:53:48 AM »
Rolling or Cat-Hang to Drop?
I was browsing APK earlier and I saw this thread:
http://www.americanparkour.com/smf/index.php/topic,38722.0.html
Matthew posed the question:  To get off a high wall, would it be better to jump and roll off, or cat-hang and drop off without rolling?
Well I thought I could use my nerdy-ness to help. I don’t have something to measure time as accurately or precisely as I would like, so I took a guess-timate on the times and the running speed.

Here’s my made up situation:

A traceur is going for a run in an unfamiliar location when he encounters a 3 meter high (about 10 feet) drop. If he is running at a constant speed of 5m/s, should he

a) Jump off ( at 5m/s) at a 45 degree angle and roll.

OR

b) Cat hang and drop down 2.25 meters (about 2.5 feet less) without rolling?

Assume that a traceur’s average roll takes around 1 second to perform and he exits the roll at a light 2m/s jog.
Assume that, for part b, the traceur absorbs the impact in .25 seconds.
The traceur weighs 77kg (around 170 pounds)

Which situation would have him feel the least average force?

Part b is easier so I’ll do that part first haha!

Through the conservation of mechanical energy, the traceur’s gravitational potential energy (GPE) at the top of the drop (from the cat hang position) should equal his kinetic energy (KE) at the bottom of the drop.

(GPE) mgh = 1⁄2 mv^2 (KE)

Where m is the mass of the traceur, g is the acceleration due to gravity (9.81m/s2), h is the height of the drop, and v is the velocity.

Solving for v gives us:

v = √(2gh)

Substituting numbers for variables gives us the traceur’s speed to be -6.64m/s (the number is negative because the velocity is pointing downwards)

His momentum would be

p = mv

Substituting numbers gives us
-511 kg*m/s (again the number is negative because it’s directed downwards)

The average force on the traceur would be:

F = Δp⁄t)
F = (pf – pi)/t

The subscripts, f and i, represent the final and initial momentums of the traceur

Substituting numbers gives us 2044 kg*m/s2, or 2044N. This is about 460 pounds of force and close to 3 times the traceur’s weight (2.7x actually).


Time for the fun part xD

The traceur jumps off the drop at a 45 degree angle; that means he’s going higher, so we must find his maximum height.
We must find the y-component (the vertical component) of his velocity; which is fairly easy because he jumps as a 45 degree angle. If you don’t know/don’t remember trigonometry just take my word for it. His vertical speed would be 3.53m/s

I could use the kinematic equation

vf2 = vi2 -2g∆y

to solve for the additional height, ∆y. vf2 is zero because the vertical velocity at the point we’re solving for would be zero (your vertical velocity at the peak of your jump is zero). This makes solving much easier. We get:
Δy= vi2/(2g)

Substituting the numbers we find that the traceur added an extra .64m to his height.

Now we must do that whole shehbang with the energy thing to find out his final speed and momentum. But I’ll save you the trouble of reading it all and save me the trouble of writing it all xD

V = -8.45m/s
P = -651 kg*m/s


We’ll assume that this downward momentum is completely transferred to forward momentum through “reverse blocking” which was mentioned in the thread.

The final momentum, calculated by multiplying the 2m/s (the traceur exited in a light jog) by his mass is:

p = 154kg*m/s

Now we use this equation again:

F = (pf – pi)/t

Except this time the final momentum is 154, the initial is 651, and the time is 1 second.
The average force felt is:

497N! That’s a little under a forth of the 2044N felt with the straight drop! And only .66 of the traceur’s weight!

TL;DR?
Conclusion:


It’s better to jump off and roll than to cat hang and drop. The math says so.

BUUUUT!

I did not account for the force it would take to shift the downwards momentum forwards. If somebody isn’t satisfied I’ll break my head trying to find out how to do that xD In fact this whole thing was half assed. Like I said I don’t have correct measurements for time or running speed (although 5m/s seems  like a light run) so this could very well have a high percent error. Also, I only considered downwards momentum for the roll. You will have some forwards momentum for the roll and I don’t know how much of a difference that could make to the average force. And the biggest variable of all is us. We need to have a good roll to make sure that momentum is dispersed safely and we don’t hurt ourselves with a 10+ foot drop.

Even so, a roll seems like a better option than a straight drop.

If anybody isn’t satisfied with my math for some reason please tell me if I made a mistake somewhere, even though I’m pretty sure it’s all right.
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Offline Anton Mesmer

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Re: Rolling or Cat-Hang to Drop?
« Reply #1 on: June 15, 2012, 11:28:44 AM »
Screech, my friend... I only wish I could speak the language of math as beautifully and fluently as you. I can speak from experience though. "Would it be better to..." seems to be worded in a way that opens up to interpretation. Am I running away from angry cyber-ninjas with a penchant for sadism, or am I just getting around. I guess either way I would personally prefer to roll. I suppose that I should assume that this is a general question and there are no sadistic cyber-ninjas. Hmmmm. I guess I've never really thought of it any other way.

High drop with forward directional momentum is a roll. High drop with a lateral change in momentum is a cat-hang to drop. I'm interested in any data that you could find though! You should really look into number crunching some more scenarios!!!

Offline Tony

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Re: Rolling or Cat-Hang to Drop?
« Reply #2 on: June 15, 2012, 11:30:19 AM »
Cat hang into a roll. Use the cat hang to get lower down, but kick off the wall, and go into a roll. Best of both worlds. If this wasn't possible, I'd go for the roll. I wouldn't want to drop 8 ft without a roll.
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Offline Nick Fernandez

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Re: Rolling or Cat-Hang to Drop?
« Reply #3 on: June 15, 2012, 11:33:46 AM »
The problem with that, Tony, is you can't get as much speed the way you would jumping off from a run. You would have more downward momentum that you would have to convert into forward momentum from the roll because you're going at the ground more directly.
http://www.youtube.com/watch?v=ykbx-yzFgBo

"If you're afraid to fall, you'll fall because you're afraid." -Daniel Ilabaca

Offline Tony

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Re: Rolling or Cat-Hang to Drop?
« Reply #4 on: June 15, 2012, 11:43:54 AM »
The problem with that, Tony, is you can't get as much speed the way you would jumping off from a run. You would have more downward momentum that you would have to convert into forward momentum from the roll because you're going at the ground more directly.
I guess that's true, didn't think about that. But if the wall was 10 ft tall, and I'm 6 ft, couldn't I hang down all the way and drop 4 feet instead? I would lose speed definitely, but if all I was trying to do is get down the wall safely, wouldn't this be a good option? I think it's what the common person would think too.
If you have a great roll and you're confident then go for it.

Btw I'm not actually 6 ft aha
Kansas.

Offline Roberto Espinoza Jr.

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Re: Rolling or Cat-Hang to Drop?
« Reply #5 on: June 15, 2012, 11:58:31 AM »
Anton:
Thank you  ;D I would like to do some more number crunching but I would need some instruments to measure quantities and shit like that xD Ya know when I graduate from high school physics is what I'd lie to study. So it's great to be able to apply one love to another haha!

Tony:
Yes I cat-hang to roll would be better of course but that wasn't really what I was looking for, and as Nick said, it'd be harder to transition into the roll. And the force needed to transfer that momentum forward could place an un-needed stress on your legs which could be avoided by having some forward momentum.

Nick:
Although it is easier to transition into a roll with more forward momentum you would not "have more downward momentum" to convert. The downward speed (and therefore momentum, because p = mv) only depends on the height. It does not matter how fast you're going horizontally; if you just drop 10 feet you'll have the same downward speed if you dropped ten feet going 50 miles/hour. Just clearing that up cause I whole lot of people seem to think like that. It is true, though, that forward momentum makes it easier to just fall into the roll.
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Offline Anton Mesmer

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Re: Rolling or Cat-Hang to Drop?
« Reply #6 on: June 15, 2012, 12:09:36 PM »
What kind of instruments would you need? I'm actually looking for that kind of stuff for my site but I don't have the personal know-how. I'd love to collaborate and I'm not beyond investing in the future!  :P

Offline Roberto Espinoza Jr.

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Re: Rolling or Cat-Hang to Drop?
« Reply #7 on: June 15, 2012, 12:29:34 PM »
Ya know I'm not entirely sure. I know that in our physics class we had this thing....darn I forgot what it's called! xD Well it measures force and we could use it to plot force as a funciton of time. The only thing I'm sure of it that it was very cheap and not really precise or accurate because we would get different results every time we'd use it with the same set up so....yeah.

Also, if I'd like to study the dynamics of things like a wall run I'd have to measure something called the co-efficient of friction (which is a quantity that says how much friction one surface can have on another) and that's actually pretty easy but the only way I know of how is to have the two surfaces on an angle that can be slowly elevated and have the angles measured. It'd probably be easiest to do that with cinderblocks since those are large enough to put a shoe on.

Also a highspeed camera would be mighty useful since we could just count the frames in which something happens then use the frame-rate to find out the time. And also large strips of measured tape or something.

It's sorta like what the Mythbusters do if you've ever seen their show.



You said you're looking for this stuff for your site? Actiontutorials right? I would love to do that for you but it'd be sweet to actually meet you in person which I don't think would happen anytime soon haha! It's an exciting offer but I just don't think it could happen right now sorry. Haha. One day Anton. One day.
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Offline Nick Fernandez

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Re: Rolling or Cat-Hang to Drop?
« Reply #8 on: June 15, 2012, 12:47:43 PM »

Nick:
Although it is easier to transition into a roll with more forward momentum you would not "have more downward momentum" to convert. The downward speed (and therefore momentum, because p = mv) only depends on the height. It does not matter how fast you're going horizontally; if you just drop 10 feet you'll have the same downward speed if you dropped ten feet going 50 miles/hour. Just clearing that up cause I whole lot of people seem to think like that. It is true, though, that forward momentum makes it easier to just fall into the roll.

I guess that's not really what I meant to say. You would have the same amount of downward speed either way, but with the horizontal momentum from the jump actually gives you a reason to roll, due to that "reverse blocking" idea by Levi Meeuwenberg. If you were to just fall straight down and roll from a cat, there's really no point because the roll won't absorb much of the landing, it would turn more into a "jump, land, squat, roll out" as opposed to "jump, land, spring into roll" http://www.youtube.com/watch?v=0JoBLxFKkbM (2:25)

EDIT: I think we already went through this in the other thread :P
http://www.youtube.com/watch?v=ykbx-yzFgBo

"If you're afraid to fall, you'll fall because you're afraid." -Daniel Ilabaca

Offline Roberto Espinoza Jr.

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Re: Rolling or Cat-Hang to Drop?
« Reply #9 on: June 15, 2012, 01:03:03 PM »
Haha yeah huh? Sorry 'bout that.

Actually I think I just read your post wrong so it was my bad.
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Offline NMPK

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Re: Rolling or Cat-Hang to Drop?
« Reply #10 on: June 16, 2012, 01:00:17 PM »
You're value for the force in a roll is quite a bit off. You can't use impulse momentum in this case because you're using vertical and horizontal components. You're taking his downward falling velocity as your initial p value and his presumed horizontal exit speed as your final p value which is why you're getting such a small number.

Aside from this the more I think about it the more I dislike the impulse-momentum as a way of approaching a roll anyway giving the rotational, vertical and horizontal terms involved. Experimentally at least it's much easier to do with a pressure pad or accelerometer (which is how the oft quoted Fight Science crowd handeled it). Because of the complexities of the human body as an object (i.e. multiple limbs, even more hinges, uneven mass distribution etc.) coming up with an accurate theoretical description is tough. It might be profitable to just assume that in the limit of "perfect technique" the roll becomes spherical and then you could just model it as a ball with some given Young's modulus based on the squishiness of human flesh.

Will give this more thought and get back to you, as well as in regards to the numbers on the "reverse blocking" concept. I think there's a power loss in there somewhere i.e. 1-1 downward to forward velocity isn't even possible theoretically  let alone in actual application but again, this is gonna take some sketches.

Offline Roberto Espinoza Jr.

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Re: Rolling or Cat-Hang to Drop?
« Reply #11 on: June 16, 2012, 07:39:54 PM »
You're value for the force in a roll is quite a bit off. You can't use impulse momentum in this case because you're using vertical and horizontal components. You're taking his downward falling velocity as your initial p value and his presumed horizontal exit speed as your final p value which is why you're getting such a small number.

Aside from this the more I think about it the more I dislike the impulse-momentum as a way of approaching a roll anyway giving the rotational, vertical and horizontal terms involved. Experimentally at least it's much easier to do with a pressure pad or accelerometer (which is how the oft quoted Fight Science crowd handeled it). Because of the complexities of the human body as an object (i.e. multiple limbs, even more hinges, uneven mass distribution etc.) coming up with an accurate theoretical description is tough. It might be profitable to just assume that in the limit of "perfect technique" the roll becomes spherical and then you could just model it as a ball with some given Young's modulus based on the squishiness of human flesh.

Will give this more thought and get back to you, as well as in regards to the numbers on the "reverse blocking" concept. I think there's a power loss in there somewhere i.e. 1-1 downward to forward velocity isn't even possible theoretically  let alone in actual application but again, this is gonna take some sketches.

Yes I knew most of this already which is why I said "BUUUUT!" at the end of my post. I also mentioned how this was half-assed. Haha! And I did mention that I assumed the "reverse blocking" to shift all downwards momentum. I know this is basically impossible but I didn't want to deal with doing everything else. Although I do think that you could use the impusle-momentum method because this method is to find the average force isn't it? Also, if I had accounted for the horizontal momentum (I'd have to use a real-life example where a traceur would slow down), couldn't I still use the impulse-momentum method? I could just use the different x and y components of the momentum to find the average force in each axis, then use trig to find the resultant force, as well as the average angle it acts through, couldn't I? Of course, like I said this would be an average force on a person as a whole so...yeah. As you said the human body is very complex so it'd be hard to isolate any one part, such as the force exerted by a calf or quad.

And I have to admit I never even thought of the rotational motion. To tell you the truth I never really studied up much on rotational motion in my physics class. It was an Advanced Placement class, ya know the one where you take an exam towards the end of the school year and if you pass some colleges take it as college credit? Well since we had a lot to cover, our teacher thought it'd be best for us to only go over what's most likely to appear on the exam. I tried reading up on it myself but our book didn't go in depth. Plus I had to study what we were actually doing in class xD Not to mention my other classes.

Funny part is that I'm taking the class again my senior year just so I can read the book and learn more xD That way I can mostly concentrate on what I want to read since I would already know most of the material :)

I wish I did have a pressure pad or an accelerometer. That'd be sweet! xD

Although I am curious. How off do you think I am in my guess-timates? I really really would like to make more accurate measurements and calculations but I don't yet have the resources (or the smarts apparently there's a whole lot more I need to learn haha!) to actually do something like that.

It's cool to know another physics geek lurks APK haha!
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Offline NMPK

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Re: Rolling or Cat-Hang to Drop?
« Reply #12 on: June 17, 2012, 10:36:23 AM »
I could just use the different x and y components of the momentum to find the average force in each axis, then use trig to find the resultant force, as well as the average angle it acts through, couldn't I? Of course, like I said this would be an average force on a person as a whole so...yeah. As you said the human body is very complex so it'd be hard to isolate any one part, such as the force exerted by a calf or quad.

Yes you're exactly right on how you would go about it. My point was simply that in your calculations you treated horizontal and vertical velocity components as interchangeable when they are not. You seem to have a solid understanding of why though, i.e. perpendicular vectors are independent. It's why your value for the roll was tiny and you got .66 g's for average acceleration which is just way to low.

If we instead treat these momentum components separately we get a vertical impulse = m√2gh and a horizontal impulse of m(Vroll - Vjump. If you plug and chug this out you're going to see a couple of interesting phenomenon. First off the roll reduces your force in two ways the first of which is by giving you a greater time to decelerate. This aspect is the same in both the straight absorbed landing and in a roll longer interaction time is going to reduce your felt force.  Well according to this it would seem rolling serves no purpose as long as you're straight job takes equally long or longer to decelerate you, but how can that be?

The difference comes in the remaining aspects of the roll post foot contact. Remember how we seperated out the horizontal impulse term? Now neglecting air resistance your horizontal velocity when you first reverse block and punch the ground is gonna be the same as when you first jumped. This means that any horizontal impulse has to occur from said punch. This is the key to getting the values you're looking for impact force. If we plug numbers in it should be easy to determine an average value for horizontal force on the punch (and since this is such a short interaction time relative to the rest of the phenomenon we're observing we can treat this as the total force applied). From there we can use trig to determine how much force our punch applied vertically. Theoretical maxima for forward acceleration is at a 45 degree impact angle but since we have a lot more vertical force to worry about then a need to come out of the roll quicker, I think most traceurs tend to impact in the 60-80 degree range.

So now we have the total absorbency we're gonna need in the vertical sense. We also have a way to determine reverse blocking force in both the x and the y directions (and since this is the same object with the same mass we're talking about any time we can find force we can find acceleration and vice versa). So essentially at this point we just subtract the vertical impulse provided by the punch from the total impulse we need to stop. The leftover amount is going to be absorbed by the reduction in CoM radius provided by the roll, and the force you feel across your back as you roll. This force on your back is further reduced by the fact that Pressure = Force/Area so we're feeling less force than if we had taken the same acceleration on our knees or something.

So as you can see the more carefully and exactly we break this down the more equations and variables we're having to consider. This is why I didn't really put specific numbers in, there's enough systematic error (without an immensely complicated differential equation called a Lagrangian which would require taking into account all those limbs and uneven mass distributions), that any value actual value you get is gonna be more guesswork and error than calculation (since we have to presume mass, presume roll time, presume exit speed, presume impact angle, ignore air resistance and ground absorbancy etc. etc.). Instead it's better to analyze the system and see WHERE the forces come in and which variables affect them then to try and get any actually values theoretically. Use the theory to decide things like how to adjust your landing angle for maximum forward speed or absorbancy, or to determine why we tuck tightly for rolls, let it give you a better understanding of why you're doing the movements you're doing.

If you want actual numbers with something like this the experimental route is just worlds easier.

Haha and yes it is cool discussing the physics of parkour with those similarly interested. After all the "rules" of parkour are just the laws of physics!  8)

Offline Roberto Espinoza Jr.

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Re: Rolling or Cat-Hang to Drop?
« Reply #13 on: June 17, 2012, 11:58:27 AM »
Wow that was a nice read xD I actually had to read it twice to take it all in.

While reading that I also thought of the angle your center of mass, your feet (contact point/fulcrum), and the ground make. Was this the angle you were referring to? Because I understood that the angle you said (The 60-80 degrees) to be the angle the velocity makes with the ground.

Well anyways. The angle I'm talking about.....

Since your body is acting as a lever pivoting around your feet, which I presume would help shift some of the vertical momentum horizontally (am I correct on this?), your muscles' main job during the "impact" portion of the roll would be to keep your legs as straight as possible (by pushing down on the ground and of course absorbing some of the momentum in the process) in order for this lever, basically you, from working efficiently?

We also completely forgot to mention the roll (pun intended) our arms play. I'm sure they absorb some of the vertical momentum, right? Probably too small of a force compared to everything else, and in such a small amount of time to even consider. You definitely were right when you said that the more we break this down the more complicated it gets xD

Damn I've never even heard of something called a Lagrangian equation. I'm not even entirely sure what a differential equation is yet. There's very much to learn. But I've got time, I'm only 17 (actually 16 but my B-Day is in less than a month haha), to learn everything. And Google. Google is a very good learning tool when used correctly.

Let's see....opening Google....Lagrangian equation..... :o

I must learn this one day xD
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Offline NMPK

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Re: Rolling or Cat-Hang to Drop?
« Reply #14 on: June 17, 2012, 02:02:34 PM »
Wow that was a nice read xD I actually had to read it twice to take it all in.

Thank you, this has been quite an illuminating discussion. I was not actually talking about the angle your velocity vector takes with respect to the ground. This, if we remember our projectile motion is going to be outside of our control and dependent entirely on our velocity and height at initial jump. What we CAN control is the angle I was talking about and the angle which you brought up the angle between our body (imagined exactly as you say like a lever) and the ground and this is the angle which is going to determine how we feel the force. 45 degrees is the angle at which the force will be applied equally in vertical and horizontal components, 90 degrees being obviously pure vertical (the standard straight drop).

The other points you mention seem to fall into the distinction between the basic parkour roll and what is often described as the advanced roll. In the basic roll the main force mitigation comes from the increased interaction time in the impulse, which is why it has some added protection then a straight absorbed drop/slap but not very much. The "advanced" roll uses the lever mechanic you described to absorb a chunk of the downward momentum from the initial punch and convert it to forward momentum. Then it uses the arms to absorb a bit more force (you could describe this with an impulse momentum relation same as the other absorbing steps) and finally displaces the rest of the force along the back (though you can disregard what I said earlier about pressure I was confusing myself, if you think about it your back is only contacting the ground at a single point anyway). The more I analyze it the more I think the difference between the two is not in extra force mitigation but rather the much greater boost to horizontal momentum the advanced roll has going for it.

I'm impressed that you're only 17, props for taking ap physics in high school it's definitely worth it. Don't ever stop teaching yourself.  ;D

Offline Roberto Espinoza Jr.

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Re: Rolling or Cat-Hang to Drop?
« Reply #15 on: June 17, 2012, 02:43:14 PM »
Thank you :) As I mentioned earlier Physics is what I want to study in college when I graduate next year so I don't think I'd ever want to stop learning new things. Plus I'm a traceur so I have that make-yourself-better-every-day mentality :P

What would you say the "basic parkour roll" is? Because I've seen Levi Meeuwenberg's advanced pk roll tutorial a couple of times and I never thought that this was actually a different roll. I felt like his video was just for people who already knew how to roll but needed a couple of tweaks to get their roll better/perfect.

I'm guessing that the basic roll is the one where you use the stance to get the roll instead of the reverse blocking?

And I do think that the pressure thing was spot on though. You yourself mentioned the "squishiness of human flesh" :P So I do think that you'd cover quite a bit of surface area.
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