G-Force question

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>What is really causing the type of problem you describe is that the
>forces are applied in a non-uniform manner to the non-rigid system . . .

Well, actually I think the problem is applying a uniform field to a body which is not uniformly restrained. A common injury in impact, for example, is the aorta separating from the heart, because the two structures (aorta and heart) are not equally attached to the skeleton (the 'rigid' part of the system.) A very short high acceleration pulse may cause the heart and aorta to translate, but not over enough distance to cause them to separate. A longer pulse might.

In the elevator example the issue is onset, or jerk. A rapid onset pulse would cause the person to be rapidly accelerated towards the wall (well, in relation to the elevator at least) and then decelerated very, very rapidly when he hit the wall. A slow onset pulse would cause him to fall relatively gently against the wall and stop there; while on the wall he can better deal with the acceleration.

I don't see any fundamental relationship involving jerk that corresponds to Newton's 2nd law with acceleration. I haven't come across any constitutive relations for any material that involve jerk either. Surely you can analyze a non rigid system (modeling it with masses, springs and dashpots if necessary) using only the constitutive laws of the elements, the forcing function which is usually defined in terms of forces or displacements, and Newton? How does the use of jerk help the analysis? Does it simplify the system of equations or lead to some new insight in some way?

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Once again, strain-rate sensitivity is a very specific materials property, not just a response to varying stress - "jerk" has nothing to do with it.

Agreed. Jerk has nothing to do (in the sense that it does not affect them) with a material's properties, including its sensitivity to strain rate. However, I stand by my position that jerk is directly related to strain rate. So a material which, by definition, is strain-rate sensitive, I would also consider "jerk-sensitive".

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I don't see any fundamental relationship involving jerk that corresponds to Newton's 2nd law with acceleration. I haven't come across any constitutive relations for any material that involve jerk either. Surely you can analyze a non rigid system (modeling it with masses, springs and dashpots if necessary) using only the constitutive laws of the elements, the forcing function which is usually defined in terms of forces or displacements, and Newton? How does the use of jerk help the analysis? Does it simplify the system of equations or lead to some new insight in some way?

Honestly, a "jerk-inclusive" mathematical analysis of a real-life situation is probably slightly over my head at the moment. But one reason I've always loved physics is because it's so intuitive (parts of it, at least). I'll use my simple car driving example again. In a car which is being decelerated at a very large magnitude, my torso will be pressed forward against the seatbelt and my head may even be hanging forward with my neck bent, if the "G-forces" are too strong for my neck to hold my head upright. But as long as the deceleration is applied smoothly and then held constant, I don't think my neck would break. But a very rapid onset of deceleration (jerk), while my torso was constrained by the seatbelt, would give me whiplash, or if severe enough, break my neck.

You are right that the fundamental rules of force-acceleration dependence (Newton) are not altered by jerk. The surface force exerted on your torso by the seatbelt is determined ONLY by the deceleration and doesn't care about the jerk. And if your body was truly rigid (which nothing is, especially not a body), the whole system would not care about jerk. But intuitively I can see a less than rigid body getting whiplash as I described above. My guess is that a detailed analysis of the situation would need to describe the time-domain motion of every single part of the body. The overall difference in translational response (due to inertia) of the head and torso would be such that it would generate certain forces in the neck, and these forces would be higher in the high-jerk case, to give you whiplash. That's what I suspect... as much as I love discussing this I'm not gonna even attempt that analysis right now...

If you want to analyze the situation without considering jerk, and it is a situation where acceleration is dynamically changing, then you will only be able to analyze one moment of the entire situation at a time (a=constant), and I don't think that would be sufficient to see the overall picture.

Keep in mind it's not actually the force of the seatbelt on the torso that's causing the guy's neck to break (that seatbelt force isn't dependent on jerk)... it's the tensile force in his neck that his own head and torso are respectively exerting on each other... and this force comes from the dynamic response of each member to the jerking and deceleration of the car. This dynamic response will be different in a situation with or without jerk.

I think that's the center point of this whole debate. The actual simple forces transmitted from car to seatbelt to human are independent of jerk, as you and Newton would both agree. :) But the flexible body would respond inertially to its "one-point constraint"... and it would respond different based on different jerks (a phenomenon of motion, which would help describe the subsequent motion of the not-entirely-constrained body). These different motions of the different parts of the body would generate different internal impulse forces from momentum. Just like billvon pointed out with the heart and aorta separating.

And since it is impossible to constrain any system entirely, I think jerk will always come into play in determining the interal forces which build up in the system. But fundamentally, you are right... the jerk does not affect the forces transmitted to the constraint points between the "force giver" and the "force receiver". But if the force receiver is flexible and only connected to the giver at one point, the internal forces which arise will be dependent on the subsequent motion of all particles in the system, and inherently, dependent on jerk.

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If you want to analyze the situation without considering jerk, and it is a situation where acceleration is dynamically changing, then you will only be able to analyze one moment of the entire situation at a time (a=constant), and I don't think that would be sufficient to see the overall picture.

Keep in mind it's not actually the force of the seatbelt on the torso that's causing the guy's neck to break (that seatbelt force isn't dependent on jerk)... it's the tensile force in his neck that his own head and torso are respectively exerting on each other... and this force comes from the dynamic response of each member to the jerking and deceleration of the car. This dynamic response will be different in a situation with or without jerk.

I don't dispute that, but it just seems like giving a name to something for the sake of naming it.

I disagree that the analysis you describe would be limited to one instant in time, all you need to do is set up the time-dependent system of diffeqs describing the system in terms of Newtonian mechanics and behavior of the elements describing the body, and solve as f(t). That's how we model crystal lattice vibrational dynamics, and they are as complex as anything. Prolly need a numerical solution for a complex non-linear body.

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The only sure way to survive a canopy collision is not to have one.

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I'm very edit-happy in case you hadn't noticed. I edited my post about 298 times and was hoping I would finish before you read it. Make sure you read the last part. I'll reply more later, I have to go to bed. I enjoy this. :)

Hi Jennifer!

To much to read it all so maybe someone beat me to it but why don't you try contacting Larsen&Brusgaard (Dytter, ProTrack) or Airtech (Cypres)?

They should have done at least some testing of their devises (at least I hope so) and have a good grip on the amount and type of forces that occur.

My .02 anyway.

/M

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I don't dispute that, but it just seems like giving a name to something for the sake of naming it.

I disagree that the analysis you describe would be limited to one instant in time, all you need to do is set up the time-dependent system of diffeqs describing the system in terms of Newtonian mechanics and behavior of the elements describing the body, and solve as f(t). That's how we model crystal lattice vibrational dynamics, and they are as complex as anything. Prolly need a numerical solution for a complex non-linear body.

Yeh, my comment about having to analyze one instant in time was kind of a half-joke... because if you consider acceleration as a function of time (which as you pointed out would be necessary), you are admitting that jerk matters. But I see where you're coming from when you say that it seems unnecessary to name jerk. You're right that the whole situation could be analyzed without explicitly naming jerk, but it would be present in the variation of a(t), and I think that an in-depth anaylsis of situations where flexible bodies are subjected to low and high da/dt at a single constraint point, the results would show what my intuition feels... that the high da/dt situation results in higher stresses in the weak points of the flexible body.

That, to me, is why jerk is worthy of a name. Also, because it is something that you can physically "feel" pretty well. Admittedly there are 4th, 5th, and 6th time derivatives of position that have been jokingly called snap, crackle, and pop... this is obviously ridiculous because it is very hard (for me at least) to physically imagine the "real-life" results of one of these things. But jerk is very real to me... I get motion sick in cars when someone else is driving (depending on how good or bad they drive)... and it is not the acceleration at all which makes me nauseous, but the jerk (which is very well-named, since it causes the car to visibly "jerk" around!). I, on the other hand, drive like a jerk... but I think that's from your other definition.

One last thing, I think I will rescind my previous statement that there is a direct relationship between jerk and stress. As I stated above, the high da/dt situation results in higher stresses in the weak points of the flexible body, i.e. jerk can result in higher stress. But this is really a result of the complex dynamics across the body and its different particles reacting to each other's motions. In a direct, single-particle situation, jerk will have no affect on force applied to the system, and therefore I can't really say there is a relationship stress=f(jerk). Though I do still think jerk affects stress, it's more of a thing that happens unique to each body's construction (the stresses occurring at different locations than the jerk is applied) and there's not some missing law of physics that considers jerk. You are right about that. :) Hopefully this paragraph made sense... I was thinking about the seatbelt/whiplash example for most of the things I tried to explain...

I guess a simple analog to my mistake (when I said stress=f(jerk)) would be saying (incorrectly) that stress=f(velocity), because it was experimentally observed that the faster you drive a car into a wall, the higher stresses you create in the car's structure. While the observation is very true, it doesn't imply a relationship between the two. Velocity on its own creates no stress, it's the specifics of this situation which are allowing stress to be generated, and all of those specifics can be described by a Newtonian system of DiffEQ's. :)

In case you guys haven't noticed, malin is fine... her doc has signed her off to jump.

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In case you guys haven't noticed, malin is fine... her doc has signed her off to jump.

Mailin? Jump? Wha?

LOL!
Glad Malin can Jump!
Malin I think the biggest thing you need to be aware of is the placement of the generator. Most of them are placed in the sub-q space below the left clavicle and that could be uncomfortable during the initial phase of deployment as you get "jerked" outta the belly to earth position. Padding to spread that force across the area of the generator, maybe in a donut shape, could be helpful.
I also heard that a bad opening most of the time, as well as most malfunctions, can be attributed to bad body position at deployment. So be aware at pull time and make sure your slow and stable.
Good luck and keep us posted to your progress!

Blue Skies, Soft Openings, and Sweet Landings

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In case you guys haven't noticed, malin is fine... her doc has signed her off to jump.

That's nice. Now back to physics...