It isn't relavant to his question what the speeds in this case may have been. His question is entirely about where does using 1.0 as the CoF come from, and why this is so.

It also not relevant how the body came to be rolling, flopping and bouncing this way. It plays no role in evaluating this.

Ken, I don't know that using 1.0 is the right way to go. 2 reasons, you're indicating by the 0 that this number is derived from a piece of equipment sensitive enough to calculate/measure out to the tenths place, but that it just happened to be 0. I doubt that's the case.

Now onto the 1 part. If the CoF is 1, this indicates that 100% of the pull of gravity is being used. Remember that static friction is greater than dynamic friction. Static friction occurs when two objects have a common velocity. But I don't see how that relates to a rolling body as there's no extrinsic retarding force applied to the body So, it's essentially a rolling, uneven wheel that bounces and flops and stuff like that.

Though I don't know where they got that 1 from, I can only say that something stopping by using 100% of the gravitational grounding capacity will stop faster than something using a lesser percentage. We know this from watching sliding cars.

But this body isn't sliding. It's flopping, rolling, bouncing and all kinds of other fun stuff. So, it doesn't fit as a skidding object. Nor does it fit as a rolling object. Nor will airborne equations help you, at least not *during* the part where he's sliding, bouncing and what not.

Though I agree with Blue that anything which can make a human body roll for a football involves some reasonably high speed, it isn't relevant to your question.

Here's where the problem comes in. The mass of the human body is insignificant when compared against the forces acting on it in a situation like this. Since this is the case, the body will tumble in completely unpredictable ways, meaning that its rotational velocities with respect to the instant moments will change quite rapidly based on the orientation from one bounce to the next. This will dramatically alter the CoF at all of those indefinitely many contacts. So, you can't get really get the CoF at any specific point.

All you can do in this case is get an average over a long period. This will require multivariate calculus to do. And I can't type that in here because we have, still, no equation editor here.

Let me think on this and see if I can use simpler math to explain what's going on.

Ok, I'm back. I'm not having a lot of luck after mulling this over a smoke and coffee. I've gotten a general case from calculus that's relevant, but I'm not sure how best to explain it. That isn't to say that I can't explain the math, I just can't figure out how to make it understood in this context.

Also, we'd need a lot of data point, which we can't have here since you showed up afterwards.

By the way, I'm more talking this through to myself right now. Don't mind me.

Ok, sorry about that. It's true that body isn't in contact with the ground during parts of this. It's more the case that the body is rarely in touch with the ground during this, which is to say that most of the time it's airborne. So, from that we can conclude that most of the time during this, there is negligible loss of speed. This in turn requires f to be extreme in the few instances when the body hits the ground. That does, incidentally, account for the extreme rotational velocities we expect and see as well as the other odd behavior.

To come up with a number for f, there would have to have been some experiments done. I haven't seen them if they exist.

I'll have to think more on this and write about it later. I don't have a readily available solution for you more than what I've written, which is decidedly inarticulate and unhelpful.

Well, if you can pinpoint when the body was ejected, and where it first landed, you needn't consider the tumbling bit.

The speed at ejection will be roughly the same as the speed at the first touchdown.

You can use all of that to solve the system for your purposes, but I'm still mulling over the original question.

Since we'll have some initial condition and an ending one, the problem is simplified considerably as we can more or less model the deceleration of the body with some function.

The average value function which would then apply is [1/(b-a)] [integral f(x)dx], where f(x) is the velocity function found to model the deceleration of the body, b is the upper bound and a is the lower bound of integration, in some units of time.

It's late and I'm tired. I'm still going to have to do more thinking on this.

I must say this is an interesting questionl; thank you for bringing it up. ^_^

The vehicle entered a critical speed yaw and yawed to the left. The vehicle began to roll to its right side over and immediately there is a blood trail that begins and follows a straight line to the body at final rest. i said 300 feet but the exact measurement was 268 feet. I put the 268 feet into the slide to a stop formula with a COF of 1 and the result is 89.6mph which would be the point from body impact to body final rest. Since he was ejected out of the moving vehicle then I would assume that the vehicle was traveling at least 89.6 mph even though witnesses said that he was doing 100 before he even entered his yaw.

I don't have the measurements from the yaw and this witness is VERY reliable. I wish I could give more details but this is a criminal case awaiting trial. It involves high speeds, alcohol, drugs, and death. You know, plenty of job security for us all.

Ken,
I have to agree with Ashman.  If you get the speed of the vehicle from the yaw, trust me, the body was ejected at that speed as well.  If a vehicle is moving at 60 MPH, so is everything else inside of it.  If you try to explain the drag factor of a body tumbling when it is not necessary to do so, you may open up a can of worms that does not need to  be opened. 
The yaw mark is going to be critical for your case.  That absolutly needs to be measured using a 30-50 foot chord.  Critical speeds obtained from yaws, if done properly, are very accurate.  Make sure you obtain a good CoF from the surface the yaw was made on.  (If I sound condensending, I'm sorry, but I don't know what your level of expertise is.)
As for obtaining a 1.0 CoF for a tumbling body, I'm sure that figure was obtained through a series of tests.  I was looking through my reconstruction manual on pedestrians (IPTM) and they have the Cof as being between .90 and 1.0.  But like I said, don't go there if you don't have to.
I don't know what type of vehicle you have but have you considered downloading the Event Data Recorder?  The information you obtain would give you a good information to let you know your investigation is going in the right direction.  Depending on the type and age of the vehicle, it can give you such information as speed, Delta V, braking, acceleration, throttle percentage, and maybe even more.  Even if the airbags did not go off, there could be a "non-deployment event" recorded.  You still have to investigate and gather data to support what the EDR recorded but like I said, it lets you know that what you are doing is correct.  Your information will not be exactly what the EDR recorded but it should be close.  Just something to think about.

Craig

-- Edited by omegacrash at 21:50, 2008-09-19

-- Edited by omegacrash at 21:53, 2008-09-19

Ken,
appreciate your comments on the reliable witness, but even well versed police officers who deal with asessing speed against known devices still have prblems getting the figures close as the speed of the vehicle increases, especially when they may not be expecting to have to asess the speed, ie sudden accident.
Do have a cof for locked tyreroad surface in which case you could consider some other options or will that be estimated as well
In terms of the body tumbling along the road, was it lots of time in the air or on the road.
Appreciate your initial comment was asking how to explain the tumble, but no it seems it is to do with trying to asses the veh speed ( Sorry already rasied this earlier)Try some simple calcs, so a 45 trajectory ( optimal agle) gives an initial velocity of @ 64mph, but a lesser angle (22.5 degrees) does give a slightly higher speed but of course one would have to justify anything other than the optimal and horizontal angles.
Presumption of sliding the whole distance on the ground where mu is assumed at .6 gives about 70mph. Even raising the mu to 1.0 is 90mph, but you make no mention of significant entanglement or big hits to the ground so perhaps 1.0 is not so easily justified.
Looking back at the numbers, I would be very careful to make sure I am doing the sums to ascertain a speed we can jsutify rather than simply look at how we can agree with the witness whom we already know is likely to exaggerate the vehicle speed.

ashman165 wrote:

---

How do you figure either an optimal angle or a horizontal angle doesn't require justification but any angle which is a departure from this alleged normative angles does?

There is nothing of particular specialness about 45º and 180º which makes them presumptively correct and any other angle presumptively unusual.

-- Edited by ashman165 at 14:57, 2008-09-21

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In many instances of dealing with trajectory, if the angle is not known or approximated, then 45 is the usual number to use.  And of course, it is about mid way between horizontal and vertical

Blue, I'm fully aware that when the angle isn't known, it's common for people to use 45º as the default angle. Thank you for bringing that to my attention and entirely neglecting to answer the question I asked of you.

Now, back to the question: how do you figure there isn't anything particularly special about 45º? True, it is about midway between 0º and 90º. This, however, doesn't make it a particularly special angle in collision dynamics. It is a special angle in mathematics; particularly this is so in trigonometry and its progeny.

I'm not trying to bust your ba . . um, whatever you have. I'm just trying to figure out why people use 45º as a default angle instead of trying to actually determine the proper angle to use, or a rough approximation.

I wish we could somehow get posts from the old forum so that we could copy them into here because I had a nice run down of angles and their importance.

It is, of course, true that angle nearing 45º are less sensitive to error than angles nearing the horizontal, or even the vertical. But the absolute error between, say, 1º and 45º is significantly greater than absolute error between .5º and 1º, but the relative error between 35º and 45º is substantially less.

This doesn't, however, provide any reason to think that assuming 45º is a safer bet than assuming any of the other angles as they're all nearly as equally likely to occur.

I could well be missing something here, which is why I'm asking what about 45º makes it a better angle to guess than say, 72.5º.

Ken, it's my pleasure to be a part of this discussion, and to read all of the replies in here.

I have only a minor point to make: 45º is not halfway between 0º and 180º. It's a quarter of the way there. 45º is halfway between 0º and 90º.

I understand the logic behind behind the thinking though.  It's that at 45º, the sine and cosine values are equal.  So the horizontal and vertical components in the vector are equal.  I understand the temptation to say that because those two are equal, it should be the least amount of force required to launch a projectile a certain distance.

Now, it's true that given a particular force, we will optimize the distance traveled by launching something at a 45º.  If we use an angle less than that, the object doesn't have enough height with respect to its horizontal velocity to travel far.  If we use an angle greater than 45º, we get too much height and not enough horizontal velocity so the object doesn't go as far.

That's the reasoning behind the assumed take off of 45º.  God, I've been thinking about this for days off and on and it just came to me why that assumption is made.

It's moments like this when I like to remind my friends why I wear shoes without shoelaces in them. ^_^

This is a good time to note there are great reasons why we mathematicians work in groups.

-- Edited by ashman165 at 07:40, 2008-10-03

Huh?