Thanks Omegacrash,

I'm not an engineer but, I think I know what most of what you are saying.
I have some info as follows about the two vehicles involved.
Pre-Impact
V1 is traveling south in a relatively straight line and weighs 1900 kg.
V2 is traveling north and turning left (at 30 degrees) and weighs 1200 kg.

The medium worn pavement is damp.
The PDOF (principle direction of force) on V1 is 30 degrees, making V2 PDOF 210 degrees ( as I understand it for V2).

Post-Impact
V1 is rotated (to its right) about 30 degrees to its right and travels about 24 meters.
V2 is rotated (to its left) about 140 degrees so it is now traveling south and traveled about 26 meters.

It is difficult to say how much braking was involved. How can one determine the slide to stop speed, what goes into the formula?

Regarding the crush analysis we do have most of that info. It seems that 'stiffnes' is the determining factor (along with the crush depth/length). What is this derived from when, V1 has damage 1/3 of the front corner wrapping around past the front axle, twisting the vehicle front end to its right? V2 has a nice V pattern to front end but, it also twisted to its right.

So, it appears that the angle of departure is the best option in this sample.  If, anyone can share the 'angle of departure' formula that will be appreciated.  I'm just some guy trying to figure it out, no dragging, I'm using Crash-Zone.

Well, the departure angles for each vehicle is something that has to be figured out.  It won't follow that if two vehicles meet at some angle, then the departure angles will be the complements of those angles.

This is usually done by having a scale diagram of the collision and using a protractor like you see here.

Sorry I can't be of more help, but I don't really understand your baseline angles to start with.  30º? 30º from what?  I haven't a good idea of what kind of coordinate system you're using, but I only know that you're not referencing your angles from standard position.

The work would be greatly simplified, I think, if you reorient your axes such that one vehicle or another is traveling at 0º.  Any information you can give on how you're setting up your frame of reference and what not would be quite helpful.




Fish wrote:

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More info:
The attack angle of V1 is 175 degrees, weight distribution F/R is 57/43. PDOF 30 degrees.  Deepest crush is 12cm
The attack angle of V2 is 35 degrees, weight distribution is 60/40.  Deepest crush is 30cm.
Angle of Departure is?

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Fish,
Breaking down the info a bit, in terms of the 'slide to stop', if you know that the vehicle was under maximum braking effect or for some reason all the wheels had locked then you can use a slide to stop formula. You suggest both vehicles 'slid/skidded about 24-26 metres to come to rest. The diagram suggets that one vehicle slid forwards, so just taking the slide forwards, the veh would be doing high 30's -low 40's mph when wanting to make the turn, and thats before accounting for any additional speed that may be credited towards the other vehicle. Firstly is that achievable on the approach to the junction?
The chances are that the vehicles were not under maximum braking for all that time post impact, so the values from the calcs become less reliable.
As mentiond above, small changes of the angles can make a big difference to the answers and it would be sound workings to have some variation in the angles to show how sensitive that aspect is.
Perhaps what I am trying to put over is that one can use the calcs and software to get answers, but you must also be prepared to accomodate the real world into it.

Looking at the plan, it seems too many profiels are labelled as veh 1.

Thanks for the diagram.  The scale and all that looks great, but I have a minor nitpick. Actually, it's not really a nitpick so much as something which confuses me greatly.

I'm going, for the sake of simplicity, change your angles to comport with the orientation of the protractor.  And I'll use directions (left, right, up or down) since North isn't on the map.  All of that is to say that on this picture, 90º will be my "north" (to the top), with 0º being my "east" (to the right). 

Now, on this, I see a car traveling along 0º (from left to the right); another one traveling along 180º (from right to left).  I presume these would be the original cars in question.  But you have them both designated as the same car "v1".  Now, I suppose that wouldn't be that much of a problem all on its own, but then there are two more cars, which I presume are the same ones after the collision, but you have one of those also marked "v1" and the other one unmarked.  And then in the middle of it all, where the collision happens, one of them has somehow become "v2".

Now, I know someone will say to me that it's obvious "v1" (which was later, I think, called "v2") is the car traveling left (westward) being spun around and pushed there, and the unnamed one is the car which was originally traveling eastward being the downward most one.  True enough, and I'd be willing to go along with that as one reasonable interpretation.  But, to my mind, it's going to get complex really fast once we start talking about the behavior of each car since 3 of them have the same name.  In other words, if I say "v1" appears to be doing _____, the question will naturally arise:  which one of the three "v1" are you talking about?  I suppose we can cure this by referring to left "v1", top right "v1" and bottom right "v1", but since we're going to have to do something to parcel them out somehow, I suggest we just give each one a different name.

In collision dynamics, it's pretty standard to let "v1" represent one of the cars pre-crash, "v2" represent the other car pre-crash, "v3" to represent "v1" post crash, and "v4" represent "v2" post-crash.

Anyway, I hope you won't think I'm being pedantic by bringing this up; it's really just so that we can all first agree on which "v1" we're talking about once we get into it.

Also, and I know you're doing this within the frame of reference of the direction "v1" (or I think what was supposed to be "v2" - see, confusing, huh?) is traveling, but the angle isn't actually 35º; it's true that the interior of the angle between "v2" and the horizontal is about 35º, but the angle with respect to its motion is about 215º.
Now, you can argue for using either as a reference point, and I'm fine with doing it whichever way you ultimately think makes the most sense to you, but one thing we can't do is change our reference point.

So, we'll have to set up a baseline and measure all things relative to that.  For instance, if the westward traveling vehicle is turn left and we're calling that 35º, then we can't turn around and call the other vehicle's angle of motion 175º because that would have the vehicles oriented in the same general direction. That is to say, of course, that would be traveling towards the same side of the paper, which means we'd have to turn around one of the cars to account for the angles as they appear.

In general, we want to pick one car's direction of motion as the reference and then work from that, which is to say that the eastward moving car has an angle of either 355º, or -5º, and the westward moving one has an angle of either about 210º, or -150º.  Now, that's in the mathematical sense which doesn't purport to speak for the actual direction of motion; it only deals with the direction of the angle with respect the standard position on a Cartesian map.  If we factor in the physics bit, then the negative is going to indicate the direction of motion with respect to some fixed point, which isn't what we're doing here.  For the mathematics of it, the sine and cosine values we care about will work out the same.

This is why I yesterday (or the day before?) suggested that when dealing with this, we take one car's direction of travel to be 0º and work from that.  This greatly simplifies the trigonometry by artificially forcing the axes to align how it's convenient for us.

If anything isn't clear here, please let me know and I'll be happy to clarify it.

Thoughts, anyone?

Fish:

Thank you for the additional data.  Off to the south, where the vehicles came to rest, does the surface they travel over change?  Or is it all the same?  Is it a grassy area?

The reason for asking is that dirt, grass, sand, whatever will have different properties, and the crux of solving this momentum problem is going to involve the summation of partial coefficients of friction over various surfaces, unless of course, it's all the same surface.

Did "v2" have its brakes fully applied, or did it coast to a stop? Or were some of the wheels locked and some not?

Thanks in advance, and sorry to ask so many questions (but a lot goes into making these things work)

Ok, thanks.

I'll have to play with this for a little while (which I think I'll do tomorrow first thing).  Tonight's a raiding night, so I don't think I have time.

Anyway, with the information we have, I'm not seeing why you'd want to use a crush analysis anyway.  Crush analysis is also an inferior method of gaining useful information, if it indeed can even give any useful information.

This situation can be elegantly handled with just momentum.

Does either vehicle have anti-lock braking systems on them?
Is there an elevation in the terrain - a slope or anything?
And what kind of asphalt is the roadway?

I plan on ranging the distances of sliding anyway, but it occurs to me that I don't have a range of coefficients of friction.  If you don't know what it is, that's fine, I'll make a best guess.  But any information would help.

I hadn't planned on using a database about the vehicles.  There is one potential source for error that can throw this all out of whack:  the momenta differences in the cars might be too great for momentum to work well.  I haven't done any calculations because I started making a list of knowns and unknowns and realized I was missing some information.

Sorry for the delay in all this, but it's summer and a boy has stuff to do!

-- Edited by ashman165 on Friday 31st of July 2009 08:18:58 PM

Fish wrote:

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Hi Ashman165,
After a raid party (not sure what that is) and these hot days-- summer fun has got to set precedent--that said I do appreciate your enthusiasm.

Oh, among my many activities to waste time, I play World of Warcraft.  I'm in an end-game raiding guild (basically, we deal with the hardest content in the game).  Raids require the coordination of 25 people to carry out a set number of tasks in a reasonable order in response to a the fights' mechanics.  In any given fight, there is a predictable set of events, and then there are the events generated by the random number generator, which require extremely complex mathematics to create.  The variable for any given player's character to maximize his damage, threat or healing is boggling, but taken in conjunction with 24 other players who have to fight server lag and computer limitations, this gets more difficult.  Add to that the fact that there are non-player controled characters (the bad guys generated by the game), and things get even more challenging.  The most challenging thing, I'd suggest, is that you have two prime components to game interaction:  your attempt to interact based on when you get data, and the server's response to your actions.  Sometimes there's a lag component of a few tenths of a second, which is the difference between success and failure.

As such, raids can take several hours to progress through "farmable" content (content which has been done successfully so many times that it doesn't require as much focus).  But then there are progression nights, where we can spend many, many hours failing on the same fight while we try to learn its mechanics and develop strategies to overcome the unknown.

I'm beginning to understand the Conservation of Linear Momentum idea, to get the angle of departure. One reconstruction guy pointed out that the PDOF of 30 degrees for the Van is if, the Van was stopped and got hit by the Car but, both vehicles were moving. Secondly, he pointed out that the PDOF should be a shallower angle about 15 degrees because of the depth of crush and lateral scuffing.

Yeah, it's not the easiest thing to wrap one's mind around.  And there are further issues which compound anyone's ability here to be of precise help to you:  we have to rely on second or thirdhand information.  That isn't to say you're misleading us or anything, but in science, primary information is always preferred.  Plus, you don't know what we need to know at various stages in the process.  And I don't think far enough ahead to predict what I'll need to know that I don't know right now.  The list what I need to know comes along as I play with the scenario.

I suppose I should give you fair warning; I don't do this professionally, though I used to.  I'm a cop turned mathematician, thus a lot of what interests me doesn't have a great deal to do with the actual arithmetic.  That's why I'm not a professional engineer or physicist.  I prefer dealing in abstract mathematics, and I tend to put off doing the actual calculating bit as much as possible.  It's just tedious to me. *shrug*

That said, I'm not sure if I understand this one reconstructionist's reasoning.  He might be thinking about what the angles are when the vehicles finally reach a common velocity, in which case I'd agree that angle will be different than the approach angles.  But it's far from certain that the angle would be less eccentric.  How the angle shapes itself during the initial part of the collision through maximum engagement will largely depend on how the materials deform.  This, in turn, depends on overlap of the surface areas of the vehicles when they collide.  Since these things aren't knowable to us, we don't ordinarily work through the tensor analysis of the situation.  We reduce the behavior of the vehicles to what their centers of mass are doing simply because orienting the vehicles precisely at each moment of the collision is arduous, and not usually that important.

The only time it becomes exceptionally important to make sure that the approach angles are as precise as possible is when the original angles are extremely small.  Of course, it's intuitive to think that because 15 is half of 30 that a change in the angle by a factor of two will necessarily halve or double some other part of the system.  That's not necessarily the case because we aren't dealing with the angles themselves per se; rather, we're dealing with their sines and cosines, which aren't linearly scaled.  In some cases, a change of half a degree can result in several orders of magnitude of difference, in other cases, a change in an angle of fifteen degrees doesn't make a great difference.  Yes, there will be a difference in all of the, but the degree of the difference isn't intuitive.

All of that being true, I see no reason why this case isn't solvable.

 

BlueB wrote:

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So, the question is.... what ae you trying to achieve and what range are you hoping to ascertain?

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Excellent question; here's why. On V1

The opposing engineer took measurements of the crush damage.  More importantly gathered up the airbag system to subrogate the  airbag manufacturer because the passenger side airbag broke the plastic surround and cut the 'driver'. (Snide Comment here: who drives from the passenger side of the vehicle?)

The V1 'driver' says the seat belt was being used properly and their engineer does not oppose that. Witnesses say 'driver' is not the driver.

The airbag system should have some of the missing data, impact speed on airbag deployment, throttle position, brake pedal position etc.  Number of face prints on airbags as V1 had only one occupant.  Non the less that info is not available to us, yet.

On V2 the crush measurements have been taken.

Therefore, we are looking for speed analysis that is a reasonable, and correlates to the amount of crush damage to the vehicles in question.  We are sticking to the facts that we have and not on fantastical stories and lucky charms...

The answer Veh 1 = 23mph Veh 2 = 42mph numbers seem very close if, you mean the turning vehicle = 23mph and straight moving vehicle = 42mph.  A small range is probably the best we can do with th the info at hand.

 

-- Edited by Fish on Saturday 1st of August 2009 07:28:58 AM

Sample two seems to be some sortof reconstruction. Alas to me it had absolutely no value compared to the info you have gioven above. It seems that the veh which continued through the jucntion had also impacted the veh turning left, but has never been mentioned or involved in th eincident.

i only gave the speed of 23mph/42mph as examples, not based on calcs as a means of asking how close you want the result to be. On the info given, you may be able to get some indication of speed loss during impact, but what happened before and after impact is so unclear and 'ffy' that you would not reasonably be able to utilise it

Ok, now I'm confused nine ways to Sunday.

You keep talking about crush analysis.  If that's what you're interested in, then none of this information is relevant.  Crush analysis is the least accurate method of determining speed there is. 

I also don't know about the advice which purports a range where the upper bound is twice that of the lower bound.  That is of absolutely no use.  If a range so large is the best one can do, then one needs to work in another field as it will be the very, very rare case where a speed range of use can't be determined.  Indeed, I can't think of any set of circumstance where it can't be.

I'm also confused; you have a reconstruction guy working for you, right?