DeltaV

Probie · Member

DeltaV

ashman165 · Veteran Member

Hi, guys! I'm not quite sure what to think of the new forum, but I'm sure I'll get used to it.

Anyway, on to the question.

I'm taking PDOF to mean the principal direction of force, which in this case is confusing to me because:

it's a side impact collision; and
you can't have an angle of incidence greater than 180 degrees, at least in a purely mathematical sense.

From what I can imagine, since it's a side impact collision with an angle close to 180 (which could be either 170 degrees to 180, or negative 170 degrees to negative 180 - a post I had on the old forum which is too lengthy for me to want to write out again explains this in more detail), one of the cars is sliding sideways?

Now if my imagination is properly envisioning the orientation of the cars, I get confused about your impact speed with respect to at least one, possibly both, of the cars.

Now, as far as my statement goes about not being able to have an angle of incidence greater than 180 degrees, I'll just say to let me worry about the quadrant issues for my own calculations - meaning we can stick with your 190 degree PDOF.

But, to actually work this through, I'd need approach and departure angles for both vehicles, but in general:

change in velocity for vehicle 1 is approximately equal to:
sqrt{[(v1^2)+( v2^2)] - [2(v1)(v3)cos(theta)]}; and,

for vehicle two we'll have:
sqrt{[(v2^2)+(v4^2)]-[2(v2)(v4)cos(beta)]} where beta is the difference between the approach and departure angle for vehicle 2.

This series of equations will tell you the CHANGE in the speed of the vehicles *at* impact, which isn't saying they'll you the speed of each vehicle *at* impact - the former being the change in the rate of the speed (acceleration) while the latter is change in the vehicle's position with respect to time.

Not to add more pressure for you, but when you're dealing with angles near 0 degrees or near 180 degrees, it's extremely important that you be as precise as possible because even a minor error in the angles can yield relatively dramatic alterations in the speed reported from the calculations.

If you have more questions, or want to provide more information, post here and I'll take a look at it next time I remember to log in and read up.

Regards,
Johnathan

Probie · Member

Johnathan, I thank you for your time in answering my question and I will study you equation and put it to my problem.

I will have to play with it a bit to find out what the V3 and V4 in your equations stand for.

As for the PDOF... what I meant to say was that after impact veh2 had a dep. angle of 170 deg. Veh1 maintained the path it was on prior to POI.

Thanks again, it is muchly appreciated.

-- Edited by Probie at 15:03, 2008-05-30

lewpytel · Newbie

Delta-V is simply the difference between the incoming and outgoing speeds.

In other words it is the difference between the impact speed and the post-collision speed.

ashman165 · Veteran Member

Oh, I'm terribly sorry for the confusion. I should have defined my variables in the original e-mail. Vehicles 3 and 4 are used to designate vehicles 1 and 2 post impact, with vehicle 3 being vehicle 1's departure and vehicle 4 being vehicle 2's departure. Again, sorry about that.

CrashXprt · Member

BE CAREFUL! Delta-V is a vector, and as such, it has magnitude and direction. That means that there is a bit more to it than simple subtraction unless the speed change does not also include a direction change. DV can be very confusing, but a good way to get your head around it is to calculate it using vector diagrams, at least until it becomes familiar. If you use a CAD program to draw the vectors, it makes it much easier than using a pencil and a scale.

Some would argue that when a vehicle experiences a rotation in its postimpact trajectory, the angular component must be taken into account as well (another vector), and many simulation type programs do so. Another caveat to delta-V is that it is a localized phenomenon, i.e. different locations on the vehicle can have radically different delta-Vs especially (or only) when there is a rotation induced by the impact. In general, however, for most crashes the rotational component can be ignored when calculating DV - unless you have a high number of postimpact rotations or there is some other reason you need such precision (like for those pesky bio-mechanics experts).

I'm sure you are aware of all of this, I just wanted to post a message to the new forum. It's been a while since I was on the ARC site. biggrin

-- Edited by CrashXprt at 09:18, 2008-07-10

ashman165 · Veteran Member

Indeed, David.

Ok, this will be my third post on this topic - the latter two of which were to address my first post. I was writing in haste and was lax in my language, and notably, structure. I apologize for any confusion I might have caused.

David brings up a point alluded to in my first post - velocity versus scalar quantities.

Velocity, by definition, is always a composite vector quantity (or even quantities) whereas speed can only ever be scalar.

As I said above, speed deals only with the change in position with respect to time. That is to say that a vehicle has occupies some space, call it p1, at some particular time, call it t1. Now at some other time, call t2, the same vehicle now occupies a space, call it p2. The speed is a measure of the two spaces (and p1 can equal p2) as compared against the difference in time.

Velocity is a little trickier because it's a vector quantity. That is to say that this concept takes into its consideration both speed (called magnitude), and direction. That essentially boils down to the fact that when we speak of velocity, we must not only state the speed, but also the direction of that speed. This is why the approach and departure angles become important.

Actually, reading over my first post, I shouldn't have posted it.

Delta V is math shorthand for "change in velocity", which means that we have to factor in all components of what a velocity is (speed and direction). So, delta V can further be described as shorthand for "change in speed and direction) before and after a collision. Keep in mind that the change in either part of this component can potentially be 0 - but not in both. That is to say that the angle of approach may be the same angle as departure, or that the speed befoer and after may be the same - meaning only one changes. But it can't be true that both remain unchanged. At least one has to change, usually - but not always - both.

David is, of course, correct when he says that different areas of a vehicle might have different deltas V. Not only might that be the case, it will always be the case in the type of collision we are currently discussing; namely in that, we're dealing with non-straight angle collisions. Since that is going to cause some rotation (in at least dimension), different parts of the car will travel at different speeds, implying that different parts of the car will have to change their velocity faster or slower than other parts.

David is again quite correct that in most crashes, we ignore rotational analysis and speak about the center of mass of the vehicle and what it's doing. Besides, it would be wholly unworkable if we had to account, in all reconstructions, for what the front driver's side fender is doing in relation to the passenger side seatbelt anchor.

And on that note, I'm heading to bed.

Regards,

CrashXprt · Member

Johnathan,

Excellent point. I suppose I did not consider that (in theory) a change in direction without a change in speed can be described in terms of delta-V. Of course, this is a rare bird in traffic accidents, but I suppose it does come up from time to time. Along those lines, I am curious to get your take on the relationship between delta-V and the restitution of a collision. There are various definitions and formulas that seek to describe e, and many of them involve delta-V, momentum, and/or energy. If you have a minute, see my other post and any comments you might have would be greatly appreciated.

ashman165 · Veteran Member

The restitution of a collision? That's usually handled by the court. *chuckle*

Sorry, I couldn't resist.

To answer this question even adequately could be quite a lengthy conversation given that concepts of energy and momentum, while related, are entirely different - and often not well, if at all, understood by most people.

But, I'm going to assume that for the sake of brevity (and your working in this field) that it's understood by all. If not, I suppose we could start a new thread discussing them in greater detail.

I have learned to shy away from writing out mathematics here because the applet here isn't exactly friendly with symbolic notation beyond basic mathematics. So, I guess words will have to do as well as they can. (Can we please get an equation editor here?!)

Without doing any actual emperical study of this, I'm going to speak from my first guess perspective on delta v and the restitution of the system based on what seems to be the likliest expected outcome.

I think we're all aware that behavior at high speeds is different than behavior at lower speeds. Similarly, obligue angles are more eccentric than straighter angles when a collision occurs. This is probably true both from a relative perspective as well as an absolute perspective.

The relative perspective has to deal with the potential of vehicle materiel to deform thus absorbing the forces without altering trajectory - only speed. Like, say low speed rear end collisions. Now, the force absorbed there and the deformation of the materials accounts for the bulk of the force available. So, it's a relatively great portion of the quantities.

At higher speeds, the ability of the materials to deform is neglible compared to amount of force brought into the equation. This is what leads to trajectory changes.

This, of course, makes intuitive sense. We expect higher speed collisions to result in more violent behavior upon impact.

After all, every substance has a maximum potential to deform. After it can no longer deform (which we call maximum engagement), we get the separation and all that fun stuff. This is the thrust behind making "softer" cars. The idea being that we want softer materials which have greater capacities to deform so as to reduce the eccentric behavior of the vehicles when they separate.

Now to your point about delta v and restitution. As has been pointed out in this thread, delta v takes into account both speed and direction. Restitution can be understood as to the ability to absorb energy. The less energy we have in the eccentricity during the collision, the less the delta v likely will be. At least in the middle cases - the extreme cases won't really matter much because either the force absorbed is so great as compared to the forces brought into it that the materials don't really matter, or the forces absorbed are so small in comparison to the forces brought in that the mitigation is neglible. Basically, if it's a 1 mph collision it doesn't matter. If it's a 100 mph collision, it won't really matter.

The first case we don't really care about. The second case happens so rarely that it's not worthwhile to invest the funds in the technology to mitigate it - assuming that we could seriously mitigate it with modern technologies.

So, that brings us to the momentum/energy concerns (force through time, or force through space) issue. The greater the time (or distance) we can dissipate the energy or momentum through, the better. This is directly related to the coefficients of restitution of the vehicles. In turn, the delta v is directly related to stiffness of the vehicles in question. There's more to consider than just that: surface areas, approach vector and the like. But that's my general take on it.

About the definition/formulae thing, yeah. That's true with many things because we like to define things in convenient (insert laugh here) terms relevant to what we're interested in at the time. From that, we generally work to more and more abstract rules. But, in essence, they're all really the same thing - just situationally adapted for brevity's sake.

I'm going to track down your other post and have a look.

- Johnathan