Safe Speed Forums

I've been pondering the graph that shows the frequency distribution of crash impact speed.

It's going to be a very strange graph indeed.

There's a bit of Australian junction crash research that showed about a quarter of crashes taking place without braking. (But that doesn't mean that the crashes took place at "free travelling speed" - in some, possibly many, cases speed will have been reduced in the danger area.)

Our own accident severity figures show that high severity outcomes are comparatively very rare. See this page: http://www.safespeed.org.uk/ten.html

The braking distance graphs appear to suggest the opposite:



We'd expect very low speed impacts to be rare because the distance covered at lower speed is less. Or is the time based view more useful?



The time based view doesn't show the bias towards higher speeds.

(graphs from http://www.safespeed.org.uk/braking.html )

Pedestrian crash data does not support the idea that crashes at free travelling speeds are frequent. See the panel "30mph is a deadly speed" on page: http://www.safespeed.org.uk/why.html

This is the graph referred to:



Finally, the number of non-impacts is absolutely enormous. so do we have a very high frequency of 0mph impacts?

So what shape is the damn graph? Let's start with a simplified case, where the free travelling speed is 35mph - a pretty typical urban situation.

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Paul Smith
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on figure four, would it help to put a time line,


at 30 mph there is less time to impact than at 70 mph.,

this may allow two things to happen

car driver to brace himself, or duck !

pedistrian to jump out of the way..

or on the other hand the time graph superimposed on this one may not help.


the opther thing that interests me ( as an idiot, ) is the line that can be drawn from about the 10 mph spot upwards where the curve starts in each speed shown.. thats going to mean something.. not quite sure what .. got to rush, so will pose the question and look for the answer later !

rgds
bill

I sugest that the question may be slightly counter-intuitive, since it is an attempt only to analyse accidents which have occured, not situations where accidents have been avoided.

I'd go for something like the df=3 line on this page
http://www.math2.org/math/stat/distribu ... i-dist.htm

I don't understand what the distribution is intended to represent, but it has the correct sort of shape.
The line must pass (0,0) - no impact can occur at speed=0.
There is a rapid rise in the probability of an accident having occured at a low speed, since the majority of accidents are 'almost avoided'. This is likely to differ from a graph of 'free' speeds for the location, which might be closer to the df=4 line.

Above some point, the probability of an impact occuring at a specific speed will tend to exponentially decay to zero, becoming <1 in 3000 at maybe 150mph...

Given a impact speed distribution, and a known relationship between impact speed and fatality rate it shouldn't be too hard to determine the median of a suitable distribution (we already know that a delta distribution requires a mean of 12mph)

Sean

I agree with tsh. There is no possibility of an impact at 0 mph, so the probability on the distribution model has to drop to nothing before 0 mph. There can be impacts of one kind or another at any speed over zero, although your average free-traveling speed 'limit' of 35 mph means that there will be few instances of cars at (say) 55 mph (especially if there are cops or cameras around!), so I would expect the tail of the distribution probability to trail off to near zero somewhere around that point. So there are the two end limits. But where would the peak of the graph be, and what would be it's shape? Some accidents will happen as the Australian research shows, (hazard became real so quickly that the driver could do nothing). But I'd expect most hazards to become real slowly enough to allow most drivers to both recognize it and do 'something', which would lower the speed at which the greatest number of impacts happen down somewhat. Intuitively, without evidence of any kind, I would suggest this point to be in the range 10 to 15 mph. This would result in a graph that ramps up rapidly from zero to peak at (say) 13 mph (the point where most impacts are expected to happen) with a long tail, extending to 55 mph. This fits tsh's chi squared df=3 model quite well.

A non-impact is harder to conceptualize. That is because non-impacts happen all the time at all speeds but zero. It does no good to talk of impacts and non-impacts when there is no relative movement at all, as far as I can see.

There is no definition of a non-impact, other than to say that

As the NumberOfPossibleImpacts is near infinity (one happens every time you pass near any object), while the NumberOfActualImpacts is very finite, NumberOfNonImpacts is a colossal number, so the probability of one happening to you in your car at a certain point in time and space is also colossal. So one could say we have a very high frequency of > 0mph non-impacts. I think!

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I stole this .sig

I would disagree with the proposition that there is a finite upper bound on impact speed even for our 35 mph free travelling speed (was that supposed to be a 30 or 40 limit?). Excluding artificial factors, a significant proportion of vehicles will be in the 55mph bracket. Some (1 in 10000???) may even be over the 70mph bracket.

Take as an example the guy who put his scoob through a house, flat out in 3rd - in a residential area!

Another data point I have is some (not very significant) data indicating that partial closure of a road in cambridge reduced traffic flow, and increased accident rates (without significant speed increase). The adjoining road which took the diverted traffic became more conjested and provoked a drop in accident rate. (see cam.transport newsgroup). I think this shows that whilst impact speed distribution might be interesting, the connection to the normal traffic speed distribution might be not well correlated.

Sean

I broadly agree with the analysis posted by tsh and basingwerk, But I'm very worried by the likely "moderate" frequency of crashes at free travelling speeds. Let's make a wild guess and say that 10% of crashes take place at free travelling speed, and let's assume for the sake of discussion that all our causing vehicles are travelling at 35mph in a 30mph zone. This would give a much higer than expected frequency at the top end of the scale.

I also happen to believe that we should epect smooth continuity between crashing conditions at finite speed and missing condition at a "by definition" 0mph. If we can't "get our heads around" this discontinuity problem, then let's instead look at a distace representor of crashing. In this model, we list impacts or non impacts by reference to the stopping distance. If there's no impact we have stopping distance in hand and the measurement is positive (the distance between where we stopped and the point where we would have crashed). If we crash then we are within our stopping distance and the distance is negative (measured to the theoretical stopping point without the crash). Where's the discontinuity now? It's gone right?

If you want my opinion, we're in deep trouble trying to make sense of this. I'm guessing that the problems we're facing come from the psychological domain, and don't fit well at all into the physics domain.

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Paul Smith
Our scrap speed cameras petition got over 28,000 sigs
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I am not up to all the maths u guys are talking about,

so going back to my first post..

looking at the line I wanted to draw, but u ignored

I guess it crosses with the following numbers of feet to go before impact.

6, 15, 20, 25 35,

the curve is turning down, ie speed. there is still a distance to run, suggesting to me, that there is more time in the last split seconds to react and avoid an accident..

bear in mind , we look where we are going to be driving, the faster we drive the further we look ???

must be bollox.. but maybe it will spark u into making a better examination than I have .

rgds
bill

How do you guys feel about this:



See my post of 6:40pm today.

Damn - I see I've transposed the signs. The negative values on the x axis are the misses.

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Paul Smith
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I am paying close attention, Bill, and I appreciate your input. You haven't triggered anything yet, but please don't let that stop you from trying.

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Paul Smith
Our scrap speed cameras petition got over 28,000 sigs
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Just found this again that I was looking at months ago:



I suspect that there may have been impacts at the low end of the distribution that simply were not severe enough to be recorded.

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Paul Smith
Our scrap speed cameras petition got over 28,000 sigs
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Incorrect, a 30 mph limit road layout is very limited on time to impact. As you would normally be in a built up area, and not spot a hazard until you are on top of it. Thus giving you less time until impact.

A 70 mph limit road layout, however is in the open with good visibility for all approaching hazards. Thus giving you much more time until impact.





Damned jay walkers

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Steve

I've verified that all crashes in the red speed distribution curve were "serious injury, casualty removed from scene in ambulance" crashes.

It seems obvious, therefore that there were crashes at the low end of the speed distribution that were completely excluded.

It's entirely probable that the red curve of impact speed (irrespective of injury) would be high at 10, 20 and 30 km/h impacts.

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Paul Smith
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Hi all,

I might be getting somewhere with this. If we start with this "psychological" distribution:



It leads to an impact speed distrubtion estimate like this:



I haven't done the calculus/integration thing yet required to accurate assess the size of the buckets, nor the work required to "run it backwards" and determine the slope of the psychological distribution based on some real world data, but it's looking very interesting.

It does look as if the physics is massively subservient to the psychology. (Thank god for that!)

I also need to run it with "impact time" as opposed to "impact distance", and see what that looks like.

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Paul Smith
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It seems to follow tsh's df=3 curve well, and fits with an intuitive assumption of 13 mph as the peak. Is this related to data derived from some observations or experiments, or is it a stab in the dark, based on what we think might be the curve?

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It's not based on any real data at all, except the braking physics stuff and the psychologically based "log scale" of error degree. I didn't do ANY fussing or tweaking to get that result. As soon as I put in the single data element (the blue curve in the other new graph), this is what popped out.

Next stage is to put some real data in and see if it can be made to match up on "both sides". My bet is that it will.

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Paul Smith
Our scrap speed cameras petition got over 28,000 sigs
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Paul,

If you don't mind a former expert chucking a few more stones into the pond...

You are probably trying to group a number separate graphs into one, which won't actually go too well. For junction collisions like the Australian one, you can have a couple of major reasons why the accident happened:

1) Looked but failed to see
2) Looked but failed to appreciate speed on oncoming vehicle

1) Is undoubtedly carelessness on the part of the vehicle emerging/crossing while 2) can be carelessness on the part of the emerging vehicle or due to excess speed on the part of the 'bullet' vehicle. Both will have very different results in terms of impact speed distribution, because of the time and distance issues alluded to in http://www.safespeed.org.k/braking.html but taken separately will probably be more or less normally distributed. Your last graph, with a bit of squinting looks a bit like that.

As for the Ashton & Mackay study graph, it helps to know exactly how the study was performed. It only took into account serious PI and fatal accidents (i.e. ones where the Police AI unit were involved) where an exact measure of the car's speed at the point of impact could be made (from debris and skid marks). I seriously doubt if there was much data below 15 mph so you can pretty much ignore the bottom end of the chart.

Unfortunately, my experience was solely in the serious injury/fatal arena, so I can't really quote any sensible statistics - the vast majority of my cases involved impacts at 30mph plus, and with a distinct jump at 60+ (in 30 mph limits)

Hi Dave,

I'm really happy to recieve any input.

I'm not certain you've exactly appreciated my purpose in this. What I'm hoping to do is to broadly characterise the statistically average crash. Individual crash causes don't matter in such an approach.

The problem we face presently is that there's an "official assumption" that there's a general relationship between speed and the risk of crash involvement. I'm hoping to end up with a realistic model that shows that the real relationship is between "degree of driver error" and crash severity. I've already taken a dozen or so views of this and the message is always the same. Driver error is the primary determinant of crash outcome, and speeds selected by responsible drivers are almost completely insignificant.

Work continues...

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Paul Smith
Our scrap speed cameras petition got over 28,000 sigs
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I'd agree with that. I'm just not sure you can characterise the 'average statistical crash' and link it directly to degree of driver error. You might be able to disprove the direct link between vehicle speed and risk of accident involvement easily, but generating a suitable metric for degree of driver error is going to be interesting. Finding suitable data for such a metric will be even more interesting.

It may be considerably easier than you think. Have a look at:

http://www.safespeed.org.uk/ten.html
http://www.safespeed.org.uk/12mph.html

We have various "links" and various relationships to explore. If the Joksch equation is in the right ball park we have a startling weighting towards low average crash speeds (I believe we do). The same applies to chasing the proportion of pedestrian fatalities backwards across the Ashton Mackay curves.

Since I don't believe that it's possible to create the "ten" relationships with a physics model of crash causation we know we have to look elsewhere (we need a psychological model instead).

Matching a psycological model to the simplest crash physics model and checking it against real world data has to be revealing and may lead to further hypotheses. For example, the psychological error scale is steep - tiny movements along the curve (i.e. improvements in average driver quality) will lead to relatively huge improvements in road safety results.

Unfortunately I have a hell of a lot on this week and it'll be next week before I get to play with the linking model again.

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Paul Smith
Our scrap speed cameras petition got over 28,000 sigs
The Safe Speed campaign demands a return to intelligent road safety