Safe Speed Forums

Pete317 did some work on this and sent it along. I fitted it in with some other data and the Aston Macay curves are proved to mean something different from the usual claim:



Spreadsheet: http://www.safespeed.org.uk/inj3.xls

The red trace is the Ashton Mackey curve.

The green trace is the result of combining a speed distribution (purple) with the 4th power curve (yellow).

The blue trace is the Minnesota re-evaluation of the A&M data.

The goodness of fit between the red and green curves is remarkable.

The goodness of fit between the blue and yellow curves is remarkable.

It's extraordinarily likely that the underlying 4th power relationship in A&M was CORRUPTED BY a speed distribution in the sample data.

The Minnesota re-evaluation of the A&M data is remarkably close to the 4th power curve.

The spreadsheet couldn't be simpler. There's no scaling or manipulation AT ALL to get these curves to fit so well. I'm quite sure we could fuss with it and get it even closer.

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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

I think a clarification is in order here, for the sake of those who don't know what the fuss is about:

What Paul has shown here is that the A&M graph is really a cumulative distribution of impact speeds taken from a sample of fatal pedestrian collisions - a percentile graph. This much is stated in the A&M research.

The only thing wrong with it is that it has been misquoted and misused by the authorities and others.

What the graph really says is that 50% of fatal pedestrian collisions occur at impact speeds of around 32mph and below.

What it does not say is that a pedestrian has a 50% chance of being killed if hit at 32mph.

Yet the latter version is the one we hear ad nauseam.

According to the 4th power graph as well as the Minnesota graph, a pedestrian has a 50% chance of being killed if hit at around 42mph.
And hit at 32mph, a pedestrian has around a 15% chance of being killed.

And that's impact speed, not travelling speed.

The new THINK! ad goes as far as to use data from both sets to make their case look good. In it they say that a child hit at 30mph has a 85% chance of surviving, whereas they have a 90% chance of being killed if hit at 40mph.
This is pure chicanery. The 30mph figure is roughly right, but the 40mph figure is way, way out. And then they exacerbate this by implying that they're talking about travelling speed. (the 30mph speed limit is there for a good reason).

Regards
Peter

On a further note, I listened to the new(ish) "if you hit me at 40mph" ad today and thought about it a little harder.

Basically the two scenarios they play don't really add up.

Here is the advert:
http://www.thinkroadsafety.gov.uk/campa ... 5radio.mp3

The first one (40mph) has a long screech and a loud bang

The second one (30mph) has a much shorter screech (1/3rd the length) and a quieter bang.

Two errors I can see:

- The longer screech means that in that scenario the driver would have had MORE warning of hitting the child.

- In both cases the car would have LOST speed while braking/skidding, so what was the starting speed and how does THAT relate to the 30mph speed limit?

Gareth

I'm not sure the length of the screeches and the magnitude of the bangs is meant to be absolutely representative, I reckon you're trying to read too much into this element of the ad. The difference is far too subtle and few people will notice it. The significant sound -so far as the commercial is concerned - is the that of the child crying in the 30mph collision i.e. it lived.

Brilliant. Thanks for the clarification Peter. I was really running out of steam when I posted the first message in the thread.

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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

This may be true, but would it have affected the message the ad was trying to convey if the sound effects were accurate? See, the problem I (and I suspect Gareth) have with ads like this is that, in trying to portray a genuine problem, the apparent message being given out is so riddled with flaws and inconsistencies that you can't be sure whether or not the problem actually exists.

If the sound effects were more accurately matched to the scenarios the ad is suggesting, then those people who didn't pick up on the inconsistency in the current ad wouldn't notice anything different about the accurate ad. HOWEVER, those people, like Gareth, who DID spot the error, wouldn't have anything to point out to those people who didn't spot it...

To put it another way - if the government continues to rely on lies, deception and figure-fudging to push their version of road safety, how much longer will it be before a significant number of people just stop listening and end up missing a genuine message that needs to be heard?

Sadely I may have read too much into a lucky match.

See this graph:



And this spreadsheet:

http://www.safespeed.org.uk/inj5.xls

The yellow curve is the accumulation of the purple curve. The Red curve is the original A&M data. Since the A&M curve exhibits the frequency plot of a normal distribution, coincidental matches are highly probable. This isn't, in itself, evidence of a speed distribution in the sample. I thought it was, but that's not a safe assumption.

It's still incorrect to try and read fatality risk from the A&M curve (of course).

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

I don't think you have. You have highlighted the reason why the A&M graph is not an indicator of fatality risk.

A cumulative distribution curve (what the A&M graph is) is highly sensitive to the distribution curve, but little else. The small difference between the curves in the first and second graphs is a measure of the effect of the 4th power risk function - hardly any.

If we somehow changed the risk function, say by making the front ends of cars out of marshmallow, there would be a lot less fatalities, but the distribution would not change - so the cumulative distribution curve would hardly change.

If, on the other hand, we changed the distribution, say by fitting 20mph speed limiters to all cars, the cumulative distribution would change. It would then show that 100% of fatalities take place at impact speeds of 20mph or less. But, as you can see, this would not tell us anything about the risk vs speed.

Regards
Peter

I believe you are msitaken... Try this thought experiment.

We line up a few thousand pedestrians and we cause 10 collisions at 1mph, 10 at 2mph, 10 at 3mph and so on.

We're stil going to get something that looks like A&M when we count up the bodies by speed bucket.

So we KNOW there's a something like an accumulated normal distribution in the fatality risk curve. But this time there's an entirely flat distribution in impact speeds.

I thought we'd found evidence (in the first post above) of a normal speed distribution. We hadn't. It was a leap too far.

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

OK, we haven't shown any evidence of a normal distribution, but that's not what we were trying to do.

What we set out to do was to show that the A&M curve tells us little about the risk of fatal injury vs impact speed - I believe we have succeeded in this.

However, FWIW, there are a few points worth mentioning. We may not be able to show that a normal distribution exists, but neither can we say that it doesn't exist.

In research papers I've seen which plot the number of pedestrian fatalities against impact speed (eg McLean) , the plots do resemble a normal distribution curve - any deviation being easily explained by the statistically small number of samples.

Your example does indeed give a flat line distribution, but what you have done is to artificially create a very large deviation from mean. A large deviation from mean applied to a normal distribution will also give something resembling a flat line - plus the fact that, with a straight line, the mean value could be anywhere.

Regards
Peter

THe likelihood of death in the graphs is based on averages.

Of course the likelihood differs with the height of the pedestrain and the vehicle type.

The shape of the front of most light passenger vehicles is such that adults are hit at or slightly below the knee. Hence their torso and head is not subject to high initial accelerations and they survival depends on the outcomes of hitting the bonnet or windscreen and /or the consequences of subsequent trauma if they bounce off the impacting vehicle. Older people, because of loss of elasticity in their arteries et cetera.

However for a small child of 3 years or less the front of the vehicle may impact the torso directly so the accelerations of the torso and head will be much higher and concequently the likelihood of death.

The analogy for adults is being hit by a bus, or a child up to 10-12 years being hit by an all whell drive style vehicle with a vertical front.

In these three cases (<3 years and car, up to 12 yrs and blunt front of AWD, or up to adults and bus) the speed limits at which death will occur will be low. Where the front of the vehicle is rigid, there will be a high chance of death at an impact speed of 35 km/h or 20 - 25 mph.

Hence it might be true that SMALL children have a 90% chance of being killed if hit at 40mph or 65 km/h. But not based on the Ashton et al data

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John Lambert

The A&M curve under discussion is the adult curve (I believe).

You may well not have seen the "Minnesota" re-analysis of the A&M data. It's here: http://www.lrrb.org/pdf/200223.pdf

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

Further explanatory note

My calculations are based on the physiological ability of the human body to survive impacts. It is well known that somewhere in the range of 20g - 40 g acceleration or deceleration the chance of survival beckoms low, with older people surviving lower g forces.

Using these figures one can calculate the speed at which death is likely to occur where the compression of the human body is providing most of the deceleration distance for a pedestrian, Assuming some deflection of the vehicle structure the acceleration distance when hit by a bus with a flat front wil likely be in the range of 0.1 - 0.2 metres. At vehicle speed for a 40 g average acceleration with a dsitance of 0.1 m is about 32 km/h, and 45 km/h with 0.2 m distance. That is 20 mph and 30 mph respectively. But this only applies to those pedestrian cases where the torso and head are hit by a flat close to vertical front of a vehicle.

And to emphasise again, these are impact speeds, not travelling speeds.

The front of a modern sedan is neither flat of vertical except in the bumper region. For large sedans the height of the top of the bumper may be at 0.5 metres, a height which is at or above waist height for children up to about 3 years. And if hit at waist height or above waist height the body will be caught by the vehicleand not bounce up on to the bonnet.

For adults the centre of the knee will be at a height of 380 - 520 mm in 95% of cases (360 - 460 mm inm Asian countries). So an adult body bounces onto the bonnet and is hence subject to much lower accelerations.

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John Lambert

Thanks, John, interesting. It's more or less my understanding also.

However, some real world data may be a poor fit with our shared understanding. See: http://www.safespeed.org.uk/pedrisk.html

I do note that buses and light goods vehicles are the closest to flat fronted, and also close in the severity ratios.

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