Safe Speed Forums

Following on from this forum topic:

Is there a relationship between speed and crash severity?

I created a spreadsheet model to examine "pedestrian incursion":

http://www.safespeed.org.uk/pedinc.xls (updated)

Basic description:

Imagine a line of pedestrians all along the kerbside to your left as you drive along. At some instant they all start crossing the road without warning. You brake hard. How many do we hit and how hard? What are the parameters that have a big effect? Note that some peds will be able to cross in front of you before you get there.

Input parameters:

driver reaction time: How long after the peds start moving do we start braking?
Distance to kerb: How far has a ped got to move to get into our path?
Pedestrian speed: How fast do the Peds move?
initial vehicle speed: How fast are we driving?
vehicle width: How wide is our vehicle
braking effort: How hard do we brake?

Have a play around and see what you think. Comments welcome.

Sensitive factors are: distance from kerb, pedestrian speed and driver reaction time.

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

This is useful for showing the effects of incursion time in situations where pedestrians are within the braking distance of the car.

It must, however, be pointed out that it's not a real-life simulation, and one which doesn't take into account the fact that the probability of being at the wrong place at the wrong time is inversely proportional to speed.
The resulting number of collisions will therefore be biased towards higher speeds, but the other results (collision severity etc) should be OK.

I would suggest that to eliminate this bias, the resulting number of collisions should be divided by the initial travelling speed.

I'll have a good play around with it later on.

Regards
Peter

I'm hoping to make it the best possible physics model for average cases. By leaving out psychological factors completely, I'm hoping that we'll be able to show that physics fails comprehensively to offer us the right result.

This in turn tends to support the important assertion that we must address crashes in the psychological domain.

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

But that probability is in the physical domain, not the psychological domain. Therefore it should be included.

Sorry. Now I understand your point. Several years ago I argued the same point, but I was wrong. The contra-argument that convinced me was considering the number of crashes that would take place at effectively infinite speed.

Suppose we covered 100 miles in a 1/10th second. We'd collect everyone crossing the road in that 1/10th second.

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

Paul

There's something not quite right with your calculations, but I don't know what (I had a skinful last night so my brain isn't working properly )

I wanted to check that, under conditions of zero incursion time and zero driver reaction time that you'd get four times the number of collisions when you double the speed - as expected. So I input the following values:

driver reaction time 0 seconds
Distance to kerb 0 ft
Pedestrian speed 0.001 mph
initial vehicle speed 60 mph
vehicle width 6 ft
braking effort 0.9 g

The reason for making pedestrian speed 0.001 mph is that I wanted to make it zero but got a divide by zero error.

I got the following results:

number of impacts 150
potential impacts 134

and at 30 mph:

number of impacts 150
potential impacts 34

The number of impacts is the same in both cases, which strikes me (no pun intended) as being wrong, especially as it's greater than the potential impacts figure.
The potential impacts seems to change by a factor of four, as expected.

Edit: That may have been an invalid set of conditions, If I input a pedestrian speed of 1mph and instead change vehicle width to 600ft, then the results appear to be OK.

Regards
Peter

It's just the effect of the column B "time to vehicle arrival" fudge for "the vehicle has stopped and will never arrive". I set in a value of 1,000 seconds (approx infinity) but your ultra low speed pedestrians wouldn't have got out of the way in 1,000 seconds.

I'm not worried that you can break it by putting in funny numbers

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

Another (more realistic) way of putting it is, if you start a 30 mile journey at 12:00 you'll finish your journey at 13:00 if you do 30mph. If a pedestrian runs across the road somewhere along that 30 mile stretch at 12:45 there's a possibility that you might hit them. But if you do 60mph, you'll finish your journey at 12:30 so there's no possibility of you hitting them.
But the pedestrian could choose 12:15 as the time they run across the road, so you could hit them at either speed. So the probability is really half at twice the speed.
Note, this is without taking stopping distance into account - taking stopping distance into account but assuming zero reaction time, would double the actual collision risk when doubling the speed (ie it does NOT quadruple, as some people might think)
My simulation which I described in another thread shows that this relationship between speed and probability holds true even when you have lots of vehicles and lots of pedestrians crossing - the probability per vehicle is inversely proportional to speed.

Regards
Peter

Well, someone's going to, so it might as well have been me - sod's law.

I realised my slip after I posted, which is why I put the edit in.

Regards
Peter

You're saying that if we go fast enough we'll never be able to run anyone over. Clearly that's wrong.

Most road hazards are "location based". This includes all normal hazards like pedestrians, bends and other vehicles.

A few hazards are "time based". One is falling asleep. If we spend more time on a journey then clearly our risk of falling asleep is increased.

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

I'd like to add fatality risk to the pedestrian incursion spreadsheet.

There's a data tale in this spreadsheet based on Ashton and Mackey 1979:

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

But I don't know any easy way of automating the process of reading acros the table data. Suppose a calculated result is 32mph. How can I get to the answer 52%? Obviously I can calculate a straight line approximation between every data point pair, but it's huge - I'd be working on it for a couple of days!

I tried a polynomial approximation with excel's trendlines but the approximation is pretty crap.

I thought of a "three straight lines" approximation, but that's pretty crude as well.

Anyone got any ideas?

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

No, that's not what I'm saying.
If you double your speed you'll halve your risk of encountering a time-based hazard, but there's no speed this side of infinity that you cannot double it again - so the risk never falls to absolutely zero. Certainly not within the practical range of vehicle speeds, although I understand that if you're travelling at the speed of light you'll pass right through the hazard without touching it.

And, because braking distance increases with the square of speed, the actual collision risk increases with speed, although not with the square of speed.



Bends and junctions are location based, as are pedestrian crossings. But pedestrians and other vehicles are also time based. Actually, pedestrians cross the road pretty much anywhere. And, although you'll usually only encounter a vehicle encroacing into your path at a junction, you have to be approaching the junction at the time that it pulls out.

So I'd say that most hazards are principally time based, the exceptions being things like bends, trees lamp posts etc.

Regards
Peter

OK. I solved the problem of the fatality risk curve using the Excel "PERCENTILE" function. It's a little crude, and I might be able to improve on it. I've uploaded a revised spreadsheet.

But I've discovered something amazing.

If you set the driver reaction time to zero, the results suddenly get realistic

Is this because road safety depends on anticipation?

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

You could always try, a) a massive IF statement, b) write a VB function macro, or c) reference a cell number index according to speed.
The last one is the easiest, although I've forgotten how to do it.

But the A&M graph doesn't give you the risk vs speed anyway, as I think I've pointed out to you.
It's a graph of the the percentile of fatalities etc.
So the 52% at 32mph doesn't mean that a pedestrian has a 52% chance of being killed at a 32mph impact speed, rather it means that 52% of the fatalities in their dataset occured at impact speeds of 32mph and below.

So I don't think that the A&M graph would give you anywhere near the true figures.

But other research (I'll scratch out the references, if you like) indicates that the risk of fatality increases as the fourth power of impact speed, serious injury as the third power, and slight injury as the square.

So I'd calculate the fatality probability as follows:

p = (s ^ 4) / (a ^ 4), where s is the impact speed, and a is the impact speed at which a fatal injury is virtually 100% certain. (50mph?)

Regards
Peter

You did. I'm still trying to get my head around it. How did you find this out? Any documents you can refer me to?

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

The document: "The case for speed cameras" by our old friend, Rob Gifford, (I've just emailed you a copy) contains the following:



This appears to have been taken verbatim from the A&M document. I've not seen the original so cannot confirm this, but why should he lie? - particularly as this would weaken his case considerably.

Regards
Peter

You get the same thing if you reduce pedestrian speed to around 2mph, or increase distance to kerb to around 11 ft.

It's incursion time minus reaction time wot does it.

regards
Peter

Paul,

Can you tell us what conclusions you draw about the effects of variations in "initial vehicle speed" compared to variations in the other variables (I imagine pedestrian speed, vehicle width and braking effort can be treated as constants, for practical purposes)?

I've been expecting to show that the phyics model is so unrealistic as to be indicative of cause and effect.

The critical contribution of attention / reaction looks as if it might swamp all other variables (within a realistic normal real-world range).

But I'm not (this minute) drawing any conclusions. Work continues...

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

OK. Here's a small sample of results playing with 3 variables. I haven't tested the accuracy of the calculations so take that for granted.

Inputs:

Driver reaction time (DRT) - varaible as results table
Distance to kerb (DTK) - variable as results table
Pedestrian speed - constant 4mph
Initial vehicle speed (IVS) - variable as results table
Vehicle width - constant 6ft
Braking effort - constant 0.9g

Results:

Average impact speed (AIS)
Number of impacts (I)
Potential impacts (PI)

1. DRT variable; DTK 5ft; IVS 30mph

This table uses standard inputs to evaluate the effect of reaction times.

DRT AIS I PI
0.5 15.4 20 56
0.75 19.6 27 67
1.0 23.9 34 78
1.25 27.0 39 89

2. DRT 0.75s; DTK 5ft; IVS variable

This table uses standard inputs to evaluate the effect of varying initial speeds.

IVS AIS I PI
25 15.3 19 51
30 19.6 27 67
35 24.5 34 85
40 29.2 42 104

3. DRT 0.75s; DTK 8ft; IVS variable
In this table, our driver has positioned himself 3ft further away from the kerb. His reaction time is the 'standard' 0.75s and we evaluate the effect of varying speeds.

IVS AIS I PI
25 8.9 6 51
30 11.9 12 67
35 15.6 19 85
40 19.6 27 104

4. DRT 0.5s; DTK 8ft; IVS variable
In this table, our driver has positioned himself 3ft further away from the kerb AND sharpened his concentration, becoming more 'hazard aware' thus reducing his reaction time to 0.5s. We evaluate the effect of varying speeds.

IVS AIS I PI
25 5.1 2 42
30 8.4 6 56
35 11.5 12 72
40 15.4 19 89

If these results are accurate (I have no reason to think they're not), they show:

at 30mph, reducing reaction time by 0.25s will have approx. the same effect as reducing speed to 25mph

at 30 mph, increasing reaction time by 0.25s will have approx. the same effect as increasing speed to 35 mph

at 40mph, increasing kerb clearance by 3ft will have approx. the same effect as driving at 30mph without the addditional kerb clearance

at 40mph, sharpened concentration and increased kerb clearance will have approx the same effect as reducing speed to 25mph

Please note I'm NOT suggesting that 40mph is a recommended safe speed in any particular circumstances. What I think these results indicate is that the defensive driving qualities of concentration/observation and road positioning far outweigh speed alone as influencing factors in impact severity. Another interesting result indicated by the results is that a driver who uses concentration/observation, road positioning AND speed reduction is a 20 x better risk (measured by number of impacts) compared to a driver at 30mph who is distracted for 0.5s (by a speed camera?). However, distract the advanced driver for just 0.5s and his risk (measured by number of impacts) increases by a factor of 5.

Interesting model which deserves more study than I have time or expertise to give to it.