Safe Speed Forums

I think it's extremely dangerous to imagine that we can hold all conditions constant except vehicle speed. Clearly we can't. The only available means of speed reduction affect the driver, who then in turns responds. It's extemely unlikely that we can alter his speed without altering "other things" too.



I appreciate this problem. The ultimate question is:

Is it reasonable to expect that we can reduce average crash severity through speed enforcement?

I think we're (reasonably) trying to address a component of that question.

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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

Actually that's a specious argument, which makes perfect sense until you start analysing it.

Impact speed, if braking takes place, depends on how much braking has taken place. If you're doing 20mph and you manage to brake for a quarter of a second before impact, the impact speed will be 15mph. On the other hand, if you manage to brake for one and a half seconds from an initial 40mph, the impact speed will be 10mph.

I know the scamerati will then say something like, "But if you're doing 40 you won't have one and a half seconds."
Maybe you will, maybe you won't - it depends on a lot of random factors, such as precisely what time both parties involved started their journeys, and how far they had travelled.

Then they'll say, "But, given the same circumstances, you'll have more time and space to stop from 20 than you will if you're doing 40."
Wrong. In any set of circumstances, you cannot just change the speed without changing everything else as well. In other words, you cannot rewind to some fixed point some distance back along the road and just change the speed of the car without also changing its position. The laws of physics simply will not allow it. No two sets of circumstances are the same, nor can they be. Additionally, the laws of probability dictate that the longer you spend on the road (the slower your speed) the more likely you are to be in the wrong place at the wrong time.

But still we hear, ad nauseam, "At 35mph you need an extra 21 feet...", as if it means something. If someone walks in front of you when you're at such a distance from them that you're just able to stop from 30, it doesn't mean that you'll hit them if you're doing 35. If you're doing 35 then, in all probability, you'll be way past that point in the road at the time that that same someone walks into the road. Someone else may run them down, but it won't be you.

If you want to test this theory, and you know how to write programs, write the following simulation:

1) Have cars passing a fixed point at fixed intervals, say one every three seconds, all travelling at the same fixed speed.
2) Have a hazard appearing at fixed intervals, say one every ten seconds, but at a random point along the road, say up to half a mile either side of the fixed point.
3) Whenever the hazard appears, calculate where the nearest car is in relationship to the hazard (but, obviously, not the one that's already passed) At this point you can, if you wish, build a little 'intelligence' into the equation - like, for example, to take.
4) If the hazard is within the stopping distance of that car, record a collision. For good measure, you can also calculate the impact speed and record it. At this point you can, if you wish, build a little 'intelligence' into the equation - like, for example, to take into account that the hazard takes a finite amount of time to get into the path of the car so, if the car is very close it will probably miss the hazard.
5) Run this simulation for say, 10 million (simulated) seconds, and then check the number of collisions vs the number of cars past the point.
6) Repeat the simulation at a different car speed.
7) Compare the results. You may be surprised.

You can write the simulation with some scripting language, but it will take forever to run. Better to use a compiled language.

Regards
Peter

This isn't a good argument. It's spurious to hold the position of ONE of the road users constant when re-running a crash scenario.



There's a simpler way to write this. We can just chuck out obstructing pedestrians at ALL the potential positions along a vehicle's route. Some are too far away to be hit, and some are too close to allow time fro braking. Ultimately we end up calculating the area under the speed-distance (or speed-time) curve.

But in the real world road users observe one another and the probability of a collision is massively influenced by this behaviour. Even the probability of seeing one another at all is influenced by speed and distance. Ultimately the physics models do little to illuminate the real world situation.

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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

Yes, yes. That may all be true but it's not relevant to the question posed. That's why I said the question's wrong.

That seems a bit more like it. But having asked the question you did, I think you have to dispose of it, unanswered or inadequately answered, a bit more effectively. Otherwise it looks like you're avoiding a difficult question. The answer to the question you did pose is as I gave it. And it's the question that is/will be asked by those who we are seeking to persuade that indiscriminate speed enforcement is not the right/best/only answer to imroving road safety.

Afraid my IT skills aren't up to that so go on - surprise me.

Actually, that looks like the principal question ('ultimate' in a sense). In order to answer that, we have to start with and dispose of a number of implied questions, the first of those being the one you originally posed - to which the uncomplicated, straightforward answer is "yes".

It's reasonable to hold the position of one of the road users constant - after all, if a pedestrian steps into the road without looking at precisely 12:15:00 for example, they'll do it regardless of the whereabouts of the other road user. What's NOT reasonable, however is to hold the position of ONE of the road users constant while changing their speed - which WILL also change their position at that point in time. You can't get away from that, it's physics.

Having said that, I do hear what you're saying - the actions of one road user will affect the actions of the other road user, well, most of the time anyway.



Yes, I know. It's actually the speed-time curve. But it's not very intuitive, and as most people unfortunately think in terms of the speed-distance curve, they'd be inclined to mistrust the maths. But taking the laws of probability into account changes the speed-distance curve into the speed-time curve.
The simulation PROVES this to people who may have their doubts, which is why I mentioned it rather than going into the maths.



The physics tells us more than you may realise.
I agree that road users are massively influenced by the actions of other road users, but I believe that that only influences the probability of them getting into a situation where a collision is likely to occur. At that point, this relationship breaks down and the laws of physics take over.

Regards
Peter

The answer from the physics is very wrong for the real world. For example, assuming simple values for the area under the graph we mentioned earlier we get

at 60mph: (60*.75) + (0.5*60*(60/20)) = 135

at 30mph: (30*.75) + (0.5*30*(30/20)) = 45

(speed*reaction time) + (0.5*speed*braking time))

Yet we know that the chances of getting run over on a 60mph are neither 3 times greater nor 3 times more severe.

The fact is that we can see further in the general 60mph case and this more than makes up for the increased stopping times.

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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

Bringing the laws of probability into the equation, it becomes:

((speed * reaction time) / speed) + ((0.5*speed*braking time) / speed)

which, simplified, becomes:

reaction time + (0.5*braking time)

This gives:

at 60mph: (.75) + (0.5*(60/20)) = 2.25

at 30mph: (.75) + (0.5*(30/20)) = 1.5



Quite correct. This (the fact that cars are driven by thinking humans, rather than just being propelled missiles) goes even further and takes speed completely out of the equation - your actions completely compensate for the negative effects of speed - or should do.

Having taken speed completely out of the equation, it can now be said that the longer the time you spend on the road the greater your probability of encountering a hazardous situation, so the faster you go the safer you are (within the constraints of always being able to react appropriately to the hazards you do encounter)

But, my point was that collisions only tend to happen when all the other mechanisms - psychological or otherwise - have broken down and the only thing you have left is the physics. But even then, I have shown that the physical relationships are not as some people would have us believe.
And, more to the point, at the end of the day it's the physics which dictates the impact speed - which is what this thread is all about.

Regards
Peter

Here's something I've been pondering over from a maths perspective for quite a while now...

Lets take a fairly simple "accident model" of a pedestrian stepping off a pavement in front of us. Now leave all factors the same apart from the speed of the car, thus we can see in isolation what effect varying that speed has on the potential outcome. We will also assume that the driver is "fully attentive" - ie his reaction time between seeing the emerging pedestrian and hitting the brakes doesn't vary.

Now in the "intuitive" model, we tend to think in terms of anything within the overall stopping distance of the vehicle as being at risk, and that the closer they are to us the higher the risk, as we clearly will have had less time to react, and therefore to reduce speed.

So we can say that at speed x with an overall stopping distance of y that any pedestrian betweeen the current location and a distance y away is at risk of being run over if they should step out. Taking this assumption further, it is equally clear that if the speed increases then so does the stopping distance, thus there is now a longer section of kerb which might contain an "at risk" pedestrian.

But what this simple model fails to consider is that there is also a minimum distance to consider, for whatever the current speed is. In other words anyone stood on the kerb within a certain distance wouldn't be able to step in front of the car before it had passed them, therefore they drop back out of the risk zone. Of course this also increases with speed.

So in a theoretical scenario where we are driving parallel to a kerb lined with people stood shoulder to shoulder, then at any given speed only a certain number of them are within a danger zone by which they are far enough away to be able to step in front of us, but not so far away that we can stop before hitting them.

(Clearly, in a real situation we try not to get into this situation at all, which we generally do by driving far enough out into the road to ensure that the minimum distance increases to a point where it overlaps the maximum distance, with the result that there is no longer any "at risk" zone anywhere along the kerb. This is what we are actually doing when we instinctively veer away from a crowded kerb - amazing how good our intuituion is, isn't it?)

Anyway, the interesting points here are...

1. Taking our theoretical number of "at risk" pedestrians, then does this number increase or decrease when we increase speed? I think it increases, but...
2. This "at risk" zone is further complicated by the fact that the near end of it represents a higher risk, in that the pedestrian who steps out from there will be struck at a higher impact speed than one who steps out at the far end of our "at risk zone". So we could notionally go a step further and calculate an impact speed for each person sized section of kerb. Close to us the impact speed is high, further away it is lower. Now what happens to these numbers if we vary the speed? Do they go up? I'm not sure...
3. The worrying bit. If we follow this through to its logical conclusion we realise that slowing down can actually bring people into the "at risk zone" who weren't there when we were travelling faster! When we slow down, someone relatively close to us may now have time to step in front, whereas at a higher speed we'd have already gone past.

Ok, so I can almost hear Steve Callaghan clearing his throat in readiness to accuse me of building a ludicrous argument to support the idea of travelling faster to avoid pedestrians . Clearly this is not the case, but it does illuminate an interesting point: We know that when we drive faster we need to look further ahead, but what this shows is that the opposite is equally important - when we slow down we need to look closer too.

And finally...

I know I said "all else remains the same", but I can't resist thinking about what effect the other real life variables have on this scenario. Instead of thinking about a fixed "reaction + braking time" model, we ought to also consider what happens to our "at risk zone" when we vary other things. What effect does distraction have? What effect does avoidance have? My suspicion is that whilst speed has a steady incremental effect on the outcome, attention level will affect it dramatically, and avoidance (ie road positioning) will affect it wildly. Indeed, in a crowded street, road positioning is the only thing that can wind our "at risk zone" right back to zero.

It would be fascinating to model all this properly, but in the meantime just playing the idea over in our minds tells us a huge amount about the relative importance of speed, and of the C and S of COAST...

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CSCP Latin for beginners...
Ticketo ergo sum : I scam therefore I am!

Duplicated posts.

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Make everything as simple as possible, but not simpler - Einstein

I think there is a relationship, but it's easily affected by other things so it's a fairly weak relationship.

First, as bmwk12 says, the difference between initial speed and impact speed will be greater if the hazard is spotted early and smaller if spotted late. If the driver fails to see it entirely then the two might well be the same. If spotted sufficiently early (ie on the margins of braking distance or perhaps too close to brake but enough space to steer round) a collision might be avoided altogether. Impact speed=0! Observation has a very strong effect.

Having seen the hazard the driver must react to it quickly and appropriately. Reacting appropriately will itself be down to different factors - experience, quality of driver training, driving talent (for want of a better term), how well the driver has assessed the situation and so on. Reaction times between drivers may vary as well, though it's probably only slightly.

Then we have the vehicle itself. From the point when a driver hits the anchors how long does a car take to stop? About as long as a piece of string, right? My car stops faster than Mrs Gatsobait's, in spite of an extra 70 odd kilos (and no, that's not all because of my beer belly ). It's nothing more than slightly better brakes, but that changes the relationship between initial speed and impact speed. Even among the same make and model there can be significant differences. Maintenance may vary, and if that's on brakes and tyres we could have a scenario where the well maintained car at 35mph reduces impact speed more than a poorly maintained one doing 30. What if one car has had the brakes improved? What about a slower car, four up and full of luggage against a slightly faster one with only the driver?

I'm sure there's more, but off the top of my head that's a handful of things that will change the relationship between initial speed and impact speed, and in a big way. The question shouldn't be whether or not there's a relationship, but is it important when compared to other factors? Pro-scamera folks probably think so, and I'm sure rabid anti-car sandalista types would swear it. But I feel there's a very strong argument that observation is probably the most important, and though I'm not sure what order the rest are in I think it's likely that initial speed is near the bottom (not at the bottom as I can think of one thing that ought to be lower).

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Make everything as simple as possible, but not simpler - Einstein

Speed reduction will not effect impact speed

The relationship that effects impact speed is solely reliant on when a person makes the error.

At present all the focus is on the speed we travel on.

The latest advert, which is a joke, stating that 80% of pedestrians survive at a free traveling speed of 30 mph. This is complete nonesense, we have no way of knowing the traveling speed of a vehicle prior to impact after an accident has taken place.

Their stat's are based on mainley assumptions. The 35 mph claim is also complete tosh, and they only wish to support the number of fines they are imposing.

When an accident involves a pedestrian stepping into the road, the error is the Pedestrian, yet why do we have no warnings to pedestrians. They have a duty of care.

We should concentrate on the root cause of accidents, not one of the factors.

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Steve

When we are talking about crash severity here, we are talking about average crashes are we not? Thus, it stands to reason that altering the mean speed of vehicles involved in any of the sub-categories of incident classification (i.e. no injury, minor injury, major injury and fatality) by even a few mph will not greatly affect the overall figures. This is what happens when you average out the data and statistics in this manner.
But what about the incidents that occur at the threshold of each group? There must obviously be a cut-off point where the injuries received by one or more parties involved in an incident are only just classified as (say)major; any less severe an impact and they may very well not have been major at all, they would have been minor. And so it goes at each threshold, minor injuries that would have resulted in no injury at all, fatality incidents in which the individual would have survived albeit with major injuries. In fact, this is the very point being made by the latest Think ad isn’t it?
So, let us suppose that by subtle persuasion we are able to reduce the speed of vehicles on the UK roads by 1mph across the board, in every situation. There is no reason to suggest that drivers would suddenly behave any differently, any more than they would if speed cameras were turned off at midnight on Sunday, so I’m convinced that the threshold incidents would be affected and as a result, lives would be saved.

The number of speed camera convictions raise year on year, Speed cameras do not reduce speed

Speed does not create an accident in 95% of our accidents. It is driver, pedestrian error, remove the error, you remove the accdient, thus you reduce the death rate on our roads.

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Steve

Why have you taken that one little bit of my post and placed it totally out of context.? The only point I was making about speed cameras is one Paul himself made, turn them off and it won't affect the way people drive.
Similarly, create a 1mph reduction in speeds across the board and you won't affect the way people drive either, apart from the fact they'll be going imperceptibly slower. This won't affect the severity of the average crash, but it will affect those that occur on the cusp of incident classification thresholds.

The only defined point within it



Based on what exactley

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Steve

Quite right.
However, the effect is much greater than most people imagine. A difference of just one quarter of a second to the time the hazard is spotted, or to reaction time, will make a difference of around 10mph to the impact speed, and one second will make a difference of around 40mph.
This alone is enough to make the relationship between travelling speed and impact speed more-or-less completely random.

Regards
Peter

The only element that decides when the hazard is spotted, is when an error takes place

The relationship is between the error and impact speed.

everything else is mere factors, which will have no effect.

When & where a driver / pedestrian decides to make their error, decides the impact speed.

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Steve