Safe Speed Forums

You are way off the mark. Pete317 said nothing anything about different classes of roads - he claimed that "your risk increases less than linearly with speed, i.e. twice the speed increases the risk less than twice".

I have demonstrated that, over the same stretch of road in the same conditions (his drive-way!), his claim is utterly false, and you are trying to deflect things away from his false claim.

But it happens that is also false in many hazardous, congested situations. If his claim is wrong in some circumstances, he shouldn’t make it without clarifying that.

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I stole this .sig

Is lateral thinking the same as topsey turvey thinking

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I stole this .sig

I don't fully agree with bw but I do not accept pete317's reasoning. AIUI, his argument is that the risk of any given collision decreases with speed because, if the vehicle had been travelling faster, it would not have been at location X at the time the hazard materialises.

That may be true but, by the same argument, it is equally true that the vehicle would not have been at location X if it had been travelling more slowly.

It seems to me that a 'risk of collision' is essentially a random occurrence being the result of two moving objects (each of whose movement/intention is unkown to the other) having an unadjusted course and speed that would result in them arriving at the intersection of their intended tracks at the same moment in time (or within a 'window' of time). We cannot usefully define risk of collision by reference to speed because of the random element.

The point where speed comes into play is when a risk of collision exists (i.e. a collision would occur if both objects maintained their respective course and speed). At that point, higher speed necessarily means greater stopping distance and more limited ability to change course.

So, it seems to me that speed does not influence risk of collision (or, at least, that it's unhelpful to consider it in that way) but it does influence ability to avoid collision once a risk of collision has materialised.

And that is where all of the SafeSpeed material comes into play. In order to avoid a collision, one has to be aware that a risk of collision exists sufficiently to take appropriate avoiding action. That 'awareness' is encapsulated in 'COAST' and, if COAST is applied, everything else, including speed selection, necessary for effective collision avoidance falls into place.

You misunderstood me slightly.

The point about not being at location X at time Y if the speed is different is a point which is ignored in the studies I've seen. They assume that a given vehicle would be at location X at time Y regardless of speed - which, of course, is complete nonsense - and leads to the wrong conclusions.



Precisely.



Precisely again. The 'window' of time is the time from when the driver realises the need to brake to the time they're stopped. If the intersection of their intended tracks happens within that time, a collision is unavoidable. That window of time, otherwise known as exposure, defines the risk. It does increase with speed, but certainly nowhere near the square of speed - as some would have you believe.



Agreed.

Cheers
Peter

Just as an aside, can you tell me why faster roads are safer?



You have demonstrated nothing except that it's lunacy to do 60mph down your driveway. Even if it were remotely possible, I seriously doubt that anyone ever has or ever would try it. So do you mind telling us how this little piece of fantasy of yours relates to the real world?



It holds true in situations where one road user collides with another. Enough clarification for you?

Quite rightly IMO. Being at a different location along your route at any particular time has no systematic effect on your risk of accident. Setting off on your journey a few minutes earlier or later also changes where you are along your route at any particular time, and also has no systematic effect on your risk of accident. For every accident that is randomly avoided in this way, another will be randomly encountered instead, given a large enough sample. Thus, this factor is of no relevance in a study about risk factors for accidents.

But suppose we have a scenario where a hazard materialises 100m in front of two drivers on a motorway - a lorry overturns due to a freak gust of wind, say. One driver is in the middle lane doing 70mph, and stops in 96m (distance obtained from highway code). Another driver is alongside him at the time the lorry overturns, and is doing 90mph in the outside lane. This driver won't be able to stop before reaching the lorry that is now sideways across the motorway. Here, the increased speed has led directly to increased risk.

Precisely. Risk is proportional to exposure, and if we're talking about colliding with another road user, the exposure is equivalent to the stopping time. But ignoring that point leads to the wrong conclusions - fixing risk to a fixed set of parameters which aren't fixed in real life.



You've just fallen into the same trap.
Your scenario depends on the faster vehicle just happening to be alongside the slower vehicle at the precise time that the lorry overturns - which, at that same moment, just happens to be 100 metres ahead, which just happens to be the distance within which the slower driver can stop but the faster one cannot.
I'm sure you'll agree that the probability of everything being just so is pretty low - alter one of the parameters a bit and everything changes.
It says nothing about the risk.

Cheers
Peter

Total nonsense!
What if there simply wasnt time to react, no matter what speed you were going. You could even argue that the biker should have been going faster, as that way he would have been further down the road when the twat in the box screwed up, and thus no collision.

It's not a trap, your logic is incorrect. I've described a scenario where speed has a systematic effect on the outcome. These are the only scenarios that are relevant. Out of all the possible scenarios, positions of vehicles, speeds etc, if you were to count up the number of scenarios where the 70mph driver couldn't stop, and the number of scenarios where the 90mph driver couldn't stop, the 90mph driver would hit the lorry more times, because there are more possible starting locations where he will be unable to stop. This says everything about the risk, indeed it's the very definition of it - the number of scenarios where a particular outcome will occur out of all the possible scenarios.

Just thought of another way to explain it, but I'll have to use 50mph and 70mph, as I need both stopping distances.

At 50mph, stopping distance is 52.9m.
At 70mph, stopping distance is 95.4m.

Let's assume that the lorry in my scenario is going to get blown over, that's a given, what we want to establish is the relative risk of driving at different speeds along the route where it happens. The risk is determined by the relative likelihood that each driver encounters the incident whilst at a location, and travelling at a speed, that together cause them to not be able to stop in time. This window of opportunity to be involved in the accident is determined by the length of time they spend driving along the section of road that is between the start of their safe stopping distance and the point where the lorry will end up across the road.

For the 50mph driver, it takes him 2.37 seconds to cover his 52.9m, but it takes the 70mph driver 3.05 seconds. The 70mph driver thus spends 28% more time in his window of opportunity where he will be unable to avoid hitting the lorry, and this is the increase in risk.

You may well laugh, but the road on which I see this phenomenon the most (the A374 between Antony and Trerulefoot in Cornwall) has claimed the lives of five bikers in as many years. It's a stretch of road favoured by some owners of high-powered bikes for its delicious sweeping bends. In my biking days, I used to love that road - so I'm not surprised that it gets more than its fair share of bikers!

For info, I posted the piece you quoted having just come back from a trip on that road and having been obliged to brake and swerve rather sharply to thwart one more biker's attempt at hari-kiri on my A-pillar. This is something that I see nearly every week. In my youth, I fell into the same trap - G-forces play tricks on your perception of up and down, and hence your spatial awareness. My post was meant as a warning, not a criticism. As an ex-biker, I am very pro-bike - but I'd rather not see the A374 closed by the emergency services for yet another motorcycle fatality.

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Will

And I've absolutely no hope of even beginning to count the number of times that I, whilst riding quite properly and safely, have had to make allowance and take compensatory action for the total lack of appreciation of the abilities and handling limitations of a motorcycle by car drivers.
This is perhaps because many car drivers seem only to be looking no further than half-way along their own bonnets.

It isn't the increase in risk in the real world. In the real world time to react is CREATED by sound driving practice. We have crashes when drivers fail to observe or plan. The number of crashes caused by bizarre and 'suddenly materialising' obstructions is really very small. Certainly less than 10%.

In the real world crashes are caused in the psychological domain, and trying to prevent them in the physics domain is doomed to fail.

It follows that it's a mistake to compute relative risk based on speed unless speed and psychological factors take place independently of one another. Clearly they do not. They are closely tied - speeds are chosen based on observation, skills and attitudes, and in turn concentration is affected by speed.

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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 apreciate how annoying it is for you. But this is something almost magical for road safety.

By and large, one road user error doesn't make a crash. By and large two road users have to make errors at the same time. If we all had a 1% error rate then suddenly the risk of crashing become 1%*1% or 100 times safer than it would have first appeared to be. It's because of this that we have drivers who can make mistakes every day, but survive for a lifetime without crashing.

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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 totally agree - this is only the risk for this specific scenario that I constructed to illustrate the invalidity of the "different time, different place" argument. For other types of accident, the calculation would be different, and much more complex. The "different time, different place" argument will still be invalid for those other types of accident, though, as it will still not systematically alter the risk.

You've desribed one tiny subset of all possible scenarios.
I'm not disputing that the risk is greater at a higher speed. What I am disputing is the degree by which it is greater - according to them.

By their reckoning, risk is proportional to stopping distance - which is braking distance plus reaction distance, and so the relative risk works out at something approaching the square of the ratio of the two speeds. But this does not take into account the probability of being at a certain place at a certain time.
With probability taken into account, the risk is proportional to the stopping time, or more accurately, the sum of reaction time and half the braking time - which makes the RR something approaching the ratio of the two speeds.
The half the braking time is a bit confusing at first glance, but in fact that's the time it would take to cover the braking distance at the pre-incident speed. And it's that which determines the risk. Anything that happens once you've started reacting to an incident (the apparent 'slowing down' of time), is already fait accompli and no longer plays a part in the risk.

How it works mathematically is as follows:

Stopping distance is reaction distance plus braking distance, so

D = ( s * r ) + ( ( s * s ) / ( 2 * g ) )

where: s = pre-incident speed, r = reaction time and g = deceleration.

As a worked example, the stopping distance D from 30mph (13.33m/s) assuming a deceleration of 0.9g (8.82m/s/s) and reaction time of 0.6s is:

( 13.33 * 0.6 ) + ( 13.33 * 13.33 / ( 2 * 8.82 ) ) = 18.078m

and the stopping distance from 60mph (26.66m/s) is:

( 26.66 * 0.6 ) + ( 26.66 * 26.66 / ( 2 * 8.82 ) ) = 56.312m

So, according to them, the relative risk at 60mph compared to 30mph is:

56.312 / 18.078 = 3.11

But the laws of probability tell us that the probability of being between two points at a particular time is proportional to the time spent between the two points, ie inversely proportional to speed.

So modifying the first equation gives us:

( ( s * r ) / s ) + ( ( s * s ) / ( 2 * g * s ) ) = r + ( s / ( 2 * g ) )

At 30mph we get a figure of:

0.6 + ( 13.33 / ( 2 * 8.82 ) ) = 1.356

which, incidentally, is the time taken to cover 18.078m at 30mph

and at 60mph we get:

0.6 + ( 26.66 / ( 2 * 8.82 ) ) = 2.112

So the risk ratio is actually:

2.112 / 1.356 = 1.557

which is half of what they say.

This is not difficult to prove, if proof is needed, by writing a fairly simple computer simulation as follows:

1) Simulate a stream of vehicles passing a fixed point P at an interval of V. V can be fixed (say every 3 seconds) or random

2) Simulate hazard appearing in the road at an interval of H. H can be fixed (say every 10 seconds) or random. The point at which the hazard appears is A, which can be fixed, or random (say up to half a mile either side of point P)

At this point I must add that it makes no difference whether V, H or A are fixed or random, just as long as at least one of them is random.
Also, they should be chosen to be valid for the whole range of interest - for example it makes no sense to make V one second if, at the highest speed being considered, the stopping time is two seconds, as this will result in a collision in every case.

3) At every interval H, calculate whether there's a vehicle approaching point A, and within its stopping distance of point A. If this is true, record a collision. You could, at this point, also calculate the impact speed and record it.

4) Run this for as long as is necessary to get a good spread of random values (suggest in the order of a million times)

5) Divide the number of collisions by the number of hazards and the number of vehicles passed point P. This will give the number of collisions per hazard per vehicle.

6) Run the simulation again with a different vehicle speed. The risk ratio will be the ratio of the two results obtained.

You can try different variations of the simulation, just as long as you're careful not to artificially skew the results. You could even add other parameters if you so choose.

Cheers
Peter

Peter, I think we are in complete agreement, I suspect I wrote my follow-up post while you were busy writing your lengthy and informative post. If I've understood you correctly, you will agree with my figure of 28% that I calculated for 70mph vs 50mph (in this particular scenario of a suddenly appearing hazard).

Absolutely.

What I'm talking about is the physical risk attributed to speed - which is the only thing considered in the research I've come across so far.
And that they inflate this risk to double what it actually is by ignoring the laws of probability.

But cars are not driven by machines which only respond to speed limits and hazards already diectly in their paths, they are driven by thinking human beings.
Properly applied by drivers, the SafeSpeed rule, COAST, or whatever else you want to call it (not implying anything, Paul - the principle's the same) will virtually 100% compensate for the physical risk imposed by speed - ie it takes speed out of the equation, for practical purposes.
With the risk factor from speed removed from the equation, the risk depends purely on the amount of time spent on the road - which is inversely proportional to speed.
So it can actually be said that a faster (on average) SafeSpeed driver is less likely to have a collision than a slower (on average) SafeSpeed driver.

Cheers
Peter

Yes, I only read your follow-up after I had worn out my keyboard.
I don't know why we were at cross-purposes before - I agree with your 28%.
What I was actually trying to point out is the flaw in the so-called 'research', which would put the figure from your example at 80%

Now if only basingwerk would try my computer simulation for himself, he might stop bothering us so much.

Cheers
Peter