We use figures from official sources and well respected research to show that we could reduce all UK speed limits to just 12 mph and still have the same numbers killed on the road.

Bong! Including only car drivers excludes one of the principal groups affected by excessive speed - vulnerable road users. These are significantly more likely to be killed, and speed plays a very large part in turning an injury into a fatality for these vulnerable road users. So excluding vulnerable road users essentially invalidates the argument right at the outset.

This is made clear by the source Smith uses: "The relationship between impact speed and crash severity is particularly critical for pedestrians, the most vulnerable road users. In a recent review of the issues, the European Transport Safety Council (1995) report that only 5 percent of pedestrians died when struck by a vehicle travelling at 20 mi/h; however, the proportion of fatalities increased to 45 percent at 30 mi/h and to 85 percent at 40 mi/h."

A thought for you: each year something over 200 children die on the roads, while about 80 children are murdered - 73 of them by their parents or close relatives. On average less than ten children per year will die at the hands of strangers. The papers are full of stranger danger, right opposite adverts for cars.

Notice how we can use these figures to deduce the probability of death in a collision. If you add up all the figures and compare the total to the number killed you can deduce that drivers in injury accidents have a 1 in 125 chance of being killed.

How reassuring for them. Pity about two other road users who die for every driver, really. When seat belt wearing was made compulsory the result was the largest recorded rise in pedestrian, cyclist and rear-seat passenger fatalities. There seems to be a touch of "I'm alright Jack" going on.

We realised that these two pieces of information could be combined. We can calculate the average crash speed from the proportion of drivers killed. We know the proportion of drivers who are killed, and we can use the equation for fig 2 to calculate an average impact speed.

From the first graph (Fig 1) we know the real probability of death to a car driver from an injury accident. 

Turning Joksch's equation around we calculate as follows:

     * speed = 71 * (fourth root of) 0.0079706 = 21.21 mph

We've calculated the average speed required to kill 1 in 125 drivers is 
21.21mph"

This part is utter rubbish.  Why?  Two fundamental problems.
One, you're using the formula for V when it's clearly meant
to be applied to delta V.  Please change the formula to use
V.  Oh, you'd have to ditch the whole page as it's entirely
based around delta V == V?  Shame.

Secondly, you can't apply this formula to the average speed,
and here's why:

A worked example, using your method of equating V to delta V:

Two cars, one with a delta V of 20mph, one with a delta V
of 50mph.  V = delta V, so average value to be used is thus
35mph.

The individual probability of death in the 20mph and 50mph
cases are:

(20/71)^4 = 0.00630
(50/71)^4 = 0.24595

We apply the same formula to the average of these two delta Vs,
and we get:

(35/71)^4 = 0.05905

Note that the proability of death for someone involved randomly
in either a 20 or 50mph incident would be (0.00630 + 0.24595)/2
or 0.126125).

Let's reduce those speeds by 10mph.

(10/71)^4 = 0.00039
(40/71)^4 = 0.10074

Average of these: 0.050565

Improvement: 2.4x less deaths

Applying the formula to the average delta v:

(25/71)^4 = 0.0153

Improvement: 3.85 times less deaths.

So it seems that your method of using the formula underestimates
the death rate and overestimates the benefit of reducing speeds.

We've shown without room for doubt that the average speed of a fatal accident on a UK road and affecting a car driver is less than 12 mph.

Bong! Oh no "we" haven't. The fatality line is effectively flat (i.e. zero within the limits of experimental uncertainty) below about 20mph, and certainly below 15mph. Joksch says: "These relationships are based mainly on speed limit and speed changes on high-speed roads. More research is needed to assess their applicability to low-speed urban roads." This is not even a formal equation, merely a "rule of thumb." So the equation is clearly not applicable at low absolute speeds.

Why might this be? One reason is that drivers of modern cars can normally survive a 12mph crash into a stationary object without fatal consequences. Another is that I for one can run faster than 12mph. What is Smith's proposed mechanism for causation of fatality in all these 12mph crashes? The equation is being misapplied, and the misapplication is then being erroneously extrapolated beyond its limits of experimental uncertainty.

Since 12 mph bears no relation to any free travelling speed used on UK roads "something" must intervene between free travelling and the actual crash. This "something" is of course driver response. No one wants to crash. Most drivers, most of the time have effective strategies for avoiding crashes. In practise the failures of these crash avoiding strategies are not normally massive blunders resulting in impacts at free travelling speeds. Instead they are subtle misjudgements followed avoiding actions leading to mostly minor crashes. The ratio of minor crashes to fatal accidents is probably greater than 1,500:1.

Perhaps you might wonder if speeding is a separating factor between the 1,500 survivors and the 1 fatal? With 70% of drivers exceeding the speed limit at sample sites it would be an entirely unreasonable conclusion.

Bong! The 70% don't speed all the time. To quote Smith's source (my italics), "Vehicles exceeding the 90th percentile speed or traveling more than 7 km/h faster (4 mi/h) than the speed limit and median speed had above average injury crash involvement rates." Note that in a 30mph limit the median speed is 31 and Gatsos are usually not set below 36mph. This is fully consistent, therefore, with catching only those drivers at greatest risk of crashing. A safety win!

It isn't speed that kills. We can reduce the speed limits endlessly or enforce them perfectly without ever hoping to get close to the thresholds where free travelling speed will play a larger part in the outcome than driver based factors like skill, attention, attitude and training level. In fact, small variations in these factors will have far more effect on accident rates and outcomes than big variations in limited or enforced speed. See elsewhere on this web site.

Bong! The figures on which Smith bases this very page show that accident probability increases with increasing speed and reduces with reducing speed - in fact they suggest that numbers of crashes should be significantly reduced if everybody obeys the speed limit. His referenced source says "When the consequences of crashes are taken into account, the risk of being involved in an injury crash is lowest for vehicles that travel near the median speed or slower and increases exponentially for motorists traveling much faster." And the equation on which he bases the entire shambolic argument specifically states that the probability of fatality given an accident rises with the fourth power of speed. In what way does speed, then, not kill?

So far we've only looked at injury accidents. Perhaps we should make things a little more realistic by looking at all accidents? One problem is that damage only accident figures are not gathered nationally. There's some data from the insurance industry, but we'll need to do a little intelligent guesswork. There were about 4,000,000 motor insurance claims for the last year on record (2,000). We'll assume that 75% were vehicle accidents, and 50% of those applied to private motor cars. So we have 1.5 million accidents (give or take)