In a collision between a car and a pedestrian, it's not the speed of
the vehicle which makes it more likely for the collision to kill the
pedestrian, it's the kinetic energy (œ mv²) of the vehicle, so faster
cars will be more likely to kill you, but so will heavier ones. So,
this
idea is for
cars to have kinetic energy gauges instead of
speedometers, and for kinetic energy limits, rather than speed
limits. Thus, instead of the 30mph limit in most UK towns, there
would be a 135KJ limit and lighter cars would therefore be
allowed
to travel faster than heavier cars.

This would have the benefit of conveying to people the
dangerousness of going faster as it would show that driving at
30mph
your car has more than twice the kinetic energy as it does driving
at
20mph. Also, note that driving a light, flimsy car fast is more
dangerous *for you* than driving a heavy car slowly but that's your
choice - this idea is about protecting other people.

//so faster cars will be more likely to kill you, but
so will heavier ones.// No, not really. What
counts is the kinetic energy _absorbed by the
pedestrian_.

The absorbed kinetic energy does indeed go up as
the square of the velocity, but isn't much affected
by the mass of the vehicle, at least over a certain
mass.

Imagine being hit by a truck at 40mph.
Unless it's a glancing blow, you will end up
travelling at close to 40mph - the truck is barely
slowed by the impact. If you're hit by a typical
saloon car at 40mph, the car is slowed a little (say,
to 35mph), but not significantly. You wind up
absorbing very nearly the same kinetic energy.

The mass of the car only becomes important for
very, very low mass cars (say, less than a few
times the weight of the pedestrian). In these
cases, the car is significantly slowed by the
impact, and hence it (by being slowed down)
absorbs a significant amount of the energy of the
collision.

If this isn't clear, let me ask you a question.
Would you rather be hit by a 10,000kg truck doing
10mph, or by a 1000kg car doing 33mph, assuming
(in each case) that you're not being crushed
between the vehicle and a wall? Both vehicles
have the
same kinetic energy, but you're not going to walk
away from the 33mph impact with a car, because
you will have absorbed roughly 10 times more
kinetic energy.

So, although the absorbed energy does indeed
depend on œ mv², the relevant "m" is the mass of
the _pedestrian_, not of the _vehicle_. Just mark
your speedo in v² regardless of the vehicle mass.

Incidentally, obese people are significantly more
likely to be injured when hit by vehicles than are
skinny people, precisely for this reason. Children
(being lightest) absorb the least kinetic energy
but, unfortunately, they are also very fragile.
(They also have lower centres of mass, and are
hence more likely to wind up under the wheels.)

Really the way to decrease kinetic energy delivered is with a big triangular spike on the front of the car. If it hits you perfectly that would not be good, but more likely it will be on one side or the other, pushing you aside rather than transferring kinetic energy directly to you.

Plus that spike would be styling! Please illustrate your idea but with this spike. It should be blue, or bluish.

I believe that making laws on the sole basis of just one very limited type of traffic incident is a flawed approach. Flawed to the point of failing to consider any other ramifications, such as what happens when that lighter car traveling faster fails to navigate the corner at high speed and plows headlong into the heavier car, or if the drivers of lighter cars are somehow blessed with the power to see objects obscured from their vision and the prescience to know when people will pull out of parking spaces and blind alleys better than their heavy vehicle peers.

So, that's a closing speed of 18mph, and suppose the
truck weighed 10,000kg. By [hippo]'s reckoning, that
would be equivalent to being hit by a 1,000kg car at
54mph, from which you wouldn't have walked away.

Consider a spherical pedestrian (since we are fresh out right now of spherical chickens), with mass m, standing still. And a truck with mass M moving at speed V. Total momentum then is MV. After the collision, if head-on, the pedestrian is traveling at –v and the truck at V’. Total momentum is MV’-vm, which must equal MV. Also energy is conserved, so MV^2 = MV’^2 + mv^2. Solving, we find:

KE (pedestrian) = mv^2 = 4mV^2 (M/(M+m))^2.

For M >> m, we find KE (pedestrian) = 4mV^2, which is indeed independent of the truck’s mass, proving Max correct once again.

Braking distance and drivers reaction distance are far
more important factors. If you're going to adjust
speed limit, you're probably better off basing it on
driver's age.

Unless you're on a motorway in the UK the speed
limit of 30mph is entirely theoretical. The road
system of the whole country is a convoluted,
tortuously narrow traffic jam.

Ah, but then it would have to be calibrated for the
mass of the pedestrian you're planning to hit, rather
than for the vehicle (from the original idea: "faster
cars will be more likely to kill you, but so will
heavier ones").

But the idea of a speed-
squared scale would be good.

Yes, maybe a speed-squared scale would be sufficient. Of
course we'd need bigger speed limit signs to fit the extra
characters, as "30" would now be "900", but that's easily
done.

// so: in this 135KJ speed limit zone (nominally 30mph),
an 80kg rider on a 120kg motorcycle could drive at about
80mph. hmm. //

Therein lies the rub: the potential damage of a collision is
not the only factor involved in the calculation of a speed
limit. Traffic engineers must also take into account the
manueverability and stopping distance of various vehicles
(stopping distance formulas are surprisingly complicated),
as well as the wide range of
experience of vehicle operators. A motorcycle rider with
100 hours of riding may have more trouble avoiding a
sudden obstacle at 30mph than a rider with thousands of
hours in the saddle, but neither of them will stand a
chance to avoid it
at 80mph because they cannot react quickly enough or
turn as sharply.

One of the nice things about the Halfbakery is that, for the most part, it's very polite when compared with other forums (fora?). So, where mild disagreement might be communicated elsewhere with "YOUR A MOREON!!", on the Halfbakery we get the more civilised "Therein lies the rub...".

Aha - I had to look up the reference before remembering where it was from:

From Hitchhiker's Guide to the Galaxy. "R is a velocity measure, defined as a reasonable speed of travel that is consistent with health, mental wellbeing, and not being more than, say, five minutes late. It is therefore clearly an almost infinitely variable figure according to circumstances, since the first two factors vary not only with speed taken as an absolute, but also with awareness of the third factor. Unless handled with tranquility, this equation can result in considerable stress, ulcers, and even death."

But yes, R as a trickily defined measure of speed (including both personal lateness vector, but also one describing the current road conditions and general level of safety) should very much be the one shown to users on their dashboard - one element of which very likely ought to be the kinetic energy currently possessed by the vehicle in question.

I like the "the idea of a speed- squared scale," since in operation it would have exactly the same effect as a speed scale, but the speedometer would look cooler.

Wow. It's not just speed and energy imparted you silly mechanical engineers. Accident fatalities are totally dynamic, sometimes death results from tiny tears or lesions, aneurisms, thrombosi, ruptures, where the injury was apparently very slight. In other cases the body suffers severe trauma, dissipates massive amounts of energy and the victim survives. Factors such as which way you are looking, what you had for lunch, if you see the car coming and resist the impact all play roles, but the final outcome is impossible to predict.

Howevertheless, to a first approximation, injuries
tend to increase as the square of the impact
speed.

By strange coincidence, the terminality of
electrocution also goes as the square of the
applied voltage (all other things being equal),
because the energy delivered (V^2/R) goes as the
square of the voltage.

But this may be all by the by since, as discussed
above, the only useful part of this idea is the
speed-squared-ometer part, which has been
explicitly halfbaked as per [scad]'s link.