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# Kinetic energy limit

 (+12, -3) [vote for, against]

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.

 — hippo, Feb 08 2013

Momentum Limits
[xaviergisz, Feb 09 2013]

x^2 Scale speedometer x_5e2_20scale_20speedometer
The speedometer was already halfbaked in this anno. [scad mientist, Feb 10 2013]

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Annotation:

 I like it.

 For trucks, you could put a strain gauge in the transmission to measure how much it is carrying to recalibrate the read out.

Also, i think a pedestrian is just dead when hit by anything, so that would not matter- but it does matter against other cars.
 — Kansan101, Feb 08 2013

 //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.)
 — MaxwellBuchanan, Feb 08 2013

 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.
 — bungston, Feb 08 2013

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.
 — WcW, Feb 08 2013

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.
 — MaxwellBuchanan, Feb 08 2013

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.
 — sqeaketh the wheel, Feb 08 2013

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.
 — MechE, Feb 08 2013

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.
 — UnaBubba, Feb 09 2013

Haven't we done this before? I remember reading a momentum limit idea.
 — DIYMatt, Feb 09 2013

 //since we are fresh out right now of spherical chickens

Come on, there's always a few spares in the box to the left. Jutta has a cron job running that tops it up from time to time.
 — not_morrison_rm, Feb 09 2013

[Max-B] Yes, yes, yes, I know all that - really I just wanted a speedometer calibrated in KJ
 — hippo, Feb 09 2013

 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.
 — MaxwellBuchanan, Feb 09 2013

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.
 — hippo, Feb 09 2013

so: in this 135KJ speed limit zone (nominally 30mph), an 80kg rider on a 120kg motorcycle could drive at about 80mph. hmm.
 — sninctown, Feb 09 2013

[DIYMatt] We briefly did the speed^2 speedometer before, and one annotation requested to have it multiplied by mass. See Link/
 — scad mientist, Feb 10 2013

 // 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.
 — Alterother, Feb 10 2013

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...".
 — hippo, Feb 11 2013

A less scientifically callibrated speedo might be enumerated with values such as; Ponderous, Ticking Along, Toe Curling and ARRRRGHH!!!
 — zen_tom, Feb 11 2013

When you say "ARRRRGHH!!!", do you actually mean "R17"?
 — hippo, Feb 11 2013

 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.
 — zen_tom, Feb 11 2013

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.
 — sqeaketh the wheel, Feb 13 2013

Asymptotic speed scale.
 — UnaBubba, Feb 14 2013

 Vehicle specific speedometer marked in "will kill a ..."s: human, horse, rhino, bull elephant, etc.

Street signs appropriately posted.
 — FlyingToaster, Feb 14 2013

Don't forget 'Impulse' and 'Standard Warp.'
 — RayfordSteele, Feb 14 2013

 //        Vehicle specific speedometer marked in "will kill a ..."s: human, horse, rhino, bull elephant, etc. //

I insist upon the omission of the noble rhinoceros from the scale.
 — Alterother, Feb 14 2013

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.
 — WcW, Feb 14 2013

 // 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.
 — MaxwellBuchanan, Feb 14 2013

//rhinoceros// well, we could go the other way: "hitting this at this speed will kill you" speedometer.
 — FlyingToaster, Feb 14 2013

The rhinoceros thanks you, I'm sure.
 — Alterother, Feb 14 2013

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