I have just had a brief argument with a (highly annoying) cow-orker about car crashes. The basic point of it was that I thought that speeding in a built up area (30 mph zone) was worse than speeding on a motorway (70 mph zone). My reasoning was that if you did 40mph, for example, in a 30mph zone you were going 25% faster than the speed limit and were also more likely to encounter pedestrians etc. I also added that doing 80mph in a 70mph zone was only a relatively small 10% faster than the speed limit and that the difference in speeds would have a negligible effect on the resulting carnage. Basically if you crash at 80mph when you should be doing 70mph will effectively make little difference to your chances of survival. Now this is where annoying cow-orker stepped in with his usual counter argument (I swear this guy would argue that black was actually white if you asked him) containing a lot of long words and physics that to be honest I didn’t understand (I am not entirely convinced he did, I just think he tries to baffle people into submission). Now I know that the majority of road fatalities occur in built up areas and I also know that doing 35mph instead of 25mph results in a far higher death toll (I don’t remember the exact figures but it was from a road safety campaign run by the government) so I know that my argument is sound at least in that respect. Can anyone in the know give me as much info. as possible behind this subject as the guy really cheeses me off and I’m convinced he is talking out of his ass.
*I know I haven’t given his ‘argument’ but that is simply because I didn’t really get his point also his voice offends me and I find it hard to listen to him without wanting to scream.
Well, your coworker is probably arguing that kinetic energy increases as the square of the velocity, so if you hit something on the expressway, there’s more energy to spread around in the form of mayhem. There are probably other factors that become increasingly borderline at high speed – for example, braking distance and reaction time.
However, you are right in that suburban or built-up areas are a more target-rich environment and are likely to present more unpredictable events such as cars entering from driveways or kids chasing balls into the street.
But without knowing what point your coworker was actually making, and then grovelling through a whole bunch of statistics (which will probably prove to be interpretable in a myriad of ways), there’s no way of giving you a definitive answer.
Yes, that sounds like the jist(sp?) of it. Does 10mph extra make that much difference at that speed though?
The fact that a 10 mph increase is a smaller percentage increase at higher speed outweighs the squaring effect IF you are talking about the percentage increase.
A car at 35 mph has about twice the kinetic energy it has at 25 mph.
A car at 40 mph has about 78% more kinetic energy it has at 30 mph.
A car at 80 mph has about 30% more kinetic energy it has at 70 mph.
But the extra 10 mph actually provides much greater energy at high speeds. If we arbitrarily call the kinetic energy of a car at 10 mph “1 unit of kinetic energy”
A car at 35 mph has 12.25 units; at 25 mph, it has 6.25 units (5.75 units increase)
A car at 40 mph has 16 units; at 30 mph, it has 9 units (7 units more energy)
A car at 80 mph has 64 units; at 70 mph, it has 49 units (15 units more energy)
In short, the increase ALONE when you go 80 instead of 70 mph is more than the TOTAL energy of going 40 mph.
Absolute energy is much more related to the amount of damage you’ll do to yourself and all the cars around you. (Freeway accidents are more likely to be multicar, rather than two-car.) Absolute energy is also more relevant when you consider the chances of losing control (you tire friction on the road and braking capacity will be smaller by comparison). Higher speeds might also contribute to the chances of a blowout (however heavily you weigh that possibility).
Also, all the cars around you are also going at a higher speed, and if you careen into one of them, the total energy of ALL the cars might be important. If the accident were bad enough to make all of you lose control (i.e. a domino effect that ends with all cars at a full stop). The total energy of several cars would add to the lethal potential. However, in a fender bender, even at highway speeds (e.g. you swerve after a blowout, and bang into another care, but both of you recover and maintain highway speeds) the difference in velocity is more important.
I agree that lower speed, more populated roads are target rich environments, and laso present more traffic hazards. I see roughly the same numbers for highway fatalities per vehicle mile and overall traffic fatalities (roughly 1 fatality/160 million vehicle miles in 1997) but without looking at the source data, I’m not sure if they’re comparing apples to apples.
Only you can decide which factor is more important to your argument. Often the most important factor is “the position I already took in this argument.”
Yeah, you are right it is usually the most important factor…(I found this very amusing, thankyou!)
I still can’t quite get my head round the figures though (I admit i’m a bit thick when it comes to maths), is it really that much worse to crash at 80 rather than 70? Either way I will bow to your greater knowledge, I just get annoyed at this guy because he seems to be deliberatley obtuse when it comes to discussions like this.
I would guess that speeding by a certain amount leads to more accidents in low speed limit areas than high speed limit areas. That is if you are going 40mph in a 30 zone you are probably going too fast to deal with the area. This is especially true when there are kids about. Likewise people are going to be pulling out of their drive way and the like. Going 80mph when the speed limit is 70mph probably isn’t going to lead to more accidents - unless of course you are going significantly faster than the rest of traffic. In that case you probably are going to have some trouble if you hit dense patches.
Actual collisions are worse at high speeds, and in high speed areas. To figure out a combined how bad value you could calculate chance of accident and multiply it by consequence of accident. This is your expected accident value of various speeding scenarios. Go to your coworker and say that and make up numbers. It generally works as a way to win arguments. If he challenges your numbers refer him to various government websites and google to find traffic statistics.
A few points of clarification (I should know better than to post at 3 a.m.)
The difference in energy between 70 and 80 mph (15 units) is ALMOST as much as the total energy (16 units) at 40 – not “more than” as I said.
The equation for kinetic energy is 1/2*(mass)*(velocity squared). Since the mass of a car doesn’t change appreciably at speeds much less than the speed of light, and the 1/2 is a constant that divides out, the relative energy of different speeds is proportional to just “velocity squared”. This may help you see how I got the figures above e.g. (80^2)/(70^2) = 6400/4900 = 130.6% or roughly a 30 percent increase.
The reason I compared “highway fatalities per vehicle mile” with “overall fatalities per vehicle mile” was to see if highway driving was safer per mile than nonhighway driving. The federal government collects separate statistics for federal Interstates, but local roads aren’t federal, so I could only check if highway driving was more dangerous than the “overall average”. However, since the numbers were almost identical, I wonder if the people who put together the gov’t charts I linked were so careful about labelling the exact stats they were copying.
I really find it hard to believe all driving is equally dangerous. Of course, since I would have been equally willing to accept “highway is safer” and “highway is more dangerous”, there’s no logical reason NOT to accept that they may be the same.
Absolute energy [the total kinetic energy of the car] is related directly to damage by collision with a stationary objects. Impacts with other vehicles at a similar speed are more complicated, so I simply assumed a “serious” impact, where both cars eventually come to an uncontrolled halt. In those cases, the total energy of both cars can play a role in whether they skid out of control, hit other cars or rails, or roll over. It’s probably not the most representative case, though.
Brake pads/drom/rotors turn your [absolute] kinetic energy into heat through friction. Too much heat, too fast, will make them overheat, and they’ll be useless. Your ability to steer (mostly whether your tires will grip the road) depends on a combination of momentum and energy, and momentum is directly proportional to the speed (if a car goes twice as fast, it’ll have twice the momentum) However, at high speeds, you often can’t move the steering wheel/tires turn fast or far enough to keep up with anything but minor controlled turns, so we may as well assume it’s roughly proportional to the energy, which goes up much faster than momentum.
The real factor is psychological, as you noted in your OP: drivers don’t think “I’m going 33% too fast”; they think “I’m only going 10 mph over the speed limit” partly because mph are reported on the spedometer, while percentages aren’t. As you said, speeding by 10 mph is a bigger deal when the speed limit 30 mph (vs 70), but that’s not how many people think. Some drivers feel that “45 is a safe easy speed for me” and treat speed limits of 25 or 30 as pointless nuisances – schoolchildren be damned. People get some seriously odd notions behind the wheel.
WILLASS, you are correct, mainly because you are a Doper and the other person is just a cow-worker, but in my opinion, for other reasons as well. I will try to provide some statistics and reasoning to back up my/your argument.
By the way, I design roads in the US but learned to drive in England, have a British Driving Licence and love the UK roads.
The safety issue of traveling (please excuse the American spelling) over the speed limit has nothing, or little, to do with the physics (mass and velocity) of vehicles but instead has to do with the driving environment. The environment consists of design standards (if any), surroundings and potential for conflict (e.g. hitting another vehicle, bicycle, pedestrian, etc.).
A bit of background – Pedestrians and bicyclists make up 45% of UK fatalities. I do not know for sure if these are included in the fatality rate statistics, but would believe so. Among motorized traffic, the highest rate of fatalities and injuries is among motorcyclists. Sources for this information are:
http://www.safecarguide.com/exp/statistics/statistics.htm
http://www.etsc.be/STATS5dec.pdf
Motorways, and in the US, Interstate Highways, were built to be forgiving to accidents. There is a safe area alongside the road that allows most run-offs to recover without hitting an immovable (killing) object, and there is a lack of pedestrians, bicycles, animals and adjacent oncoming vehicles to run into. A measurement of safety is the accident rate, often measured in accidents per 100 million kilometers traveled by vehicles. In the UK, for 1998, the rates were Motorways – 10; Trunk (A) roads – 29; All A roads – 55; Other roads – 75. (For US readers – Trunk A roads are like non-Interstate highways. A roads are major roads but not highways.) So, you are 5.5 times more likely to have or cause a fatality on an A road than on a motorway for every mile/kilometer you drive. http://www.highways.gov.uk/aboutus/corpdocs/strat_plans/safety/02.htm
So, on a motorway, although a vehicle traveling at 80 mph in a 70 mph speed zone has more potential for damage based on kinetic energy, the construction of the road is more forgiving and the distance you can see an object that you need to safely stop for is farther than in the Town Centre or hedge surrounded lanes.
Where are pedestrians and cyclists typically found? In towns, usually where speed limits are lower. These are also areas that are much more susceptible to accidents. For any increase in speed you also increase your “stopping distance” and decrease your reaction time. On the motorway, if your visibility is 1000 feet, a speed difference of 80 mph vs 70 mph does not matter that much. Among the local shops, if someone can step out from between parked cars 100 feet away, 40 vs. 30 mph does make a big difference.
For a UK/US comparison, in 1996 the listed fatality rate for the UK is 0.86/100 million vehicle km and for the US it was 1.1. http://www.fhwa.dot.gov/ohim/hs97/in56.pdf
Another bit of information – In the US, at least in Minnesota, the highest fatality rate areas are rural roads. A big reason for this is the amount of time for accidents to be discovered and responded to by emergency crews. There are other factors as well, but this reason surprised me when I found out.
Mycroft H., great post.
I, too, used to think in terms of % when driving over the limit. I believe it counts because usually limits are designed around the conditions of the road (not always though).
Speed isn’t really the issue. People can shout all the numbers then want about energy at certain speeds. The fact of the matter is, the better roads are the high speed roads. They were designed for 75 mph (the old “limit”) and have been reduced to “PC” levels which are too low for most, if not all, drivers. Most highways could easily set their limits to 85 mph without a huge change in accident numbers (ok, maybe not in MOST cities, but along the more rural highways).
Thanks for all the information guys, I really have learnt something! The problem is what to do with this new found information? I can’t bring myself to be so petty as to bring up the argument again just to prove him wrong so I will have to hope that he does it himself (this is quite likely as he is exceptionally petty) and when he does I shall quote stats. like a man possesed. Thanks again guys, I love this place - you can get really detailed explanations, they are just 24hrs too late to inform my cow-orker Tim ‘The Winter of Discontent’ Winters.