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    Unleaded Foot On The Gas Pedal
    By Enrico Uva | January 9th 2013 11:00 PM | 22 comments | Print | E-mail | Track Comments
    About Enrico

    I majored in chemistry, worked briefly in the food industry and at Fisheries and Oceans. I then obtained a degree in education. Since then I have...

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    People on highways interpret speed limits as a minimum velocity. On certain stretches of the Florida interstate 95, the speed limit is 70 miles per hour or 113 kilometers per hour (31 m/s). But several times, except for the odd truck carrying a herd of elephants, we were the only ones actually moving at 70 mph.

    The gaps between us and other cars kept increasing. Yes, the lanes are wide and numerous. The road is flat and likely to be free of ice for at least 364 of 365 days. It's also not a good idea to lag too far behind the rest of traffic. But none of this makes driving fast rational.

    1. Why do People Drive Fast?

    The primary reason seems to center around the issue of time. I found data for New York State. When using a personal vehicle, the average length for a long distance trip was 488 miles. Depending when the data is collected, specific location and other variables, this number will vary across the country. But assuming immediate access to a highway, no construction and no traffic tie-ups, on average the total maximum time "saved" on a 488 mile-trip by going 70 mph instead of 60 mph is about 1 hour and 10 minutes.

     Of course the term "wasted" is very subjective. If that extra hour is spent talking to a spouse or child, listening to music or to an audio book--- or better still, simply thinking,  how is it ill-spent? The idea for the polymerase chain reaction came to Kary Mullis while he was driving and his girlfriend was asleep.

    But many people on the interstate are not driving on long distance trips, especially when the highway approaches major urban centers, where most of the speedsters probably live. If they're traveling to a workplace 5 to 20 miles away, by going ten miles above a 65 mph speed limit, they are saving a whopping 0.6 to 2.4 minutes!

    Since most drivers as novices once feared a loss of control when moving too fast, going over the speed limit and maintaining the car on the road gives them a sense of mastery over the elements. The competition-thrill and the joy of having no other drivers ahead of them gives drivers added incentive for having a heavy foot on the accelerator. A sense of power is accentuated even at constant speed by the following kinematics reality: if the driver is moving at 75 mph instead of 65 mph, the time it takes to catch up to a 55 mph driver is cut to half. *see end of article for the simple mathematical details.

    2.    Reasons to Drive Slowly

    Anyone who's been to driving school has been reminded that speeding is risky. Moving at 75 mph instead of 55 mph gives the car (77/55)or almost twice as much kinetic energy, something of consequence in case of a collision. Since the work needed to stop a vehicle is related to its kinetic energy, breaking distances and speed are not associated though linear relationships either. According to this braking calculator, on dry asphalt 145 feet are needed to bring a 55 mph car to a stop. At 75 mph, 269 feet are required---again almost a factor of 2.

    On snow, the distances mushroom to 337 and 627 feet, respectively! But the need for speed digs a ditch between thought and action, not too differently from the way high-speed, violent impacts persist in the NFL and NHL because fans enjoy them.

    Another reason to keep an unleaded foot on the gas pedal centers around fuel efficiency. The minimum speed at which the highest gear engages is where the least amount of fuel is consumed per mile traveled. Minimizing fuel consumption is great for both pocket books and the environment. For most car models efficiency peaks close to 55 mph. In 2009, Consumer Reports found that fuel efficient car models experience, on average, a 12% drop in fuel economy at 65 mph and a 25% drop at 75 mph.


    Driving more slowly also widens central vision while increasing peripheral vision, both of which help prevent accidents. Although it's not advisable for a driver to engage in sightseeing while driving, moving slowly also gives passengers a better chance to enjoy the scenery and take photographs. Finally there's less noise generated at lower speeds:


    *
      A-------------------------------B---------------------------C
    Let x = the separation distance between driver A and driver B.
    and let C represent the position where A catches B. 

    Let y = distance from B to C.
    With no acceleration:
    y = VBt
    x + y = VAt.
    Substituting:
    x + VBt = VAt.
    x =  VAt -VB
    x = t(VA-VB )
    t = x/(VA-V)
    so if the difference in velocity is doubled, the time to catch the slower car is cut to half.

    Sources:

    https://www.dot.ny.gov/divisions/policy-and-strategy/darb/dai-unit/ttss/repository/trend%20highlight%202_28_06.pdf

    http://www.transportenvironment.org/sites/default/files//docs/presentations/2005/2005-01_clean_car_seminar/2005-01_p6_reducing_noise_pollution_from_cars_brouwer.pdf


    http://www.roadtraffic-technology.com/features/feature126199/feature126199-3.html

    Comments

    vongehr
    Another scary set of calculations gives the paths/times that one drives basically unconscious at high velocities due to the ~ 0.5 seconds it needs to react consciously to anything unexpected that one has no trained unconscious response for (say tire blow out), which often increases reaction times dramatically.  The brake path is only that long if we brake, or the collision brakes us in more sense than one.

    BTW: Velocities are always relative velocities, so 75-55=20 while 65-55=10 is enough.  Involving x only adds confusion.
    UvaE
    Another scary set of calculations gives the paths/times that one drives basically unconscious at high velocities due to the ~ 0.5 seconds it needs to react consciously to anything unexpected that one has no trained unconscious response for (say tire blow out), which often increases reaction times dramatically.  The brake path is only that long if we brake, or the collision brakes us in more sense than one.
    Thanks. It's a good one.
    Involving x only adds confusion.
    Yes, but as a former math teacher and otherwise loyal husband, x is my mistress. :)
    Brent1178
    Good article. Not nearly enough people really understand the relationship between speed, and stopping distance, reaction time and fuel economy. 
    The competition-thrill and the joy of having no other drivers ahead of them gives drivers added incentive for having a heavy foot on the accelerator.

    I really think that the subconscious drive to speed comes more from that competitive nature than  time pressure most of the time, especially for us males. have you ever noticed that no matter what speed you're doing, if you have a truck in front of you it feels too slow and you want to be in front?
    or that rush of blood you get when someone passes you at speed, (particularly if they do it on a blind corner and cut you off)? It's like a personal insult. The testosterone fuelled part of you wants to reassert your dominance by chasing them down, even while the rational part of you reasons that the speed you're doing is just fine, and that he's using twice as much fuel and is four times as likely to kill himself. Of course it makes you feel much better if you see him 5k down the road pulled up by a cop!

    Since becoming involved in Solar Car racing, I've come to far better appreciate the relationship between speed and energy consumption. I like to think that the rational part of me is much stronger these days than in my teenage years, and I drive slower than I used to  but I still feel the testosterone fuelled part trying to take over at times especially if someone just pissed me off.
    UvaE
    Since becoming involved in Solar Car racing, I've come to far better appreciate the relationship between speed and energy consumption.
    That must be fun. Do you have any speed vs. fuel* consumption numbers for solar cars?
    *meant "energy" :)
    Brent1178
    Fuel consumption? Zero at any speed, energy consumption? approximately 600W at 60 kph and 2200W at 100 kph. There is quite a lot of variation with road surface, also the slightest gradient makes a big difference. We found the best speed for our car was between 60 and 65 kph, going faster than that meant covering less distance on a days energy. If we were driving at 100 for example, we would cover less than half the distance before running out of energy. Since we designed the Solar Fern, the rules have changed and solar cars are now smaller, and aerodynamics are still improving so the top cars now can use as little as 1600W at 100kph.
    The car was designed and built for the 2007 world solar challenge. Basically we were a bunch of friends who decided it would be fun to have a go, no University backing, very little sponsorship, and a very small budget. When we ran out of money and failed to get a major backer, we used borrowed polycrystalline solar panels which were already 15 years old and obsolete, so we were far from the fastest in the race, but we came 12th out of 18 in our class, ahead of some teams who had spent several times our budget, so we came away happy and it was a very educational experience. Since then we set a record in 2011 by being the first to drive a solar powered car the full length of New Zealand, which proved to be a bigger challenge than Australia because of the terrain and weather. Now the car is obsolete as a racer, but I keep it road registered and often drive it to work. It's entertaining looking at the expressions of fellow motorists!


    UvaE
    Fuel consumption? Zero at any speed, energy consumption?
    Sorry! I wasn't necessarily thinking of some sort of hybrid by using the word "fuel' instead of "energy".  
     600W at 60 kph and 2200W at 100 kph. 
    The efficiency definitely drops. The car needs 2200W/600W = 3.7 times as much power to get only (100kph/60kph)2 = 2.8 times as much moving energy. 
    Beautiful car, though. It looks like an airplane wing on wheels.

     but I keep it road registered and often drive it to work. It's entertaining looking at the expressions of fellow motorists!
    I must confess that I've long wanted to add such a feat to the list of transportation modes that I've used to get to work---legs, bicycle, cross-country skis, dog(not a sled; he just pulls hard and I sometimes glide on the ice!) 
    Brent1178
    The efficiency definitely drops. The car needs 2200W/600W = 3.7 times as much power to get only (100kph/60kph)2 = 2.8 times as much moving energy. 


    The problem is that aerodynamic drag increases with  the square of the speed, so doubling the  speed results in four times as much drag, and the power requirement increases with the cube of the speed. Eight times the power over half the time, means energy spent on aerodynamic drag is still four times as much over a given distance at double the speed. or 2.77x the energy at 1.66x the speed as in 60kph/100kph. If all the drag was attributable to aerodynamics then you would expect the car to use 1.6666^3 = 4.63x as much power doing 100kph compared to 60kph. Fortunately the aerodynamic drag on this vehicle is very low. Drag due to rolling resistance, the other factor,  remains constant, so the power required to overcome rolling resistance increases in direct proportion to the speed. The faster you go, the more dominant the aerodynamic drag as a proportion of the total.


    The reason you don't see such a dramatic difference  in fuel consumption in an ordinary car (though it's still significant) is that an internal combustion engine is at it's most efficient close to full power and the efficiency drops off dramatically at very low power settings . At idle with the motor burning fuel but producing no power the motor is zero percent efficient. At 50 kph (roughly 30 mph) the engine is barely working above idle and is probably only about 5% efficient, while at 100 kph, the car requires 6-7 times as much power (depending on the ratio  of rolling resistance to aerodynamic drag), but the motor may be operating at more like 15% efficiency, and the result is a relatively small increase or no increase  in fuel consumption  over the trip. Above 100kph, the power requirement keeps increasing at close to the cube of the speed but there is less to be had in efficiency increase, so you start to see the fuel consumption rising more spectacularly.


    Beautiful car, though. It looks like an airplane wing on wheels.


    Thanks, I did a lot of the work on the aerodynamics and body design and I'm quite proud of it :-)




    Brent1178
    Fuel consumption? Zero at any speed, energy consumption?
    Sorry! I wasn't necessarily thinking of some sort of hybrid by using the word "fuel' instead of "energy". 
    It's OK I knew what you meant :-)  I thought it might be interesting to convert the energy consumption to a petrol/gasoline equivalent as a comparison, so;

    Petrol has an energy density by volume of 9.7 kWh per Litre. (varies a little by composition, ethanol blends aren't as good)
    1 Litre per 100km = 235.21 miles per (U.S)gallon
    2200W at 100kph = 2.2kWh per 100km or equivalent petrol/Gasoline consumption  0.227 L per 100km or 1036 miles per gallon
    600W at 60kph = 1kWh per 100km or equivalent petrol/gasoline consumption 0.103 L per 100km or 2283 miles per gallon!


    Of course achieving such fuel economy in practice with an internal combustion engine is rather difficult since the electric motor in the solar car is about 95% efficient and no one has managed to build a 90+% efficient petrol engine. This is where electric cars have such an advantage in terms of energy consumption, especially at low speeds where the internal combustion engine is so inefficient.









    MikeCrow
    Very cool!
    And I've noticed the difference between level roads, and any sort of up-grade, if you could go downhill everywhere it'd save lots of fuel ;)
    Never is a long time.
    MikeCrow
    Then this might be the wrong thread to point out my old car still got near 27 mpg while averaging 85-90 mph????????
    Never is a long time.
    UvaE
    What did your old car get at 60 mph? 
    MikeCrow
    28-30 mpg, but on flat ground, 6 gear @~ 40-45mph I would see instantaneous averages in the +40mpg range. All from a 405 hp Corvette. Which I haven't replaced yet.
    Never is a long time.
    Brent1178
    Interesting, so 30mpg at 60mph =2 gallons per hour, 27mpg at 85mph = 3.148 gallons per hour.

    If the Corvette uses 15kW or about 20hp (at an educated guess ) to push it along at 60mph, and energy density of petrol is 9.7 kWh per litre or 36.6kWh per US gallon, so energy consumption of 2gph= 73.2 kW, then the motor is working at a respectable 20.5% efficiency.

    If of that 15kW 5kW is rolling resistance  and the other 10kW is aerodynamic drag (again the proportions are a guess) then increasing the speed by 1.416x to 85mph would cause the rolling resistance to increase to 7kW and the aerodynamic drag to 34.2kW (speed cubed), so the total power requirement would be 41.2kW. Fuel consumption of 3.148gph= 115.2kW would make the efficiency of the motor an unbelievable 35.7%

    I know the motor isn't actually going to be 35.7% efficient, so maybe my educated guesses aren't too good, all the same 27mpg at 85mph is pretty amazing.
    MikeCrow
    From what I've read, they are getting close to that number. In general, hi-performance engines tend to have lower internal losses, low friction rings, roller rockers, etc, Plus being capable of pumping a lot of air, they have lower pumping losses.
    In the case of the Corvette, it's pretty aerodynamic, has a top speed ~165, to maybe a tick more and weighs 3050 with about 8 gal's of gas. Mine dyno'd a tad over 350 hp at the rear wheel, manual transmissions seem to have lower internal losses, as well as (many anyways) low numerical final gear ratios.
    I also have a GMC truck with a 300 hp version of the 3rd gen v8 (a variant of the corvette engine), all wheel drive, automatic, and probably weighs 4,000-4,500 lbs, and it gets about 17 mpg. The engine isn't going to be as efficient as the vette, but much of it's internals are the same.

    But it's near half the mpg highway is going to be because of aero, a bit more drive train loss and gear ratio (cruise rpm). Weight comes into play starting and stopping, and therefore driving style makes a huge difference.
    I had a 1986 Dodge Shelby Charger (~170 hp 4 cyl turbo), it got about 33mpg highway, a day on a road course yielded about 8.
    Never is a long time.
    In the case of the Corvette, it's pretty aerodynamic, has a top speed ~165, to maybe a tick more and weighs 3050 with about 8 gal's of gas. Mine dyno'd a tad over 350 hp at the rear wheel.

    I was thinking perhaps I over estimated the drag, the corvette is pretty sleek, but knowing the top speed and power at the wheels, (assuming that 165mph uses the full 350hp at the wheels) we can calculate it a little  more accurately. At 165mph, (2.75 x 60 mph) the power to overcome rolling resistance is 2.75X higher than at 60 and the power to overcome aerodynamic drag is 2.75^3 = 20.8 x higher than at 60.So again using the assumption of 5kW rolling resistance at 60, 13.75kW at 165mph.  350hp = 261kW. - 13.75kW rolling resistance leaves 247.25kW being used to overcome  aerodynamic drag.  Reduce the speed to 60mph and 247.25kW/20.8= 11.88kW, not too far off my estimate. You can see that if my estimate of the  rolling resistance at 60mph was out significantly, it wouldn't make much difference to the calculation, you can also see the huge difference that speed makes to drag, especially at the higher end. 
    Weight comes into play starting and stopping, and therefore driving style makes a huge difference.

    Too true, I've been being a bit simplistic by assuming a constant speed on a level highway, otherwise it gets a whole lot more complicated. One of her biggest wastes of energy is heavy braking, as you dump all your kinetic energy into the brakes and then replace it by burning more fuel as you accelerate again.

    UvaE
    One of her biggest wastes of energy is heavy braking, as you dump all your kinetic energy into the brakes and then replace it by burning more fuel as you accelerate again.
    You've just described my wife's driving!....Not to mention the cost of replacing brakes.

    MikeCrow
    assuming that 165mph uses the full 350hp at the wheels
    With my car it was a little more complicated (but I suspect your calculations are close enough).
    It is rpm limited in 5th @~165, but 6th was too much of a step, so it couldn't really pull 6th to redline (or even peak hp). I had seen people say they managed to get close to 170, but myself I don't think I ever had it much over 140 or so (on a very fun trip to the airport playing with a 911).
    Never is a long time.
    Brent1178
    How does your new car compare to that? any better? if so, is the car a similar size? I guess that question isn't really relevant to this thread, more so to Hank's "Cash for Clunkers" thread, but just curious.
    vongehr
    I think his sneaky meaning was something like this:
    His new car gets 27 mpg at an average of 110 mph.  ;-)
    MikeCrow
    No new car, but the old one would spin the tires shifting into 4th at about 120!

    Oh, and my bike probably get over 30 at 110mph :)
    Never is a long time.
    rholley
    Driving more slowly also widens central vision while increasing peripheral vision
    Something which registers true to me from experience, though I wonder whether that’s something to do with concentration.
    Robert H. Olley / Quondam Physics Department / University of Reading / England
    Bonny Bonobo alias Brat
    I think that the speed we drive at often reflects our state of mind and in turn affects it even more. Overloaded, stressed, unhappy people seem to drive much faster than overloaded but resigned to be relaxed and happy people, I know that I do anyway. 

    One day a couple of years ago I realised that on most of my car journeys around where I live, I seem to randomly encounter the occasional queue or traffic jam, roadworks, traffic lights, slow truck or driver etc and regardless of how many there are, the difference between my arrival time after driving as fast as I can within the speed limit, compared to my arrival time when I have driven in a relaxed and safer manner, is normally just a matter of minutes. 

    So now I rarely stress out when I'm driving and just enjoy my music and often usually let out the many people who get stuck on side junctions or trying to cross the busy road. Everyone always smiles and is very grateful, except for the occasional lead footed, overloaded, stressed out driver driving two feet behind me of course :)

    My latest forum article 'Australian Researchers Discover Potential Blue Green Algae Cause & Treatment of Motor Neuron Disease (MND)&(ALS)' Parkinsons's and Alzheimer's can be found at http://www.science20.com/forums/medicine