Stoplights revisited

I get frustrated when I'm cruising down a major thoroughfare at the speed limit on cruise control, say at 40 m.p.h. and the light turns yellow at a point that forces me to stop. Often, a lot of cars behind and in front of me will also have to stop and a single car will pull out from the cross street. Or I'll stop and there's nobody at the light on the cross street. What a waste!



So, it's frustrating, it loses time for me (and others of course), and it does waste fuel. But how much? And if we could figure out a way to eliminate them altogether, what could be saved? Sounds like a time for estimates and calculations since I can't find figures on how many stoplights are stopped at each day. I've repeatedly mentioned Fermi and so-called Fermi problems where plausible estimates are made. I'll give it a try.



Fuel is wasted in two ways at a stop light. First, the kinetic energy at speed is wasted, though the waste from this can be minimized by utilizing coasting to a stop. While your kinetic energy still goes to zero, you use less gas in getting there. But you still have to extract the potential energy from the gas to change to kinetic energy in getting back to speed. Then, you waste fuel idling at the light. I mitigate this to an extent by shutting off the engine at some long lights (the efficacy of this is controversial and the subject of future experimentation). But I'll ignore that technique for this analysis.



I'll calculate figures for what I think are average cars, drivers, and routes. I'll figure a 3000 pound car (including fuel and payload)and accelerating to 32 m.p.h. (my typical average speed over a tankful). I estimate that the average driver stops at 12 stoplights each day (is this high?) and spends 45 seconds at each. Finally, I'll estimate that an average car burns 0.35 gallons of fuel per hour at idle.



Using these numbers, I have to add 139,350 joules of kinetic energy to get the vehicle up to speed. This means I need to burn about 557,400 joules worth of gasoline, about 0.00446 gallons to add back this lost energy (since I have to burn four joules worth of gasoline to get a joule of useful work, with the 25% efficiency of the engine). And 45 seconds of idling at 0.35 gallons per hour burns 0.004375 gallons of fuel. I'll add another 0.00097 gallons for the fuel used during the coast to a stop. Thus, as an approximation, a single stoplight will waste about 0.009805 gallons of fuel. In a day of 12 stoplight encounters, this is 0.11766 gallons.



Now, I'll figure about 125,000,000 people do this in a day, for a burn of 14,707,500 gallons nationwide, representing $44M. At 19 gallons of gasoline in a barrel of oil, this is represents the gasoline in 774,000 barrels of oil. Of course, the other 25 gallons of oil are used, so all of this wouldn't be saved. Figure 1/2 of this, or 387,000 barrels. This is about 1.8% of our daily oil use.



Of course, it's not possible to have no traffic lights, so if proper sequencing and traffic management logic could reduce stops at lights by a third, 0.6% of our oil use might be saved. And the carbon in a gallon will combine in the engine with atmospheric oxygen to create about 19 pounds of carbon dioxide, so this would save 139,700 tons of CO2 per day.



For me, adjusting the figures to reflect my vehicle, I waste about 0.195 gallons per day at an approximate cost of $0.59. A little under a nickel per light. In a year, this is about $213. Not a fortune, obviously. In fact, my time at the lights is worth considerably more (depending on whom you ask). And, as above, it's impossible to live in a world with no traffic signals, so reducing my stops at lights by a third would save me about $71. Again, not a huge amount of money. But, if asked, I'd rather have $71. than not have it.