I timed some of my snail-like starts, timing how long, on average, it takes me to go from 0 to 10, 10 to 20, etc. and finally from 50 to 55 (the fastest I ever go). I took the average of four times for each interval and plugged them into a spreadsheet. Then I graphed them and found a regression curve that had the best fit.
It turns out that it takes me, on average, about 53 seconds to go from 0 to 55 m.p.h. I'm guessing, from their wailing and gnashing of teeth, and their honking, flashing of lights and gesturing, that this seems kind of slow to many of my passengers and fellow drivers. Ah well, anything for science.
In any event, I took the regression curve and integrated it twice from 0 to 53 seconds and determined that it takes me about 890 meters, or about 2900 feet to accelerate from a stop to 55 m.p.h. I then plugged times into my spreadsheet that fit the same shape of curve but that totalled 9.7 seconds (I was looking for about 10 seconds) to model fast acceleration from a standstill. This isn't flooring it, I determined a long time ago that the Jeep will go from 0 to 60 in about 7.4 seconds minimum.
Utilizing the same mathematics, I determined that it would take about 150 meters or 490 feet to go from 0 to 55 m.p.h. Now, in each case, I have changed the potential energy of the chemical bonds in gasoline into an amount of kinetic energy of the car that is identical for each acceleration regime (a little over 600,000 joules). As I mentioned in an early post in this blog, the energy of burning fuel goes to overcoming the forces working against the motion of the car and to adding kinetic energy to the car.
So I've gone about 2400 feet farther on the same amount of fuel by accelerating slowly. That's about 0.45 miles. Supposing I do the equivalent of this amount of accelerating about 15 times per day, I get something like 6.75 miles extra by accelerating slowly. At 32 miles per gallon on the highway, that's about 0.21 gallons of fuel saved.
I'm saving something like 1.5 gallons per day compared to my old driving methods, so I'm estimating that about 14% of my fuel savings come from leisurely acceleration. The rest come from some combination of lower freeway speeds and extremely conservative energy management, that is, coasting to stops, coasting in neutral when going downhill, turning off the car on long downgrades and at long stops, etc. I'm not sure of the division here, but I'll try to figure it out.