Prius Math

So, as many of you know, I drive a 2004 Prius a good bit. One thing that has bothered me about achieving the best fuel mileage is this: people normally tell you to accelerate fairly slowly to save gas. But I wonder, when accelerating onto the highway is it better to use full throttle or less? My thinking is that, even though during the moments of acceleration you use more fuel, the less time you spend accelerating the less power (and therefore less gas) you would need. Obviously, in city driving this is more of a moot point, since you don't have long periods of time at speed, but otherwise it is a difficult question.

To try and find an answer, I made some calculations. At a zero to sixty time of around 30 seconds, probably the slowest reasonable acceleration one could put up with, the car averages about 25mpg according to the onboard computer. At 10 seconds, about the fastest the car can go, it averages about 5mpg. To maintain speed, I assume the car is running at 50mpg (this is actually probably too low, given my experience, but it is most important that the remaining distance's MPG be constant for this problem). The biggest assumptions here are the veracity of those two numbers, my assumption of a linear relationship between MPG and 0-60 time, and that the final MPG will be a relative constant, even though the battery's state will be different depending on acceleration. If I have a chance, I'll have to try and fill in better data later. But for now, with rudimentary physics formulas and rudimentary python, I can present you with this data:

MPG Scale over 1/2 mile, Prius Acceleration:

0-60: 35 ; Total time: 65.0 s; MPG: 41.9230769231
0-60: 30 ; Total time: 60.0 s; MPG: 40.0
0-60: 25 ; Total time: 55.0 s; MPG: 38.6363636364
0-60: 20 ; Total time: 50.0 s; MPG: 38.0
0-60: 15 ; Total time: 45.0 s; MPG: 38.3333333333
0-60: 10 ; Total time: 40.0 s; MPG: 40.0

So it would seem, interestingly, that hard acceleration is as effective, for highway merging, as Grandma acceleration. Again, take this data with a grain of salt, but I do think that the numbers are so close as to negate the importance of your acceleration run. If I get a chance, I'd like to run the same tests for city driving, as well as get better data, but for now, enjoy your highway merges. It seems like you can without much incident.

By the way, someone should probably check my math as well as my methodology, so I'm attaching the simple Python script as well. Advice is always welcome.

mpg.py1.06 KB