Ok I've played around with this a couple times, but it doesn't seem to work out.

Let's say I am driving at 30mph. I reset my trip meter and acellerate for 1 mile with the MPG pegged right at 30 mpg (halfway between 20 and 40).

Then, after 1 mile, I feather the gas pedal and settle in at 60mpg cruising. I hold 60mpg for 1 mile.

So, 1 mile at 30mpg, 1 mile at 60mpg.. and at the end of the 2 miles, my average MPG reads around 38-40mpg.

Now, shouldn't it read 45?

I tried this a few times after noticing that if I acellerate and my average MPG moves down .4mpg (clicks down), then it takes a LONG time to get it to "click back up".

There's been times where there's been, say 100 miles on the tripometer and I'm getting 51.8mpg.... then I get a stoplight and as I acellerate it moves down to 51.4mpg... we're talking about 1/4 mile of acelleration -- and then I need to drive 5 or more miles at 60mpg to get it back to 51.8mpg. Doesn't seem right?

 

You drove 1 mile at 30mpg which means you used 0.03333 gallons for that mile then you drove 1 mile at 60mpg which used 0.01666 gallons for a total of 2 miles and 0.05 gallons which equates to 40 mpg.

 

Your sample size is too low, and accelleration is less efficient. A slightly different test that would give completely different results would be to reach cruising speed at 60mpg, reset the meter there, then change to 30mpg and compare. I'll bet your "average" will instead be closer to 50 rather than 40 in that situation. As the sample size (trip miles) gets larger, the mpg swings in either direction will get smaller.

 

Shiloh is right, listen to him. One mile of 60 mpg plus one mile of 30 mpg means an average of 40 mpg, not 45. Maybe it is easier to realize why by using more extreme figures, for example what would the average mileage be if you did one mile of 10 mpg, followed by one mile of 1 000 000 mpg.

Btw, in the metric system, using l/100km, averaging like this works out nice. So 100 km with 4 l/100km followed by 100 km with 6 l/100km means an average of 5 l/100km.

 

This is a perfect exampe of the flaw of using a reciprocal unit to describe fuel efficiency, that is using miles/gallon instead of gallons/100-mile for overall economy or gallons/hour for cost to run accessories. This alone has led to much of the confusion I hear/read about fuel efficiency.

On a lot of websites I see people saying things like "expect this air conditioner to cost 1-2 mpg" which is absolute nonsense. The difference between going from 50 to 49mph vs going from 20 to 19mpg is almost a 3 to 1 in actual fuel consumption, but that does not mean a Hummer's air conditioner is more efficient than the one on the prius, just because it costs one .25 mpg and the other 4mpg. The most accurate way to describe cost to run air conditioning would be in horsepower or kW per hour, which could be approximated in gallons per hour* -- very easy to compute in dollars.

* Smaller engines may actually be more sensitive to load changes, depending on what RPM they are running at so even this isn't terribly accurate.

 

Gallons per hour is completely different from L/100km or miles/hour because it fails to take movement into consideration. If one car is burning two gallons per hour and the other is burning three per hour, which is more efficient? Well you can't say. If the 2 gph car is going 20mph and the 3gph car is going 60mph, then you know the 3gph car is in fact the more efficient one, since the first is evidently doing 10 mpg and the second is getting 20 mpg.

 

As my high school physics and chemistry teachers used to say, 'Use those Units!' Let me try to add a little more math to the already lucid discussion by Shiloh and rgx. I love numbers!

You ought to calculate it this way:

1 mile over x gallons = 30 miles per gallon (1/x = 30, so x = 1/30)
1 mile over y gallons = 60 miles per gallon (1/y = 60, so y = 1/60)

You need to calculate what two miles over x+y gallons is, so you take
2 miles over (1/30 gallons + 1/60 gallons) = 2/(3/60) = 2/(1/20) = 2*20 = 40 mpg.

Your original math, in words, has the numerators and denominators reversed, and it's like you're trying to add fractions by saying

a/x + a/y = a/(x+y), which just isn't so. [side note: in fact, a/x + a/y = a(y+x)/xy]

You were thinking of this equation:
a/x +b/x = (a+b)/x, but you have a direct proportion instead of an indirect one, which you can tell by checking the units (measuring in inverse gallons instead of gallons, for instance).

If this helps you understand it, I'm glad. Try chugging through it with different numbers if you like.

1 mile at 2 mpg + 1 mile at 200 mpg- Could it get you 101 mpg?
2/(1/2 + 1/200)= 3.96 mpg.

Consider the logic. You wasted a half gallon going that first mile. No matter how crazily efficient your second mile is, you still wasted that half gallon already, and you can't get it back. So think about it- after the second mile, even if you've used barely a drop more than half a gallon, the best you could be at is 2 miles for half a gallon= 4 mpg. Twice the distance, so twice the mpg. Not 'halfway to whatever other mpg you were travelling at for the second mile,' because that could be a lot more.

One little hit has huge repercussions on the average because we're talking about inverses. Your whole 'only a quarter mile of acceleration' can still be a huge hit if you use a ton of gas to do it, no matter what your mpg is before or after that quarter mile.

Good luck!

 

I meant to specify gallons per hour for things like accessory load, which are the same regardless of vehicle speed. I often see reports that air conditioner use will cost X mpg or X% of fuel economy. However, a fixed load like an air condioner would appear smaller in proportion to a faster vehicle speed. I just now corrected my post -- you are correct in that respect though that gallons per hour would be out of context without knowing exact speed.