Can you solve Barlow's Quandary?
 

I have a problem.

Let's say my HCH averages 60 mpg during the pulse phase for let's say, one mile, and then I shut off the engine and glide for another mile. The mpg during said glide phase is...infinite mpg, since I got a mile while burning no gas whatsoever. However, the HCH computer surely can't average an infinite mpg number into the overall mpg. I theorize the mpg computer simply says to itself "the car burned x gallons of gas for one mile (during the 60mpg pulse phase) and burned no gas as it travelled another mile, thus it travelled 2 miles on the gas burned during the pulse phase, thus doubling the calculated/measured mpg for a 120 mpg average."

Now let's say my HCH averages 40 mpg during the pulse phase for one mile, and then I shut off the engine and glide for another mile. The average for the 2 miles travelled on the gas burned during the pulse phase is doubled for an 80 mpg average."

But let's say my HCH averages 40 mpg for one mile during a pulse phase, and then averages 120 mpg for the next mile during the glide phase. The average for the 2 miles is still 80 mpg, right? How?

How is it that the average mpg in these 2 examples can be the same? Is averaging 120 mpg during the glide the same/equivalent of infinite mpg for a mile while burning no gas at all?

Let's say the pulse phase averages 30 mpg for a mile, and then the infinite mpg glide with the ICE off for one mile doubles the effective/average mpg to 60 mpg for the 2 miles. But if the pulse phase is 30 mpg for a mile and the glide phase is 120 mpg for a mile, the average is 75 mpg, right?

How can it be that a glide at 120 mpg in this last example is better than a glide with infinite mpg? What am I doing wrong?

Bob :confused:

Re: Can you solve Barlow's Quandary?
 

Hi RJ:

___Sure, break it down to gallons of fuel consumed and you can play with it a lot more. This is how Krousdb was calculating FE above 99.9 before Ken1784 supplied him with the SuperMid.

___Here goes …

Case Study #1:

Pulse: 40 miles/gallon during Pulse over 1 mile = 1 mile/40 miles/gallon = .025 gallons
Glide: Infinite miles/gallon during Glide over next 1 mile = 1 mile/infinite miles/gallon = 0 gallons

2 miles traveled on (.025 + 0) gallons = 2 miles/.025 gallons = 80 miles/gallon

Case Study #2:

Pulse: 40 miles/gallon during Pulse over 1 mile = 1 mile/40 miles/gallon = .025 gallons
Glide: 120 miles/gallon during Glide over next 1 mile = 1 mile/120 miles/gallon = 0.00833 gallons

2 miles traveled on (.025 + 0.0083) gallons = 2 miles/.0333 gallons = 60.0 miles/gallon

Case Study #3:

Pulse: 30 miles/gallon during Pulse over 1 mile = 1 mile/30 miles/gallon = .0333 gallons
Glide: Infinite miles/gallon during Glide over next 1 mile = 1 mile/infinite miles/gallon = 0 gallons

2 miles traveled on (.0333 + 0) gallons = 2 miles/.0333 gallons = 60.0 miles/gallon

Case Study #4:

Pulse: 30 miles/gallon during Pulse over 1 mile = 1 mile/30 miles/gallon = .0333 gallons
Glide: 120 miles/gallon during Glide over next 1 mile = 1 mile/120 miles/gallon = 0.00833 gallons

2 miles traveled on (.0333 + 0.00833) gallons = 2 miles/.04163 gallons = 48.0 miles/gallon

___A 120 mpg Neutral Glide (as an example) over 1 mile still burns fuel at the rate of .0833 gallons/mile. Once you break everything up to gallons, you see how one can combine with another.

___Good Luck

___Wayne R. Gerdes

Re: Can you solve Barlow's Quandary?
 

Ahhh, I can't average the mpg's for the various segments, but total the fuel consumed by miles travelled, just as we do for a whole tank. Why didn't I think of that? I know why, because it requires math. :omg: I was a history major!:embarass:

Thanks Wayne.

Bob

Re: Can you solve Barlow's Quandary?
 

Fear not; the concept that one cannot average a bunch of averages is not explicitly taught until College-level probs & stats. Not your fault.

Re: Can you solve Barlow's Quandary?
 

heck, i can't even balance my checkbook

Re: Can you solve Barlow's Quandary?
 

RJ, Wayne is correct, but may I presume you cannot do those calcs in your head ?

If so desired, try this:

From your example of 40 mpg and 120 mpg, you have used 1 part gasoline pulsing, and 1/3 of that part gliding. 80 divided by 4/3 = 80 * 3/4 = 60 MPG.

Re: Can you solve Barlow's Quandary?
 

If you have seen this problem before and understand it please do not answer.

So a car is making a 2 mile trip, one mile is up hill and one mile is downhill. On the way up the hill the car averages 30 miles per hour. The driver wants to maintain an average of 60 mph for the entire 2 mile trip. How fast must the driver go down the hill for the second mile to average 60 mph for the trip.

Situation in detail:

The driver has gone one mile so he is at the top of a hill with one mile remaining on his trip.

The driver has averaged 30 mph for the first mile.

He has one mile to go.

Total trip lenght will be 2 miles.

He wants to average 60mph for the 2 miles.

How fast (average) must he go for the remaining mile to average 60mph for the entire 2 mile trip?

Re: Can you solve Barlow's Quandary?
 

Without admitting that I might be old, I'll just say that some years ago, I came across a math problem -- I think late elementary school. It has stuck with me:

Two cars race on a track -- to, and back again. One car goes 70 mph the entire route; the second goes 60 mph halfway, and then 80 mph on the return. Is their a winner, and if so, who ?

This is LakeDude's question, but better, because it is a race !

Re: Can you solve Barlow's Quandary?
 

ah! i went to art school to avoid math!

actually no not really. i like math fine.
do you have an answer? because the way i have it figured now he'd have to go the remaining mile instantly, in 0 hours...
because he does the first mile: 1mile/.03333hours and 60m/h = 2miles/.03333hours
where i'm i going wrong?

Re: Can you solve Barlow's Quandary?
 

You've got the point, IMA. Always break the averages apart and work from there.