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Old 09-18-2012, 06:14 AM   #1 (permalink)
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MPG Tool Math Help

First posting for me here ... just found this site/forum and must say it scores a wow and then some!!

I need help understanding the math in the aero-rolling resistance tool.

The conversion from Watts to MPG has me baffled.

I understand the need to use consistent units of meters, kg, and seconds in values for weight (mass), density, velocity, and area.

I can duplicate the force values in Newtons for rolling and aero and multiply by the velocity in meters/sec to get Watts.

I divide the Watts by 746 to duplicate the horse power in the chart.

Knowing the gallons per hour and the distance per hour makes MPG simple ...

However, that gallons per hour calculation using the fuel energy density and Watts has me totally confused. I am using 100% engine and drive train efficiency and zero parasitic losses to keep things as simple as possible until I understand the math from Watts to gallons of fuel. Seems like I should just multiply Watts by 3600 seconds/hr and divide by the fuel energy density in Wh/gal ... but I get crazy values doing so.

All help much appreciated.

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Old 09-18-2012, 06:32 AM   #2 (permalink)
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id help, but i have 2 physics lab reports due tomorrow morning, so my brain is already hurting, and i work later today. i can tell you that most engines are only about 20-25% efficient, transmissions are 90-95 for manual and for automatics as low as 70%, like mine, and up to maybe 85-90% for new dual clutch auto's.
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Old 09-18-2012, 09:45 AM   #3 (permalink)
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Got it now ... I think

Watts / Energy Density --> GPH

MPH / GPH --> MPG

Embarrassingly simple. Watt confused me (pun intentional) are the units of a Watt (N m / s) and a brain cell screaming to multiply by 3600 to get the hourly quantity.

This forum is going to be fun. I'll have to blow the dust off my physics book and get back into form.

The energy density's time dimension needs to match up to the consumption velocity measurement. hour <--> hour

And the energy density's power dimension's time needs to (now obvious for me) match up to the power measurement. second <--> second

Work = Force x distance

Power = time rate of work

So ... some really crazy units can be used with different units of velocity if the reported energy density is consistent with both the power measurement and the rate measurement.

Here is a crazy example:

Work = lbf * inch
POWER = lbf * inch / day
^^ Here the velocity would be inches per day

No acceleration, so distance = Velocity if the time frame of interest is same as the measurement unit. Here one day is that unit.

=======================================

Energy density = POWER (lbf * inch / day) week / wheel barrow
Velocity = inch / week

Note how the power quantity is in days and the consumption is in weeks. Inconsistent units!!

POWER / Energy density --> wheel barrow / week {volumetric consumption rate}

Velocity / (wheel barrow / week) --> inches per wheel barrow {volumetric performance}

Perhaps not another soul around that got confused as I did. This posting was for my own sorting things out and for your entertainment.
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Old 09-18-2012, 11:57 AM   #4 (permalink)
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Your engine is not 100% efficient.
Most gas burners are only around 25% efficient.
Your transmission and drivetrain could be as low as 85% efficient. The differential unit alone has about a 3% to 5% loss associated with it.

I plugged all the numbers in for my suburban and they were very close to what I get in real life.
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Old 09-18-2012, 12:29 PM   #5 (permalink)
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Welcome. A pun in you 2nd post, you should fit in well.

Lead2gold, eh?
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Old 09-18-2012, 12:33 PM   #6 (permalink)
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The default 0.22 engine efficiency seems to be right-on for our 2011 LTZ Cruze with FWD-automatic, because the program came up with 32.5 MPG at 65 MPH, and the wife's gotten 32.6 and 32.7 MPG at 65 MPH, on two different occassions--the best we've seen to date.

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