# 500 MPG, I Think Not!

**May 01, 2017**

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How PHEV's are capable of much high efficiency performance then the on board internal combustion engine because of the electric drive train.

Recently I ran across an article about a fellow driving a Ford Fusion Energi PHEV in the Omaha area who was claiming mpg as high as 500 mpg. Upon reading the article you can see right away he and the dubious reporter are only talking about gasoline consumption over the 44,000 miles of driving. They said he had consumed 106 gallons of gasoline or 44,000/106 = 415 mpg. No mention was made about the total amount of electricity required for the bulk of the distance traveled.

Since we own a Ford C Max Energi with the same drive train I can make some back calculations about what this driver was actually accomplishing with his PHEV. He claimed 40 MPG for the internal combustion engine (ICE) which I will give him, even though it is probably a high figure. That works out to 40 x 106 = 4,240 miles.

The best we can give him is 95 mpg e for EV only travel and that is including charging loses. Total miles 44,000 – 4,240 = you get 39,760 EV miles. Dividing 95 mpg e into 39,760 EV miles yields 418 gallons e. Conversion to MPG e for both systems means adding 106 + 418 = 524 gallons. Dividing total miles 44,000/524 = 83.96 mpg e.

Recently we went on a long distance run of our own from March 11th, 2017 to April 11th, 2017 or for 31 days. My goal was to get just over a thousand miles between refueling and to do a complete mathematical treatment of the comparative performance of the two drive systems. Lots of good numbers fell out that tell an important story of just how much more efficient electric drive is as compared to the internal combustion engine. I will let the detailed math explanation pages speak for themselves.

Explanation for Math Treatment on Energi PHEV energy flows.

1,011.6 ICE miles 671.4 EV mi 671.4/1,011.6 = 66.37%, 1011.6 miles – 671.4 = 340.2 ICE miles.

104.7 read out mpg 1011.6/104.7 = 9.66 gallons (10.362 actual gallons were pumped which means 1,011.6/10.362 = 97.62 mpg.

162 kWh is metered by the car, charging losses represent 82% so 100/82 = 1.23 for a multiplier, 162 kWh x 1.23 = 199.26 kWh.

Electrical gallons of gas equivalent there are 111,836 BTU in one gallon of E-10 gasoline. There are 3,412 BTU in one kWh so 111,836/3412 = 32.777 kWh in one gallon equivalent of electricity.

So 199.26 kWh/32.777 = 6.079 gallons of gas equivalent (or gals e).

Total system performance 10.362 gallons of gas + 6.076 gals ev = 16.411 gallons of gas e. 1,011.6/16.411 = 61.64 mpg-e.

ICE performance 340.2 mi/10.362 gallons = 32.83 mpg.

EV performance 671.4 mi/6.076 gal e = 110.5 mpg e.

Normalizing the performance for 1,000 miles requires 1,000/1,011.4 = .9885 x as a multiplier.

Normalizing 340.2 ICE mi 1,000/340.2 = 2.939 x for a multiplier.

Normalizing 671.4 EV mi 1,000/671.4 = 1.489 x for a multiplier.

So 10.362 gals x .9885 = 10.242 gals x 2.939 = 30.1 gals per 1,000 mi.

So 6.079 gal e x .9885 = 6.009 gal e x 1.489 = 8.947 gal e per 1,000 mi.

Conversion to MBTU as stated before there are 111,836 BTU in one gallon of E-10 gasoline.

ICE 30.1 gallons of gas x 111,836 = 3.366 million BTU (or MBTU).

EV 8.947 gal ev of gas x 111,836 = 1.000569 MBTU.

ICE watts per mile = 30.1 x 32,777 wHr = 986,587 wHr per 1,000 mi.

986,587/1,000 = 986 wHr per mile.

EV watts per mile 8.947 x 32,777 = 293,255 wHr per 1,000 miles.

293,255/1,000 = 293 wHr per mile.

Cost calculations. Gasoline is 2.199 per gallon. Electricity is 8 cents per kWh buy back tariff from EPE for Grid Tie Solar including charging losses.

ICE 30.1 gallons x 2.199 = $66.19 per 1,000 miles.

EV 8.947 gal e x 32.777 = 293 kWh x .08 = $23.44 per 1,000 miles.

Cost per MBTU.

ICE 30.1 gals x 111,836 = 3,366,263 BTU/3.366262 = 1 MBTU.

EV 8.947 gal e x 111,836 = 1,000,596 BTU/1.000596 = 1 MBTU.

ICE $66.19/3.366262 = $19.66 per MBTU.

EV $23.44/1.000596 = $23.42 per MBTU (note here, although electrical cost per MBTU are higher electric drive is 3.36 x more efficient in energy used per mile).

Since we traveled 66.37% EV miles v 33.3% ICE miles the cost break downs as follows over 1,000 miles.

ICE $66.19 x .333 = $22.04 over 333 miles, cost per mile is $22.04/333 = $.066 or 6.6 cents per mile.

EV $23.44 x .673 = $15.77 over 667 miles, cost per mile is $15.77/667 = $.0236 or 2.36 cents per mile.

Aggregate cost for both systems is $22.04 + $15.77 = $37.81/1,000 = $.3781 or 3.78 cents per mile.

Aggregate Watt Hours per mile is ICE + EV or 986.587x.333 = 328 wHr.

+ 293.255x.667 = 195.6 wHr = 523.6 wHr averaged with this driving mix of 33.3% ICE miles and 66.7% EV miles.

I hope this helps. As you can see sorting out the energy flows in a PHEV is complicated and the values I gave for the 33.3% and 66.7% mix are only true for this mix of driving.

There are some PHEV drivers who are operating with far less of an ICE component and they can return higher composite mpg e. Some are not even counting electrical energy inputs and claiming inflated mpg figures as high as 500 mpg which is completely misleading of course.

The accounting used in the above analysis is as accurate as I can make it given the uncertainties in pump metering, odometer read outs, and the on board electrical tracking in my Ford C Max Energi. It is however a good relative accounting for the two power systems.

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