“Be kind, for everyone you meet is fighting a hard battle” - Often attributed to Plato but likely from Ian McLaren (pseudonym of Reverend John Watson)

Thursday, September 27, 2012

Faulty comparison?

I follow (and link to) a fair number of energy related blogs. One of them is Consumer Energy Report, which aggregates posts from a variety of journalists and energy professionals with various specializations. A recent post was entitled "High Cost Prevents Electric Cars From Penetrating the Market." In this post, Andrew Holland discusses his thinking behind the lack of sales of pure electric cars and the financial troubles befalling some of their manufacturers. However, he's also quite complementary of the Chevy Volt, a vehicle I've considered.

But in the comment section, Buddy says

I’ve also never understood, however, how I can run a 5K Honda generator for a minimum of 2 hours ,and occasionally 4 hrs, on a single gallon of gas, that hybrid vehicles cannot achieve the 100 MPG rate easily.

Is this a valid comparison? After all, I certainly can't drive my hybrid  Lexus CT200h for 2, let alone 4 hours on a single gallon of gas. I think looking at Buddy's comment with the Lexus as the representative is quite reasonable. It's the same drive train as the ubiquitous and iconic Prius hybrid and I've gotten 51.38 miles per gallon total in the 14 months or so that I've driven it.

I wrote a simple Wolfram Mathematica program to determine an estimate for the power required at an input speed and an estimate for the mileage to be expected. The program comes gratifyingly close to my actual mileage at the speeds I've checked so I suspect that the power requirement is likely pretty close, the wild card being the engine efficiency.

In any case, let's go on. Buddy's Honda generator has a maximum rated output of 5 kilowatts, but I'm very doubtful that the two hours to which he refers is at full load. Nevertheless, I'll use it anyway because... who knows? And I suspect the two hour figure is at closer to full load while the four hour figure is at a much lesser load.

5 kilowatts is 6.71 horsepower. I calculated that, at 55 m.p.h., my Lexus requires from its Atkinson cycle internal combustion engine (and, where required, the generator and electric motor) about 13.8 horsepower and achieves about 54 m.p.g. If I assume that, at that cruising speed, the Lexus is capable of 28% efficiency, then I'd be burning fuel to release heat energy at the rate of 13.8/.28=46.4 horsepower. This is 34.6 kilowatts or 34,600 joules per second. Now, upon burning, a gallon of gasoline releases about 120,000,000 joules of heat energy so this gallon should last 3,470 seconds or just shy of 58 minutes. A quick check: at 54 m.p.g. and 55 m.p.h., a gallon ought to last an hour!

OK, so we have that I need 13.8 horsepower, a bit over twice what Buddy's generator supplies at 5 kilowatts or 6.7 horsepower. Multiplying my one hour by that 2 figure, I'd think his generator should run for about 2 hours at 5 kilowatts if it was as efficient as my Lexus. I don't think there's any reason for Buddy to be surprised!


Kit P said...

Happiness can come pretty cheap if you buy a used yacht after the fat can learns that sailing actually requires some skill and a lot of work.

I always wonder about folks who buy an overpriced Corolla. Oh, it is a company car with records being kept. This is a first for me, a HEV with real data.

What kind of driving, aggressive city, balls to the walls interstate, or country roads at 55 mph?

King of the Road said...

If you're David Lee Roth, you are the fat cat (though when I saw them a couple of months ago he was still skinny after all these years. But he certainly can afford the yacht.

As to the CT200h, I drive extremely conservatively. unless I'm going down a hill with foot off the gas and the system's turned the engine off and I'm coasting and recharging the battery, I never exceed 55 m.p.h. But that's why my combined m.p.g. is 51.4 vs. the EPA estimate of 41. And I have excruciatingly thorough records.

Kit P said...

“I never exceed 55 m.p.h. ”

Thanks for the feedback. The secret of getting good mileage and enjoying a road trip. Many places the speed limit is 75 mph and if you observe it you will be passed by over powered SUV and pick up trucks pulling trailers. Then on a strait stretch road in prefect weather, the rig and tow vehicle are wheels up on the weeds.

We have found that there are lots of highways that have little traffic because the interstate draws it away. The speed limit is lower but the goal is to enjoy the trip.