Calculated Theoretical MPG

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oilyriser

I'm playing with some numbers... Assume: A car takes 15 hp to move at 65 mph, steady speed. 1. gasoline with 140,000 BTU/gallon engine efficiency is 20%, drivetrain is 93% In this case, the car should get 44 mpg. 2. fuel 150,000 BTU/gallon diesel engine at 40% efficiency The diesel car should get 95 mpg Which of my input numbers are way off? It seems that real diesel engines might only be operating at 20% efficiency, and gas engines at 15%.

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Originally posted by oilyriser: I'm playing with some numbers... Assume: A car takes 15 hp to move at 65 mph, steady speed. 1. gasoline with 140,000 BTU/gallon engine efficiency is 20%, drivetrain is 93% In this case, the car should get 44 mpg. 2. fuel 150,000 BTU/gallon diesel engine at 40% efficiency The diesel car should get 95 mpg Which of my input numbers are way off? It seems that real diesel engines might only be operating at 20% efficiency, and gas engines at 15%.
IIRC, 100 lb total drag at 60 mph is pretty good for small car. That would be 16 hp at the rear wheels at 60 which translates to about 20 hp at 65. If you assume 80% total drive train efficiency, that's 25 hp at the crank to go 65. The energy values you gave look like high heating values (HHV), you only get to use the energy in the low heating value (LHV), about 120,000 BTU/gallon for gasoline. A modern gas engine is probably close to 25+% efficiency in highway steady state operation. A diesel about 32+%. 25% on gas is about .56 lb/hphr. I think a modern gas engine can roughly match that at highway power levels.

Engine efficiency should be closer to 26-29% but only when operated at WOT. Engines are most efficient at WOT and at the RPMs that correspond to peak TQ. You can't be cruising at 65 MPH and operating at WOT, and you are not likely to be operating at peak TQ at 65 MPH, so maybe 20% is not so bad a guess but it could still be high. Driveline efficiency (including driven tire slippage) is closer to 15% loss (10% for miserly FWD manual transmission, 15% for classical front engine manual transmission live axle rear drive, 20% for classic with automatic transmission)

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Originally posted by Mitch Alsup: Engine efficiency should be closer to 26-29% but only when operated at WOT. Engines are most efficient at WOT and at the RPMs that correspond to peak TQ. You can't be cruising at 65 MPH and operating at WOT, and you are not likely to be operating at peak TQ at 65 MPH, so maybe 20% is not so bad a guess but it could still be high.
20% efficiency is about 0.7 lb/hp-hr, pretty poor. Engines are almost never most efficient at WOT. Take a look at most any BSFC map. Figure 11 is typical BSFC map Figure 11 in the above link is a Saturn 1.9L engine, a reasonably efficient engine, but not the best. Note that for any given rpm the lowest BSFC occurs at roughly 80% of full load. That's pretty typical of IC engines. Even lot of diesels. Multiply the gr/kWhr values by 0.00164 to convert to lb/hp-hr that most of us relate to more instintively. The best bsfc island is 0.41 lb/hp-hr. If you run a line through the centers of the islands that roughly follows the peak torque curve, you can see that it is at roughly 80% of peak loak at any given rpm. At 1750 rpm, lowest BSFC is .41 lb/hp-hr when the engine is putting out 109 Nm torque which is 27hp. 0.7 lb/hp hour at 65 mph would be poor for a vehicle that was geared for economy.

Thank you! I've been looking for just such a graph. If a Saturn were geared so that the engine runs at 1750 RPM at 70 mph, the resulting 27 hp would be enough to overcome drag, with a bit to spare for climbing hills. However, the engine is probably going 2800 rpm at this speed in 5th gear, where 27 hp would put it at around 0.472 lb/hp-hr on the graph.

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Originally posted by oilyriser: Thank you! I've been looking for just such a graph. If a Saturn were geared so that the engine runs at 1750 RPM at 70 mph, the resulting 27 hp would be enough to overcome drag, with a bit to spare for climbing hills. However, the engine is probably going 2800 rpm at this speed in 5th gear, where 27 hp would put it at around 0.472 lb/hp-hr on the graph.
For some reason BSFC maps are hard to find in the public domain. They exist for every engine developed by real engine devlopment company, even B&S lawnmower engines. If you car to look for more, Google BSFC map Here's some more Notice how VVT streatches out the low consumption islands to give efficient operation over a wider speed range. The graphs in that paper use BMEP on the verticle axis instead of torque, but BMEP is directly proportional to torque for given engine, so the shapes and relationships of the curves are still meaningful when compared to others. The paper is more examples of best BSFC at close to 80% of full load, although the VVT example devlops best BSFC at about 70% of full load. Not at full load, almost never at full load.

Why does the engine have to be throttled a little bit in order to be most efficient? Does that stem from mixture enrichment at full throttle, or something like that? A variable compression ratio engine would have a very large island, allowing efficient operation over a wide range of power levels.

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Originally posted by oilyriser: Why does the engine have to be throttled a little bit in order to be most efficient? Does that stem from mixture enrichment at full throttle, or something like that?
I thnk that's most of it but don't know for sure. Diesels show the same characteristic, although you can program the elctronically controlled FI systems on some of them to limit fuel to the load level that gives best BSFC. You give up power by doing that though and spend more time below optimum.

Maximum power requires a slightly rich-of-peak mixture, just one reason for less efficiency at high power settings. A lot of these things are being "rediscovered" in this age of computer modeling and programmable electronic fuel injection. The airlines and military in the 1940's and 1950's had to learn how to operate internal combutstion engines at maximimum efficiency just to cross the oceans without running out of gas. This was done with a combination of analog instrumentation and trial and error. WOT (low vacuum, aka high manifold pressure) and low rpms (lugging) is not a good place to operate an IC engine. Theoretical pumping losses may be minimal there, but there is a lot more to efficiency than just that. You want to operate where the maximum pressure of expanding gasses is at the halfway point in the downstroke, giving the most leverage on the crankshaft. This is the torque peak. This condition varies with boresize, bore-stroke ratio, spark timing, etc.

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Originally posted by Jimbo: You want to operate where the maximum pressure of expanding gasses is at the halfway point in the downstroke, giving the most leverage on the crankshaft. This is the torque peak. This condition varies with boresize, bore-stroke ratio, spark timing, etc.
Max leverage occurs at around 76 degrees depending on stroke/rod length ratio, not 90 degrees.

Ok, but you get the idea. I forgot the stroke/rod length ratio.

I saw a car add from some fancy car of the 1930s or 1940s I believe. One of these streamlined rounded cars... I believe it claimed that it took 60hp to push a car at 60 MPH. Their claim was that the engine had 200 hp or something, so you had this magnificent power reserve. Maybe your numbers w.r.t. drag are off... JMH

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Originally posted by JHZR2: I saw a car add from some fancy car of the 1930s or 1940s I believe. One of these streamlined rounded cars... I believe it claimed that it took 60hp to push a car at 60 MPH. Their claim was that the engine had 200 hp or something, so you had this magnificent power reserve. Maybe your numbers w.r.t. drag are off... JMH
No, the old ads numbers were off.

Power required to move a car, vs. velocity. I found a neat calculator that estimates the power needed to move a car at different speeds. Photograping the front of my car, and, using measurements to calculate the area of one pixel, plus photoshop, I measured its frontal area. My car plus driver weighs 1566 kg. Maybe add 20kg for gasoline in the tank. The frontal area is 1.61 m^2, and the Cd is approximately 0.31 after adding a belly pan. Air density is about 1.2 kg/m^3. Rolling resistance is probably about 0.01 with the stock RE92 tires that are so terrible in snow. Setting min to 0 and max to 35 m/s, the graph shows a power need of 13.5 hp at 60 mph. This is power at the wheels, after drivetrain losses. 65 mph -- 15.75 hp 70 mph -- 18.9 hp

If my car takes 15.75 hp to go 70 mph, and it gets 30 mpg at this speed, and the drivetrain is 80% efficient, I can calculate the thermal efficiency of the engine under these conditions. 70 mph --> 15.75 hp = 11749.5 W One mile takes 51.42857 seconds at 70 mph 11749.5 x 51.42857 = 604260 joules of energy = 572.8 BTU to travel one mile A gallon of gas has 125,000 BTU, if you cool the resulting gases down STP. (HHV) If the car were 100% efficient, it would get 125,000 / 572.8, or 218 mpg. With 80% drivetrain efficiency, it should get 174.6 mpg. The actual mileage is 30 mpg, so this means the engine efficiency is 0.172 or 17%.

Gas engines are more efficient when at nearly WOT because they are not using fuel to provide the power to maintain vacuum. That is one of the reasons diesels are efficient - no engine vacuum - always at WOT. BSFC usually ranges from .4 to .5 lb/HP/hr. If you get 30 MPG @ 60 MPH, that's 2 gallons per hour. At about 6.8 lbs/gal, thats approx 30 HP [crank] needed. One odd thing that I've noted is that when I hold the gas pedal steady, and declutch at highway speeds, the engine doesn't rev to redline, but only increases 1500-2000 RPMs or so. That means free revving my engine at 5000 RPMs or so takes 30 HP!

The two main reasons diesels are more efficient in mpg are higher btu heat energy per gallon and much higher compression ratios. The pumping losses with a partially closed throttle plate just arent that much of a factor by comparison. BMW has taken the throttle plate out of the latest 3-series gasoline engine and replaced it with a real "Rube Goldberg" variable lift valve setup. This yields single digit percentage gains vs 20-30 percent for the diesel models (not sold in the US). I looked up my aviation sources again and have to correct myself. Maximum cylinder pressure at about 18 degrees ATDC yields the most torque and highest BSFC.

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Originally posted by Jimbo: BMW has taken the throttle plate out of the latest 3-series gasoline engine and replaced it with a real "Rube Goldberg" variable lift valve setup. This yields single digit percentage gains vs 20-30 percent for the diesel models (not sold in the US).
It still takes the same amount of air to make x hp and the engine is trying to suck y*x air. Seems like restricting it with goofy valve timing or a throttle plate makes about a much differance as the difference between strangling someone with a silk scarf or a rope. The piston doen;t know if the throttle plate of the valve timing is making it suck so much. Try some calculations on how much work it takes to suck air past a throttle plate, it might suprise you.

Oily, you have unrealistic values in there. Your result indicates about 0.8 lb/hp hour. No car engine made today is remotely that bad at cruise conditions. You have assumption piled on top of assumptions to try and determine efficiency. That doesn't work

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