Gas Mileage Calculations

Factual Questions
1

Okay, I’ve got an idea for an experimental engine that I want to build simply for shit’s and giggles. Before I build it and drop it into a car, I’d like to be able to do a rough guesstimate of what kind of fuel mileage I can expect from the thing.

Whilst I don’t have all the data necessary at the moment, I’m assuming that if I know how much fuel the engine consumes at a certain RPM, and what the RPM of the tires would be at that engine speed, I can get an idea of what the MPG of the engine would be. I realize that the aerodynamics of the vehicle the engine’s dropped into will reduce the actual MPG (and I won’t know what the drag coefficient of the vehicle is, so I can’t plug that in anywhere). Am I correct in my assumptions, or is there something that I’m missing?

2

You can’t ignore aerodynamics, it’s the biggest source of resistance. There isn’t a big variation of drag coefficient - most passenger vehicles are between 0.3 and 0.5.

You also need to predict the engine’s power output at that RPM. The vehicle speed is the point at which resistance (air + tire) equals engine power output. Better yet, predict the RPM vs. power (or RPM vs. torque) and RPM vs. fuel consumption rate. You can’t just use engine RPM and gear ratio, because you don’t know if the engine can actually achieve that RPM with that gear.

3

Well, I’ve got no way to figure the drag coefficient of the vehicle, so any guess is as likely to be wrong as it is right. And I’m not looking for something that’s within a few MPG of being right, as EPA estimates are. I’m just looking for something that’s in the neighborhood. If I can get within 10 MPG, that’s fine. I just need a rough estimate, because if the fuel economy comes out too crappy (say .005 MPG), then I need to scrap this idea and switch to something else.

The top horsepower of the engine should be somewhere around 450, though from what I’ve read, the predicted HP of the engine design is lower than the actual. I haven’t ran the numbers to figure the torque, but it should be plenty.

4

A related question:

I obsessively calcualte the gas mileage I get from my '01 Civic. Since all of the above-mentioned variables have already been worked out for the car, is the gas mileage solely a function of RPMs? In other words, no matter what the driving conditions, will 2000 RPMs for an hour always produce the same MPG?

If my question is unclear, let me know and I’ll try and rephrase.

5

A related question:

I obsessively calcualte the gas mileage I get from my '01 Civic. Since all of the above-mentioned variables have already been worked out for the car, is the gas mileage solely a function of RPMs? In other words, no matter what the driving conditions, will 2000 RPMs for an hour always produce the same MPG?

If my question is unclear, let me know and I’ll try and rephrase.

6

No, consider cruising at 55 MPH in 5th gear, going up a hill or going down a hill. The engine will be turning at the exact same speed (say 2000RPM) but it will be doing far more work going up hill, requiring more gas.

At least I assume that the computer controller will be injecting more gas into the cylinders, I admit my knowledge of engines is somewhat limited.

7

The amount of gasoline an engine consumes will be dependant upon (1) the efficiency of the engine turning energy into horsepower, and (2) the amount of work the engine has to do (horsepower).

Your 450hp engine isn’t always going to do 450hp of work, though. So the coefficient of drag you were told to look for is only valid for determining the horsepower at any given time. Less drag, less work required. Low rolling resistance tires contribute. Going up or down a hill contribute. The weight of the vehicle of course matters. Given the same vehicle with two different horsepower engines, and a constant cruising speed in all identical conditions, both vehicles will use the same horsepower. It may be the higher-horsepower engine does it more efficiently and uses less gasoline.

Alone high-horsepower won’t mean anything; that’s a measure of how much work the engine can do. You also need to work with torque, which you can say indicates the ability of the engine to deliver that horsepower in a timely manner. High horsepower should let you drive a higher-speed than low HP (given the same gearing). Torque is what will get you to that speed faster.

So to sum up: engine HP is a measure of what the engine can deliver; you need to figure out the anticpated load.

8

I think you are missing something Tuckerfan: like a couple other people have suggested, the torque output of the engine is important. Perhaps I’m misinderstanding you, but let me try to explain:

It takes power to move an automobile. The output power of the engine is proportional to speed X torque. However, the engine can put out a range of torques at any given speed. Exactly what torque the puts out depends on how much gas you feed it. More gas -> more torque; less gas -> less torque. Of course you feel this driving a car: to get up a hill at constant speed, you need more power, so you add more gas. More gas -> more torque -> more power -> maintaining speed uphill.

Perhaps a better way (better than mpg, I mean) to look at an engine is to determine its efficiency. You can construct an engine efficiency map, showing efficiency at all combinations of speed and torque. Since the map measures the efficiency of only the engine, it eliminates any assumptions about weight or drag coefficient of the vehicle. Efficiency is just power out/power in; power out is proportional to speed times torque; power in is proportional to fuel flow times heating value (with the appropriate constants, of course). Peak efficiency for a typical passenger car engine is probably in the 30-40% range (with the higher efficiencies being diesels). The peak tends to be at relatively high power levels, though, so actual cruising efficiency in an automobile is much lower.

9

I’m no scientist, but I think aerodynamics plays quite a big role. I remember reading about a German (VW? Benz?) concept car that had it’s passenger sit inline (as opposed to side-by-side) so as to achieve very high fuel efficiency (100mpg?)

Unfortunately, I haven’t found a cite, but here’s a quote from the 3/21/03 San Jose Mercury News: “Gas mileage improves by 5 percent for every 10 percent improvement in aerodynamics. ‘‘Reducing air drag is the most efficient way to improve fuel economy, which is a top priority for us,’’ said Dieter Zetsche, president and CEO of the Chrysler Group, at last year’s opening of the wind tunnel.”

10

I’ll be able to calculate the torque of the engine, along with the weight of the vehicle, eventually. At the moment, all I’ve got is a horsepower estimate. And it’s the MPG that I’m concerned about, as there’s no point in me dropping the engine in the car if I know beforehand that the thing’s going to only get 5 MPG, ya know? Oh, and Zut, this is going to be a steam engine, so the torque’s going to be a constant.

Ravenman, aerodynamics do play a significant role in the fuel economy of the car, but I’m not worried about getting a figure that’s even a few percentage points correct. I just need a ballpark figure. If I find out that I’m only going to get 5 MPG, then I’m not going to bother dropping the engine into the car in the planned configuration. I’ll make some changes to the design which should yield an improvement to the MPG, however, it’s not my preferred design.

11

She has some engine-eering skills. (Kill me for that pun NOW!)

I was going to say that if you could give us the displacement of the engine, we could give you some ballpark numbers based on RPM and throttle position.

Basically, instead of thinking about this as a fuel problem, think about it as an air flow problem. Engines can be thought as as basically air pumps, buy assuming that the engine control electronics will deliver enough fuel to match however much air you cram through them. (It’s a 17:1 air/fuel ratio, by mass. One gram of fuel per 17 grams of air.) This is not a real great assumption in the real world where fuel injectors have flow limits and other such things happen, but it’s good enough for the purposes of this thread I think.

You can work out the airflow for any RPM by multiplying the displacement of the engine by the RPM its running at, and then dividing by 2. The divide by 2 is because normal 4 stroke engines only suck in once per two downstrokes of the piston.

However, you said this is going to be a steam engine. That makes things more complicated. You’re presumably not going to burn the fuel directly. Instead you’re going to use the fuel to boil water, and use the steam to power the pistons. This gets into a whole mess of physics about heat transfer and other such issues.

The big problem with steam engines, aside from the uglyness of the math, is that they’re pretty inefficient because you’re not using the fuel directly. There’s all those inefficiencies in burning it to make heat, transferring the heat, etc.

Still, I suppose we can at least ballpark. Give us the displacement of the pistons the steam is going to drive, and an RPM, and we’ll pretend they’re gasoline pistons instead, then calculate the fuel consumption at say, full, 3/4, 1/2 and 1/4 throttle. Then we’ll halve the MPG estimate because of the inefficient nature of steam engines. This will still probably be a little more than actual, but at least it’s ballparkish.

That’s my $0.02 anyway.
-Ben

12

Ah, but you see, it’s not going to be a piston-powered steam engine (at least, I hope not)! So, in order to determine the fuel consumption, I’m going to need to know how much fuel the boiler consumes to produce a given amount of steam. Which is going to be tricky, because the most efficient boiler for a car is the Doble, and there’s not a heck of a lot of information about those on the web. Evidently, there’s not even a lot of specific data abotu them that’s printed. I won’t know for certain the fuel consumption of the Doble boiler (if at all) until I can snag a book on them, and at $55, it will be another month or so before I can get that. If that book doesn’t provide the information that I need, then I plan on using a formula based on the thermal transfer capabilities of copper, which should, hopefully, put me in the ballpark.

The biggest problem is that the folks who might know about this, are all closed-mouth on the subject because they’re all afraid that it’ll compromise any patents they’re working on. Nevermind the fact that even if one could build a steamer which got the same or better MPG than a contemporary car, none of the carmakers are going to be interested in it (they’re too busy working on fuel cell cars).

Quite frankly, I’ll be happy if I can get a steam engine which has the same MPG as the engine it’s replacing.

13

Tuckerfan, people have been telling you about the significance of aerodynamic drag in your problem, and they’re right. Without some kind of estimation of this, you’re just guessing.

But maybe you could work around it this way. You said “I’ll be happy if I can get a steam engine which has the same MPG as the engine its replacing”. Do you have an automobile picked out for this project? If so, do you know how much power it requires at cruising conditions? That is, do you know how much power its existing engine puts out (torque and rpm) at cruise?

If you knew that, you could match this power required with your engine’s capability at the same condition, (allow for changes in gearing, etc.). Then you could maybe figure how much fuel you’ll drink per unit time (or distance).

14

I’m not sure if you understand: aerodynamics isn’t a correction which you can ignore. It’s the dominant cause of friction, and must be included in your calculations, even if all you have is an guesstimate. And as I said earlier, it’s easy to estimate it: the coefficient is constant to within a factor of two (between 0.3 and 0.5) for almost all production passenger cars. The frontal area of the vehicle you can calculate if you know the size and shape of the vehicle.

15

Race, the car I’ve picked out for this is a 1970s Chrysler Newport (sample photo as I haven’t gotten the car yet, but that’ll happen in the next couple of months, hopefully). At the moment, the sole data on the engine I have is that the original engine made 255 HP.

One of the reason’s I picked this car is because it’s got a nice, big engine compartment. Additionally, the car comes with a 727 Torqueflight transmission, which, in a slightly modified form, was what Chrysler used in it’s turbine car, and since I plan on dropping a Tesla turbine into the car I can simply duplicate what the Chrysler engineers did and not have to come up with a whole new tranny design on my own. I haven’t crunched all the numbers on it’s output yet, but, in theory the size of turbine I plan on building will put out 450 HP. The actual output might be higher. (I’m basing this on the only published data I’ve been able to find which lists the HP output of a small one. It’s predicted HP was .096, the actual HP was .14 HP. This one used air as the working fluid, not steam [so, in theory I should have an even higher power rating] and had a poorly designed injector nozzle.)

If, however, the theoretical fuel consumption is unacceptably high, then I’ll either use it as a non-steam turbine in the car, or yank out the transmission and use a piston steam engine. (Finances will determine this, most likely.)

The overall fuel economy of a conventionally powered steam car is in dispute and the raw data necessary for me to perform an accurate calculation seems to be sorely lacking. (Or as I’ve stated above, being kept secret in a misguided attempt to get rich.)

16

scr4, Bucky Fuller’s Dymaxion car had a drag coefficient of .19, IIRC, and it got 30 MPG using a standard Ford V-8 produced at the time. This V-8 got something like 15 MPG in a Ford car. So whilst aerodynamics can halve the fuel economy of an engine, I’m not looking for a precise measurement. I’m looking for the ballpark. If I do some simple number crunching that says my current configuration’s going to yield 5 MPG, then there’s no need to go any farther. If it says that I’m going to get 50 MPG, then I know that it’ll be less, but at even half that level, it’s still worth doing.

17

I think you are trying to run before you can even walk. You are tryingto get from A to Z without going through the intermediate steps. You might as well pull a number out of your hat. You cannot directly calculate MPG. That is just impossible. You need to calculate first the engine specs: consumption, power, torque, etc, for different conditions and then see what that motor can do with that car.

You should be able to get a fair idea for the car’s requirements from the original engine. Get the orinal engine’s specs and see specific consumption per HPHr delivered. Now find out the same for your engine. if both engines have the same specific consumption per HPHr delivered at the shaft, then , in theory, you could get the same mileage (in practice you would need to optimise the transmission etc). If your engine has double specific consumption, then you will get half the mileage. and so on.

In summary, the number you are looking for is specific consumption. Once you have that you can try to estimate mileage but you cannot in any way estimate mileage directly. it is meaningless

And any calculations about specific consumption are probably way beyond what you can do. This is really complex stuff. We know the specific consumption of (say) diesel engines because millions have been built and they are optimised. I doubt you can make any meaningful and simple calculations about specific consumption of something so experimental. My guess is that the consumption will be extremely high when compared to conventional engines but the only way to find out is to build it and find out. Let us know how it goes.

18

That, in a nutshell, is what I’m trying to do. Since I’m going to be doing this on the cheap, I can’t afford to do a lot of mucking about and I’ve got to get it right the first time. It’d be nice to be able to slap the thing together, hook it up to a dynamo and see what the results are, but that will add years and dollars to the pricetag of this thing that I just don’t have. So I’m trying to get something which gives me an idea if this is doable or not. My gut tells me that it’ll work, and some of the data I’ve seen tells me that it’ll work, but I’ve got nothing approaching hard evidence at the moment, and I’m really going to need that when it comes time to build the thing.

19

Hmmm. According to this, the standard steamer burner is fed fuel at a rate of 4 GPH, while it looks like the average electric fuel pump feeds a carburetor at 32 GPH. So that might mean I can expect better fuel economy. Anybody care to take a guess?

20

That 32 GPH has to be a max flow rate, not a real world average.

For example, my car has about a 16 gallon tank. I get about 28 mpg while running at around 80 mph on the road, which gives me a range of about 450 miles and a fuel consumption rate of a shade under 3 gph.

32 GPH would drain my tank twice in one hour. Unless I’m going 800 mph, that’s going to be pretty crappy mileage.

Or did I misunderstand this entirely?