Hypothetical mpg question fo a 90 mile journey.

Joe_Horner

Norman_Castle wrote: »

So first gear@2000 rpm and 10 mph for nine hours would be cheaper?.

almiller, the engine will be running for three times as long at 30mph and be in a lower gear.

But it would also be running at a MUCH reduced throttle opening (or pump delivery for a diesel). In fact, for that sort of gearing (15mph per 1k revs), most cars would need the throttle opened barely more than idle.

That has far more effect on the rate an engine consumes fuel than its speed does, so the car at 2000 rpm in 4th on a low throttle will use much less fuel per hour than the one at 2000 rpm in 6th with an open throttle.

Ultrasonic

Norman_Castle wrote: »

So first gear@2000 rpm and 10 mph for nine hours would be cheaper?

Almost certainly not, but it is overly simplistic to conclude this purely on the basis that it would take a very long time to get anywhere. You have made me think though, and I do see where time does factor into the way I was thinking about this.

Before getting bogged down in detail I will though say that for my own car, 2,000 rpm is about 60 mph in top (5th) gear and 30 mph in 3rd gear. Going by instantaneous mpg figures on my ScangaugeII (which I believe to be fairly accurate) fuel economy is a little better at 60 mph, by about 10% or so I think. But I do believe that if I had additional gears such that I could do 90 mph at 2,000 rpm that this would give worse mpg, but I'll admit I can't be absolutely certain.

Let me have a stab at reducing some confusion in this thread, although I realise I risk introducing a load more ;-)

There are two factors worth considering - aerodynamic drag and the variation in engine efficiency with load (Brake Specific Fuel Consumption, or BSFC). That is, how much fuel it takes to generate a certain amount of mechanical energy. Higher engine efficiency means less fuel needed per unit energy output.

As discussed above, the faster a vehicle is travelling the greater the force exerted on the vehicle as a result of aerodynamic drag. To overcome this force the engine has to do more work, which is achieved by burning more fuel per engine revolution. (Note that more fuel being used per cycle is why getting there 3 times as fast at 90 mph DOES NOT mean that it uses a third of the fuel at 30 mph. That shouldn't need saying, but it was mentioned above...)

It takes a particular amount of energy to move a particular car a fixed distance at 30 mph. A portion of this is due to overcoming aerodynamic drag, and a greater amount of energy is required to do this at higher speed. If this were the only cosideration then travelling at 30 mph would obviously use less fuel to travel the distance considered. The complication is that overcoming the extra aerodynamic drage increases engine load, and typically increases the engine efficiency.

In order for travelling faster to give a higher mpg requires an improvement in BSFC which more than offsets the change in energy taken to overcome aerodynamic drag is required. This is what needs to be considered in this debate. As we're talking about a hypothetical vehicle and engine we can't decide this for certain (it would be tough even for a specific vehicle!) Here are some example BSFC plots though to give an idea of the variations though:

http://ecomodder.com/wiki/index.php/Brake_Specific_Fuel_Consumption_%28BSFC%29_Maps

Thinking about it I now realise that the time considerations above are a factor reflected in the BSFC variations. If you drive 10 miles at 10 mph or 30 mph but both at 2,000 rpm then there are three times as many engine revolutions required at the slower speed for the same trip. The amount of energy wasted on frictional losses as the engine turns will therefore be greater at 10 mph, which will act to reduce engine efficiency. But there are other factors affecting BSFC as well, and less fuel will be burnt per revolution at 10 mph, so it is not possible to simply conclude what is optimal on the basis of journey time.

My best guess remains that 30 mph would be more economical than 90 mph but I do now appreciate that it is perhaps a little less clear cut than I first suggested.

Norman_Castle

Joe_Horner wrote: »

But it would also be running at a MUCH reduced throttle opening (or pump delivery for a diesel). In fact, for that sort of gearing (15mph per 1k revs), most cars would need the throttle opened barely more than idle.

That has far more effect on the rate an engine consumes fuel than its speed does, so the car at 2000 rpm in 4th on a low throttle will use much less fuel per hour than the one at 2000 rpm in 6th with an open throttle.

The extent the throttle is open depends on whether the gear is suited to the engine torque and the aerodynamic load.

Norman_Castle

Herzlos wrote: »

Yup. You'd use a lot less fuel to move the car. You'd use more fuel for fixed items like A/C and the radio, but that shouldn't have much impact on the overall fuel economy.

Would the extra eight hours the engine is running affect the amount of fuel used?

Richard53

There is some interesting discussion here, and I am probably not qualified to disagree with some of the experts. But here goes.

I look at this from the opposite end of the telescope. Logic says that to move a certain mass (i.e. a heavy car) a certain distance (90 miles) represents a certain amount of work, which will take a certain amount of energy. If you discount air resistance, frictional losses etc, it will take exactly the same amount of fuel, regardless of speed and the gear selected. One hour at 90 mph, 9 hours at 10 mph, same work done, same energy required, same fuel used.

Than you come to the additional loads which come with the changes in speed and gearing. Air resistance is the big one which, as others have said, goes up with the square of the speed. It affects a moving vehicle at any speed (ask a cyclist) but for an average car the effects become noticeable above about 60 mph. At 90 mph, it needs 9x the energy to push the air aside as it does at 30 mph. Frictional losses in the engine and transmision, and between the tyres and road, will increase with speed too, although I don't know to what extent these are linear or exponential.

Bottom line is, it will take exactly the same amount of fuel to move the mass of the car whatever the speed, but doing it faster increases the additional energy costs out of proportion to the speed. Faster = more fuel for the same distance.

The most energy-efficient speed would seem by this reasoning to be as low as possible - say running the engine in a low gear at just above idle for many hours. But then you get into issues of the actual efficiency of combustion. An engine at idle isn't operating very efficiently. Best efficiency comes at maximum bmep, or roughly maximum torque, so you would probably be better running the engine at about 2000 rpm (depends on the engine) and gearing for a lowish speed. Bear in mind that the throttle would barely need to be open and the engine would be sipping fuel as the actual load on the engine is tiny. (To achieve this, you would only need a small engine, which would reduce frictional losses even more.)

ETA: Ultrasonic has made many of the points I was making, only better. We cross-posted.

Ultrasonic

Richard53 wrote: »

ETA: Ultrasonic has made many of the points I was making, only better. We cross-posted.

It's good to know I wasn't the only one thinking along these lines . (And I'm not at all sure I made any points better, but thanks.)

Herzlos

Norman_Castle wrote: »

Would the extra eight hours the engine is running affect the amount of fuel used?

You'll waste a lot of fuel running the car for the extra 8 hours. But you'll be using a lot less fuel to move the car, so it should still be less fuel overall. There's maybe a lower bounds where the fuel wasted with the extra running time exceeds the fuel used to move the car, but I don't know where that'd be.

Assuming you're running the car at the optimum revs (peak torque) and all else is equal, then going faster will use more fuel per mile.

WTFH

There comes a point where you have to evaluate the overall cost, not just of the fuel.
There's the driver's time - could 8 extra hours behind a wheel be spent more productively? I mean, 8 hours is a working day. Even at minimum wage you'd earn more working than the extra cost of the fuel.
And then there's the depreciation of the car. That is based on the car's age, and at 10mph, by the time you get there the car will be 8 hours older than it was at 90mph.

Yes, I'm being a bit flippant with the second point, but sometimes the analysis of costs gets so deep into one piece of detail it misses a lot of other bits.

Richard53

But your first point is a good one. I usually try to drive economically* but if I need to hustle I justify it to myself by telling myself that I am saving more of my own time (by hourly rate) than I am wasting on extra fuel. Sometimes I even believe myself.

* In the car, that is. On the bike it's different.

Ultrasonic

Herzlos wrote: »

Assuming you're running the car at the optimum revs (peak torque) and all else is equal, then going faster will use more fuel per mile.

It isn't quite that simple I'm afraid, you need to consider engine load not just revs when considering what is optimal. (See my comment re. BSFC above.)