Why does it use more gas to accelerate more rapidly?
 

I think I'm missing something obvious here, but let's see...

Steady state gas milage is roughly due to two factors, the air resistance which goes with the square of speed, and rolling resistance which goes with the speed. So, roughly, milage is the fuel use at idle dividend by the cube of speed. Roughly. Then you add in things like hills and such.

The part I don't understand is acceleration. It would *appear* that the amount of energy needed to accelerate to a given speed is a fixed, it's simply 1/2*m*v^2. There's no "t" term in there for the time you take, nor an "a" for the acceleration. It's just initial vs. final velocity.

But that certainly isn't the case in practice. "gunning it" up to speed appears, according to my milage readout, take considerably more gas than doing so leisurely. And every reference on gas milage says the same thing.

I know that gas engines have performance curves, and this might be the cause of the problem. Yet most curves I have seen peak at numbers far higher than what I use in my car to get the best milage (54.2 US mpg right now BTW).

So can anyone out there offer an authoritative answer to this?

Part of the answer is a combination of engine RPM and gearing. Generally, vehicles get the best fuel economy cruising in the highest gear at the lowest possible engine RPM. Brisk acceleration normally demands lower gears are held longer while the engine runs at higher RPM (particularly true if you're driving an automatic).

At higher RPM, your fuel economy display shows you the cost of increased internal engine & transmission friction and accessory drag, to start.

People are going to correctly point out that you can accelerate with a high engine load and moderate RPM (manual transmissions work best for this) and take advantage of the engine's "performance curve", as you say, to minimize fuel consumption while generating the higher power needed to accelerate ("performance curve" in this respect = Brake Specific Fuel Consumption (BSFC): Brake Specific Fuel Consumption (BSFC) Maps - EcoModder).

But operating an engine close to its best BSFC point on the "curve" (map) does not equal lowest overall fuel consumption. Some people will tell you that it's always best to accelerate briskly for best overall fuel economy, but it's not as simple as that, as your dash display shows. A lot depends on "what happens next" (after accelerating) in your particular driving scenario.

Having said all this, I think people worry far, far, far too much about acceleration technique. Much more fuel savings are to be had by most drivers by focusing on the brake pedal (minimizing its use) and by cruising at moderate speed after accelerating (on the freeway).

That's what I like the most about driving a hybrid - the high amount of "engine braking" from the generator. After a few weeks I got really good at estimating the deceleration at various speeds and the amount of time my brake pads actually grip metal are probably reduced by 100 times.

Well that's just it, if my meter is at all accurate, it's the exact opposite. For example; there's an onramp I use every morning to get onto Highway 401. If I goose it right up to 105 km/h (I rarely go over that :-) and then settle into cruise, my milage will go down 0.2 or 0.3 over that few hundred meters. If I accelerate more slowly and use up the entire ramp lane plus a little of the slow lane before getting to 105, I can keep this down to 0.1.

Now mathematically, the two should be *very* close to equal, but they are not even remotely close in practice. Which is why I think I'm missing some obvious factor... or not so obvious maybe!

I'll try to keep this short.
Too roughly. It's not (air resistance)times(rolling resistance), it's (air resistance)plus(rolling resistance). So, roughly, gas milage is Av^2+Rv, where A and R are coefficients. By roughly I mean that there is more to that equation, like varying engine efficiency depending on rpms, load, etc.

The formula you gave is for (kinetic) energy, ie that is the energy of a vehicle with mass m and speed v. Much better would be to use force and acceleration: F=ma. Acceleration a has time in it (time squared, actually), so the greater the acceleration, the more fuel had to be burned to produce enough more force.

"Grannying" isn't what you'll find here, nor will you find us telling you to floor it, either. Each engine has a "sweet spot" of efficiency - a certain range of loads (usually ~80%) and rpms (close to max torque) when the amount of fuel used to produce a certain amount of power is lowest. Trying to keep your engine close to that sweet spot yeilds highest efficiency. Search for BSFC maps for more reading.

Edit: MetroMPG beat me, grrr.

You're on to something there. ;)

You may simply have illustrated the difference between operating the engine closer to its most efficient point on the BSFC map (slower accel), vs. higher accel. I assume your hybrid (what kind is it?) has a CVT, and it will try its best to adjust gearing during acceleration to stay close to the engine's "sweet spot", which is generally at a relatively low RPM. But when you put your foot in it and demand higher RPM/more power, it will concede, and overall fuel economy will drop.

It's physics, if it takes a certain amount of energy to get from point A to point B, it will take more energy to get from point A to point B faster.

Ideally you would accelerate at optimum speed, kill the engine and coast down to a low speed and repeat. We call in Pulse and Glide. Then the engine is only ever running at peak efficiency.

My experience of driving in Phoenix these past 12 years - our streets are unbent by lake or stream so we have a near perfect grid throughout the whole city -

I have always left a stoplight quickly and reached the speed limit very rapidly, probably around 90% throttle and shifted in the low 4k's ... then when I reach the posted speed limit I stop accelerating and maintain that speed.

I am apparently the only human being in Arizona who does that, because no matter what car I drive, how low its horsepower, I pull out WAY ahead of everyone else and much later, when I've reached the 45mph speed limit and settled there for quite some time, all the people I left behind blast past me at 55-60mph, only to stop again at the next light and repeat the process.

I don't do any "hypermiling", I simply get up to the speed limit quickly and then stay at one speed until it's time to stop. I consistently get higher than the EPA mileage on whatever vehicle I drive.

Sorry, this is not correct. There is no relation between force and fuel use.

Perhaps I should have mentioned I'm a physicist. Because I am :-)

Ok, I'm going to operate under that assumption, as it makes sense. Although that often means little (ie, it makes sense that eating eggs, which are filled with cholesterol, results in higher blood cholesterol... except that it doesn't actually do that).

Anyone suggest a good book on this in general? I'm also thinking of adapting my wife's 2003 Echo to all-electric, so I'd like to read a lot more on the engineering and energy use side of things.

It's a 2006 Civic Hybrid. Generally very happy with it, and I'm getting 54.3 mpg over the last 3700 miles (I reset at the last oil chance) as of this morning. In the winter that goes down to about 42 mpg, which is also interesting. My only complaint is the low seating arrangement, which doesn't agree with my back so much.