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.

On what? BSFC? There's a decent article about it on Autospeed.com: link

It is interesting - and there are lots of reasons for it. Here are a dozen or so:

http://ecomodder.com/forum/showthrea...leage-220.html

first, the wind resistance is cube of speed, but you get to divide by miles covered, so your MILEAGE is a function of speed squared.

Mileage and acceleration are indeed sort of unrelated, but they do tie together.

The faster you accelerate, the more time you spend at "top speed", which means you burn more fuel simply because you are going faster.

Second, the ECU computer in the car richens the mixture drastically above a certain point. It goes "open loop" and throws gas at the engine, because extra gasoline gives more power. You REALLY want to stay out of "open loop" for mileage.

Third, an automatic transmission will stay in low gears longer, meaning more average RPM's, which means more gasoline burned.

Fourth, driving conditions can mean you burn more gas as a systems point of view. If you and I are next to each other, and the light turns green, and you rabbit out there and get up to 45mph , only to stop 1/4 mile on for the next red light, and I ease out, and my top speed is only 30 mph, you burned well over twice as much gasoline on that single section of road than I did. First, you accelerated to 45 which takes twice as much gas as it takes to accelerate at 30mph, and second, you spent time at 45 mph which burns twice as much gas as it does for 30mph if you look at only wind resistance.

Hope this helps

and yes, i'm also a math/physics major.

But that's not what's happening here. The problem is getting to the same speed - say 60 mph - and then staying at that speed. So obviously (at least I hope it's obvious) if you accelerate 0-60 in 8 seconds, the point A at which you reach 60 is a lot closer to your starting point than the point B at which you reach 60 if you do the 0-60 in 16 seconds.

I must admit I've wonder about it myself, and whether it's merely the effects of the IC engine/powertrain. What would a pure electric do? Anybody have a Tesla and want to run some tests?

How about a Nissan Leaf? My Nissan Leaf Forum • View topic - Faster acceleration vs slower acceleration

I stated above that I always accelerate much more rapidly than basically everyone else on the road (this is 6 stoplights per morning and 6 stoplight per afternoon 2-3 days a week at least when commuting by car.. and the hundreds of thousands of other stoplight accelerations ever since I began driving in 1995) and have always returned better than EPA-listed mileage without using any deliberate hypermiling techniques.

All I do is get up to the speed limit fast, then stay there. I drew a crappy graph in mspaint to illustrate where I believe the difference lies:
http://img571.imageshack.us/img571/5...elerationy.jpg

Even if other drivers maintained the same maximum speed, they spend a much longer duration at acceleration-level fuel consumption, and a shorter duration at cruise level fuel consumption. I believe based on the feedback loop (with its necessary lag time) engines use to regulate combustion, a steady cruise rate will necessarily result in a more accurate and thus more efficient level of regulation. It's worth noting that this particular difference may not be relevant to electric vehicles because even if there is a feedback loop, it operates at the speed of light rather than at the speed of combustion gases.

Here is an example, not based on any actual measured data but just my guess at why greater acceleration may not actually be a big culprit, even if the same cruise speed is attained - even when that means maximum cruise speed is maintained for a longer duration on the car that gets up to that speed first. Pay attention to the relationship between the green region and the yellow region as illustrated:
http://img26.imageshack.us/img26/6804/acceleration2.jpg

There is, and it's called the engine ;)

The acceleration is generated by the fuel, and more precisely by how (in)efficient the engine converts that fuel into acceleration.

I'm doing something wrong here. I accelerate @ 80-95% load and upshift @ 1500-2500 RPM, depending on conditions. I use cruise control EXTENSIVELY, and use it to engage DFCO @ lower RPM. I NEVER EOC, I RARELY P&G or DWL, and I NEVER draft another vehicle.
My lifetime average is over 47% over EPA combined. What am I doing wrong?

Your driving a manual transmission.

Despite being a physicist the op has little understanding of how our engines behave real world, there are volumes past and present about how inefficient most engines are, how many losses there are in various drivetrains, how most engines run efficiently near only one high level load, etc, etc.

Simply put if you drive a manual transmission you can load up your engine to its most efficient level, which is usually somewhere between 75-90%.
It may be more or depending on auto/manual and whether your car richens up dramatically.

Anyway Your motor inevitably makes power most efficiently near its design limit (least losses VRS power created) so accelerating along that curve is ideal if you can do it and your automatic doesn't twart your efforts.

This means if you pulse at max efficient power and kill the engine you will get the best FE out of your platform.

If you instead drive at low load levels your motors power will be wasted on parasitic losses AKA, throttling losses, compression and other internal engine efficiency losses and more on friction than at a high load level where internal friction is less of a percentage of total engine power.

Cheers
Ryan

Let me throw one more variable in the mix. The a/f mixture under heavy acceleration is significantly richer than during cruise or light throttle acceleration. Thet could account for some of difference in the results achieved by the 2 techniques. Is this not true?

You control the power an engine produces by regulating the air delivery, which in turn regulates the timing and fuel delivery, except in Diesels which have no air delivery restriction.

Engines are most efficient when they have maximum air delivery at fairly low RPM, without full load enrichment. I remember a Dyno test of a 2.5 L GM engine. At 1500 RPM producing 20 HP the engine required a specific volume of fuel. When the load was increased to 50 HP (same RPM), the fuel requirement rose by 50%, while the power produced rose by 150%. That is the essence of best BSFC, you get more work out of the same amount of fuel by making the engine work harder but not at maxumum for that RPM.

This is the essence of pulse and glide. Long before the term "Hypermiler" was ever adopted this principle was known. Using the "cheaper" (fuel wise) higher load capabilities of engines people who were not constrained by traffic and speed used P&G to extend the range of their cars. It mostly started in WW2 (but was done before that) Use the higher efficiency load to store energy in your car as inertia, then kill the engine and coast.

80% load is the ideal load range, becasue it does not use enrichment. Lower RPM does not encounter the much higher friction losses of high RPM.

Why does it use more fuel to accelerate at higher rates?
You are doing more work to increase the inertial state of the vehicle.

My Insight would use 12 times the fuel at maximum acceleration than it did at lower constant speeds. The secret is to minimise the fuel used in acceleration then use the additional inertia to travel considerable distance with little or no fuel consumption.

regards
Mech

No. From a pure physics POV (neglecting engine inefficiencies, etc) you're doing exactly the same amount of work to accelerate to a given speed: Work (physics) - Wikipedia, the free encyclopedia You're using a greater power, but applying that power for a shorter time: http://en.wikipedia.org/wiki/Power_(physics)

Sure, but what about fuel consumption vs rate of acceleration? Then with the Insight, there's still another factor, which is that if you accelerate hard enough, the electric assist comes on, using energy that you'll (partially) recover in the next braking. But if your battery charge is below about 3/4, the engine will be charging the battery, and thus using more fuel...

I think we're getting closer to the answer.
Keeping engine efficiencies aside, since greater acceleration means more power, but for a shorter time, then we need to know if twice the power (let's assume twice the instantaneous fuel consumption) will result in half the time needed to accelerate? In theory yes, but after factoring in aero and rolling resistances?

In my case this represents perhaps 1 km over a 100 km one-way route, so the effect on overall would be perhaps 1% if this was simply a geometric effect.

Looking at the instantaneous gauge, mpg goes from about 65 cruising at hiway speed, to about 15 to 20 mph during acceleration.

Ahhhh, now *that* sounds like we might have hit on it...

Is this purely linear? IE, is 2x RPM and 1/2x the gearing to get the same end speed using twice as much fuel?

Maury

Quote: Why does it use more gas to accelerate more rapidly?

Because you are injecting a larger amount of fuel with more losses to heat, friction and the force of the rapid acceleration.

Simply put the more pedal you give it the more fuel it waste.
Much like doing 70 on the highway compared to doing 55 on the highway.
Use less hp and you will also use less gas

But you are doing that for a proportionately shorter length of time, so - assuming your engine &c is equally efficient at all loads & RPMs - you should wind up using exactly the same amount of fuel.

...theorectically, that would be true, but nothing is 100% efficient, so accumulating 'losses' cause our realworld results to be otherwise!

This is silly to think that a bunch of physickists and mathemagicians can't understand the difference between energy and power?

A 3200 lb car accelerates from rest to 60 mph (88 ft/sec).

The "work" or kinetic energy is .5mv^2 = 387,200 lb-ft regardless of how long it takes to get up to that speed.

But power is the time rate of the change in work or energy, dKe/dt.

So 0 to 60 in 5 seconds = 77,440 lb-ft/sec = 140 hp
and 0 to 60 in 20 sec = 19,360 lb-ft/sec = 35 hp.

How much more fuel does it take for your engine to make 140 hp versus 35 hp?

Look at the dyno data--the torque-speed curve and the volumetric efficiency-fuel consumption curve to find the actual number, but it will be at least a factor of 4.

BTW this is why stop and go traffic kills mileage--it takes so much more power to get up to speed than to just maintain a constant speed.

In this case if your mileage gauge normally reads ~40 mpg for the slow acceleration, then it will drop to ~10 mpg for the faster accel.

35hp average is a pretty low number for a 3200lb car. Typical cars are geared so that cruising on the highway is less efficient than wide open throttle 100% load acceleration, at very high rpms they're about even.

3200 lbs, Cd = 0.36, Area = 20 sqft, Crr = 0.030

Cruising at 60 mph constant speed on flat asphalt road, the power loss due to aero drag and rolling resistance is about 25.7 hp. Drag force ~65 lbs, Roll force ~96 lbs.

I already hit the thanks button but I wish I could repeatedly - that is the BEST article i've ever seen on BSFC, finally explaining part throttle BSFC (which I see so much more rarely discussed) and singlehandedly making alot of things "fit" in my mind about why things work the way they do.

Thank you x10

IMHO, this chart:

http://us1.webpublications.com.au/st...112611_7lo.jpg

and this chart:

http://us1.webpublications.com.au/st...12611_10lo.jpg


summarize "...the tale..." quite well.

• The first illustration shows that moderate (1/2) throttle is better than either light (1/4) or full (100%) throttle.

• The second illustration shows how the most economical engine speed lies between 1,000-2,000 rpm.

You have it backwards, 35 hp is high for a 3200 lbs car.
Wide open throttle High RPM 100% load will consume fuel at the fastest rate possible and cover the least distance possible.
Guaranteed that all North American passenger cars will consume the most fuel and travel the least distance at full throttle.
Highway cruising is the most efficient, 55 down to 40 mph will give you the best mileage.

Very high RPM consumes very much fuel, the two are joined at the hip.

If you have a fixed maximum speed (the speed limit) and you spend very little time in the high consumption mode of heavy throttle, then settle into the low consumption-per-distance full cruising speed for the longest duration per interval (between stops), that should use less fuel overall than accelerating for a very long period of time and cruising for a shorter time.

Exactly.
I like to accelerate at a reasonable pace, slower than molasses is not required, either is jack rabbiting.
I use very little throttle in my driving, short shift at 1500 rpm when accelerating and still get up to speed fast while maintaining low rpm.
Its the RPM's or even driving it in too low of gear that sucks back the gas.
My driving motto is if it doesn't stumble its going into 5th.
From 30 mph on my car is in 5th gear.

I found a great quote from Katy Levinson, the drunken roboticist, speaking at Defcon 20
Personally, when the light changes, I clear the intersection as quickly as possible (as a courtesy to other drivers :) ) and then think about that last 1% of gas mileage. And I'll burn a little extra gas to not have to sit at that long light in Thurston. It's all about position in traffic.

I drive faster in traffic and slower when the road is clear. If everyone did that traffic wouldn't bunch up.

Thinking is just physics, accellerating a given mass from 0 to 55 is the same amount of work in terms of kinetic energy. But doing it slowly you had to go a longer distance so more work is done. So more fuel is used accelerating slowly but more work has also been done.

Proper accelerating is better though, open throttle, but low rpms and short shift. Almost never beat out of a light with my auto's, shifting at 2k the cobalts not so quick.

No, the WORK is the same
 

No, No, No...
Are you another one of them physickists or mathemagicians that don't know the difference between energy and power?

The Work done is exactly equal to the Kinetic energy.

Kinetic energy = 0.5mv^2 = Work = F x distance = m x accel x distance

Power = Work / time

You go a longer distance but the acceleration is lesser, and the Work is the same.

No need for erroneous clutter--do you want to delete your post, then i'll delete mine...

Energy required at the wheels is equal
 

Clarification: The amount of energy expended at the wheels to accelerate to a given speed is identical (assuming you're not burning rubber on the launch). However, in an internal combustion powered car, the efficiency of the engine in converting fuel to usable wheel power varies. Optimal MPG therefore depends on accelerating at the rate of maximum engine and transmission efficiency.

For an electric car it's simple. The energy expended has zero relation to the rate of acceleration.

Ex: If you drive a distance of one mile with a maximum speed of 40 MPH, the total energy consumed will be ~300 watt hours regardless of if you accelerate to 40 MPH in glacial 30 seconds or in just 3. Note that I have confirmed this countless times in my Tesla S.

Hahaha
 

lets dumb this down to under grad level LOL!
Your question is, "Why does it use more gas to accelerate more rapidly?"
The simplistic answers may be insulting so I wont go there, But I think you ask about reworded why Does it absorb more energy to accellerate fast v/s slow.
It does not., the big difference is that engine tuning is designed for what?
Thats the kicker see?', All engines are purpose designed and sacrifices must be made to conform to its intended application, to epa to carb etc etc etc.
My dodge R/T actually does more economy to accelerate quick then glide.
This is pulse and glide basis and It has big effect with cars designed for acceleration foremost .
others it doesnt do so good for because it switches ECM into WOT mode and just dumps fuel unceremoniously.
Unless You have fancy car that has special programs and optimizes itelf better than the standard cars up till about 2005?

Ok its deep its open and its simple I cant break it apart much better without becoming specific.

Here are the results of 70%, 82%, and 90% engine load P&G cycles with my xB. The 90% engine load gave the best results.
http://i1179.photobucket.com/albums/...B/PGSGdata.jpg

Here are the rest of the testing results, and the discussion.