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I've often heard that accelerating harder makes for bad fuel efficiency, but have yet to be given a sound explanation of why. Naturally this makes me question this advice. Now obviously when you accelerate harder, more fuel is being pumped into your engine, but you'll sooner get to that cruising sweet spot where fuel consumption is a lot less. So is the payoff worth it or not?

This question needs some parameters, as obviously if you fly off at the lights only to stop hard in 100 metres, you'll certainly be facing some very bad fuel efficiency. I'm more talking about lights at the beginning of a long open road, where how you accelerate has no impact on the eventual braking that will have to happen.

I think the crux of this question has to do with power output per fuel input at varying engine RPMs. I've been thinking about this as my car has very low torque at low RPM, but once it's around 3,000+ RPM it's great (old BMW 320i). Might it be that my car's engine runs more efficiently at 3,000 RPM, and as such slightly harder acceleration than normal will improve fuel efficiency? Or am I dreaming?

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As you said the crux of the issue has to do with getting every last amount of energy out of a unit of fuel. You can consider this your total fuel efficiency.

Accelerating your vehicle from rest to 60mph or 100km/h will require a fixed amount of energy based on the weight of the vehicle. (excluding wind, friction and rolling resistance).

So you need to utilize your engine in the most efficient way to produce that amount of energy. For example you could just floor the accelerator and rapidly produce the energy required but there is no way for you to know whether that path is more efficient than building that energy over a longer period of time.

To know this you need to know your engine. Specifically you need to know your Brake Specific Fuel Consumption (BSFC). The BSFC measures how much energy your engine produces per unit of fuel (usually a gram of fuel). Your engine will have different BSFC at different RPMs and Torque values. You want to run your engine where it has the lowest BSFC (lowest fuel consumption per unit of energy produced). So if you look at the BSFC chart I have linked you will see that for that engine its lowest BSFC value is 206 at about 2100-2200 RPM at close to peak torque.This means that this engine runs most efficient in that operating range.

In general engines run most efficient close to their peak torque at wide open throttle and at the lowest RPM possible. This range will be different for every engine and vehicle because all engines are different and every vehicle has different parasitic loads. You could probably calculate it for your vehicle if you run the vehicle on a dynamometer to measure the hp (energy) and then also monitor the fuel consumption and then do a division accross the curve to see where the engine was most efficient.

Now that you know at what operating conditions your vehicle is most efficient the difficulty then becomes running your engine in those conditions at all times during acceleration. This becomes difficult with a transmission because the rpms have to rise as your vehicle accelerates.

With a manual transmission what I would do with the above example curve would be to have the accelerator at wide open throttle from 1500-2500 rpm and shift at 2500rpm for each gear. I am sure that it is possible to calculate the exact shift points for maximum efficiency but I am not willing to put that much effort into it.

With an automatic transmission this is very difficult because if you try to run the engine at wide open throttle the automatic transmission will extend your shift point up to the high RPM range and you will get very bad BSFC and in turn efficiency. With an automatic transmission you have to accelerate much slower so that the transmission will shift at the appropriate points to keep your engine in an rpm where it can operate at its highest efficiency. Maybe pushing the accelerator at half throttle can achieve this but you would have to do it by feel.

In conclusion I would say the best way to accelerate is to accelerate as fast as possible in the lowest RPMs.

Hope this explanation helped somewhat.

Wiki Brake Specific Fuel Consumption

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Wow what an answer. I'm going to need some time to have a good look at this, but I think this information is what I've been looking for! –  andrewb Mar 16 '13 at 2:51
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"(excluding wind, friction and rolling resistance)." Those exclusions remove all of the real world concerns of this question. This isn't an abstract physics problem. BSFC is useful to determine the most efficient engine speed on an engine stand. It does not directly translate to the most efficient speed over ground (frictional losses are important). It gives you no information about efficient acceleration as the loads and fuel consumption profiles vary wildly (e.g., increased fuel added to cool the charge under boost). –  Bob Cross Mar 18 '13 at 12:03
    
If you use the BSFC values generated from a wheel type dynamometer then most drag innefficiencies would be included. Wind resistance will be minimized by getting up to the required speed sooner so that energy loss should be less if you accelerate quicker. Same with rolling resistance and friction. So I assumed to remove those from the assumptions because generally speaking you can't control them and would generally favor accelerating quicker. BSFC will give you lots of information about what range your engine is most efficient accelerating in that range will also be the most efficient. –  Mike Saull Mar 18 '13 at 14:18
    
BSFC gives you information about your engine at a steady state, not during acceleration at different throttle positions with varying tuning parameters. Fuel consumption is easily measured using the OBD II port. Rabbit starts are less efficient than gradual acceleration. –  Bob Cross Mar 19 '13 at 2:50
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I agree with the statement that rabbit starts are less efficient only if you accelerating at a higher rpm where the engine is essentially "wasting" fuel more than required. However I believe that accelerating from 0-60 at 20% throttle from 1500-2500 as opposed to 100% throttle 1500-2500 that the 20% throttle will be less efficient in getting up to speed. Just because the engine is producing much less energy and the fuel consumption would not be less than 1/5th of the 100% throttle option. –  Mike Saull Mar 20 '13 at 15:06
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Does accelerating faster worsen fuel efficiency?

Yes.

Now obviously when you accelerate harder, more fuel is being pumped into your engine, but you'll sooner get to that cruising sweet spot where fuel consumption is a lot less. So is the payoff worth it or not?

No.

This is easily measured via the OBD II port. For example, my Accessport gives me immediate readings on instantaneous fuel consumption. The Automatic dongle + smart phone combination purports to give you information that's just as detailed (though without the capability of reprogramming your ECU). As they say in their product tour: "Rapid Acceleration - Stepping hard on the gas pedal decreases fuel efficiency and wastes money." With a device like this, you'll be able to measure exactly how much money you're losing with rabbit starts.

Accelerating requires more energy than steady state cruising, therefore requiring more fuel. Accelerating quickly requires more energy than accelerating slowly. There is a super-linear releationship between rate of acceleration and rate of fuel consumption (more fuel consumed per meter/second^2 at higher rates of of acceleration).

If you'd like a practical demonstration of how turtle acceleration can save fuel, I refer you to Jeremy Clarkson's demonstration in his epic drive from London to Edinburgh and back on one tank of fuel in a twin turbo V8 Audi (scroll down to episode 4 of season 4). He describes in detail how to avoid the wasted fuel of acceleration. Most importantly, he kept the revs under 1200 rpm.

These are measurable quantities. There's no fuel efficiency justification for rabbit starts at stop lights.

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It takes a specific amount of energy to accelerate a specific amount of mass to a specific speed. So just looking at those factors, you'd be right to assume that it matters little how quickly you accelerate said mass.

But that's not how the real world works. The problem here is that combustion engines and the many things we connect them to are astoundingly inefficient. There is a substantial amount of friction involved. In order to accelerate your car quickly, your engine Has to move faster. The faster a piston has to oscillate, the greater the force that the bearings are subjected to. The work required to pull air into and out of the cylinders through the valves is much greater at high RPMs, exponentially so. And the list goes on.

On top of that, your car engine has to waste even more energy at high RPMs turning the alternator, the water pump, steering pump, etc.

If you put all these factors together, it's quite obvious why your engine is more efficient at lower RPMs.

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s/high speeds/high RPMs/g :) –  jensgram Mar 15 '13 at 8:01
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