The Case for Coasting: Energy-efficient Driving

by David S.Lawyer mailto:davylawyer1@gmail.com More transportation articles by David Lawyer

August 2008, minor revision 2012

1. Copyright

2. How to Drive Efficiently

3. Engine Efficiency

4. Energy Storage

5. Analysis of BSFC Maps.

6. More Tips on Efficient Driving.

7. Problems and Suggestions

8. Why High Torque is More Efficient

9. Why Doesn't my Efficiency Double?

10. Author's Notes on Searching for BSFC Maps

11. Bibliography


1. Copyright

Copyright 2008-12 by David S. Lawyer. Feel free to make copies but commercial use of it is prohibited. For example, you can't (except to an insignificant degree) combine it with advertising on the Internet. Please let me know of any errors or suggestions for improvement.

2. How to Drive Efficiently

Most people erroneously think that to save gas they should take it easy on the gas pedal, accelerate slowly, and maintain steady speed. But in reality one should do just the opposite combined with lots of coasting.

To drive efficiently, keep a heavy foot on the gas but when you wind up going too fast, shift to neutral and coast. It would be even better if you could coast with the engine off but in most cases it may hurt your transmission. And it usually disables the power part of the brakes and steering which may not be safe. The brakes and steering still work but you have to use a lot more muscle to operate them. Except if you should have a hybrid, it's designed to coast with the engine off.

Also, coast downhill as much as possible and also coast when you need to reduce speed or stop. With the exception of downgrades steep enough to coast down, and also with the exception of upgrades where you have to keep the accelerator pedal pressed down hard (say over about halfway to the floor) to make it up the grade, you can "pulse and glide" (also called "burn and glide", "accelerate and coast", etc.). This is done by accelerating at near maximum acceleration (pulse or burn), and then when you reach a high speed, shift into neutral and coast (glide) until speed is reduced by say 15 mi/hr. Then repeat another pulse and glide and so on.

It takes skill to do this safely and in heavy traffic it may not be feasible. Make sure that you are not obstructing traffic behind you. Note that coasting in neutral is illegal in many states but shouldn't be. In some states, only coasting downhill in neutral is illegal so "pulse and glide" is legal if you are not going downhill.

3. Engine Efficiency

The reason that the above works is that while automobile engines are about 33% efficient (thermal efficiency), the typical efficiency while driving is more like about 17%. The efficiencies at various RPMs and torques are found on brake specific fuel consumption maps. But since they are often kept secret (if it exists at all) you probably will not find one for your engine (as of 2015). Looking at such a map, for example, may show that engine efficiencies range from 0% to 33% and that the best efficiency (33%) is only obtained at a certain RPM and torque. By using this map you can find the most efficient torque for the RPM your engine is currently turning, if you were able to apply that torque (using the gas pedal) you will obtain the maximum efficiency for that RPM. If you are not in the highest gear, then you have another option besides adjusting torque: change the RPM by shifting gears. Of course the car's computer could assist in all this if only the car makers designed it so. But as of late 2015 a few car-makers are taking out patents on such technology so it may someday actually happen.

While doing the above, you would get 33% engine thermal efficiency only at a certain RPM (like 2,500). However, at other RPMs efficiency doesn't drop off that much except at very high RPMs. For example, any RPM below say 3,500 might give say at least 28% efficiency provided you also provide the right torque with gas pedal. If you wind the engine up to 4,000 RPM, the maximum efficiency possible may drop to 26%. And higher rpm's will be significantly worse. This is all still a lot better than the typical 17% people get out of their engines while cruising at moderate speeds (at low torque).

To actually optimize how much you depress the gas pedal you really need the help of the car computer, which isn't set up to do this. But without such a computer, you can still significantly improve efficiency but making educated guesses as to how much to depress the gas pedal.

Where do you find a "brake specific fuel consumption map" (BSFC map) for your engine? Good question. Car manufacturers may keep them secret and don't distribute them although it's possible that some auto-makers don't even have them. But by about 2010, several such BSFC maps found their way onto the Internet. See BSFC maps

In the past before such maps were available, the alternate ways of getting a BSFC map were not very feasible: You could buy an engine, put it on a dynamometer test stand and test it yourself at various speeds and torques and create your own map. Or you could try to get a BSFC map from an automotive engineer that was involved in engine performance testing (as the author of this article did), especially from an engineer that no longer works there. Or you could try to get laws passed to require release of such information (although such a law may be unconstitutional since the claim will be made that companies have a right to trade secrets). Or you could try to get the EPA to come up with these maps when vehicles are tested for fuel economy. The last two ideas are still good ones today and EPA is now publishing some figures that may have come from such maps (or the like).

Even without a BSFC map for your car, it's possible to do reasonable efficient pulse and glide since the best fuel economy happens in most modern cars at near maximum torque. You get ths by pushing the accelerator pedal at least halfway to the floor. One problem is that you do not want an automatic transmission to automatically downshift since then RPMs will then be high and high RPMs generally give lower fuel economy. Also, if it downshifts, then it has to upshift again and all this causes needless wear on your transmission. Of course, if you have a manual transmission then you don't have this problem and can pulse at near maximal torque.

So selecting a torque is fairly easy. For an automatic, press on the gas pedal so that the automatic transmission is just on a verge of down-shifting, but don't push it far enough to actually downshift. At low speed, downshifting is not so detrimental since the engine speed will likely not be too excessive even after it downshifts. At high speed (if you're lucky) automatic downshifting may not happen if you keep torque under perhaps 2/3 of the maximum.

4. Energy Storage

The methods for fuel economy described above are quite simple and easily understood. One operates the auto engine at near its maximum efficiency (at high torque) and stores the excess energy in the momentum of the auto for later use while coasting. This momentum represents "kinetic energy". For an auto to coast downhill, it must first go uphiil, storing "potential energy" as it gains elevation and then utilizes this "potential energy" for coasting downhill.

A hybrid auto operates in a similar way by storing energy in an electric storage battery. It saves the excess energy by generating electricity in a generator, storing the energy in a battery and then later withdrawing the energy from the battery to power the auto. This process is by no means 100% efficient like kinetic energy storage is. There are losses in each stage of the power flow: generator-battery-electricMotor that are not present in either the kinetic (or potential) energy storage schemes. That's why some hybrid owners (that are hypermilers) don't use the hybrid in it's normal mode of battery charging/discharging, but pulse-and-glide instead since it's more efficient even when carrying a load of heavy batteries. But with the hybrid it's feasible to coast with the engine off resulting in a more efficient pulse-and-glide.

5. Analysis of BSFC Maps.

These maps can also be used to find the efficiency for the case of driving at steady speed without utilizing pulse-and-glide. Then one could find the efficiency during pulse and compare it to steady speed. This part of this report is somewhat technical and to fully understand it you need to understand the basic physics of forces, etc.

Note that aerodynamic drag will be higher when using pulse and drag since such drag is nearly directly proportional to the square of the velocity. For example if you start the pulse at 60 mi/hr and start the glide when you reach 70 mi/hr then you will travel at an average speed of about 65 mi/hr. But the average aerodynamic drag at the two extreme points of 60 and 70 mi/hr will be higher than if you just cruised at 65 mi/hr: .5(60^2 + .5(70^2) > 65^2. This inequality also holds true at 61 and 69 mi/hr and at all similar pairs of points. However, the gain based on the BSFC map will likely be many times more than the loss due to higher aerodynamic drag.

5.1 Steady Speed

For better analysis, the BSFC maps need to have a road load curve drawn on them for high gear on level ground. The following will describe how to construct such} a curve and should make it clear what it represents. Let's assume that the horizontal axis of the BSFC map is RPM and the vertical axis is engine torque. (The BSFC map has iso-efficiency contours drawn on it just like a topographic map has iso-elevation contours drawn on it.) So thus in high gear each RPM corresponds to a given car velocity. And every velocity on a level road creates a known resistance force impeding the forward motion of the car, consisting of aerodynamic drag and rolling resistance. The force applied at the points where the rubber of the tires meets the road surface must be equal to this resistance force in order to maintain steady speed. This force times the radius of the driving wheels (including the tires) gives the torque needed. Dividing this torque by the drive train ratio (including any transmission ratio) gives the engine torque needed for this RPM which determines a point on the road load curve of the BSFC map. Do this for a number of different RPMs and then connect up all such points into a smooth curve and you have the road load curve. A correction needs to be made to account for drive train losses (including the transmission).

The above implicitly assumes that there is no acceleration of the car, since if there was, the torque required from the engine would need to be higher than just the force needed to overcome car resistance (rolling and aerodynamic) and keep the car moving at a steady speed. Once you have a load curve drawn on the BSFC map, with velocity values appended along the RPM axis you can then see what the efficiencies are obtained a given cruising speed (in high gear). You will observe the they are poor at low speed and improve at higher speeds. But at the higher speeds vehicle resistance increases with the square of the velocity. This explains why steady speed fuel economy increases as speed increase up to a certain point and then decreases. Hopefully, people will do this for various cars and post such enhanced BSFC maps on the Internet.

5.2 Heat of combustion

Today specific fuel consumption uses the metric system and is usually in units of grams of fuel per kilowatt-hour. Knowing the heat value of fuel and using conversion factors, it's trivial to convert specific fuel consumption to thermal efficiency in percent. Note that the U.S. often uses the "higher heat of combustion" which results in a lower value of efficiency than would be reported using the "lower heat of of combustion" as is common in non-U.S. countries. The efficiencies (in %) reported in this article are likely based on the "lower heat of combustion". Thus efficiencies in the U.S. reported a decade or two ago will likely appear be lower in value (for the same engine) since they used the higher heat of combustion. "Transportation Energy Data Book" by the US Department of Energy is still using the higher heat of combustion. So the same engine can have, for example, either 30% or 33% maximum thermal efficiency depending on which "heat of combustion" is used.

5.3 Enriched fuel/air ratio

Traditionally, gasoline engines enriched the mixture of fuel/air at high torques. This is one reason why fuel economy drops off at maximum torque. But today some engines may no longer do this. It was formerly done to increase power for passing, which would partly explain why maximum efficiency is sometimes shown to be obtained at somewhat less than maximum torque.

6. More Tips on Efficient Driving.

Pulse and glide is also good for road sections other than level. For uphill sections, the pulse will be longer and the glide shorter. If the uphill grade is really steep, there may be no glide phase: It will all be powered climbing and you might want to cease pulse and glide when the glides become too short on an upgrade. For downhill, the pulses will be shorter and the glides longer. And if the downgrades are moderately steep, it will be all coasting with no power from the engine needed. If downgrades are still steeper you may wind up braking with the engine with the transmission in gear.

For going over the crest of a hill where engine power is not needed for going down the other side, try to go over the top of the hill at a slower speed since the downgrade itself will speed up the auto from the slower speed of going over the crest. This may mean coasting just a bit as you approach the crest of a hill.

Since hills can be used to store energy, it turns out that driving in hilly areas may result in higher miles-per-gallon, provided of course that the downgrades are not steep enough to require braking. In fact, even without any coasting in neutral and pulse/glide, fuel economy on a mountain (or hilly) road (with the start and end of the run at the same altitude) should be better than on the level since even if one doesn't coast in neutral but lets off on the gas pedal, much of the potential energy is still recovered on the downhill sections.

7. Problems and Suggestions

The main problems with the coasting part of "pulse and glide" are: laws, failure to design autos for coasting, and the effects on other traffic. The last problem (high traffic) may improve as the amount of driving is reduced due to both higher oil prices and possible population decline due to a poor economy, etc. Also, computer controlled cars could communicate with each other and "pulse and glide" in unison so as to keep traffic flow steadily moving.

The need for changes in the laws speaks for itself. It might be feasible to have a pulse and glide lane where all cars in this lane would synchronize their pulse and gliding, possibly under computer control or by colored lights on the roadway.

But major changes are needed in the design of autos to support coasting. First, it should be possible to prevent automatic downshifting of automatic transmissions when the driver doesn't want it. Autos should be able to coast safely with the engine off which means electric power steering and possibly manual hydraulic brakes. A super-high overdrive gear ratio would help too, allowing cruise at high speed with the engine at slow RPM and with high torque for economy.

8. Why High Torque is More Efficient

One reason why high torque is more efficient is because with higher power output (due to higher torque), the engine parasitic losses: friction, pump, and alternator power are a lower percentage of the useful output power. It takes fuel to just turn the engine when it's not supplying any output power. This "parasitic" power is used to overcome friction in the sliding parts of the engine such as the pistons, to power the alternator, and to power the following pumps: water, oil, power steering, and air conditioning. The energy used by an idling engine is all parasitic: The power produced is all used just to keep the engine turning (at idle) and the pumps, etc. pumping. No power (or torque) is transmitted to the wheels. Thus the efficiency is zero.

There are actually 2 types of power produced by the engine: brake power and indicated power. The power on the rotating output shaft of the engine is the "brake" power. If, with the car stationary, you put a brake on the output engine shaft and braked the engine at constant engine speed (like driving with the brakes applied), the power dissipated by this brake would be the "brake" power. Now the use of the word "brake" in "brake specific fuel consumption map" should be clear. Unless otherwise specified, engine power and torque, etc. mean brake power and brake torque.

The power produced by the pushing down of the pistons by the exploding fuel mixture (assuming the pistons had no friction with the cylinder walls) is "indicated" power. It called "indicated" since if you put a pressure gauge on each cylinder, read a pressure indicator as the piston goes down on the power stokes, and calculated the work done by this pressure, then the power of this work would be the indicated power. It's pretty obvious that to find indicated power in practice you would use a computer to read the pressure gages, rpm, and make various calculations, etc. As indicated power goes up, so does fuel consumption.

Now imagine that you are driving with a manual transmission in high gear, with the engine engaged and turning but not supplying any torque to the wheels since you are essentially coasting. This might be the case if you were driving down a moderate downgrade where the velocity you are maintaining is the same as if you were coasting down the hill in neutral. The engine is essentially idling, but at high speed and it is burning more fuel than if it was idling normally (slow). Your engine is producing indicated power but no brake power. If you press down on the gas just a little more, then your engine might use 1% more indicated power, most of which would be applied to moving the car faster downhill. The result would be that about 99% of the indicated power is still being used for parasitic purposes: friction, pumps, alternator, and only 1% is being used for moving the car and producing output torque. Even if the indicated power was being produced with 35% thermal efficiency, the brake efficiency would only be 1% of this or 0.35% (nearly zero). This extreme example shows one reason why internal combustion engines are inefficient at low torque.

There's another reason too. When the engine has low torque it also has high vacuum due to the throttle value restricting air flow into the engine so as to burn less fuel on each engine cycle. In contrast, at high torque, the gas pedal pushed nearly to the floor so it has low vacuum. High vacuum means that the engine is like a vacuum pump, expending energy to draw air thru the slightly open throttle valve into the cylinders (pumping losses). So low torque implies high vacuum which implies high pumping losses which implies lower efficiency.

9. Why Doesn't my Efficiency Double?

If by pulse and glide I could double thermal efficiency of the engine from say 15% to 30% why doesn't my miles per gallon double?

One reason is that you may not be applying enough torque during pulse. And if you do apply sufficient torque, your automatic transmission may downshift which greatly increases the RPMs.

Another problem is that while you're coasting, the engine is likely idling, thus consuming energy when the car isn't getting any energy from the engine. Also, there is more aerodynamic drag using pulse and glide. If you coast from 70 mi/hr down to 50 mi/hr the aerodynamic drag, which is directly proportional to the square of the velocity, will be greater than if you just maintained a steady 60 mi/hr.

If due to traffic behind you and/or slow cars ahead you can't pulse and glide all the time, this traffic interference makes it less efficient. Also in urban driving a high percentage of energy is wasted in braking and much of this is hard to avoid. So even if cruising efficiency doubles using pulse-and glide but half the energy of normal driving is wasted in braking, then miles-per-gallon would only go up 50% instead of double.

Thus while pulse-and-glide might double your mi/gal under ideal conditions, under real condition you are lucky if it increases it by say 40% or so. 50% has been reported but it's likely not typical..

10. Author's Notes on Searching for BSFC Maps

While the author has had some access to such maps for decades, searching the Internet in 2010 found no real BSFC maps, a search in early 2012 found several such maps along with a website that collects them. Some of these maps indicate that maximum efficiency happens at almost maximum torque. Peak engine efficiencies for gasoline-fueled engine are over 30% with perhaps an average of 33%. Diesel is somewhat higher, about 38%.

11. Bibliography