Model Engine Builder magazine , a go-to resource for building model engines, recently included a very complimentary article on the Brickley engine. It is featured in Issue 25 of the RICE Report (Really Interesting Combustion Engines), a frequent piece written by Ron Cairns. I look forward to helping any of the model engine builders build their own particular version of the Brickley engine.
Some have asked,”What about the valve train for your engine?” Being that reducing mechanical friction has been an important consideration in the design of the bottom end, it only makes sense that this would as well be the case for the valve train. For an engine operating at part-load and low speed, valve train friction can be a significant portion of total engine friction. Of the various components of valve train friction the most dominant under the described conditions is the friction generated at the cam lobe/ follower interface. This element can be easily addressed by employing a roller follower. One simple valve train for the Brickley engine would consist of two camshafts, one for the valves in each cylinder head. Each camshaft would be parallel to the crankshaft and between the pair of cylinders it operates. In this case push rods and rocker arms would actuate the valves. This arrangement allows a great deal of freedom for the placement of the intake and exhaust ports. Also it allows both exhaust cam followers (on one side of the engine) to be driven off one cam lobe as well as both intake cam followers (on the other side of the engine) to share a cam lobe. This approach also allows for easy VVT when the cam drive chain or belt is driven off the exhaust cam side of the engine.
The Nissan Leaf is built on the same platform as the Nissan Versa. The Versa can be bought for about $11,000, while the Leaf is about $27,000 after rebates. Check this out; with the average vehicle miles driven per year at 15,000, and an average fuel consumption at 30mpg, the Versa consumes 500 gallons of fuel per year. Even at $4/gallon that is $2,000/yr. Eight years of free fuel to get to $27,000. Add in the fact that you will have to have another car (maybe a new Versa anyway) in addition to the Leaf in order to drive further than 60 miles in the summer and it is no great mystery that the sale figures are as stands:
Recently I presented a document on my engine configuration and I thought it might be helpful to include a condensed version of it here.
The development and use of the Brickley Engine would provide the world with an affordable, earth friendly engine applicable to everything from automobiles and trucks to farm machinery.In a relatively short amount of time it could address the following current and urgent world problems:
- The efficient use of petroleum, and
- The ever-increasing problem of the production of CO2 through the consumption of petroleum.
I will begin with a brief introduction of my design and then proceed with a more detailed analysis.
The focus of the Brickley Engine is to reduce fuel consumption and CO2 emissions by 15-20%. This is accomplished by significantly reducing engine friction: turning energy normally lost in heat into useful work. The area of concentration for reducing friction is localized in the bottom end of the gasoline or diesel internal combustion engine.
In a typical engine the bottom end is the mechanism that captures the energy of the hot expanding gases in the form of cylinder of pressure and turns it into mechanical work. For example, in a typical four-cylinder engine the bottom end is comprised of four pistons, four connecting rods, and a crankshaft (see Brickley Engine video for engine animations).
Each piston, by way of a wrist pin is linked to one end of a connecting rod and the other end of the connecting rod is attached to the crankshaft. Each piston moves back and forth within a cylinder as the crankshaft rotates. These components are contained within a cylinder block and comprise the foundation of the engine.
As there are various ways to arrange the pistons about the crankshaft there are just as many different engine configurations. Among the most common are in-line (as in the video), V, opposed, and radial configurations. Automobiles and trucks typically use one of the first three.
The Brickley Engine configuration changes the way the pistons are connected to each other and to the crankshaft, thus eliminating a great deal of friction. The configuration employs a combination of pinned linkages to determine the paths of the pistons and thus eliminates the piston skirts and their associated friction.
Additionally, by connecting the pistons to each other in a more efficient manner, it reduces the type and number of bearings on the crankshaft for further reductions in friction.
At first glance a casual observer might find my engine configuration seemingly more complex than a conventional configuration. For many, it’s not clear how an engine configuration that has more moving parts results in less friction.
So let’s talk about friction…
Imagine that the floor is a smooth steel surface. On the floor is a wooden box that weighs 100lbs. What we are going to do is observe how much effort it takes to push the 100 lb box just one foot across the floor. Now compare that amount of effort to the amount of effort it takes to move a 100 lb box that is suspended like a pendulum from the ceiling. The 100lb box never touches the floor and is simply swinging on a nail that allows it to pivot at the ceiling.
Which scenario moves more freely and with less friction?
Obviously the one suspended from the ceiling.
Let’s examine why…
While the materials and the load of 100 lbs are the same in both cases, the friction is significantly reduced in the second case. The reason for the reduction in friction is in the distance the area-supporting load has to travel. In the first case it travels one foot. In the second case, while the 100 lb box travels a foot through the air, the supporting area only travels .014 inches at the pivot (the nail).
So if one divides 12 by .014 the quotient reveals that friction work is smaller by a multiple of over 850. By reducing the distance that the loaded areas have to travel there is a significant reduction in friction.
This principle is the focus of my engine configuration.
However, before we take a look at the engine configuration, let’s first examine how it fits into a larger picture…
THE BIG PICTURE
In 2007 an average of 85.9 million barrels of petroleum were consumed by the world each day. At 42 gallons per barrel the world consumes 3.5 billion gallons of oil each day.
In the United States alone, petroleum consumption in 2007 was 19.4 million barrels per day, representing 24% of petroleum usage worldwide. The transportation sector in the US consumed 70% of this amount, 13.71 million barrels. Table 1 below shows US transportation petroleum consumption broken down by highway and non-highway mode ranked in order of consumption.
|Thousand barrels/day||Percentage of Total|
|Freight (Class 1)||266.6||1.9|
|HWY. + NONHWY TOTAL||13,710.2||100.0|
One can see from Table 1 that the majority of petroleum used for US transportation was burned on US roads. US automobiles are powered by piston driven gasoline and diesel internal combustion (IC) engines. While the consumption distribution is not representative for all countries, it isn’t difficult to see that if the amount of oil attributable to piston driven IC engines worldwide were significantly reduced that a great deal of fuel could be saved and an enormous amount of CO2 eliminated – 19.6 lbs of CO2 per gallon of gasoline and 22.4 lbs per gallon of diesel fuel.
From the minimal demands placed on the engine while a vehicle is idling at a stop, to a situation that requires maximum power, the amount of fuel being consumed and the efficiency with which it is used to propel the vehicle can vary greatly.
At idle, because a vehicle is not moving and fuel is being consumed, fuel economy is reduced by the amount of time an engine spends idling.
Table 2 shows the fuel economy results of a single vehicle that was simulated under five different driving cycles used around the world to project vehicle fuel economy. Each cycle has a different percentage of time that relates to the time stopped or decelerating.
|Driving Cycle||Projected fuel economy
|Percent of time stopped or decelerating|
|Japanese 10/15 mode test cycle||17.5||52.3|
|US EPA city driving cycle||19.8||43.2|
|New European driving Cycle (NEDC)||22.0||24.9|
|US Corporate Average Fuel Economy cycle||23.9||27.9|
|US EPA highway cycle||32.1||9.3|
Certainly, it is easy to see that a motionless vehicle consuming fuel reduces average fuel economy. However, not so obvious, is the role of engine friction on fuel economy.
An engine is least efficient when idling. At idle, all of the fuel being used goes toward creating enough mechanical work to equal the sum of the various components of engine friction.
Rarely is the average vehicle engine operating at its most efficient point, its ”sweet spot”. Generally, this spot exists between 1500 and 2500 rpm and at approximately 70% of full power. For anyone who has operated an automobile, it can be noted from memory that the engine is not often operating at this point.
Imagine then, that there is a continuum between idle and an engine’s sweet spot. At one end of the continuum all of the fuel is lost to engine friction and at the other end the majority of the fuel is being converted into mechanical work and only a small part is lost to friction. If an engine then is required to produce only a small amount of power, as is most often the case, a significant percentage of the amount of fuel being consumed is being devoted to friction.
Similarly, one can see that if engine friction were reduced it would have increasingly greater impact as the power output became smaller and moved from the sweet spot toward idle. Because most engines average operating point is much closer to idle than its sweet spot, reducing engine friction can be an effective strategy to reduce fuel consumption and as well CO2 emissions.
In various studies including those made by and for the US DOE, Argonne National Laboratory, FEV and many others engine friction reduction is mentioned as a reliable way to reduce fuel consumption and CO2 emissions. However, the amount of the improvement, while important, typically remains small since there are so few drastically new technologies that meet the criteria required for industry change. Most often, efforts have been directed towards small incremental improvements in existing approaches.
THE BRICKLEY ENGINE
As mentioned previously there are various components to engine friction. Typically, engine friction is broken into three components: mechanical friction, pumping losses, and auxiliaries. The component impacted by the Brickley Engine is the mechanical friction component.
Unbeknownst to most people the mating parts of an operating engine do not touch each other. Any contact between mating parts and there is enormous wear immediately, resulting in catastrophic engine failure. The parts of an operating engine are separated constantly by a very thin film of oil. The mechanical component of friction occurs from shearing this thin film of oil that separates the parts of the engine.
Maintaining a thin film of oil and separating the asperities of the engine surfaces, is a very frictionless state and is referred to as hydrodynamic lubrication. Hydrodynamic lubrication can be obtained in different manners. The most common manner for maintaining a hydrodynamic state is by maintaining a threshold velocity difference between two mating surfaces. Such is the case with the main bearings on the crankshaft and the crankpin bearings.
Another type of hydrodynamic lubrication needs no velocity differential in the surfaces being separated but is a function of the time it takes to squeeze two surfaces together and force all of the oil out until the asperities of the surfaces almost touch.
This type of hydrodynamic lubrication is referred to as squeeze film lubrication. This is the type that occurs at the wrist pin and requires an oscillating load so that before the surfaces are about to touch the load is reversed and the squeeze is in the opposite direction using the just displaced oil from the last squeeze on the opposite side of the bearing.
Since squeeze film lubrication is what occurs at the pinned joints of the Brickley Engine it is important to take a closer look at squeeze film lubrication so it can be determined how much friction can be assigned to the various pinned joints. To accomplish this let us first refer to SAE paper 2005-01-1651 which specifically deals with wrist pin friction.
The authors suggest a very important question at the outset: Because pin friction shows up as heat, how much heat can be dissipated from a bearing that is lubricated by splash (it has no oil flow to remove heat), has a very hot piston surrounding it, and has such tight clearances that it could easily seize if it became hot? Predictably, not much heat can be dissipated. Therefore, the friction work and the resulting heat generated must be very small.
Indeed wrist pin friction is so small that it is excluded altogether from the equations for predicting engine friction: SAE paper 2003-01-0725.
Because each end of a connecting rod has very similar load let’s compare the distances travelled.
If we were to take the bearing dimensions of each end of a sample automobile connecting rod, with the wrist pin end being (.866 X.913) and the crankpin end as (2.014X.914), the wrist pin end rotates through approximately 60 degrees of rotation while the crankpin rotates through 360 degrees.
Making the assumption from the previous paragraph that the coefficient of friction is in the hydrodynamic range and similar, the crankpin travels 14 times farther than the wrist pin (2.014/.866) x (360/60). That there is 14 times the friction work lost in the crankpin contrasted with the wrist pin fits perfectly within the measurement of 14.5 from a detailed breakdown of friction work associated with the various parts of an engine.
Another way of making a comparison would be to say that the friction work associated with one revolution of the crankpin would be equivalent to the friction work associated with 14 wristpins.
Based on allowable wrist pin bearing pressures the bearing dimensions were scaled accordingly to the loads at each bearing location. Table 3 represents a way to look at the conventional inline four-cylinder in terms of the distance the various bearing areas travel. Table 4 is similar to Table 3 except that it is represents the Brickley Engine. The comparison numbers show a relative comparison of the losses associated with the various bearing locations.
|Bearing Type||No. of Bear-ings||Degrees of bearing rotation/Crankshaft rotation||Bearing diameter (in.)||Bearing length (in.)||Projected area/bearing||Area travel (radians)||Total area travelled
So far, in comparing the distances and the areas of oil being sheared it can be seen that the Brickley Engine eliminates 51% (1-64.11/130.97) of the friction work associated with the bearings. The comparison number for the Brickley Engine includes the work associated with guiding the pistons. However, the comparison number for the conventional engine does not include the work associated with guiding the pistons (via piston skirts).
The friction work of the piston skirts associated with the conventional engine must be included in order to have complete comparison of a conventional engine and the Brickley Engine. In a review of the available figures, the percentages of friction attributable to the ring pack and the skirt are unclear. At or near 2000 rpm the percentage split is 60% rings 40% skirt while another will say 43% rings 57% skirt. For discussion purposes, let’s assume a 50/50 split .
A recent 2009 study that was done by Timken revealed current data regarding mechanical engine friction and the various contributing components. The numbers that create Figure 1 below are reconstructed from careful measurement from the original study’s graphics.
Using the FMEP numbers in Figure 1 we can establish a comparison. Combining the 51% reduction at the main bearings and connecting rods with a 50% reduction at the piston skirts a significant amount of friction is eliminated. In addition, roller bearings will replace the two main bearings. These can be added since they are so accessible (unlike the difficulty of adding them to a conventional crankshaft). This would reduce bearing losses at these locations by 55% and would allow the oil pump loss be cut in half. With all of these changes a comparison between a conventional inline four cylinder and a Brickley Engine configuration four cylinder would look like Figure 2.
As seen in Figure 2, at 2000 rpm the Brickley Engine provides a 43% reduction in mechanical engine friction (FMEP) when compared to current engines. FMEP is a way of comparing engine friction that allows engines of different size to be compared. The impact of this much of a reduction on fuel consumption naturally varies depending on the type of driving if one recalls Table 2.
Since the loss incurred by the oil pump is cut by one half and it is known that this provides for a 2-3% reduction in fuel consumption, a useful prediction can be made. For a given rpm there is a ratio between half of the oil pump loss and the difference in friction between the conventional engine and the Brickley Engine. That ratio ranges from approximately 6:1 and 7.5:1. This gives a fuel consumption reduction ranging from 12-18 and 18-22% respectively. Other ways of figuring the reduction  lie within this range and end up confirming this range whose center is likely between 15-20%.
Still, an actual engine must be built, tested, and closely anchored to the criteria of a particular conventional engine in order to determine with exactness the reduction in fuel consumption attributable to the Brickley Engine configuration. It is toward this goal and further that I proceed.
FURTHER POINTS TO CONSIDER
- Not only does my design reduce petroleum consumption and CO2 but equally important it does not require any rare earth minerals, as the batteries of electric cars will on a massive scale. It requires only the materials currently used in the automobile industry. While there will be some learning curve associated with its development and production, the technology is nuts and bolts engineering. Brickley Engine technology is far more simple than what has been taken on in the development of any type of hybrid electric even though it could easily be used with a hybrid system.
- Once an engine has been designed to match a particular conventional engine it will be clear how much the gains will be for larger engines and smaller ones. It could easily be expanded in multiples of four cylinders to eight and even twelve cylinders. It could be built air-cooled or water-cooled. It could be designed to fit any power range and application that engine is used currently.
- One of its major points is that it is an affordable technology. It is a simple mechanical design and not rocket science. It is predicted that India and China will be the major source of increased need for petroleum and my design’s simplicity in application to transportation could significantly aid in offsetting the increases that naturally accompanies world expansion.
- A natural drawback of my configuration is that it requires a paradigm shift and people simply have difficulty accepting anything that challenges traditional thinking. Specifically, my engine has been criticized for having increased reciprocating mass. Critics focus on doubling the reciprocating mass (an additional 5 lbs) but never mention cutting the mass of the most expensive part by 20 lbs.: the crankshaft. Simultaneously there is this perception that increasing reciprocating mass necessarily increases load and thus friction without even exploring how the efficiency of the mechanism has been impacted. As well, a counterintuitive truth must be spoken: friction power is “independent of load but proportional to viscosity; and proportional, respectively, to the first and second powers of velocity. For this reason, motoring tests of engines give reasonably correct values of operating friction.” It is the velocity that the Brickley Engine addresses since velocity is distance/time. Load plays almost no role in engine friction whether it is from inertia loads or combustion loads. Many find it surprising that at a given rpm the friction work is virtually the same at idle as it is at full throttle.
- While I have not covered the application of the Brickley Engine configuration for the Diesel engine, the role of engine friction follows similarly in that the same continuum exists from idle to the sweet spot. Diesel friction reduction is in the same range but varies slightly because the pumping losses are so small and the mechanical friction is greater. This means that resulting gains are similar for diesel automobiles (15-20%). For highway trucks reductions are smaller; on the order of 5% since they are operating most of the time at points very close to their sweet spots.
- Of note; the Brickley Engine was highlighted as one of the best new ideas in the “Year in Ideas” issue of the New York Times Magazine, December 2008 and as well in an interview podcast through IBM.
One way or another the Brickley Engine must be built and tested. Unfortunately I alone do not have the resources to make this happen. So, until it is clear exactly how much it will contribute through the development of a prototype and further steps can be taken for its use, I will continue to ask: Can we really afford to pass up a technology that has the ability to save millions of gallons of fuel each day and significantly reduce the production of CO2?
 U.S. Department of Energy, 2009. Transportation Energy Data Book, Edition 28, Table 1.4. Prepared by Oak Ridge National Laboratory.
 U.S. Department of Energy, 2009. Transportation Energy Data Book, Edition 28, Table 1.4. Prepared by Oak Ridge National Laboratory.
 U.S. Department of Energy, 2009. Transportation Energy Data Book, Edition 28, Table 1.16. Prepared by Oak Ridge National Laboratory.
 U.S. Department of Energy, 2009. Transportation Energy Data Book, Edition 28, Table 4.31. Prepared by Oak Ridge National Laboratory.
 J.-L. Ligier, P. Ragot, Piston pin: wear and rotating motion, SAE Paper 2005 -01-1651 (2005) p. 1,2
 Sandoval, D., J.B. Heywood, “An Improved Friction Model for Spark Ignition Engines,” SAE 2003- 01-0725,2003.
 Fessler, R. R., and Fenske G. R., “Reducing Friction and Wear in Heavy Vehicles,” Multiyear. Program Plan, U.S. Dept. of Energy (1999) p.12
 R.I. Taylor (2002), Lubrication,Tribology & Motorsport, SAE paper 2002-01-3355 , p.5
 SC Tung and ML McMillan, “Automotive Tribology Overview of Current Advances and Challenges for the Future,” Tribol. Int., 37, 517-536, 2004.
 Pawan K. Goenka, Rohit S. Paranjpe, and Yeau-Ren Jeng , “FLARE: An Integrated Software Package for. Friction and Lubrication Analysis of …,” 920487,p.53
 Kolarik,Robert V.II, Shattuck, Charles W., Cooper, Anthony P., Evaluation of a Low Friction-High Efficiency Roller Bearing Engine, Timken – USDOE,2009, p.4.
 FEV, Spectrum, Issue 23, April 2003, p.3.
 Dr.-Ing. Markus Schwaderlapp , Dr.-Ing. Franz Koch Dipl.-Ing. Jürgen Dohmen, Friction Reduction – the Engine’s Mechanical Contribution to Saving Fuel, FEV, 2000, p.7.
 Dr.-Ing. Markus Schwaderlapp , Dr.-Ing. Franz Koch Dipl.-Ing. Jürgen Dohmen, Friction Reduction – the Engine’s Mechanical Contribution to Saving Fuel, FEV, 2000, p.7.
 Dr.-Ing. Markus Schwaderlapp , Dr.-Ing. Franz Koch Dipl.-Ing. Jürgen Dohmen, Friction Reduction – the Engine’s Mechanical Contribution to Saving Fuel, FEV, 2000, p.1.
 Taylor, R.I., Engine Friction Lubricant Sensitivities: A Comparison of Modern Diesel & Gasoline Engines, Shell Research & Technology Centre, 2000,p.2.
 Obert F., Internal Combustion Engines and Air Pollution, Intext Educational Publishers, 1973 edition, p.661.
A few weeks ago I had the privilege of meeting the folks of Edison2. A couple of months ago Edison2 won the 5 million dollar prize for the automotive X prize competition.The team is truly an amazing group of gifted individuals and their ability sure shows in their automobiles. The cars possess a quality of well-thought out design like you might experience in a fine aircraft – safe, no wasted space, yet the right amount of everything to get the job done with elegance. Oliver Kuttner has accomplished something beyond great. Now, if only the world might see. There are plenty of opinions to go around today about the future path of the automobile. In the end, economics will demand the path Oliver has clearly shown as reasonable.
When a portion of the horsepower lost to friction is recaptured for useful work it reduces the fuel consumed for a given power output. The equation that shows the relationship between reduced friction and the improvement in the fuel consumed for a given horsepower output is: R2= R1(hp2-hpfg)/hp2; where R1 and R2 are initial and reduced friction fuel rates; hp1 and hp2 are the respective horsepower’s produced, and hpfg is the horsepower gain from reducing friction. Since hp2 = hp1+ hpfg , it can be substituted so that R2/R1 = 1- (hpfg/hp1+ hpfg). Also, since some desired gain z can be introduced, where R2/R1 = 1 – (z/100), the two equations can be set equal to each other and a series of curves plotted for any particular set of desired gains. Here are the resulting curves relating BMEP and rpm for fuel consumption improvement of the Brickley engine over a current conventional in-line four cylinder. Note that the curves have a positive slope as compared to changes that address pumping losses which have a negative slope (less improvement with an increase in rpm).
People ask me, “Why are you spending your time and energy
on the internal combustion engine? Isn’t it a thing of the past?
What about all of the new alternatives?
Well, many people talk about hybrid and electric cars, and while they
might be helpful for a part of our future of transportation needs, they
simply don’t work in all applications. Currently they subtract
a measly 2 million gallons from the 380 million we use daily.
That’s not much of a reduction.
Hybrids are also costly; and while an electric motor assists the
internal combustion engine to improve fuel mileage in the city, we
are fooling ourselves if we don’t admit that the internal combustion
engine is still the heart of the hybrid’s power.
Electric cars sound great; however, the material and production costs
associated with their batteries indicate that they will always be too
expensive for the average person to buy. 20-40 thousand dollars
for a battery is not realistic for 90% of the population.
And because two thirds of that cost is materials there is very little
room for reducing the cost through large production volumes.
It has been estimated that by 2025 electric cars might hold as much as
just 2% of the market.
So let’s face it, technological and economic facts suggest that the
internal combustion engine will continue to be the prime-mover
for decades to come, whether it runs on gas, diesel, compressed
natural gas or hydrogen.
It is critical, therefore, that the internal combustion engine be
made more fuel efficient and yet remain affordable.
This is the focus of my engine configuration.
By drastically reducing engine friction, it allows for
improvements in fuel consumption of up to 20% at a very reasonable
cost. So, here is my question to you:
Can we really afford to pass up a new technology when it has
the potential to save millions of gallons of fuel each day?
I need help to get my engine design into various forms of
production. I do not have the economic resources to do it by
myself, but I do have solid science to support my design, and I own
the intellectual property.
Please share with me your thoughts about the engine itself, the
funding of a prototype, and anything else you might think useful. I
can be contacted through my website: www.brickleyengine.com.
A much more fuel efficient internal combustion engine could resurrect
American car manufacturing, contribute to world economic recovery,
and could seriously impact the production of greenhouse gasses on a
I think it might be helpful to pass on a few graphs showing the breakdown of friction for a typical engine and a comparison of a typical engine with my configuration.
The numbers for the first graph are from the Automotive Research Center at the Univ. of Michagan. Type 1 is a typical engine and Type 2 is the Brickley configuration. The numbers for the Brickley configuration are based on reducing the the number of bearings on the crankshaft and increasing the number of pinned joints. The overall reduction in friction in this comparison is 36%. My impression is that it could be reduced even further if in the case of a four cylinder engine two roller bearings were employed on the crank and a much smaller oil pump were used because of the much reduced demands of squeeze film lubrication which used at all of the pins. There is a possibility that the oil pump could be eliminated altogether further improving the reduction.
Because the most frequent criticisms of my engine configuration concern questions involving pin friction and reciprocating mass I must say that a good SAE paper to look at regarding the losses in pinned joints (piston pins specifically in this paper) is SAE 2005-01-1651. The authors ask a very valuable question: Because pin friction shows up as heat, how much heat can be dissipated from a bearing that is lubricated by splash, has no oil flow to take away heat, has a very hot piston sitting right next to it and has very tight clearances? Regarding reciprocating mass it must be pointed out that while my configuration does involve more mass the configuration does not respond the same as a typical configuration to increased mass for a number reasons (1) there are no piston skirts (the place where much of the reciprocating friction shows up) (2) squeeze time and the movement at the joint rotation at the end of the squeeze time allows for a different friction response and (3) the connecting rod performs a very different function in my configuration because the cylinders are already connected to each other through the linkage, to mention a few differences.
Also, I am including a few additional graphs relating to the 1.9 L TDI diesel for an example of projected gains. I used a diesel so I could simply use a Willans line for the friction determination.
From this graph a Willans line for 1500 rpm looks like this:
Using y=mx +b; m=(2753-1680)/(11.97-6); m=179.7
Inserting m and solving for b we get 2753=(179.7)(11.97) +b ; b=602
602g/hr is the amount of fuel consumed at idle (zero power, y intercept)
The x intercept would then be -602=(179.7)(x) ; x=-3.35kW (friction power)
A 36% reduction in the 3.35kW shows up on the ordinate as (1-.36)(602) which equals 358g/hr now instead of 602g/hr at idle (-244g/hr)
The new formula is now very close to y= 179.7x + 358
A common point to measure for average fuel economy is 1/6 throttle 1500 rpm. In this case that point is 5.23 kW.
The fuel consumption for this point is y= (179.7)(5.23) +358 ; y=1298 g/hr.
The fuel consumption for the original engine is y= (179.7)(5.23) +603 ;y=1543 g/hr.
This is a reduction in fuel consumption of 15.8 %.
I now have a blog. I am looking forward to posting soon and communicating with everyone.