Paper Number 2006-01-0014

Analysis of an Extended Stroke, (Offset Crankshaft), Engine

John J. Jibben

copyright © 2005 SAE International

ABSTRACT

This is a fundamental analysis of an extended stroke, SI engine accomplished by comparing its performance to a typical engine with exactly the same piston data. The stroke extensions include the intake and power strokes, with longer crankshaft durations of 202 degrees, and the compression and exhaust strokes, with shorter crankshaft durations of 158 degrees.

The primary focus of the analysis is to determine the impact on performance attributed solely to the mechanical differences of the two engines. This was accomplished by using an Air Standard Otto Cycle analysis which neutralized potential differences in combustion effects. The secondary focus is a qualitative discussion on potential improvements in combustion efficiency.

INTRODUCTION

The Otto cycle engine used in most automobiles today has undergone significant improvements since the oil embargo of the early 1970’s. Improvements driven by environmental concerns, fuel costs, geopolitics, etc. have resulted in development of high energy ignition, multi-port fuel injection, turbo-charged, multi-valve breathing systems among other improvements that have resulted in significantly improved fuel efficiency and performance. However, the basic mechanical cycle defined by the Otto cycle has not changed. The pistons of a new, state of the art, four-stroke engine move up and down in the same manner as in a 1928 Ford Model A. This paper looks at a modification to the Otto cycle that may have the potential of providing improved fuel efficiency and performance.

For the purposes of this paper, we need to define two terms. The Piston-stroke will refer to the distance the piston moves in the cylinder between top dead center (TDC) and bottom dead center (BDC). The Crank-stroke refers to the degrees of rotation of the crankshaft between TDC and BDC or BDC and TDC.

The typical Otto cycle engine has four strokes, all of which have exactly the same crank-stroke duration, 180 degrees. In reality, we optimize the strokes somewhat by

firing the ignition before TDC and beginning to open valves early, but mechanically the piston/crankshaft system has four identically sized crank-strokes, each being 180 degrees.

If we could change the duration of the four crank-strokes to optimize performance what would we do? Given that the four-stroke Otto cycle consists of two complete revolutions of the crankshaft for a total of 720 degrees, and the piston moves through the same, identical piston-stroke for each crank-stroke, let’s look at each stroke individually to see what makes sense intuitively.

Starting with the intake stroke, we would want the crank-stroke to be greater than 180 degrees, (again in all cases the piston-stroke remains constant). This allows more time for better breathing, and therefore, a more efficient process of charging the cylinder with the fuel/air mixture. Of course, we could still add multiple intake valves per cylinder and turbo-charge it to further improve breathing, but the act of extending the crank-stroke beyond 180 degrees could, in itself, potentially further improve breathing.

The next stroke is compression, and here, reducing the crank-stroke to less than 180 degrees would potentially be an improvement. With the piston-stroke being constant, the compression would then occur more quickly and violently. This creates more turbulence for better fuel/air mixing and less time for compression blow-by.

For the power stroke, we would want the crank-stroke to be greater that 180 degrees. This would allow more complete combustion because there would be more time to more thoroughly burn the fuel/air mixture. Thus, one would suspect more power would be produced with the same amount of fuel, resulting in an improvement in combustion efficiency.

Finally, the exhaust stroke would probably want to have a crank-stroke that is more than 180 degrees as well to better purge the combustion gases. But to keep each revolution of the crankshaft at 360 degrees, it would have to be less than 180 degrees. This, however, is not a significant compromise, since we generally need to recycle some of the exhaust gases anyway to control NOx emissions.

This is all well and good, but how do you design an engine with two extended crank-strokes, (each greater than 180 degrees) and two with shorter crank-strokes, (less than 180 degrees)? One way to do this, without adding any moving parts, is to offset the crankshaft.

Figures 1, and 2, show the piston/crankshaft relationship for both a typical or standard (STD) four-stroke engine and the piston/crankshaft relationship of an offset-crankshaft (OSC) engine, both with exactly the same piston-stroke, bore and clearance volume.

Figure 1, Piston Crankshaft Configuration for a Typical SI Engine

Notice that for the STD engine, the longitudinal center line of the cylinder passes through the cross-sectional center of the crankshaft’s main journal. For the OSC engine, the crankshaft is offset or translated to the left. Also, with both Figures 1, and 2, drawn to the same scale, the crank circle of the OSC engine is noticeable smaller than that of the STD engine. It can be shown mathematically that offsetting the crankshaft results in increasing the piston-stroke; thus, the radius of the crank circle of the OSC engine had to be reduced to maintain the same piston-stroke.

It is obvious that with this large offset, the OSC connecting rod with its centerline on Line 1-2 will conflict with the cylinder. A bent rod approach centered on Line 1-3-2 will need to be used, as well as possibly a notched cylinder, to avoid the conflict.

Figure 2, Piston Crankshaft Configuration with Offset Crankshaft

The crank circle in Figure 2, clearly shows that the clockwise angle of rotation of the crankshaft from TDC to BDC (intake and power strokes) is significantly larger than the angle from BDC to TDC (compression and exhaust strokes). Table 1, below, shows the crankshaft and cylinder data for these two engines. The OSC engine shown has power and intake strokes that are extended approximately 22 degrees; whereas, the piston-strokes of both engines are equal.

STD Engine OSC Engine Comp. Crank-stroke 180 158 degrees Power Crank-stroke 180 202 degrees Exhaust Crank-stroke 180 158 degrees Intake Crank-stroke 180 202 degrees Bore (b) 12.70 12.70 cm Piston-stroke (d) 13.20 13.20 cm Clearance Volume (VC) 229.4 229.4 cm3 Displacement (Vd) 1901 1901 cm3 Engine Speed (N) 2,000 2000 rpm Adiabatic Pres. Increase 3447 3447 kPa Offset Distance (T) 0.0 13.97 cm Offset Angle (ρ) 0.0 30 degrees Crank Length (S) 6.60 5.08 cm Rod Length (L) 21.34 22.86 cm

Table 1, Engine Data for Comparable STD and OSC Engines

COMPARISON OF STD AND OSC ENGINES

The primary focus of the analytical analysis is to determine the effect on performance attributed solely to the mechanical differences of the two engines. Both engines operate on the Otto Cycle with exactly the same four strokes, except for changes in the duration of the crank-strokes resulting from offsetting the crankshaft of the OSC engine.

The two engines we will compare will be the STD and OSC engines shown in Figures 1, and 2, and Table 1. Although single cylinder engines are being studied, the STD and OSC engine analysis also applies to multiple cylinder engines with in-line, V-type and other configurations.

The STD engine is shown graphically in Figure 3, and the OSC engine in Figure 4. To compare the performance of these two engines, we need to compare various factors expressed as functions of crankshaft rotation such as piston motion, cylinder pressure, piston velocity, and torque. From these we can analyze and compare performance parameters.

PISTON/CRANKSHAFT MOTION, STD ENGINE

We will begin with developing equations that will describe the motion of the piston as a function of crankshaft rotation, D = f(φ), for the STD engine. For simplicity, we will look at only two of the four strokes, the compression stroke and the power stroke (one clockwise revolution of the crankshaft). The second revolution of the crankshaft, (exhaust and intake strokes), will be exactly the same.

Figure 3, STD Engine, Compression Stroke Diagram

For the compression stroke, where 0 ≤ φ ≤ 180 degrees, and from Figure 3, basic geometry shows that

Eq 1. ( )⎟⎠⎞

⎜⎝⎛ −= φα 180sinarcsin

LS

And

Eq 2. ( ) ( )φα coscos SLSLdD −+−−=

Substituting Eq 1, into Eq 2, we get D = f(φ)

Eq 3. ( ) ( )φφ cossinarcsincos SLSLSLdD −⎟⎟

⎠

⎞⎜⎜⎝

⎛⎟⎠⎞

⎜⎝⎛+−−=

For the power stroke, where 180 ≤ φ ≤ 360 and from Figure 2, basic geometry as well shows that

Eq 1A. ( )⎟⎠⎞

⎜⎝⎛−= φα sinarcsin

LS

And Eq 2A. ( ) ( )φα coscos SLSLdD −+−−=

Substituting Eq 1A, into Eq 2A, we get D = f(φ) Eq 3A.

( ) ( )φφ cossinarcsincos SLSLSLdD −⎟⎟

⎠

⎞⎜⎜⎝

⎛⎟⎠⎞

⎜⎝⎛−+−−=

Figure 4, OSC Engine, Compression Stroke Diagram

In summary, Eqs 3, and 3A, yield piston motion as a function of crankshaft rotation, or D = f(φ) for 0 ≤ φ ≤ 180 degrees and 180 ≤ φ ≤ 360 degrees respectively for the STD engine.

PISTON/CRANKSHAFT MOTION, OSC ENGINE

Developing similar equations for piston motion for the OSC engine is a bit more complex, but a similar analysis from Figure 4, yields for the compression stroke, or 0 ≤ φ ≤ 158 degrees.

Eq 1. ( ) ( )( )βρ

sinsinDdA −=

Eq 2. ( ) ( )φφβ −−−

= PALS 360sinsin

Where φP = the Power Crank-stroke, the angle of crankshaft rotation measured clockwise from TDC to BDC.

Eq 3.

( ) ( ) ( ) ( )φφ −−−+−−++=− PBSLSBSLSAL 360cos2222

Eq 4. ( ) ( ) ( )ρcos2222 BDdBDdA −−+−=

Substituting Eq 2, into Eq 1, we get an equation for A

Eq 5. ( ) ( )

( ) ( ) ( )( )⎟⎟

⎠

⎞⎜⎜⎝

⎛−−

−+−−

−=

φφρφφ

ρ

PP S

DdS

LDdA

360sinsin1360sin

sin

Rearranging Eq 4, we have a quadratic equation in the variable B as follows.

Eq 6. ( ) ( ) ( )[ ] 0cos2 222 =−−+−− ADdBDdB ρ

Since the negative root has no meaning in this application, the positive root of B is then

Eq 7.

( ) ( ) ( ) ( )[ ] ( )[ ]2

4cos2cos2 2220 ADdDdDd

B−−−−−+−

=ρρ

To calculate piston motion, D = f(φ), for the compression crank-stroke, we need to solve Eqs 3, 5, and 7 simultaneously as follows. For a specified value of φ, assume a value for D and calculate A from Eq 5. With this value of D, find the positive root of B in Eq 7, substitute it into Eq 3, and solve. If Eq 3, is not satisfied, repeat the process with a new value of D until Eq 3, is satisfied. This seems like a tedious process, but with the use of a personal computer, it is rather simple to zero in on values of D that satisfy Eq 3, with acceptably small error.

Figure 5, OSC Engine Power Stroke Diagram

Similarly, for the power stroke, 158 ≤ φ ≤ 360 degrees, the following three equations were derived, (Figure 5).

Eq 1A.

( ) ( ) ( )( ) ( )⎟⎟⎠

⎞⎜⎜⎝

⎛ +−+−−+−+=

LSSLDdDdSLSL

2cos2arccos

2222 ρθ

Eq 2A. Cφφρθα +−−−= 360

Where φC = the Compression Crank-stroke, the angle of crankshaft rotation measured clockwise from BDC to TDC.

Eq 3A.

( ) ( ) ( ) ( ) ( )[ ]CSLSLSSLDdDd φφα −+−++−=− cos2cos2 22

Simultaneous solution of these three equations through similar iterative methods yields D = f(φ) data.

SUMMARY PISTON/CRANKSHAFT MOTION

With the parameters defined in Table 1, we are now ready to plot the curves for D = f(φ) for both the STD and OSC engines, (Figure 6). This chart confirms that for these two identical engines, except for crank-stroke data, the effect of offsetting the crankshaft results in the piston of the OSC engine reaching TDC approximately 22 degrees earlier than the STD engine.

Figure 6, Piston/Crankshaft Motion

The analysis above is a complex and tedious effort, which in itself, does not yield much that we didn’t already know. However, it is the basis for a digital model that will be used for calculating and comparing performance parameters that will be very useful in showing the effect of offsetting the crankshaft on performance.

PRESSURE AND VOLUME CONSIDERATIONS

In order to calculate performance parameters, we will need to know cylinder pressure as a function of crankshaft rotation, P = f(φ), which can be developed from D = f(φ) data in the previous sections. So far the analysis is exact because it was developed from basic geometry. But to focus the analysis on the impact on performance resulting solely from mechanical configuration differences of the two engines, we will need to make some assumptions.

There are basically two variables in comparing the two engines that potentially could impact performance.

These include differences in mechanical configuration resulting from offsetting the crankshaft, and potential differences in combustion efficiency resulting from differences in crank-strokes. To eliminate the combustion variable, which will be discussed in more detail later, we will assume both engines will function using the Air Standard Otto Cycle. This is reasonable because it is a comparison of two engines rather than an analysis of one. The argument is, that if the two engines are analyzed and compared using the same assumptions, reasonably accurate conclusions in the difference in performance can be drawn.

Most engineers who have studied thermodynamics will be familiar with the Air Standard Otto Cycle, but as a brief review, here are definitions of the processes making up the cycle, (Figure 7).

1. A reversible adiabatic compression stroke. 2. A constant volume pressure increase. 3. A reversible adiabatic expansion stroke. 4. A constant volume pressure reduction.

Figure 7, Pressure/Volume Diagram for the Air Standard Otto Cycle

This series of processes, which includes one revolution of the crankshaft, is analyzed as a system rather than a control volume because there are no exhaust or intake strokes in the Air Standard Otto Cycle. Without these two strokes, there is no mass flowing across the boundaries of the system, the enclosed cylinder.

Process Number 2, the constant volume pressure increase, is shown in Figure 7, as a 3,447 kPa increase in cylinder pressure. Since the system includes a moving piston, this translates into an instantaneous pressure increase. The implication is perfect combustion where the combustion of gases completely and instantaneously occur exactly at TDC for both engines.

Since the combustion is instantaneous and complete and the expansion, (Process 3), is reversible and

adiabatic, potential differences in combustion efficiency resulting from differences in crank-stroke durations will be non-existent. Therefore, any differences in performance identified in this analysis would be contributed solely the mechanical configuration differences of the two engines. This will be more evident when we plot the P = f(φ) data.

To calculate cylinder pressure as a function of crankshaft rotation, P=f(φ), using the Air Standard Otto Cycle, we will assume the working fluid, air, acts as an ideal gas. With the ideal gas equations and geometric relationships, we can calculate the cylinder pressure, P, as a function of piston movement, P = f(D). Since we already have equations defining piston movement as a function of crankshaft rotation, D = f(φ), we can then find cylinder pressure as a function of crankshaft rotation, P = f(φ). For either the STD or OSC engine,

Eq 1. Cd VbdV +⋅

=4

2π

Where Vd = Cylinder Volume at BDC, b = Bore, d = Piston-stroke and VC = Clearance Volume.

Eq 2. k

datm V

VPP ⎟⎟

⎠

⎞⎜⎜⎝

⎛=

Where P = Cylinder Pressure, Patm = Atmospheric Pressure, V = Cylinder Volume and k = the Ratio of Specific Heats at constant pressure and volume.

Eq 3. 4

2bDVV d⋅

−=π

Where the variable D = Piston Movement shown in Figure 6, as D = f(φ).

Substituting Eq 2, into Eq 3, we get

Eq 4. ⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜

⎝

⎛

⋅⋅−

=

4

2bDV

VPP

d

datm

π

From Eq 4, which is P = f(D), along with the D = f(φ) equations, we can calculate cylinder pressure as a function of crankshaft rotation, P = f(φ), for each two degrees of crankshaft rotation, (Figure 8). Note that both engines begin their compression crank-strokes at 0 degrees and have exactly the same cylinder pressure at the end of their respective compression crank-strokes. Also, consistent with the Air Standard Otto Cycle, both engines experience exactly the same 3,447 kPa of instantaneous pressure increase at their respective

TDC. From this point, the pistons are forced down where both engines end their cycles at the same point, 360 degrees. These observations show that both engines experience exactly the same combustion process; therefore, any difference in performance that may result from the analysis below can be attributed entirely to the mechanical differences of the two engines.

Figure 8, Cylinder Pressure

TORQUE APPLIED TO THE CRANKSHAFT

In order to analyze performance factors, including energy and power developed by the two engines, we will need to know the torque acting on the crankshaft for each engine as a function of crankshaft rotation, τ = f(φ). The pressure in the cylinder exerts a force, FP, on the piston, which is transmitted as a force, F, to the connecting rod, (Figure 9).

Figure 9, Force Diagram

This force, F, described by Eq 1, acts on the connecting rod journal and can be broken down into two components.

Eq 1. ( )γcosPF

F =

One is a centripetal force, FA, which passes through the cross-sectional center of the connecting rod journal and the center of the crank circle. The other, FB, is tangential to the crank circle, passing through only the cross-sectional center of the connecting rod journal. Only the latter of these force components, FB, transmits torque to the crankshaft, (Figure 9).

Torque acting on the crankshaft can be calculated from the following equation

Eq 2. SFB=τ

Where τ = Torque, FB = Rotational Force on the Crank Arm and S = Crank Length.

By going through a force analysis for both engines, and using the data from D = f(φ) and P = f(φ), we can calculate the torque applied to crankshafts, τ = f(φ), for both the STD and OSC engines. Figure 10, shows this data graphically for two degree increments of crankshaft rotation.

Figure 10, Torque Applied to the Crankshaft

From Figure 10, the compression stroke shows negative values of torque, which indicates the torque is opposing the rotation of the crankshaft. The power stroke, however, has positive values, indicating the torque is driving the crankshaft rotation. These curves represent the instantaneous torque applied to the crankshafts of the two engines. This along with the data shown in the curves of Figures 6, and 8, indicates the two engines are quite different. In order to compare their performance, we will need to compare work and power, beginning with work on the piston.

Although the piston-strokes of the two engines are equal, the differences in crank-strokes do affect piston motion. Figure 11, shows differences in piston velocity. Comparing work on the pistons of the two engines will show the effect on performance due to piston velocity and other differences in the two engines.

Figure 11, Piston Velocity

WORK ON THE PISTON

Work is the form of energy that results from a force acting through a distance. We know the force acting on the surface of the piston, FP, is as follows.

Eq 1. PAFP =

Where P = Cylinder Pressure and A = Area of the piston face.

Knowing the force, FP, we can calculate incremental work, dW, on the piston from the equation

Eq 2. dDFdW P=

Where dD is the incremental movement of the piston.

From Eq 1, Eq 2, D = f(φ) and P = f(φ), we can calculate work done on the piston as a function of crankshaft rotation, W = f(φ), for the two specific engines defined in Table 1, (Figure 12). From the first law of thermodynamics, we can add up the incremental work for each two degrees of crankshaft rotation to get the total work per crankshaft revolution done on the piston. This is shown in Table 2, for the compression and power strokes of both engines.

STD Engine OSC Engine Work Power St. 19,265 19,265 Joules Work Comp. St. -5,470 -5,470 Joules

Table 2, Work on the Piston

Figure12, Work on the Piston

Notice that the work done on the piston for the compression stroke is negative and work done on the piston for the power stroke is positive (Table 2). This is because work is required for the compression stroke rather than being produced as it is during the power stroke. Also, notice that work, for both the power and compression strokes of the two engines are equal. This is to be expected, since it is work done “on” the piston, and both engines have exactly the same bore, piston-strokes, clearance volume and the same instantaneous increase in pressure (combustion). Work, being independent of path, will be constant as long as the beginning and end points of the piston travel are the same.

These are very important considerations because they show that for both engines, work on the piston is exactly the same. The next step is to determine the work transmitted to the crankshaft. Since both engines produce the same amount of work at the piston, work transferred to the crankshaft will indicate performance differences.

WORK ON THE CRANKSHAFT

From the torque analysis earlier and the τ = f(φ) data, we can calculate the work transmitted to the crankshafts of both engines for comparison to the work transmitted to the pistons of each engine. Rotational work is defined by a torque acting through an angle of rotation.

Eq 1. φτ ddW ⋅=

Where dW is the work produced by the torque, τ, acting through the crankshaft rotation angle of dφ. Figure 13, shows the resulting W = f(φ) data.

Notice that the curves showing work transmitted to the piston, (Figure 12), and the work transmitted to the crankshaft, (Figure 13), appear to be identical for both the STD engine and the OSC engine.

Figure 13, Work on the Crankshaft

If we add up all the incremental work in Figure 13, for each two degrees of crankshaft rotation, as shown in Table 3, we see that the work on the crankshaft for the compression and power strokes per revolution is equal to the respective values of work on the piston for the two engines, (Table 2).

STD Engine OSC Engine Power Stroke 19,265 19,265 Comp. Stroke -5,470 -5,470

Table 3, Work on the Crankshaft

Before drawing conclusions from this, we need to consider power. Horsepower or power is the rate at which work is being produced.

Eq 2. Hpdt

dW=

Where Hp = Power

Since each revolution of the crankshaft is actually a unit of time equal to the reciprocal of the average engine speed or rpm, work per revolution is actually a rate at which work is produced or power. Since the work per revolution of both engines is equal, the power will be equal as well.

The conclusion we can draw from this is, there is no difference, mechanically, in the performance of the two engines. The piston/crankshaft arrangement of the OSC engine, even with this very large offset, performs equally as well as the STD engine.

COMBUSTION

So far, we have discussed the impact on performance resulting only from mechanical changes, that of offsetting the crankshaft. The impact on combustion was taken out of the picture by assuming the Air Standard Otto Cycle. Although an in depth analysis of the combustion processes is beyond the scope of this paper, we need to address, at least qualitatively, the potential effect on combustion of extending the intake and power crank-strokes. After all, this is where all of the potential improvement in performance of the OSC engine lies.

In the analysis above, we assumed the Air Standard Otto Cycle applied to both engines, which assumes instantaneous and complete combustion at TDC. In a real engine, however, combustion occurs over a finite amount of time. The pistons of both engines follow the same path up and down within the cylinder, but since the crank-strokes are different, the piston velocity curves are different. As Figure 11 shows, the piston velocity of the OSC engine is significantly slower for the first approximately 120 degrees of the power stroke and roughly equal to the STD engine for the last 60 degrees. This lingering effect early in the power stroke would likely improve the thermal performance of OSC engine over the STD engine.

As we discussed earlier, the time required for one revolution of the crankshaft is the reciprocal or the engine speed. Assuming the engine speed is the same for both engines at 2000 rpm, the time required for one revolution is 30.00 m-sec. Therefore, for this condition the x-axis can be changed to time where 360 degrees is equivalent to 30.00 m-secs. For the STD engine, both the compression and power crank-strokes are exactly the same at 15.00 m-sec each. But for the OSC engine the compression crank-stroke (158 degrees) is 13.17 m-sec; whereas, the power crank-stroke (202 degrees) is 16.83 m-sec. At any specific rpm, the OSC engine allows more time than the STD engine to properly charge the combustion chamber (extended intake crank-stroke), and more time for combustion (extended power crank-stroke).

As was alluded to near the beginning of this paper, ignition in a real engine is timed to occur before the piston reaches the top of the cylinder. By doing this, the power stroke is artificially extended which results in significant performance improvement. But it is not all positive because the combustion that occurs before the piston reaches TDC opposes the piston motion. With the OSC engine, we have extended both the intake and power crank-strokes, (in this case, 22 degrees each), without the negative impact of combustion before top dead center. In addition, the artificial power crank-stroke extension by ignition before TDC can be included as well, as needed to maximize performance.

One can get a quick look at the impact of power crank-stroke extension simple by detuning a typical automobile

engine by resetting the ignition timing at idle speed to fire at TDC rather than the typical 8 degrees before TDC. The effect, as we all know, is a significantly noticeable reduction in performance. This will have to be borne out in testing, but one would conclude that the extended stroke engine resulting from offsetting the crankshaft would have significantly improved combustion efficiency and performance over the STD engine.

CONCLUSIONS

This paper looked at the effect on performance resulting from extending the intake and power crank-strokes by offsetting the crankshaft, the OSC engine, as compared to a typical, STD engine. It looked at a specific example involving a very large offset of 2.75 times the crank throw resulting in 22 degree compression and power crank-stroke extensions. We wanted to know if the effect of the mechanical change, in itself, would result in improved or degraded performance. This analysis shows that the performance of the OSC engine, even with a very large offset, was not degraded mechanically and its performance was equivalent to the STD engine.

The most potential for significant performance improvements from extending the intake and power crank-strokes, however, will be the impact on combustion. We have shown that extending the intake and power crank-strokes from 180 degrees to 202 degrees results in extending the time for intake and combustion proportionately. Allowing additional time for improved breathing and more complete combustion is where the potential for a significant improvement in combustion efficiency lies. The results are a potentially significant improvement in fuel efficiency and performance.

A very large offset was selected in order to provide a significant extension of the power crank-stroke, 22 degrees. There is more than likely an optimum that likely will vary for each specific engine. This will be a topic for further analysis; however, based on this analysis, the optimum offset will likely be very large and may very well be limited primarily by friction/structural considerations.

REFERENCES

1. Steve Shin, Annette Cusenza and Fanghui Shi, GM Powertrain Division, “Offset Crankshaft Effects on SI Engine Combustion and Friction Performance”, SAE Paper 2004-01-0606 2. ASHRAE Fundamental Handbook, American Society of Heating, Refrigeration and Air Conditioning Engineers, Atlanta, GA, 2005 3. Gordon J. Van Wylan and Richard E. Sonntag, “Fundamentals of Classical Thermodynamics”, John Wiley and Sons, Inc., New York, London and Sydney, 1968.

4. Edward Obert, “Internal Combustion Engines”, International Textbook Company, Scranton, PA, 1970. 5. Erwin Kreyszig, “Advanced Engineering Mathematics”, John Wiley and Sons, New York and London, 1968 6. Eduard L. Stiefel, “An Introduction of Numerical Mathematics”, Academic Press, New York and London, 1966.

CONTACT

John (Jack) J. Jibben (507) 289-1524 jackjibben@aol.com

• BS Mechanical Engineering, South Dakota State University, 1971

• MS Mechanical Engineering, South Dakota State University, 1974

• National Science Foundation Fellow

DEFINITIONS, ACRONYMS, ABBREVIATIONS

SI: Spark Ignition

TDC: Top Dead Center

BDC: Bottom Dead Center

Piston-stroke: The distance the piston moves from TDC to BDC

Crank-Stroke: The angle of rotation of the crankshaft from TDC to BDC or BDC to TDC

Power Crank-stroke: The angle of rotation of the crank-shaft through the power stroke

Compression Crank-stroke: The angle of rotation of the crank-shaft through the compression stroke

STD Engine: Standard or typical engine

OSC Engine: Offset crankshaft engine