INTAKE MANIFOLD DESIGN

FOR AN

AIR RESTRICTED ENGINE

A Thesis submitted to the

Division of Research and Advanced Studies of

The University of Cincinnati

In Partial Fulfillment of the

requirements for the degree of

MASTER OF SCIENCE

School of Dynamic Systems

College of Engineering and Applied Science

July 6, 2012

By

David Anthony Moster

BSME 2005

Abstract

The purpose of this work is to study the effects that an air restriction has on basic intake manifold design calculations. When designing an intake manifold for a combustion engine, there are several simple methods that engineers have used historically to help determine peak volumetric efficiency per engine rpm. Methods such as Helmholtz

Resonator Tuning and Pressure Wave Tuning have been used substantially to determine an engine’s operating conditions. However, these methods are flawed for the restricted engine case due to the assumption that there is an unlimited amount of air. Through experimentation of various intake manifold configurations, it is possible to determine how this false assumption affects the results of the design. Examination of each major design parameter of an intake manifold independently compared with the traditional analytical hypothesis is performed to help to determine if these methods can still be used in an air restricted environment. Based on the results from this experimentation, it appears that these calculations can still determine where peak volumetric efficiency is.

However, the area around the peak volumetric efficiency is affected significantly.

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Acknowledgments I would like to thank my advisor, Dr. Randall Allemang, for his support and guidance throughout my undergraduate and graduate studies. It is his push for educational excellence that has driven my knowledge growth. I am grateful to Dr. Kumar Vemaganti and Dr. David Thompson for taking the time to be a member of my committee. I want to thank Jeff Kenney for his work in building and testing the various intake manifold configurations as well as his support in design theory conversations. I want to express my sincere appreciation to Ryan Lake for the many hours spent discussing engine tuning theory and testing various architectures on the engine dyno that he modified; to Benjamin

Stoney for his fabrication efforts that made the testing possible and his late night rants that made for laughs down the road; and to Thomas Steed for his drive and dedication which was inspirational to me as well. Special thanks to Fred Jabs, Kevin Sobkowiak, and Andrew Gorton for their help though various stages of the project. Finally, I want to thank my wife, Krystal, for her dedication and support from the very beginning.

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Table of Contents

CHAPTER 1: INTRODUCTION AND BACKGROUND ...... 6 1.1 INTAKE MANIFOLD BASICS / ENGINE INDUCTION ...... 9 1.2 COMPOSITION OF AN INTAKE MANIFOLD ...... 9 1.3 AIMS OF A MANIFOLD ...... 11 1.4 TRADITIONAL CALCULATIONS ...... 13 1.5 SUMMARY OF THESIS ...... 16 CHAPTER 2: EFFECT OF RUNNER LENGTH ...... 17 2.1 CALCULATIONS ...... 19 2.2 EXPERIMENTATION ...... 20 2.3 RESULTS ...... 22 CHAPTER 3: EFFECT OF RUNNER DIAMETER ...... 29 3.1 CALCULATIONS ...... 30 3.2 RESULTS ...... 30 CHAPTER 4: EFFECT OF PLENUM DESIGN ...... 32 4.1 EXPERIMENTS ...... 35 4.2 RESULTS ...... 36 CHAPTER 5: OTHER CONSIDERATIONS ...... 38 5.1 FLOW PATH ...... 39 5.2 INJECTOR PLACEMENT ...... 40 5.3 RESTRICTOR DESIGN...... 41 CHAPTER 6: CONCLUSIONS AND FUTURE RECOMMENDATIONS ...... 43 6.1 CONCLUSIONS ...... 43 6.2 FUTURE RECOMMENDATIONS ...... 45 APPENDIX A: RAW TEST DATA ...... 48

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List of Figures

FIGURE 1: AIR FLOW THROUGH AN ENGINE ...... 8

FIGURE 2: INTAKE MANIFOLD ...... 10

FIGURE 3: VARIABLE INTAKE LENGTH EXAMPLE ...... 11

FIGURE 4: DUAL PLENUM EXAMPLE ...... 11

FIGURE 5: DRIVING HISTOGRAM ...... 12

FIGURE 6: PRESSURE WAVE ALONG AN INTAKE RUNNER ...... 15

FIGURE 7: THOMPSON’S DEMONSTRATION OF VARYING RUNNER LENGTH ...... 18

FIGURE 8: TEST SETUP - VIEW DOWN INTAKE PORT ...... 21

FIGURE 9: TEST SETUP - ADJUSTABLE LENGTH SLEEVES ...... 21

FIGURE 10: EXPERIMENTAL RUNNER LENGTH COMPARISON ...... 23

FIGURE 11: PEAK VOLUMETRIC EFFICIENCY – HELMHOLTZ VS. TEST RESULTS ...... 24

FIGURE 12: RELATIVE ERROR FOR HELMHOLTZ VS. TEST RESULTS ...... 24

FIGURE 13: PEAK VOLUMETRIC EFFICIENCY - PRESSURE WAVE VS. TEST RESULTS ...... 25

FIGURE 14: RELATIVE ERROR FOR PRESSURE WAVE VS. TEST RESULTS ...... 25

FIGURE 15: EFFECT OF VARYING RUNNER DIAMETER WITH A CONSTANT LENGTH ...... 31

FIGURE 16: CENTRAL LOG INTAKE MANIFOLD ...... 33

FIGURE 17: SIDE LOG INTAKE MANIFOLD...... 34

FIGURE 18: INTAKE TEMPERATURE VARIATION...... 36

FIGURE 19: INTAKE VOLUMETRIC EFFICIENCY VARIATION ...... 37

FIGURE 20: NOZZLE FLOW CFD ...... 42

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List of Tables

TABLE 1: HELMHOLTZ CALCULATION RESULTS; CONSTANT DIAMETER ...... 19

TABLE 2: PRESSSURE WAVE TUNING RESULTS; CONSTANT DIAMETER...... 20

TABLE 3: TEST RESULTS - PEAK VE SPEED AND MAGNITUDE ...... 22

TABLE 4: HELMHOLTZ CALCULATION RESULTS; CONSTANT LENGTH ...... 30

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Chapter 1: Introduction and Background

In automobile racing, several rule committees overseeing the class, such as Formula

SAE, develop rules to provide a safe environment, as well as a more level playing field.

With Formula SAE, many of the rules are intended to challenge the designers to provide a solution, from test or analysis, to a particularly challenging issue. One rule that is often imposed is a restriction on the air intake diameter. The purpose of this is to limit the amount of power the engine can produce, to reduce the speed of the vehicle, and bring the power to more comparable levels across the class for more equal competition. With the restricted air intake rule, it becomes the design engineer’s job to maximize performance, while adhering to these rules. This is a challenging issue due to the conflicting compromises that must be made when designing a manifold and a problem that covers multiple engineering disciplines such as fluids, thermal, materials, and manufacturing. A deeper challenge comes from the very limited references available to use in the design, and the majority of what is available is either not for a restricted engine, is too application specific, or too condition specific such as Blair’s articles on a restricted engine where the engine speed is well above the typical operating range [1]. The use of traditional hand calculations becomes less insightful to the solution, because these equations all operate under the assumption of unlimited mass air flow. Therefore, experimentation must be done to validate the analytical solution, as well as provide deeper insight into intake design on a restricted engine. The results from the experiments, and modern design and analysis tools, can be used to help the design engineer maximize engine volumetric efficiency (VE), and therefore performance. This work is centered on Formula SAE

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requirements, but the theory would hold valid for any internal combustion engine intake manifold design where intake restriction is required.

Before beginning, it is useful to know and understand overall engine basics, and its role in automobile racing. The air cycle of an engine officially begins at the intake, which is most often filtered to prevent debris from entering. After the air intake, is the throttle body, which controls the amount of air allowed to enter the engine, as controlled by the accelerator, or gas pedal. In Formula SAE, and several other sanctioning bodies, the air restrictor must be downstream of the throttle body, in this case 20mm for gasoline powered engines. Once the air has passed through the restrictor, it then enters the intake manifold before travelling down the intake manifold runner(s) into the engine during the induction stroke where it is mixed with gasoline either at the bottom of the runner (where the gasoline can be used to help cool the intake valve) or directly in the cylinder. The air is then compressed on the next stroke (compression or squeeze stroke), followed by the power stroke where the air/fuel mixture is ignited and burned. The air and combustion by-products are then expelled from the engine on the exhaust stroke where it will travel down the exhaust manifold, or header, through the exhaust piping and muffler and back to the atmosphere [2].

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Figure 1: Air flow through an engine [1]

The entirety of the air cycle will affect the volumetric efficiency of the engine. How the air travels, before it enters the engine and after it leaves the engine, has a large impact on how well that engine performs. In the racing world, engine performance is not always about peak power or peak torque. In road racing, especially in the restricted classes, having a long flat torque curve is more important than just a peak torque. This is because a flat torque curve will provide consistent driver feedback. A driver needs predictable, preferably immediate, engine response at any engine speed and any throttle position.

That being said, in FSAE, it is the engine design engineer’s job to focus on a broad torque curve, which is directly related to volumetric efficiency, not just a peak number.

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1.1 Intake Manifold Basics / Engine Induction

An engine intake manifold, as mentioned above, is the part of the engine between the cylinder(s) and the throttle body. In a multi-cylinder engine its primary purpose is to evenly distribute the air flow between each cylinder, and to create the fuel air mixture, unless the engine has direct injection. The intake manifold determines how much air can be pulled through, including the effects both in transients and steady state, how fast that air is moving, and how well it can be mixed with fuel. All of these set how much mass air flow can enter the cylinder of the engine. Because the intake manifold determines exactly the mass air flow, it has a large impact on engine volumetric efficiency.

1.2 Composition of an Intake Manifold

An intake manifold is composed of two major parts, in conjunction with the throttle body, which include the plenum and the runner(s). The plenum is the chamber which collects the air before it is diverted down to each cylinder via the runner. The runner not only connects the flow path between the plenum and the cylinder, it is also where the fuel is mixed prior to the engine (with the noted exception of direct injection). For the restricted engine, the restrictor is also usually a part of the manifold assembly. While the restrictor is not a part of this effort, it is an essential piece in the design of an engine, as it will affect how the air has entered the plenum chamber, and how that flow of air reacts throughout.

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Figure 2: Intake Manifold

Intake manifolds can come in various configurations, from simple to complex. There can be multiple plenums and/or multiple runners feeding a given cylinder. You can have variable runner length/volume intake manifolds, or even variable plenum volume manifolds. There are designs that try to swirl the air, planar manifolds, and log style manifolds. There are pros and cons to each of these configurations, where the balance of performance is measured for a given engine and design goal.

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Figure 3: Variable intake length example [2]

Figure 4: Dual plenum example [3]

1.3 Aims of a Manifold

A well designed intake manifold will deliver a uniform air/fuel charge to the cylinder in as direct a flow as possible, with appropriate air velocity to sufficiently maintain volumetric efficiency at low and high engine speeds. The various combinations and

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styles of manifolds are directly linked to the performance goals of the engine. For example, in drag racing, a max effort design is desired where peak horsepower, between shift points, is ideal to maintain the highest possible acceleration. As stated earlier, a road racing vehicle, where the primary focus is suspension design and driver feedback, a long and flat torque curve is desired.

Figure 5: Driving Histogram

When the driving plot above is examined, it can be seen that the vehicle spends a significant portion of its time between 6000-10000 rpm. In this application, that is where the desired torque, and therefore volumetric efficiency, would be maintained.

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1.4 Traditional Calculations

To understand the application of the equations, an understanding of the phenomenon should be acquired. As the piston completes the exhaust stroke, pushing out the spent air in the combustion process, the exhaust valve starts to close and the intake valve starts to open before the piston has reached Top Dead Center (TDC). This very short period of time before TDC (BTDC) and after TDC (ATDC) where both intake and exhaust valves are open is called “valve overlap”. Ideally, one would like to have high pressure air on the intake valve side, and low pressure on the exhaust side. This pressure differential would cause the air, without any aid of mechanical action, to move from high to low pressure and aid in exhausting any spent air from the combustion cavity, and therefore raise the effective air charge on the next cycle. Next, as the piston accelerates further away ATDC, expanding the volume in the cylinder, a vacuum is created. This vacuum causes the column of air in the intake runner to move as a whole into the cylinder at a high velocity. At the same time, the expansion (negative pressure) wave created by the cylinder vacuum propagates toward the inlet of the runner. At that point, rarefaction at the runner inlet causes the surrounding air in the plenum to rush in and fill the void, sending a reflective compression (pressure) wave back towards the cylinder. At a given

RPM the reflective timing will be such that it will arrive before the intake valve has closed near or at Bottom Dead Center (BDC) giving an extra charge of air to the cylinder and allowing for that much more air to fill the cylinder before the intake valve has closed.

After the piston passes BDC and the intake valve has completely closed, the momentum of the air charge going through the pipe is stopped. This causes the kinetic energy of the fast moving column of air to be converted to pressure energy on the back side of that inlet

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valve and another pressure wave in the pipe is created. The pressure waves from these events will again be used at a given RPM to increase volumetric efficiency at overlap, with the high pressure wave arriving at the back side of the valve as it begins to open.

The phenomenon described is the basis for intake manifold “tuning”.

Intake manifold tuning has been practiced and experimented with for nearly as long as the internal combustion engine has been around. Most of the early calculations were based only on the inlet pipe alone, and was referred to as organ pipe resonance. The theory of tuning for volumetric efficiency, using Helmholtz resonator theory, was first presented by Engelman. This method took into account the engine cylinder and his work proved much more useful, and over a wider range of engine speed [4]:

Equation 1

√ √

Where, Fp = engine speed (RPM)

K = 2.0 to 2.5 for most conventional engines

C = speed of sound, ft/s

V = displacement of cylinder, in^3

L = inlet pipe length, in

A = inlet pipe cross-sectional area, in^2

R = compression ratio

162 = constant incorporating units

The Helmholtz resonator method, and derivatives from it, has been used substantially for over 60 years.

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Another method that is also widely used is pressure wave tuning. This method is similarly based on using the pressure wave pulses created by the valve timing, where the tuned length is set to coincide with intake valve opening, providing an extra charge of air into the cylinder due to the higher pressure, and therefore increasing volumetric efficiency.

The calculation is from the velocity of an air wave in a pipe where velocity = distance/time, where distance is twice the pipe length and time is found from engine speed and associated intake valve timing. The derived equation is [5]:

Equation 2 L = ((ECD × 0.25 × V × 2) ÷ (rpm × RV)) - ½D

Where, ECD is the effective cam duration (portion of cycle)

V = speed of sound @85 F (chosen as the average measure intake temp)

RV = reflective value (count of each pulse from one end of pipe and back)

D = runner diameter (in)

Figure 6: Pressure wave along an intake runner [2]

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However, the historical and practical methods for calculating volumetric efficiency all have the same constraint in that the amount of air that is fed into the intake manifold is unlimited. In today’s racing world, this is not typically the case. Many governing bodies of racing leagues incorporate the use of restrictor plates or nozzles that limit the amount of air that can get to the engine. This is done to help level the playing field and more importantly keep engine power levels down to a more safe and manageable level.

1.5 Summary of Thesis

The chapters that follow are broken up into the major components of the intake manifold and their impact on engine volumetric efficiency. Chapter Two is the primary focus of this work and will discuss the effect of runner length, solve for peak VE using traditional calculations and compare those values with test data collected from a representative engine. Chapter Three will discuss the effect of runner diameter and show example hand calculations along with historical collected data to support the findings. In

Chapter Four the effect that the plenum has on VE is examined and some representative tests are shown to corroborate associated theory. The other major considerations that impact intake manifold design and volumetric efficiency are discussed in Chapter Five.

Finally, Chapter Six contains the conclusions from the study and future recommendations.

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Chapter 2: Effect of Runner Length

The runner of an intake manifold is the primary tuning tool for modifying volumetric efficiency. Changing the length of the runner is usually the simplest approach with a given engine design, with the cross sectional area, and therefore diameter, already known basis based on the cylinder head cross sectional area prior to the valve. Changing the runner length also has the advantage of being infinitely adjustable, where the diameter is limited to available pipe diameters unless more expensive manufacturing processes such as machining or rapid prototyping are used. For these reasons, runner length modification is practical and the basis for experimentation.

In general, as verified analytically and experimentally, as runner length increases, the peak efficiency shifts lower in engine speed. This is due to several reasons. First, as the length increases, so does the surface area of the flow stream which results in additional resistance. As the air velocity increases with engine speed, the effect of this frictional resistance increases causing volumetric efficiency (VE) to shift lower in engine speed.

Conversely, as the length gets longer, the charge column of air will get greater as it builds up over the greater length resulting in peak VE rising. This means as length increases,

VE magnitude increases while shifting earlier in engine speed, and also trails off quicker after peak VE is reached. [6] Thus, the first design trade-off is reached. A longer length will result in higher volumetric efficiency, but the usable power-band will get shorter as seen in Figure 7 below.

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Figure 7: Thompson’s demonstration of varying runner length [4]

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However, in the restricted engine case, the overall air charge is limited, which in theory would limit the charge column capability. This effect is twofold. First, since the charge column is limited, the increase in volumetric efficiency magnitude as length gets longer is diminished. Secondly, the drop in charge column mass reduces the effective resistance and the rate of reduction in VE after peak would be lessened. This can be seen when comparing the analytical calculations to the experimental results.

2.1 Calculations

Since the hand equations cannot be used to determine the magnitude of the volumetric efficiency, they will be used to determine the engine speed where the peaks would be for a given length.

Also, when determining the length, the effective length of the cylinder head port must be included, as well as a quantity of air at the mouth of the pipe that acts as part of the system. Thompson suggests this to be pi/2*R [4] . Using Equation 1, the calculations are as follows:

√ √

length (in) Peak RPM 9 8520 10 8249 11 8003 12 7777 13 7570

Table 1: Helmholtz Calculation Results; Constant Diameter

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The pressure wave tuning equation was solved for engine speed (RPM). The first four reflective waves were examined to see which applied most directly to the engine efficiency. For the system utilized, the second wave lined up most equally with the expected peak efficiency location. Using Equation 2, the calculations are as follows:

RPM=(470*0.25*1144*2)/(RV*L+.5*1.3875)

Reflective Value RPM @9in RPM @ 10in RPM @ 11in RPM @ 12in RPM @ 13in RPM @ 14in 1 18406 17303 16326 15452 14668 13959 2 9203 8652 8163 7726 7334 6979 3 6135 5768 5442 5151 4889 4653 4 4602 4326 4081 3863 3667 3490

Table 2: Pressure Wave Tuning Results; Constant Diameter

2.2 Experimentation

In order to test the effect of runner length on volumetric efficiency, a test manifold was designed and built. A simple planar manifold was chosen with removable runner attachments between the plenum and the runner base to allow variation of runner length without affecting fuel insertion location. Upstream is a nozzle with a 20mm restrictor in place. The test engine used is a Honda F4i inline 4 cylinder gasoline engine. Each cylinder has a bore of 2.64 inches (67.0mm), a stroke of 1.67 inches (42.5mm), and a compression ratio of 12 to 1. The intake duration is 245 degrees, opening at 22 degrees before top dead center. The engine was run on a Mustang Dynamometer which utilizes eddy current for resistance. Volumetric efficiency was measured as engine torque output from the dynamometer. The engine had fuel and spark tuned for each configuration to ensure the peak torque value at full throttle across the rpm range was achieved.

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Figure 8: Test Setup - View down intake port

Figure 9: Test Setup - Adjustable Length Sleeves

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2.3 Results

After experimentation was complete, the torque curves for each length tested were overlaid on top of each other, as shown in Figure 10. This plot clearly shows that as suggested, when runner length increases, the peak efficiency shifts lower in engine speed.

Though, it is noted that for the nine and ten inch length runners, that some other resonance phenomena resulted in an additional dip in the curve. This could be caused by several reasons, such as a high pressure pulse from the exhaust impacting the cylinder during overlap, resulting in a poor air charge. However the cause for this drop in efficiency is not a primary concern for this effort, but should be noted for its impact to the test results. It appears that without this phenomenon, the peak RPM location for both of these lengths may be at a different point, perhaps by a few hundred rpm if a trend line were fitted. This shift most likely causes the additional relative error from the Helmholtz calculation, as seen in Figure 11.

Test Results Length (in) 9 10 11 12 13 14 Engine Speed (rpm) 9400 9150 8520 8150 7850 7400 Engine Torque (lb-ft) 43.0 45.0 47.5 47.6 48.5 48.6

Table 3: Test Results - Peak VE speed and magnitude

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Figure 10: Experimental runner length comparison

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Figure 11: Peak volumetric efficiency – Helmholtz vs. Test Results

Figure 12: Relative error for Helmholtz vs. Test Results

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Figure 13: Peak volumetric efficiency - Pressure Wave vs. Test Results

Figure 14: Relative error for Pressure Wave vs. Test Results

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The experimental results also demonstrate the effect that the restrictor has on the system. As suggested earlier, the peak magnitude does not rise as substantially as theory would suggest. For the eleven through fourteen inch runner lengths the peak magnitude is within two percent of each other. The same is noted for the trail-off of efficiency after peak; while the shorter length does maintain VE higher in engine speed, the slope between the different lengths is approximately the same. Both of these are converse to the data collected in previous unrestricted scenarios such as in Figure 7 above. However the gain in VE towards peak is similar to the unrestricted case, where the longer runner has a steeper ramp.

When the experimental results are compared with the calculated predictions, it can be seen that the calculations do a reasonable job of predicting the location for peak efficiency, within a 5% error depending on length. However, there is a caveat to this that must be explained. Both calculations utilize an ambiguous factor that must be determined without much insight. The Helmholtz theory has the factor K which is to account for engine characteristics and seems to lie somewhere in the 2.0-2.5 range.

Thompson’s work did a short study noting how the factor K varies from engine to engine and system to system. This study used a factor of 2.0 which yielded a result with low error, but if one were to pick another number, the yielded error could be higher. The pressure wave calculation has a similar situation. When calculating the effective cam duration (ECD), it is suggested to subtract a value between 20 and 30 from the advertised cam duration to account for the time between when the valve is opening or closing and/or error in the cam.

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A change of the value in either equation results in a direct shift of peak engine speed.

When examining Figure 13 and Figure 14, it can be noted that if a larger ECD was used, the calculated peak could be shifted nearly directly on top of the experimental data. This is further evidence that the traditional hand calculations are only useful in getting the designer close to target and collected data results in a refinement of accuracy.

Understanding this, and under the assumption no other parameter will change, the designer can use the results from Figure 10 to make his design choice. At first glance, the 14 inch runner length would appear to be optimal for a Formula SAE platform, since it offers the highest magnitude of torque, but more importantly for an FSAE application, it has the longest, flat torque curve from 7,000 rpm to 10,000 rpm, where below 7,000 rpm all the lengths appear to suffer from the same resonant anomaly that results in a dip in the torque curve. However, using due diligence, the designer must remember to compare the test results with the driving histogram, such as from Figure 5, to verify the application is best. In this case, the histogram shows the driving range is between 5,000-

11,000 rpm. If a 14 inch runner length is chosen, there will be a point in the driving range in which the torque magnitude would increase by approximately 40% over a very short engine speed window. This change in torque would be felt by the driver as a sudden increase in performance or loss in performance depending on which way he was travelling through the engine speed range resulting in a very inconsistent response.

Therefore, for the engine used, with the resonant anomalies that result in the dips in the curve, it appears that a 9 inch runner length would actually give the most consistent torque across the engine speed range used by the driver, even though the overall efficiency number is lower. If the resonance that causes the efficiency loss at

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approximately 5,500 rpm didn’t exist or could be altered by changing another parameter, such as the exhaust or engine configuration, the 14 inch runner length might have been more acceptable. This longer length would have also made more sense to the designer if the driving range was above 7,000 rpm where the near instantaneous doubling of torque would not be driven across on a regular basis. This is why it is important for the designer to consider all aspects in his choices and settle on a trade that will meet the overall needs of the program.

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Chapter 3: Effect of Runner Diameter

A second approach to tuning engine volumetric efficiency is to vary the diameter of the runner. As mentioned above, the added complication to this approach, when using a given engine, is the relative cross sectional area difference created at the junction to the head of the engine. By changing the cross sectional area, in essence a nozzle is created, either converging or diverging depending on the change made. This will have the effect of either increasing or decreasing air speed at the entrance into the cylinder and affect the pressure wave pulse mannerisms slightly. However, empirically it is still an acceptable approach, providing a second option when tuning the manifold.

Generally, an increasing runner diameter will result in a shift of peak volumetric efficiency higher in engine speed. Like a change in runner length, this is due to several physical interactions. Primarily, this is because as the diameter increases, the air charge column increases in which to fill the combustion chamber. However, the increase in diameter results in more surface area which in turn creates more flow resistance. Along with this, the increasing diameter also causes the air velocity to decrease. The combination of these events has a different effect on the shape of the VE curve on either side of peak efficiency from that of a change in runner length. Specifically, the difference is that for a change in runner diameter the shape of the VE curve stays the same in slope and magnitude as it shifts due to the aforementioned reasons of friction and velocity. [6] However, once again, the restricted engine case is affected due to the limited mass air flow of the system. As the diameter increases from a nominal value, the air velocity, which is choked by the restrictor, will result in the magnitude of the peak VE to fall. Conversely, as the diameter decreases, it would theoretically reach a point where

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the air velocity is no longer inhibited by the restrictor, but by the runner diameter itself, with the restrictor diameter being small, this small value would result in a choking of the engine itself, once again reducing overall peak VE. The implication of this is that the analytical method would match the experimental method, within a given range of diameters.

3.1 Calculations

Using the same Helmholtz equation above but varying the area based on changing diameter, the shift in peak VE as a function of engine speed can be seen in Table 4 below.

Similar to the length calculations, the hand equations cannot be used to determine the magnitude of the, peak volumetric efficiency and will only be used to determine where the peaks would be for a given diameter.

Runner Peak RPM Diameter (in)

1.1250 6621 1.2500 7357 1.3875 8166 1.5000 8828 1.6250 9564 1.7500 10300

Table 4: Helmholtz Calculation Results; Constant Length

3.2 Results

The tabular results above indicate that a small change in diameter has a dramatic result in where peak VE would occur. As suggested, an experimental test is more difficult, and would be skewed by the effect of the nozzle created at the head, since this

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cross sectional area cannot be readily modified for comparative testing. However it has already been demonstrated in length testing that the traditional hand calculations yield small error when trying to determine the engine speed at which peak VE will occur. The same conclusion is also carried forward to varying diameter in that the calculations are of little use for more than this purpose. Figure 15 below shows a typical VE curve for an unrestricted engine. This data suggests that even for an unrestricted engine, the variation in diameter only has an effect on where peak VE is located, and not the shape of the VE curve. Future testing using a well-developed and correlated engine model from a computational fluid dynamics package can be used to compare the unrestricted curve to a restricted engine model.

Figure 15: Effect of varying runner diameter with a constant length [6]

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Chapter 4: Effect of Plenum Design

The plenum of the intake manifold is the chamber between the throttle body and the individual runners. It collects the air prior to being sent down the runners and into the engine. There are several configurations that can form the shape of the plenum. You can have a single plane design that feeds all the runners, a dual plane design where each chamber feeds half of the runners, or in a non-restricted case, you can have individual runners where no plenum at all is used. There are many different variations on single and dual plane manifolds, from simple log manifolds to complex cross ram designs. A dual plane design is typically only used in applications where there are 6 or more cylinders, where the pulse width between cylinders is reduced so that the velocity in the chamber has less variation.

The general design of a plenum plays an important role in the manifold design. After the throttle body, and restrictor in the restricted engine case, the air has opportunity to reduce velocity and increase density prior to being diverted down a given runner. The volume of a plenum should be sized such that it is large enough that at high engine RPM it has enough volumetric capacity to sufficiently feed each runner. It also needs to be small enough that adequate velocity is maintained at slower engine speeds. [5] There are no known standard equations for determining the ideal volume for an engine, where most design is done empirically. In the restricted engine case, the effective tuning volume in the intake manifold is reduced to the maximum amount of air flow that the restrictor will allow. A very large plenum would allow the velocity to slow down from the peak it found at the throat of the restrictor, and increase peak volumetric efficiency, as was found by Lee and Hamilton during their experimentation [7]. However, they did not test the

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transient performance. Intrinsically, a very large volume would result in poor throttle response, since the plenum acts essentially as a capacitor. Also, in most applications the volume is limited by available space constraints, as well as the philosophy of keeping weight down in racing applications.

The surrounding space of the plenum itself also creates another important factor in manifold design. The other important factor in shape and location of the manifold’s plenum deals with heat. An intake is subjected to conductive, convective, and radiant heat sources. While little can be done to impact the conductive heat transferred from the engine to the intake via the runner connection, there are more opportunities to reduce the convective and radiant heat transfer for a given design. This is demonstrated below in

Figure 16 and Figure 17.

Figure 16: Central Log Intake Manifold

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Figure 17: Side Log Intake Manifold

Plenum shape also has in impact from flow characteristics. The largest effect is not from the plenum itself, but the manner in which it collects air from the runners. Ideally, the runner would be a straight pipe with no bends, due to the associated pressure drop as the air is forced to bend in the pipe. However, it is understood that space constraints often disallow straight runners to be used, but consideration to this pressure drop should be considered during the manifold design. Another consideration to take into account is the path of the air within the plenum, between cylinders. In a log manifold, the cylinder closest to the plenum inlet from the throttle body/restrictor will see the air charge the most, while the cylinder furthest away results in a longer travel for the air. This means, theoretically, the closest cylinder would have a leaner burn than the furthest cylinder.

Because of this, often a ram effect is designed into the manifold where the cross section of the plenum decreases as you travel to the furthest cylinder, keeping the air velocity more consistent between cylinders. For a restricted engine, the impact on plenum shape

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theory is minimum, where the effect is limited by the total mass air flow allowed by the restriction.

Figure 18: Example of central log manifold designed with air flow characteristics considered

4.1 Experiments

The basic design of a central log manifold is that the air being inlet into the plenum is centered between all cylinders. The idea, in this case, is to ensure the air has a nearly equidistant path to each cylinder, so that the air charge is identical for all cylinders. The design in Figure 16 accomplishes this, while staying within the packaging envelope.

The side log manifold, as described above and shown above in Figure 17, has the air pulled in from one end of the plenum, closest to one cylinder. The noticed advantage is the smaller packaging space, and the reduced cross sectional and surface area where heat transfer from the engine can occur.

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4.2 Results

Back to back testing of the two styles of intake manifolds above show that ambient air temperatures remain 25 degrees Fahrenheit cooler in the side log manifold, while the temperature rises on the central log, as the engine heats up. The cooler air in the side log manifold will allow for great volumetric efficiency for the engine.

The testing performed demonstrates that the theory matches the actual test results very well. By reconfiguring the plenum so that it is not over the engine, the intake air temperature dropped by 20 degrees on back to back testing. This lower air temperature results in a more dense air charge to the cylinder and therefore increased efficiency.

Additionally, while a straight log manifold was not tested, it can be seen that the ram style log does produce consistent air charge between cylinders, which promotes reliability and enhanced tunability.

Figure 19: Intake Temperature Variation

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When the two different designs are compared on a dynamometer it is seen that the torque results are nearly identical. From this, as well as the exhaust gas temperature

(EGT) data, it can be concluded that there are no documentable adverse volumetric efficiency effects from the side log manifold, when compared to the central log. There is no documented increase in volumetric efficiency from the side log that would be expected from the cooler air because during a dyno test, the engine is not run for very long. The engine does not have much time to heat up in this situation in order to transfer heat into the intake manifold, so the measured ambient air temperatures are identical helping maintain similar volumetric efficiencies.

Figure 20: Intake Volumetric Efficiency Variation

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Figure 21: Exhaust Gas Temperature Measurement Example (deg F) Chapter 5: Other Considerations

With an intake manifold being composed of several components, all with many different possible variations, means there are lots of other considerations besides their basic dimensions will affect overall volumetric efficiency. This complexity is further confounded when you consider that the media is a compressible fluid, with high dynamics due to the pulsing between intake strokes. This is even more true with a multi- cylinder engine where the flow interactions cannot remain laminar throughout due to its very nature, where air is changing direction between cylinder runner inlets as the intake valve opens demanding air for that cylinder. Some of the primary affects are referenced below, and should be considered during the design of an intake manifold. [8]

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5.1 Flow Path

As mentioned earlier, the flow path of the runner has an effect on volumetric efficiency. For example, any convergence or divergence along the runner length will result in a decrease or increase in air velocity. A divergence can also result in the precipitation of fuel on the inner wall since the slower moving air makes it more difficult to be suspended. Whereas in a convergence, fuel can collect at the transition and then be drawn down in spurts as it collects resulting in a non-uniform mixture. [6] The effect of the fuel particles is also noticed when dealing with the surface finish. A smooth surface finish will result in reduced viscous drag and therefore a higher charge and a marginal increase in efficiency. The increased velocity close to the wall also means less fuel can precipitate and collect. The effect that shape has on volumetric efficiency is also based on frictional resistance. A circular cross section will have the least surface area and therefore the least frictional resistance. However, the drawback to a circular cross section is in the case where fuel is mixed with the air. The cylindrical shape will allow for a swirling effect which causes the fuel to be thrown to the wall due to the centrifugal dynamics.

Elbows, junctions and bends also reduce overall volumetric efficiency, more so than cross sectional shape and surface finish. [6] This is because these geometries impact the air charge greater. Bends and junctions for example create turbulent air flow characteristics such as eddies which will choke the flow in the pipe. Bends lower efficiency because of the pressure drop associated with them. Bends also creates a pressure difference on either side of the pipe, because as the air goes through the bend it is subject to a centrifugal effect where the air is pushed to the outer radius resulting in

39

higher pressure and velocity on one side, and lower on the other. Depending on injector placement, this can create a non-uniform air/fuel charge. The last noted shape effect to be mentioned is the inlet of the runner. Many studies, such as Blair’s article “Best bell”

[9], have been done to demonstrate that a bell mouth or “trumpet” entrance to the pipe length results in increased volumetric efficiency. This is because it allows a smoother transition for air to enter the pipe where a straight pipe end will actually choke the flow at the throat due to the turbulence created at the edge. All of these considerations hold true regardless of the restricted engine scenario or not.

5.2 Injector Placement

Where the injector is placed within the flow stream to the cylinder also has a noticeable effect on overall engine efficiency. While placing the injector further upstream allows more time for the fuel to mix and atomize with the air, it also allows it more time to precipitate and collect on the walls of the runner eventually allowing for non-uniform droplets of fuel to enter the cylinder. A close injector placement (nearer to the intake valve) may prohibit adequate atomization time before entering the cylinder.

Though many later designs have the injectors placed very close to the intake valve, spraying fuel on the back face of the valve. The idea behind this design is both to promote instant atomization of fuel to gas form by hitting the very hot valve and to help cool the valve at the same time to promote longevity and reliability. New designs are utilizing technology involving high temperature capabilities, and placing the injector directly in the cylinder head, as has been done historically in many diesel applications.

The extremely high temperatures along with the swirl in the cylinder chamber result in superb atomization for the fuel, increasing the charge and combustion efficiency.

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For injectors that are in the intake tract, there is also a lot of research and design concerning the spray pattern and spray angle into the flow path taking into account pressure and velocity differences, temperature, relative valve location, etc. All of this is done to promote proper fuel atomization, which is key to optimizing engine efficiency.

Again, this effort is useful regardless of a restricted intake or not.

5.3 Restrictor Design

When dealing with a restricted engine, one of the obvious factors in promoting volumetric efficiency is in the design of the restrictor itself. In Formula SAE, the rule simply states that air must pass through a 20mm restrictor for standard octane engines. It does not clarify how that restriction is to be instituted, other than its location is to be downstream of the throttle body. A well designed restrictor will meet the rules while maximizing mass air flow capability. Options could include a 20mm inlet, a plate with a

20mm hole in it, a nozzle, or another novel approach. For reference in this work a converging/diverging nozzle was chosen as the best approach. CFD analysis was completed in order to maximize capability for mass air flow.

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Figure 22: Nozzle Flow CFD, from Lindley’s thesis work on throttle and restrictor optimization [10]

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Chapter 6: Conclusions and Future Recommendations

The study and testing that resulted to form this work are useful to the engineer of an intake manifold design, with emphasis on the restricted case. While many of the physical laws that govern the design of an intake are applied the same for a restricted or a non- restricted engine, some of them, the runner length in particular, are impacted such that traditional methods and associated calculations are not fully realized due to the improper assumption of unlimited air capacity.

6.1 Conclusions

The engine tests performed in this study demonstrate that traditional hand calculations can be used to effectively tune for peak volumetric efficiency. However, the magnitude and shape of the VE curve are not the same as previous works suggest. The limited mass air flow impacts the ability to tune the shape of the VE curve with traditional methods. In particular, for the engine model tested, an increase in runner length does not constitute an increase in VE magnitude. Furthermore an increasing length does not result in an increased rate of decline after the peak is reached. Therefore it can be said that when tuning VE outside of the peak regions on a restricted engine, empirical data should be used to choose the optimum design characteristics for the given application.

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For Formula SAE, design considerations are as follows:

 The design characteristics described in this work are applicable to multiple

engine configurations, be it single cylinder engines or multiple cylinder

engines. The hand calculation utilized for finding the peak efficiency location

does change and the appropriate equation should be used.

 Traditional hand calculations are useful, but only for determining the peak

engine speed volumetric efficiency location.

 The shape and magnitude for volumetric efficiency across the engine range

should be determined empirically, due to the effects the restrictor has on

tuning theory, as well as unforeseen phenomena such as engine resonant

frequencies.

 When choosing the ideal runner, be sure to compare the torque curve to the

driving histogram of the vehicle to be used. Gear ratio, engine type and

design, and even vehicle dynamics will alter the histogram, so these things

must be representative of what will be utilized for the given design.

 Runner length is the simplest and most practical characteristic to modify for

intake manifold design.

 An increasing runner length will move the peak volumetric efficiency lower in

engine speed.

 On a restricted engine, an increasing length will have a marginal increase in

peak torque magnitude. Whereas an unrestricted engine will have a more

noticeable increase in peak torque magnitude.

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 On a restricted engine, an increasing length will result in a decay of

volumetric efficiency after peak torque at near the same rate. Whereas an

unrestricted engine will have a faster decay for a longer length runner.

 Runner diameter is useful in shifting the peak torque location but is limited for

a given head port diameter and shape.

 An increasing runner diameter will move the peak volumetric efficiency

higher in engine speed.

 An increase in runner diameter will not change the magnitude or shape of the

torque curve.

 Plenum volume should be as large as the space constraint allows while

considering weight and complexity, but the effect on throttle response must be

determined from dynamic vehicle testing. The rule of thumb for volume is

between 2 and 10 times engine displacement. The overall gains for a larger

volume are marginal, and must be traded against the weight, complexity, and

even visual impact to the design.

 The design of the plenum shape should consider the effects from the surround

environment, such as from thermal heat transfer.

 A well designed restrictor is important to the overall efficiency capability of

the engine.

6.2 Future Recommendations

The data collected for this study suggests that for a restricted design, traditional hand calculations are only useful in helping to determine the location, with respect to engine speed, of peak volumetric efficiency. They cannot be used to help determine the 45

magnitude or slope for VE for a restricted application. Computer technology with sophisticated computational fluid dynamic programs, developed specifically for combustion engine design, have the ability to account for restricted air flows. Use of these tools should be examined and compared with experimental test data to confirm the user built analytical model. Once the model has reached a high level of fidelity, it can then be implemented as a tool to effectively tune for the ideal peak VE location and shape as the engine system will allow. However, unknown engine dynamics such as observed in the testing done in this work for the 9 and 10 inch runners, may still pose a challenge to even the best computer models. Correlation of the analytical design should always be confirmed with the real world model to ensure the design goals are achieved.

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References

[1] "File:Four stroke cycle intake.png," 2005. [Online]. Available: http://en.wikipedia.org/wiki/File:Four_stroke_cycle_intake.png. [Accessed June 2012]. [2] M. Wan, "Autozine Technical School," [Online]. Available: http://www.autozine.org/technical_school/engine/Intake_exhaust.html#Tuned-intake. [Accessed June 2012]. [3] B. Gillogly, "Carbon Fiber Dual-Plenum LS3 Intake," November 2011. [Online]. Available: http://blogs.hotrod.com/carbon-fiber-dual-plenum-ls3-intake-16841.html. [Accessed June 2012]. [4] M. Thompson, "Non-Mechanical Supercharging of a Four-Stroke Diesel Engine," MS Thesis, The Ohio State University, 1968. [5] G. A. Racing, "Technical Articles," [Online]. [Accessed 2012]. [6] H. Heisler, Advanced Engine Technology, Society of Automotive Engineers Inc, 1995. [7] L. Hamilton and J. Lee, "The Effects of Intake Plenum Volume on the Performance of a Small Normally Aspirated Restricted Engine," SAE Int. J. Engines, 2009. [8] H. Engelman, "Design of a Tuned Intake Manifold," ASME Paper 73-WA/DGP-2, 1973. [9] G. P. Blair, "Best bell," Race Engine Technology, vol. I, no. 17, pp. 35-41, 2006. [10] D. Lindley, "Design and Optimization of a Throttle and Restrictor for Formula SAE," 2012. [11] J. Kauffmann, "Investigation of the Influence of Gasoline Engine Induction System Parameters on the Exhaust Emissions," PhD Dissertation, The Ohio State University, 1972. [12] V. Mariucci, "An Experimental and Computational Investigation of the Effect of Primary Intake Runner Geometry on the Performance of a Single Cylinder Engine," MS Thesis, The Ohio State University, 2006. [13] J. Hartman, How to Tune and Modify Engine Management Systems, St. Paul, MN: MBI Publishing Company, 2003. [14] "Technical Articles," [Online]. Available: http://mysite.verizon.net/vzezeqah/sitebuildercontent/sitebuilderfiles/inductionsystems.pdf. [Accessed June 2012]. [15] W. Eberhard, "A Mathematical Model of Ram-Charging," MS Thesis, University of Wisconsin, 1971. [16] H. Engelman, "Surge Phenomena in Engine Scavenging," PhD Dissertation, The University of Wisconsin, 1953. [17] G. P. Blair, "Breathing Easy," Race Engine Technology, vol. I, no. 2, pp. 46-51, 2003. [18] G. P. Blair, "Breathing Easy Part 2," Race Engine Technology, vol. I, no. 3, 2003. [19] G. P. Blair, "Breathing Easy - Feedback," Race Engine Technology, vol. I, no. 4, pp. 14-15, 2004. [20] G. P. Blair, Design and Simulation of Four Stroke Engines, Warrendale: SAE, 1999. [21] R. Stone, Introduction to Internal Combustion Engines, Basingstoke: Palgrave Macmillan, 1999.

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Appendix A: Raw Test Data

Data was collected directly from MDSP 7000 Series Dynamometer Controller Software which is the software utilized with the MD-95 Chassis Dynamometer that was used for runner length testing. Measured engine torque and engine speed were extracted for each test performed. 14" 13" 12" 11" 10" 9"

Engine Engine Engine Engine Engine Engine Engine Engine Engine Engine Engine Engine Speed Torque Speed Torque Speed Torque Speed Torque Speed Torque Speed Torque (rpm) (ft*lbs) (rpm) (ft*lbs) (rpm) (ft*lbs) (rpm) (ft*lbs) (rpm) (ft*lbs) (rpm) (ft*lbs) 4016.7 34.4 4025.7 31.5 4022.4 31.4 4000.6 31.4 4001.7 32.6 4003.9 33.5 4031.3 34.7 4035.1 31.8 4035.8 31.6 4009.9 31.4 4005.0 32.6 4004.2 33.4 4041.4 34.9 4046.9 31.9 4136.5 32.3 4011.3 31.4 4013.2 32.5 4010.1 33.5 4041.6 35.0 4048.1 32.0 4213.2 33.1 4028.5 31.3 4013.9 32.4 4010.7 33.6 4048.7 34.9 4048.2 31.9 4232.7 33.3 4036.9 31.4 4017.5 32.5 4011.1 33.5 4050.2 34.9 4048.6 31.8 4235.1 33.4 4040.5 31.5 4027.8 32.4 4019.5 33.4 4054.5 34.9 4049.8 31.7 4236.8 33.6 4061.7 31.5 4029.2 32.3 4021.7 33.3 4054.8 34.9 4051.5 31.9 4306.6 33.8 4063.2 31.6 4030.6 32.4 4023.1 33.3 4060.4 34.8 4052.5 31.8 4334.2 33.0 4068.3 31.6 4042.1 32.4 4027.4 33.4 4061.7 34.5 4061.0 31.9 4355.1 33.3 4092.8 31.6 4043.6 32.3 4037.6 33.4 4062.0 34.6 4062.7 31.9 4439.7 34.0 4103.0 31.8 4048.6 32.3 4040.1 33.2 4062.6 34.9 4066.3 31.9 4444.6 34.0 4117.3 32.0 4056.7 32.4 4042.2 33.3 4063.9 34.8 4070.3 32.1 4444.8 34.1 4147.2 32.1 4061.3 32.3 4043.3 33.3 4193.8 34.7 4074.7 32.4 4447.3 33.9 4158.8 32.3 4064.7 32.3 4047.2 33.2 4213.9 35.1 4075.7 32.0 4461.3 34.1 4174.5 32.5 4065.5 32.3 4050.3 33.2 4236.3 35.4 4077.4 32.2 4461.9 34.1 4203.4 32.7 4066.8 32.2 4054.3 33.2 4257.1 35.8 4077.8 32.2 4473.4 34.2 4208.8 32.9 4068.3 32.1 4056.8 33.2 4271.8 36.1 4077.9 32.2 4474.5 34.1 4219.3 33.0 4069.4 32.2 4061.4 33.1 4274.0 35.8 4078.4 32.3 4479.6 34.3 4238.7 33.4 4074.8 32.2 4066.9 33.2 4274.9 35.7 4080.9 32.1 4480.4 34.2 4240.7 33.2 4075.1 32.3 4067.6 33.1 4275.3 35.8 4083.5 32.0 4487.3 34.3 4242.9 33.4 4075.3 32.1 4069.1 33.1 4275.7 36.0 4085.0 32.2 4489.1 34.4 4254.6 33.4 4075.9 32.0 4070.8 33.1 4275.9 35.7 4086.7 32.1 4498.6 34.4 4254.6 33.4 4079.7 32.1 4072.7 33.0 4279.5 35.7 4087.3 32.1 4505.4 34.4 4256.7 33.5 4083.0 32.0 4072.8 33.1 4280.0 35.7 4094.0 32.3 4506.5 34.6 4260.1 33.3 4088.0 32.1 4084.5 33.0 4281.9 36.2 4094.5 32.5 4506.6 34.4 4264.5 33.3 4093.7 32.2 4084.5 33.0 4282.0 35.8 4096.5 32.3 4511.4 34.5 4284.7 33.2 4096.3 32.0 4108.4 32.5 4282.5 35.8 4096.9 32.1 4514.2 34.5 4303.2 33.3 4097.3 32.2 4119.9 32.5 4282.9 35.8 4098.5 32.3 4517.6 34.7 4312.0 33.4 4102.2 32.0 4129.4 32.5 4283.6 35.6 4102.1 32.5 4517.8 34.5 4326.5 33.4 4103.1 32.1 4153.8 32.3 4283.6 35.7 4103.8 32.2 4525.3 34.7 4354.1 33.5 4104.8 32.1 4156.8 32.4 4283.7 35.6 4104.6 32.2 4528.2 34.7 4360.7 33.6 4104.8 32.0 4163.2 32.3

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4284.2 35.7 4112.1 32.5 4530.3 34.6 4368.3 33.7 4105.6 32.1 4188.8 32.2 4284.3 36.4 4116.1 32.7 4531.4 34.7 4389.0 33.7 4109.1 31.9 4199.2 32.3 4285.8 35.7 4116.7 32.7 4532.3 34.7 4398.3 33.8 4110.3 32.0 4202.7 32.2 4286.2 35.7 4119.4 32.6 4532.5 34.7 4398.8 33.8 4110.9 32.1 4228.2 32.2 4286.5 35.7 4124.5 32.5 4533.1 34.7 4404.5 33.8 4111.9 32.0 4233.2 32.1 4286.6 35.7 4124.7 32.3 4535.0 34.6 4413.5 33.8 4114.1 32.0 4234.8 32.2 4286.9 35.7 4125.2 31.9 4539.5 34.7 4414.7 33.8 4114.3 32.0 4249.8 32.0 4287.4 35.7 4127.4 32.4 4555.7 34.0 4418.2 33.7 4115.5 32.1 4260.7 32.0 4287.5 35.7 4129.6 33.0 4576.3 34.1 4425.6 33.7 4118.6 31.6 4260.7 32.0 4287.8 35.7 4135.2 32.8 4606.7 34.2 4429.8 33.8 4123.3 31.5 4273.9 31.9 4287.9 36.4 4139.4 32.6 4621.6 34.4 4433.2 33.8 4150.1 31.4 4290.2 31.8 4288.0 35.8 4143.5 33.0 4625.1 34.4 4434.4 33.8 4173.2 31.6 4292.3 31.9 4288.1 35.7 4146.8 32.7 4631.7 34.3 4435.3 33.7 4183.2 31.6 4300.6 31.8 4288.2 35.7 4147.3 32.9 4643.7 34.3 4435.9 33.8 4211.4 31.6 4315.7 31.8 4288.2 35.7 4153.7 33.1 4653.1 34.3 4437.5 33.6 4232.7 31.7 4317.4 31.8 4288.6 35.7 4157.4 32.9 4655.0 34.4 4437.5 33.3 4247.5 31.8 4334.3 31.6 4288.7 35.8 4159.7 33.0 4655.6 34.3 4437.6 33.6 4270.9 31.8 4336.2 31.7 4289.0 35.7 4163.0 32.9 4666.5 34.2 4438.0 33.6 4294.1 31.9 4337.7 31.7 4289.0 35.9 4164.8 33.1 4667.9 34.1 4438.0 33.7 4304.0 32.0 4343.3 31.5 4289.2 35.7 4166.6 33.2 4668.3 34.2 4440.6 33.6 4318.7 32.0 4346.5 31.5 4289.2 35.7 4168.8 33.0 4670.6 34.2 4441.5 33.7 4325.3 32.0 4349.6 31.4 4289.2 35.7 4171.0 33.4 4678.7 34.0 4441.7 33.5 4329.0 32.1 4351.4 31.5 4289.3 35.7 4175.8 33.2 4687.3 34.1 4442.9 33.6 4337.8 32.4 4363.9 31.4 4289.4 35.7 4176.4 33.2 4688.5 34.0 4443.1 33.8 4379.9 32.7 4366.5 31.5 4289.8 35.8 4178.4 33.1 4689.5 34.1 4444.7 33.6 4407.1 32.8 4367.1 31.4 4290.8 35.8 4179.2 33.2 4703.9 34.1 4445.7 33.7 4412.5 33.3 4377.2 31.4 4291.3 35.7 4180.3 33.1 4705.7 34.0 4445.8 33.7 4419.0 33.4 4379.9 31.4 4291.4 35.8 4180.7 32.9 4706.8 34.1 4445.9 33.7 4438.3 33.4 4381.8 31.3 4292.8 35.9 4183.0 33.2 4713.3 34.0 4446.1 33.6 4448.7 33.6 4385.9 31.3 4293.0 36.6 4183.5 33.0 4714.0 34.1 4446.9 33.4 4466.4 33.9 4390.9 31.3 4297.6 36.6 4183.7 33.2 4718.6 34.0 4447.2 33.6 4477.4 33.8 4391.4 31.3 4298.4 36.7 4185.9 33.3 4722.9 34.1 4447.9 33.7 4492.3 34.7 4397.6 31.3 4302.2 36.8 4191.1 33.2 4727.3 34.0 4449.0 33.6 4530.2 34.5 4398.2 31.3 4304.3 36.9 4191.2 33.1 4730.5 34.0 4449.2 33.7 4545.0 34.6 4406.2 31.3 4306.7 37.1 4195.5 33.5 4731.9 34.0 4449.8 33.8 4545.9 34.3 4406.4 31.2 4310.7 36.9 4206.5 33.2 4732.9 34.0 4452.2 33.6 4546.5 34.1 4407.5 31.2 4313.2 37.2 4213.9 33.8 4737.3 33.9 4452.4 33.5 4549.0 34.3 4408.8 31.3 4315.0 37.2 4215.1 33.6 4739.4 34.0 4452.5 33.7 4552.8 34.6 4409.1 31.3 4318.4 37.2 4218.5 33.5 4739.6 33.9 4453.2 33.6 4553.2 34.2 4415.5 31.2 4438.2 36.7 4236.2 33.9 4742.0 33.9 4455.8 33.6 4557.1 34.4 4415.7 31.2 4446.3 36.9 4248.0 33.6 4742.0 33.9 4457.6 33.2 4559.9 34.1 4418.9 31.2

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4454.1 36.8 4253.4 34.0 4743.6 33.6 4458.6 33.7 4561.4 34.7 4420.2 31.1 4462.5 36.9 4254.6 34.1 4744.7 33.6 4460.3 33.7 4562.7 34.6 4422.0 31.2 4467.3 36.9 4262.2 34.2 4745.3 33.9 4469.9 33.3 4563.4 34.3 4422.5 31.3 4474.4 36.8 4265.7 33.9 4746.7 33.7 4479.3 33.3 4563.6 34.3 4423.4 31.1 4477.9 36.8 4269.4 34.1 4747.1 34.0 4507.5 33.2 4574.2 34.9 4425.3 31.2 4479.6 36.8 4271.7 34.1 4747.2 33.8 4528.2 33.4 4581.3 34.5 4430.6 31.1 4483.2 36.7 4275.7 34.2 4747.3 33.8 4537.0 33.4 4583.0 34.4 4432.0 31.2 4483.6 36.7 4278.8 34.1 4747.7 33.6 4556.8 33.4 4595.1 34.9 4432.1 31.1 4486.0 36.5 4282.6 34.1 4748.8 33.7 4579.9 33.4 4599.3 34.7 4447.1 30.8 4487.8 36.5 4287.6 34.2 4749.1 34.0 4591.9 33.5 4599.6 35.0 4451.2 30.8 4494.2 36.5 4326.2 33.2 4749.3 33.6 4599.4 33.6 4602.0 34.9 4469.0 30.7 4496.1 36.5 4345.8 33.5 4750.3 33.8 4601.3 33.3 4604.8 35.0 4502.6 30.7 4496.3 36.5 4372.6 33.6 4750.5 33.9 4613.1 33.5 4609.5 34.8 4522.5 30.8 4499.0 36.4 4395.0 33.8 4750.6 33.6 4629.2 33.5 4714.9 34.3 4533.3 30.9 4500.0 36.4 4405.0 33.9 4750.8 33.6 4634.0 33.5 4723.3 34.4 4550.9 30.8 4503.2 36.4 4416.7 33.9 4751.0 33.6 4636.0 33.5 4731.6 34.3 4560.5 31.0 4503.7 36.4 4423.8 33.4 4751.1 33.8 4642.4 33.4 4746.6 34.3 4563.9 31.3 4504.6 36.4 4429.5 33.3 4751.3 33.7 4660.8 33.4 4747.4 34.4 4579.0 30.9 4505.8 36.3 4429.6 33.4 4751.4 33.9 4665.3 33.5 4747.4 34.4 4580.5 30.8 4507.7 36.4 4431.6 33.4 4751.8 33.9 4665.8 33.4 4751.9 34.4 4587.9 31.9 4509.6 36.3 4431.7 33.4 4752.4 33.8 4672.5 33.4 4753.6 34.2 4615.1 31.5 4510.2 36.1 4432.0 33.4 4752.5 33.8 4680.3 33.3 4754.1 34.0 4635.5 31.9 4511.0 36.3 4432.2 33.5 4752.8 33.8 4684.7 33.3 4755.0 34.0 4641.2 31.5 4511.0 36.3 4433.4 33.3 4753.9 33.8 4685.6 33.3 4755.3 34.2 4659.7 31.8 4511.2 36.4 4434.0 33.3 4754.2 33.9 4686.0 33.2 4755.7 34.0 4662.4 31.7 4511.5 36.3 4434.2 33.4 4754.6 33.8 4703.6 33.2 4756.4 34.1 4665.1 32.5 4511.9 36.2 4434.8 33.3 4754.9 33.7 4705.1 33.3 4756.8 34.2 4672.0 32.1 4512.3 36.3 4435.0 33.4 4754.9 33.9 4705.4 33.3 4756.9 33.9 4685.7 32.2 4512.3 36.3 4435.6 33.5 4755.6 33.7 4709.1 33.2 4757.4 34.3 4687.4 32.4 4512.8 36.3 4436.2 33.4 4755.7 33.8 4717.1 33.2 4757.7 34.0 4703.1 32.8 4512.9 36.2 4436.3 33.4 4757.8 33.8 4719.3 33.2 4758.8 34.2 4706.0 32.7 4513.1 36.2 4436.5 33.4 4758.9 33.8 4719.8 33.3 4758.9 34.0 4731.0 33.0 4514.5 36.3 4436.6 33.4 4759.0 33.8 4723.9 33.2 4759.6 33.7 4731.4 32.6 4515.8 36.3 4436.9 33.5 4759.0 33.8 4726.7 33.2 4760.5 33.9 4736.1 33.0 4522.7 36.2 4437.1 33.3 4759.1 33.6 4727.6 33.1 4761.0 34.0 4748.1 33.3 4531.3 35.7 4437.2 34.0 4759.2 33.7 4731.1 33.1 4761.5 33.9 4754.8 32.9 4550.3 35.6 4437.2 33.3 4759.6 33.6 4733.3 33.2 4761.9 34.2 4767.6 33.2 4566.9 35.6 4437.4 33.5 4760.2 33.7 4737.5 33.1 4762.1 34.0 4774.7 33.6 4582.2 35.6 4437.4 33.3 4761.4 33.7 4738.4 33.1 4764.1 34.0 4795.7 33.5 4595.9 35.6 4437.5 33.4 4764.3 33.7 4738.6 33.1 4765.8 34.0 4800.5 33.8 4608.8 35.6 4438.3 34.1 4771.9 33.3 4738.6 33.0 4766.3 33.9 4813.0 33.7

50

4623.4 35.6 4438.4 33.5 4785.1 33.3 4738.9 33.1 4767.5 34.0 4824.7 33.9 4634.1 35.6 4438.7 33.3 4793.1 33.3 4739.3 33.1 4768.2 33.9 4834.8 33.9 4646.0 35.6 4439.2 33.3 4802.1 33.3 4740.8 33.0 4768.7 34.2 4835.9 34.1 4656.6 35.7 4439.2 33.4 4822.3 33.3 4744.4 33.0 4768.9 34.0 4842.1 33.7 4661.0 35.7 4439.8 33.3 4842.1 33.3 4746.9 33.0 4769.8 33.9 4856.1 33.9 4667.9 35.6 4439.9 33.6 4857.1 33.4 4749.1 33.1 4771.8 34.0 4859.6 33.8 4674.2 35.5 4440.2 33.3 4859.4 33.4 4750.4 33.0 4771.9 33.9 4861.1 34.0 4679.7 35.5 4440.2 33.6 4872.9 33.3 4750.9 33.0 4777.2 33.6 4869.0 34.4 4685.3 35.5 4440.5 33.3 4891.4 33.3 4752.8 33.0 4800.5 33.6 4871.2 34.1 4688.4 35.4 4440.6 33.4 4903.4 33.3 4753.9 33.1 4809.3 33.6 4876.3 33.9 4693.5 35.4 4440.7 33.4 4913.5 33.4 4754.2 33.0 4817.4 33.5 4884.7 34.2 4700.1 35.4 4441.0 33.4 4925.1 33.4 4754.2 33.0 4830.8 33.4 4886.8 33.9 4702.8 35.4 4441.2 33.6 4930.0 33.4 4754.5 33.0 4850.4 33.4 4888.5 34.0 4710.5 35.3 4441.8 33.4 4956.6 33.4 4754.5 33.0 4862.1 33.4 4888.5 34.4 4711.0 35.3 4441.9 33.4 4969.7 33.5 4757.8 33.0 4866.2 33.4 4896.2 33.8 4714.2 35.3 4442.2 33.3 4978.3 33.6 4760.2 33.0 4874.5 33.3 4896.7 34.0 4719.0 35.3 4442.3 34.1 4988.3 33.6 4762.3 33.0 4881.1 33.2 4898.9 34.5 4723.2 35.3 4442.3 33.4 4991.1 33.6 4764.9 33.0 4900.1 33.1 4902.1 33.6 4723.4 35.3 4442.5 33.2 5006.1 33.5 4766.1 32.9 4904.9 33.1 4903.0 34.3 4725.5 35.2 4442.5 33.4 5011.8 33.5 4773.0 32.6 4909.4 32.9 4903.3 34.5 4727.8 35.2 4442.6 33.4 5013.7 33.5 4791.5 32.5 4909.5 33.2 4912.5 34.6 4729.1 35.2 4442.7 33.5 5017.1 33.6 4801.4 32.6 4922.7 32.8 4921.4 34.6 4729.7 35.1 4443.1 33.5 5019.1 33.5 4816.8 32.6 4929.3 32.9 4935.5 34.6 4729.7 35.2 4443.4 33.4 5027.2 33.5 4830.4 32.5 4938.7 32.8 4938.2 34.6 4730.1 35.2 4443.4 33.7 5036.4 33.5 4849.1 32.5 4944.7 32.8 4939.1 34.6 4730.9 35.1 4444.0 33.4 5037.1 33.5 4865.4 32.5 4946.6 32.7 4942.4 34.6 4734.5 35.1 4444.3 33.3 5039.6 33.5 4878.3 32.6 4966.0 32.7 4943.1 34.5 4735.0 35.1 4444.8 33.5 5041.3 33.5 4895.4 32.6 4970.3 32.6 5033.2 33.7 4736.8 35.0 4445.0 33.4 5045.7 33.4 4917.1 32.6 4970.4 32.7 5058.3 34.0 4738.2 35.1 4445.2 34.0 5047.5 33.4 4945.8 32.7 4972.8 32.6 5071.8 34.1 4738.9 35.1 4445.4 33.3 5048.3 33.4 4960.6 32.9 4975.1 32.5 5084.5 34.2 4739.6 35.2 4445.4 33.4 5050.1 33.3 4969.4 32.9 4988.1 32.4 5091.7 33.6 4739.8 35.2 4445.8 33.5 5050.4 33.4 4974.5 32.9 4993.8 32.4 5092.2 33.8 4740.2 35.3 4445.9 33.8 5052.2 33.4 4979.9 32.8 4995.4 32.3 5092.4 33.8 4740.6 35.3 4446.0 33.1 5055.5 33.3 4992.0 32.6 4997.0 32.4 5092.4 33.7 4740.8 35.1 4446.1 33.4 5056.9 33.2 4992.7 32.8 5000.0 32.5 5092.9 33.8 4744.0 35.0 4446.2 33.3 5057.4 33.3 4993.5 32.7 5003.1 32.2 5094.1 33.8 4758.3 34.3 4446.3 33.4 5057.6 33.3 4994.2 32.7 5014.7 32.2 5094.6 33.7 4781.2 34.4 4446.8 33.4 5057.6 33.2 4999.4 32.5 5015.4 32.1 5094.8 33.7 4796.7 34.4 4447.1 33.3 5058.4 33.3 5005.4 32.4 5016.4 32.3 5095.3 34.2 4815.3 34.5 4447.3 33.4 5059.7 33.2 5006.4 32.5 5017.8 32.3 5095.6 33.9

51

4830.6 34.6 4447.6 33.5 5060.8 33.3 5007.6 32.4 5019.7 32.2 5095.8 33.7 4846.2 34.6 4447.9 33.6 5062.4 33.3 5008.3 32.5 5025.5 32.1 5095.8 33.8 4863.6 34.6 4448.0 33.4 5064.5 33.3 5011.5 32.3 5026.4 32.0 5097.0 34.1 4877.4 34.8 4448.0 33.9 5064.9 33.2 5017.5 32.2 5027.1 32.1 5097.2 33.8 4891.4 34.9 4448.2 33.2 5065.2 33.2 5023.4 32.2 5027.5 31.9 5097.3 33.7 4900.4 35.0 4448.7 33.7 5066.6 33.1 5023.5 32.3 5028.0 32.0 5097.3 34.1 4909.4 35.1 4448.8 33.6 5067.2 33.1 5026.4 32.1 5034.3 31.9 5097.3 33.7 4921.4 35.2 4448.9 33.5 5068.4 33.3 5027.4 32.0 5034.6 31.9 5097.4 33.8 4928.1 35.3 4449.0 33.9 5068.5 33.3 5029.4 32.0 5039.8 32.0 5097.7 33.7 4936.9 35.3 4449.1 33.4 5073.0 33.2 5033.5 32.1 5040.6 31.9 5097.8 33.7 4945.1 35.4 4449.2 33.4 5073.3 33.3 5034.4 32.1 5041.1 31.8 5098.4 34.2 4949.6 35.4 4449.2 33.9 5073.5 33.2 5035.4 31.9 5041.7 31.9 5098.4 33.8 4954.2 35.4 4449.3 33.5 5073.8 33.3 5037.8 31.8 5045.7 31.4 5099.7 34.2 4954.9 35.4 4450.0 33.4 5075.1 33.1 5038.8 31.9 5048.7 31.9 5099.9 33.8 4955.1 35.5 4450.1 33.6 5075.2 33.3 5040.6 31.9 5051.3 31.9 5100.3 33.7 4955.1 35.4 4450.5 33.7 5075.5 33.3 5040.7 31.9 5052.7 31.8 5101.6 33.7 4959.9 35.3 4450.6 33.3 5075.6 33.2 5040.9 31.9 5066.9 31.3 5102.0 33.8 4964.0 35.1 4450.9 33.4 5081.5 33.1 5042.3 31.8 5084.4 31.2 5102.1 33.7 4964.1 35.3 4451.0 34.0 5090.0 33.0 5044.8 31.8 5093.3 31.1 5102.4 34.0 4965.2 35.3 4451.6 33.4 5101.9 32.9 5046.1 31.7 5105.7 31.0 5102.6 33.9 4965.3 35.3 4452.3 33.7 5119.0 32.8 5046.3 31.8 5109.9 30.8 5103.9 33.7 4966.0 35.2 4453.0 33.4 5131.0 32.8 5050.6 31.7 5125.2 30.6 5104.3 34.0 4966.1 35.4 4453.5 33.4 5133.5 32.7 5051.3 31.8 5142.5 30.5 5104.6 34.0 4966.4 35.2 4453.9 34.0 5139.6 32.6 5051.6 31.7 5155.4 30.5 5105.4 33.8 4966.4 35.2 4454.4 33.5 5151.8 32.6 5052.1 31.6 5160.5 30.4 5108.3 34.0 4966.6 35.3 4455.0 33.4 5166.9 32.5 5053.3 31.8 5171.9 30.3 5108.3 33.9 4966.7 35.2 4455.4 33.8 5180.5 32.5 5053.8 31.8 5185.8 30.2 5120.1 33.4 4966.7 35.2 4455.7 33.4 5188.6 32.5 5054.4 31.6 5201.0 30.1 5134.8 33.4 4967.4 35.2 4456.0 33.8 5193.2 32.4 5055.9 31.6 5218.4 30.1 5142.0 33.4 4967.6 35.2 4456.0 33.5 5199.8 32.4 5058.2 31.7 5231.4 30.1 5152.8 33.3 4967.8 35.4 4456.0 33.4 5207.7 32.3 5059.5 31.7 5242.6 30.1 5158.3 33.2 4969.0 35.2 4457.6 33.9 5218.2 32.2 5060.2 31.7 5256.0 30.1 5169.6 33.2 4969.0 35.2 4457.8 34.1 5227.4 32.2 5060.2 31.7 5266.7 30.0 5184.1 33.1 4969.1 35.2 4459.0 33.5 5239.2 32.1 5061.4 31.6 5282.4 30.1 5189.4 33.1 4969.2 35.2 4459.9 33.6 5239.5 32.2 5061.7 31.6 5298.0 30.1 5193.2 33.0 4969.4 35.4 4461.9 33.5 5243.4 32.1 5061.7 31.5 5306.1 30.1 5199.1 32.8 4969.4 35.2 4463.5 33.1 5250.9 32.0 5063.9 31.6 5318.7 30.2 5200.7 32.9 4969.8 35.1 4473.5 33.2 5253.4 31.9 5064.5 31.6 5325.7 30.2 5204.6 32.7 4969.8 35.1 4492.6 33.2 5267.9 31.9 5065.0 31.7 5332.8 30.2 5219.7 32.6 4970.3 35.2 4518.8 33.2 5272.8 31.9 5065.5 31.5 5334.3 30.2 5227.6 32.6 4970.5 35.2 4546.7 33.4 5275.6 31.8 5065.6 31.7 5338.0 30.1 5234.1 32.6

52

4970.6 35.1 4564.6 33.6 5279.3 31.8 5066.1 31.6 5344.1 30.0 5237.2 32.5 4970.9 35.1 4599.4 33.8 5285.8 31.7 5067.1 31.6 5353.2 30.0 5239.1 32.4 4971.1 35.2 4650.6 34.1 5286.7 31.7 5067.6 31.6 5353.2 30.1 5242.0 32.3 4971.6 35.1 4684.7 34.4 5286.7 31.6 5068.6 31.6 5353.3 30.1 5246.9 32.2 4971.8 35.2 4701.2 34.7 5298.7 31.5 5068.8 31.6 5354.4 29.9 5257.4 32.1 4971.8 35.2 4717.2 34.8 5305.1 31.5 5069.8 31.6 5354.7 29.9 5262.3 32.1 4972.2 35.3 4735.4 34.8 5308.4 31.5 5070.3 31.5 5356.2 29.9 5265.3 32.0 4981.3 34.7 4739.1 34.9 5309.7 31.6 5070.4 31.7 5358.4 29.8 5266.1 32.1 5000.9 34.6 4739.8 34.8 5311.7 31.5 5071.2 31.6 5364.4 29.8 5270.3 31.9 5020.8 34.6 4744.3 34.9 5315.8 31.4 5071.5 31.6 5368.0 29.7 5273.2 31.9 5039.2 34.7 4746.9 34.6 5316.6 31.4 5071.6 31.5 5368.1 29.8 5280.5 31.8 5052.6 34.8 4747.8 34.6 5322.8 31.3 5071.7 31.5 5371.9 29.8 5286.9 31.7 5064.1 34.9 4749.0 34.7 5330.2 31.3 5071.8 31.6 5372.3 29.9 5289.7 31.8 5075.3 34.9 4750.5 34.6 5333.4 31.3 5072.0 31.6 5372.5 29.8 5289.9 31.6 5089.9 34.8 4752.2 34.7 5334.3 31.3 5072.0 31.5 5373.8 29.8 5292.2 31.6 5103.9 34.9 4752.9 34.5 5335.3 31.3 5073.6 31.6 5375.7 29.6 5298.2 31.6 5113.4 34.9 4753.9 34.5 5336.6 31.2 5073.6 31.6 5377.9 29.6 5300.4 31.4 5118.2 34.9 4754.6 34.4 5339.9 31.2 5073.8 31.6 5382.1 29.7 5311.7 31.4 5120.8 34.9 4756.2 34.6 5344.5 31.2 5073.9 31.6 5383.8 29.7 5314.8 31.4 5126.9 34.8 4756.4 34.6 5351.7 31.2 5074.2 31.6 5384.1 29.7 5315.0 31.4 5138.2 34.7 4757.2 34.8 5352.7 31.2 5074.3 31.6 5385.4 29.8 5315.7 31.3 5141.9 34.7 4757.5 34.5 5354.3 31.1 5074.3 31.6 5385.7 29.7 5316.0 31.3 5144.3 34.7 4759.7 34.6 5354.6 31.2 5075.6 31.6 5387.4 29.7 5318.4 31.1 5148.2 34.6 4760.2 34.5 5355.5 31.2 5075.8 31.6 5387.9 29.7 5320.2 31.2 5150.6 34.6 4760.5 34.5 5356.5 31.1 5075.9 31.5 5393.3 29.2 5324.9 31.0 5155.5 34.6 4761.5 34.4 5362.4 31.1 5076.2 31.7 5404.0 29.1 5331.3 31.1 5161.6 34.5 4762.6 34.5 5368.0 31.1 5076.3 31.7 5422.4 29.0 5332.2 31.1 5165.7 34.5 4763.0 34.4 5368.9 31.1 5076.6 31.6 5434.3 28.9 5333.7 31.0 5166.2 34.5 4763.1 34.4 5372.0 31.1 5076.7 31.6 5435.1 28.7 5334.3 31.0 5167.2 34.4 4763.9 34.5 5372.2 31.2 5077.0 31.6 5448.2 28.5 5334.8 30.9 5167.3 34.5 4764.5 34.4 5372.9 31.1 5077.5 31.6 5456.8 28.3 5338.6 30.9 5175.6 34.4 4765.6 34.4 5372.9 31.1 5078.1 31.6 5471.0 28.2 5344.2 30.9 5176.1 34.4 4765.7 34.5 5374.5 31.1 5078.3 31.6 5485.5 28.1 5346.6 30.9 5177.8 34.3 4767.8 34.5 5376.0 31.1 5078.3 31.6 5494.9 28.0 5349.9 30.9 5177.9 34.3 4769.0 34.4 5377.4 31.1 5079.1 31.7 5497.4 27.9 5351.5 30.9 5178.4 34.3 4770.1 34.4 5377.9 31.0 5079.1 31.6 5504.0 27.7 5353.3 30.9 5180.2 34.3 4771.0 34.4 5382.0 31.1 5079.6 31.6 5520.9 27.6 5353.5 30.8 5180.4 34.3 4773.4 34.5 5382.1 31.1 5080.8 31.8 5526.8 27.2 5368.4 30.4 5182.5 34.2 4774.1 34.5 5383.5 31.1 5081.0 31.8 5532.1 27.7 5378.1 30.2 5182.9 34.2 4774.4 34.4 5390.4 30.6 5081.2 31.7 5552.2 27.2 5393.8 30.1 5186.0 34.1 4774.8 34.2 5408.2 30.6 5081.3 31.6 5563.5 27.3 5402.6 30.0

53

5186.1 34.3 4778.2 34.4 5424.0 30.5 5081.4 31.6 5574.3 27.2 5407.1 29.8 5186.3 34.3 4783.2 34.2 5441.7 30.6 5082.0 31.8 5582.1 27.1 5410.6 29.5 5186.5 34.2 4794.5 34.1 5456.8 30.6 5082.2 31.6 5586.3 27.2 5422.1 29.4 5186.5 34.1 4811.4 34.0 5469.5 30.5 5082.5 31.7 5597.2 26.9 5441.6 29.2 5187.3 34.1 4821.4 34.0 5485.9 30.5 5082.8 31.7 5606.1 26.9 5455.1 29.2 5189.6 34.2 4827.3 34.0 5496.9 30.4 5082.9 31.6 5612.6 26.8 5466.8 29.1 5189.9 34.1 4834.6 33.9 5519.7 30.4 5083.3 31.8 5626.3 26.8 5473.0 28.9 5190.3 34.1 4843.5 33.8 5540.6 30.5 5083.6 31.7 5632.6 26.9 5480.6 28.8 5195.3 34.1 4856.9 33.7 5559.8 30.5 5083.7 31.6 5666.8 27.0 5491.4 28.7 5205.5 33.4 4863.5 33.8 5579.6 30.6 5084.2 31.7 5668.8 26.9 5502.0 28.6 5221.1 33.3 4872.9 33.7 5598.4 30.7 5084.3 31.8 5778.4 28.0 5511.2 28.5 5235.0 33.3 4884.2 33.7 5614.8 30.8 5084.5 31.5 5857.1 29.9 5515.0 28.4 5251.1 33.3 4901.3 33.6 5635.8 30.9 5084.7 31.9 5992.7 31.2 5524.9 28.2 5267.3 33.2 4911.8 33.7 5658.1 31.1 5085.1 31.7 6159.8 32.9 5534.8 28.1 5275.2 33.1 4914.9 33.6 5679.3 31.2 5085.1 31.7 6433.4 35.0 5538.8 28.0 5280.6 32.9 4917.6 33.5 5680.7 31.4 5085.5 31.8 6506.2 35.4 5549.8 27.9 5288.6 32.8 4925.2 33.5 5681.6 31.3 5085.9 31.8 6585.6 36.1 5563.6 27.9 5298.8 32.7 4942.7 33.4 5681.8 31.3 5086.6 31.6 6631.9 36.3 5575.4 27.9 5311.4 32.6 4947.9 33.5 5683.2 31.4 5086.7 31.8 6668.7 36.7 5589.4 27.7 5316.6 32.5 4949.2 33.4 5683.9 31.4 5086.7 31.8 6674.3 36.6 5589.7 27.9 5319.4 32.3 4953.8 33.4 5684.8 31.4 5087.7 31.7 6703.7 36.8 5593.5 27.9 5325.8 32.2 4955.8 33.3 5685.1 31.4 5087.7 31.7 6729.6 37.0 5601.5 27.6 5331.4 32.1 4970.4 33.2 5688.3 31.4 5088.1 31.9 6739.5 36.9 5610.9 27.6 5340.0 32.0 4977.4 33.3 5689.7 31.4 5088.6 31.8 6753.9 37.0 5854.3 28.9 5345.2 31.9 4981.0 33.3 5690.6 31.5 5089.2 31.7 6771.0 37.3 5931.9 29.9 5349.3 31.8 4982.7 33.3 5691.4 31.5 5090.0 31.8 6781.3 37.2 6045.1 31.8 5350.8 31.8 4985.3 33.2 5691.7 31.5 5090.2 31.8 6788.4 37.2 6137.2 32.7 5360.9 31.7 4994.1 33.1 5694.4 31.6 5090.3 31.8 6812.3 37.4 6334.7 34.8 5364.5 31.6 4999.5 33.1 5694.8 31.5 5090.8 31.8 6819.9 37.3 6730.2 37.7 5366.8 31.5 5005.1 33.1 5696.3 31.4 5092.3 31.6 6823.0 37.4 6943.3 39.3 5367.5 31.5 5008.1 33.1 5696.9 31.4 5093.6 31.7 6845.5 37.5 6967.4 39.4 5374.2 31.5 5008.3 33.1 5698.5 31.6 5099.4 31.5 6870.9 37.6 7301.0 41.5 5382.6 31.4 5013.1 33.0 5705.3 31.5 5104.0 31.4 6889.5 37.8 7342.4 41.9 5382.9 31.4 5022.2 33.0 5711.2 31.6 5119.2 31.2 6938.2 37.9 7362.2 41.8 5383.8 31.4 5023.0 33.1 5713.1 31.6 5132.3 31.1 6963.2 37.8 7416.7 42.1 5385.8 31.4 5023.7 33.0 5720.3 31.5 5144.2 31.1 6968.6 37.6 7427.6 42.0 5390.6 31.2 5024.3 33.1 5720.8 31.9 5154.0 31.0 6986.6 37.6 7477.1 42.2 5390.8 31.2 5030.0 32.9 5725.2 31.9 5158.1 30.7 7001.0 37.6 7484.4 42.4 5392.4 31.3 5033.2 32.9 5726.1 31.9 5170.9 30.6 7066.7 38.1 7490.3 42.1 5394.0 31.3 5037.5 32.9 5727.6 31.6 5185.0 30.5 7130.5 38.6 7525.9 42.3 5395.0 31.1 5037.9 33.0 5731.0 31.9 5190.0 30.4 7184.2 39.0 7530.6 42.4

54

5398.1 31.0 5040.8 32.9 5735.8 31.9 5195.3 30.3 7231.9 39.2 7538.7 42.4 5399.1 31.1 5042.6 32.9 5737.2 32.0 5202.9 30.1 7279.3 38.8 7570.1 42.4 5399.8 31.0 5052.2 32.9 5742.1 32.0 5204.0 30.2 7330.0 38.0 7571.5 42.2 5401.1 31.1 5052.4 32.9 5742.7 32.0 5213.9 30.0 7365.8 38.3 7577.8 42.3 5402.0 30.8 5053.7 32.9 5751.3 32.1 5226.4 29.9 7398.4 38.4 7713.8 41.9 5403.1 30.8 5053.9 32.9 5756.5 32.1 5237.5 29.9 7431.0 38.5 7763.8 42.1 5403.7 31.0 5057.3 32.9 5760.5 32.2 5243.8 29.9 7467.4 38.5 7793.9 42.2 5403.9 30.9 5070.1 32.9 5762.8 32.0 5248.9 29.8 7497.2 38.5 7831.2 42.1 5406.2 30.9 5075.5 32.7 5769.0 32.3 5253.9 29.7 7523.5 38.4 7859.1 41.9 5408.1 30.8 5088.4 32.6 5777.4 32.3 5259.6 29.6 7534.5 38.3 7939.4 41.2 5411.2 30.9 5102.6 32.5 5778.7 32.3 5262.8 29.5 7547.2 38.1 7996.9 41.3 5411.8 30.9 5121.5 32.4 5779.4 32.3 5271.6 29.4 7549.8 37.5 8021.6 41.2 5412.4 30.9 5142.3 32.4 5784.2 32.4 5271.8 29.4 7582.0 37.0 8026.9 41.0 5414.0 30.8 5160.9 32.4 5788.0 32.4 5282.9 29.3 7590.5 37.1 8103.1 40.6 5418.8 30.1 5172.5 32.4 5791.5 32.4 5291.4 29.3 7595.7 37.0 8125.8 40.7 5437.1 29.9 5186.5 32.4 5795.3 32.4 5297.7 29.3 7603.1 37.0 8222.3 39.1 5458.7 29.9 5197.2 32.3 5798.6 32.4 5300.4 29.3 7608.6 37.1 8228.6 39.1 5477.9 29.9 5212.0 32.3 5816.4 31.6 5306.3 29.2 7615.0 37.1 8232.5 39.1 5488.0 29.8 5231.7 32.2 5839.0 31.7 5307.7 29.2 7616.4 36.8 8234.0 39.1 5498.7 29.8 5244.7 32.3 5857.6 31.8 5315.4 29.0 7616.9 36.7 8234.7 39.0 5514.9 29.8 5256.5 32.3 5874.6 31.8 5316.8 29.1 7618.6 36.7 8240.0 39.0 5534.1 29.8 5270.1 32.3 5887.9 31.9 5316.9 29.1 7621.0 36.7 8240.2 38.8 5541.5 29.8 5280.3 32.4 5901.5 31.9 5317.8 28.9 7623.4 36.7 8244.1 39.1 5546.3 29.8 5292.8 32.3 5909.5 31.9 5328.2 28.8 7625.4 36.7 8245.9 38.9 5556.2 29.8 5303.1 32.4 5918.6 31.9 5334.3 28.9 7762.1 36.7 8246.1 39.0 5568.4 29.7 5318.1 32.4 5927.4 31.8 5335.9 28.8 7798.7 36.8 8246.8 39.1 5570.1 29.6 5330.8 32.5 5933.9 31.8 5337.7 28.8 7841.3 37.0 8246.9 38.9 5573.5 29.6 5342.2 32.6 5937.0 31.7 5338.1 28.8 7871.3 37.3 8247.1 38.9 5583.9 29.6 5348.8 32.6 5940.9 31.7 5340.9 28.7 7885.1 37.5 8248.2 39.0 5589.5 29.4 5354.6 32.6 5944.6 31.6 5342.5 28.7 7917.0 37.6 8248.3 39.0 5593.5 29.5 5361.3 32.6 5948.3 31.6 5346.5 28.7 7924.0 37.6 8248.4 38.8 5594.8 29.4 5364.8 32.6 5954.3 31.6 5352.8 28.6 7924.0 37.7 8248.7 39.0 5605.3 29.4 5372.4 32.6 5957.7 31.6 5355.5 28.6 7924.9 37.6 8250.7 38.9 5607.9 29.3 5380.0 32.6 5963.1 31.5 5355.8 28.7 7925.0 37.6 8251.0 39.0 5607.9 29.3 5380.0 32.6 5966.7 31.5 5356.1 28.6 7927.2 37.7 8252.3 39.0 5608.8 29.3 5383.0 32.7 5968.8 31.5 5358.0 28.5 7927.2 37.7 8252.4 39.0 5611.1 29.1 5383.7 32.6 5972.6 31.4 5358.6 28.7 7927.5 37.6 8252.4 39.1 5615.3 29.1 5385.8 32.6 5972.8 31.4 5360.7 28.5 7929.4 37.6 8252.5 39.1 5617.3 28.9 5387.0 32.6 5980.3 31.4 5360.7 28.4 7929.4 37.6 8254.9 39.0 5619.3 29.2 5387.9 32.6 5983.3 31.3 5362.9 28.5 7930.9 37.7 8256.2 38.8 5621.0 29.0 5396.1 32.6 5984.8 31.3 5364.5 28.4 7935.5 37.7 8258.5 39.0

55

5624.8 28.9 5396.7 32.6 5985.0 31.4 5366.1 28.5 7936.0 37.7 8260.7 38.9 5626.8 28.8 5398.1 32.6 5989.9 31.3 5367.2 28.4 7937.5 37.8 8261.6 38.5 5627.0 28.6 5398.8 32.5 5990.3 31.3 5367.3 28.5 7937.7 37.7 8264.2 39.0 5627.5 28.7 5400.4 32.6 5991.6 31.2 5370.3 28.5 7938.7 37.6 8266.5 38.9 5627.8 28.9 5400.5 32.6 5991.7 31.2 5372.9 28.4 7939.5 37.7 8267.5 39.0 5628.1 29.0 5400.5 32.6 5991.9 31.2 5387.5 28.0 7939.9 37.6 8268.8 39.0 5631.0 28.9 5401.1 32.7 5994.5 31.1 5405.3 28.0 7942.4 37.7 8294.2 38.5 5633.5 28.5 5401.9 32.6 5996.2 31.1 5416.4 27.8 7944.6 37.6 8299.7 38.5 5634.6 29.0 5402.7 32.7 5996.5 31.1 5431.9 27.7 7949.3 37.8 8324.7 38.6 5635.1 29.0 5403.3 32.7 6000.6 31.0 5438.2 27.5 7953.6 37.9 8359.3 38.7 5635.2 28.8 5404.1 32.6 6000.6 31.1 5444.1 27.3 7956.4 38.0 8361.1 38.7 5635.4 28.7 5404.9 32.6 6004.4 31.1 5468.1 27.2 7957.3 38.1 8381.3 38.8 5636.3 28.7 5405.9 32.7 6006.2 31.1 5489.3 27.2 7969.3 38.2 8410.7 38.7 5636.3 28.6 5406.9 32.3 6008.2 31.0 5502.4 27.2 7974.6 38.3 8412.2 38.8 5636.7 28.6 5425.4 32.2 6008.5 31.0 5516.1 27.1 7977.1 38.3 8445.2 38.9 5637.0 28.8 5442.7 32.2 6009.6 31.1 5526.3 27.1 7981.6 38.3 8466.2 39.0 5637.4 28.6 5454.5 32.1 6011.0 31.0 5538.6 27.0 7984.1 38.4 8474.8 39.1 5637.8 28.7 5470.0 32.1 6015.5 31.1 5549.6 26.9 7997.7 38.4 8509.9 39.3 5638.1 28.6 5478.7 32.1 6016.6 31.1 5562.6 26.9 8002.3 38.4 8511.7 39.2 5638.1 28.7 5488.8 31.9 6020.7 30.7 5568.4 26.8 8088.5 38.5 8519.1 39.3 5638.9 28.7 5496.3 31.8 6031.9 30.6 5662.9 27.5 8113.6 38.5 8532.3 39.3 5638.9 28.6 5509.2 31.8 6045.1 30.5 5667.7 27.5 8123.4 38.8 8538.6 39.3 5639.0 28.5 5525.0 31.7 6064.1 30.3 5685.0 27.4 8143.4 39.4 8550.6 39.4 5639.5 28.7 5533.8 31.7 6078.8 30.3 5685.5 27.5 8160.3 39.0 8558.0 39.4 5639.5 28.6 5542.7 31.6 6090.5 30.2 5701.8 28.0 8187.8 39.4 8561.5 39.4 5639.7 28.7 5546.1 31.6 6108.9 30.2 5704.5 27.9 8192.9 39.8 8567.1 39.4 5640.0 28.7 5550.4 31.4 6127.0 30.2 5783.9 29.0 8204.6 39.6 8569.0 39.4 5640.0 28.6 5559.1 31.3 6138.2 30.2 5803.6 29.2 8232.6 39.9 8576.3 39.4 5640.1 28.7 5563.9 31.3 6147.3 30.1 5809.1 29.3 8245.6 39.9 8580.4 39.4 5640.4 28.8 5569.2 31.2 6160.6 30.0 5817.6 29.5 8246.4 40.2 8584.9 39.4 5642.8 28.6 5575.4 31.1 6174.3 30.0 5819.4 29.4 8272.2 40.7 8587.6 39.5 5643.5 28.5 5582.1 31.0 6181.8 29.9 5827.1 29.6 8275.3 40.2 8788.9 39.5 5643.9 28.7 5590.4 31.0 6196.9 29.9 5842.9 29.8 8277.1 40.5 8811.2 39.8 5643.9 28.5 5596.3 30.9 6212.0 29.9 5934.9 30.6 8292.2 40.4 8834.1 39.8 5644.1 28.6 5600.4 30.9 6222.9 29.9 5953.8 30.7 8326.6 41.0 8844.8 39.9 5644.5 28.6 5602.2 30.7 6232.7 29.9 5959.0 30.7 8336.1 40.7 8845.4 39.8 5646.4 28.8 5602.6 30.8 6245.9 29.9 5960.9 30.8 8362.8 40.7 8854.5 40.0 5646.5 28.7 5608.6 30.6 6256.3 29.9 5964.5 30.9 8364.4 41.0 8854.7 40.1 5647.0 28.1 5616.6 30.6 6260.8 29.9 5980.3 31.1 8373.3 41.0 8861.2 40.1 5647.5 28.7 5619.9 30.5 6262.9 29.8 5988.9 31.2 8375.9 41.1 8870.3 40.1 5647.9 28.7 5622.1 30.5 6274.4 29.8 6038.7 31.6 8389.6 41.1 8870.9 40.1

56

5648.0 28.6 5623.7 30.4 6281.9 29.8 6061.2 31.7 8412.0 41.2 8874.2 40.2 5650.2 28.8 5623.9 29.8 6287.0 29.8 6062.5 31.8 8416.4 41.3 8878.3 40.3 5650.5 28.8 5628.8 30.4 6296.3 29.9 6064.3 31.8 8425.5 41.2 8885.3 40.3 5650.5 28.8 5636.0 30.3 6297.1 29.8 6066.0 31.9 8426.0 41.3 8898.1 40.5 5653.9 28.7 5638.7 30.3 6305.3 29.8 6075.7 31.9 8426.9 41.4 8905.7 40.4 5666.9 27.7 5641.4 30.3 6308.7 29.8 6099.9 32.0 8435.8 41.2 8910.7 40.5 5693.3 27.8 5647.4 30.3 6314.5 29.8 6100.0 32.1 8437.0 41.2 8918.8 40.7 5726.4 28.1 5647.8 30.3 6331.9 29.8 6128.0 32.3 8442.6 41.1 8931.7 40.6 5743.3 28.4 5651.6 30.2 6334.5 29.8 6129.3 32.4 8447.7 41.2 8936.8 40.6 5757.5 28.6 5653.8 30.1 6335.8 29.9 6133.4 32.4 8451.1 41.4 8949.0 41.0 5778.2 28.7 5655.0 29.9 6335.8 29.8 6135.4 32.5 8453.5 41.2 8962.0 40.9 5789.1 28.8 5671.4 29.5 6337.1 29.9 6135.7 32.4 8461.1 41.3 8966.3 40.9 5795.1 28.9 5676.4 29.6 6338.1 29.8 6148.2 32.6 8463.5 41.4 8973.8 41.1 5810.1 28.9 5692.9 29.4 6339.9 29.9 6155.3 32.6 8465.0 42.1 8975.5 41.1 5822.4 28.9 5716.0 29.3 6341.5 29.7 6174.2 32.7 8468.2 42.1 8977.1 41.1 5823.7 29.1 5733.1 29.2 6342.5 29.9 6176.1 32.7 8487.4 42.1 8978.0 41.1 5831.4 29.0 5750.4 29.2 6343.3 29.9 6180.7 32.7 8499.7 42.0 8978.3 41.1 5836.8 29.2 5777.7 28.9 6344.4 29.8 6180.7 32.9 8503.5 42.2 8998.2 41.1 5836.8 29.1 5798.9 28.9 6345.8 29.7 6181.2 32.7 8551.8 42.1 8999.6 41.1 5844.6 29.0 5813.9 28.8 6360.0 29.4 6185.6 32.9 8606.6 42.6 9004.1 41.1 5844.6 28.9 5830.5 28.8 6382.4 29.3 6205.8 33.0 8644.1 42.9 9167.3 41.2 5848.7 29.0 5842.9 28.8 6409.6 29.3 6206.8 33.0 8699.3 43.2 9183.3 41.2 5851.1 29.0 5860.4 28.7 6447.7 29.5 6212.5 33.0 8715.0 43.5 9184.9 41.2 5851.9 29.0 5868.3 28.7 6473.1 29.7 6212.6 33.0 8776.1 43.8 9185.6 41.2 5854.6 28.6 5884.4 28.6 6499.2 29.7 6216.8 33.0 8798.6 44.1 9187.8 41.2 5872.2 28.9 5893.8 28.6 6531.7 29.9 6220.2 33.1 8831.1 44.2 9188.8 41.2 5876.6 28.9 5906.2 28.6 6572.7 30.2 6220.9 33.2 8861.7 44.4 9197.6 41.3 6027.9 29.1 5918.8 28.6 6606.4 30.7 6240.6 33.2 9130.9 45.0 9207.0 41.3 6033.5 29.5 5931.8 28.6 6607.5 30.7 6243.9 33.3 9136.4 45.0 9212.2 41.4 6228.7 30.1 5941.9 28.6 6610.4 30.6 6248.7 33.2 9154.7 45.0 9214.2 41.6 6302.1 32.0 5945.5 28.6 6610.9 30.9 6249.6 33.2 9161.8 45.2 9227.0 41.6 6315.6 32.2 5955.4 28.5 6633.6 31.1 6251.3 33.4 9171.9 45.2 9245.3 41.7 6485.1 32.9 5964.8 28.6 6639.2 31.2 6254.1 33.3 9189.6 45.2 9246.5 41.8 6487.4 32.4 6254.6 29.9 6644.5 31.2 6255.6 33.4 9414.6 43.4 9248.3 41.9 6487.8 32.8 6448.9 31.9 6644.8 31.2 6268.9 33.3 9420.4 43.3 9250.3 41.8 6488.0 32.6 6532.9 32.6 6646.4 31.3 6273.9 33.4 9431.8 43.2 9252.6 41.9 6498.4 32.7 6564.2 32.8 6652.9 31.4 6274.6 33.0 9434.1 43.3 9260.1 41.9 6505.9 32.8 6589.3 32.9 6661.2 31.4 6276.2 33.4 9434.8 43.3 9260.7 41.9 6514.3 32.9 6599.5 32.5 6672.4 31.5 6278.4 33.4 9444.7 43.3 9271.8 41.8 6515.2 33.3 6601.4 32.8 6676.5 31.6 6280.3 33.2 9448.2 43.2 9273.7 41.8 6519.6 33.5 6712.2 31.3 6681.3 31.7 6283.0 33.4 9453.8 43.2 9277.0 41.9

57

6521.9 33.5 6800.8 32.5 6691.9 31.8 6283.9 33.6 9454.2 43.3 9279.7 41.8 6522.5 33.4 7123.7 43.7 6703.1 31.5 6287.2 33.6 9458.2 43.2 9283.5 41.9 6526.2 33.4 7188.4 45.9 6708.1 32.0 6289.3 33.6 9459.3 43.0 9290.4 42.0 6529.2 33.1 7200.3 45.9 6727.5 32.2 6289.5 33.5 9468.0 43.0 9413.8 41.9 6529.6 33.3 7364.1 47.2 6736.5 32.3 6297.9 33.5 9472.9 43.0 9480.3 42.0 6531.5 33.1 7372.1 47.3 6753.1 32.4 6301.4 33.5 9476.8 43.1 9483.4 42.3 6532.7 33.6 7507.0 48.1 6755.3 32.3 6304.3 32.5 9479.3 43.0 9505.5 42.3 6554.0 33.7 7516.9 48.0 6756.2 32.3 6306.2 33.5 9482.5 42.9 9506.6 42.3 6613.5 35.1 7623.1 48.3 6756.8 32.3 6309.0 33.6 9483.0 42.9 9508.8 42.4 6741.8 36.2 7633.5 48.6 6757.3 32.2 6337.7 32.4 9485.8 43.0 9511.2 42.4 6852.6 38.2 7639.2 48.5 6764.6 32.3 6337.8 32.4 9488.6 42.9 9512.1 42.4 6908.2 40.7 7839.4 48.5 6765.3 32.3 6338.1 32.4 9488.7 42.9 9515.7 42.4 7009.8 43.2 7918.5 48.8 6811.7 34.8 6338.4 32.5 9489.7 42.8 9521.4 42.4 7126.9 46.9 8012.6 48.7 6961.2 36.2 6338.5 32.5 9492.6 42.8 9524.2 42.5 7311.9 48.5 8158.6 47.8 7088.4 37.5 6340.0 32.5 9495.1 43.0 9528.4 42.6 7459.0 48.4 8263.3 47.2 7389.7 42.8 6340.2 32.3 9495.3 42.9 9535.3 42.6 7611.5 48.4 8566.7 46.8 7547.2 43.8 6340.2 32.5 9497.2 42.9 9545.0 42.6 7824.0 48.2 8751.8 44.6 7606.9 44.2 6340.3 32.5 9497.2 42.8 9545.5 42.8 8062.2 48.2 8753.5 44.8 7715.9 44.9 6340.4 32.3 9498.5 43.0 9557.2 42.7 8252.9 47.5 8785.7 44.8 7756.3 45.2 6340.7 32.4 9501.8 42.8 9561.3 42.8 8690.0 46.2 8789.6 44.8 7921.8 46.3 6342.0 32.4 9502.0 42.8 9570.9 42.9 8784.3 45.7 8816.0 44.9 7941.3 46.4 6342.1 32.5 9502.0 42.9 9577.3 43.0 8958.4 44.8 8824.1 44.9 8013.6 46.8 6342.3 32.4 9503.5 42.7 9580.5 43.0 9022.5 44.6 8842.1 45.0 8025.2 46.8 6342.9 32.3 9504.0 42.8 9585.0 43.0 9032.7 44.1 8844.6 45.0 8139.3 47.5 6342.9 32.6 9506.3 43.0 9591.5 43.0 8845.7 44.9 8144.7 47.5 6343.0 32.5 9508.5 42.7 9602.5 43.0 8848.7 45.0 8161.0 47.5 6343.2 32.5 9508.7 42.7 9613.0 43.1 8856.2 44.9 8222.2 47.7 6343.6 32.4 9509.1 43.0 9763.5 42.8 8865.8 44.9 8547.9 46.7 6343.7 32.4 9510.5 42.7 9773.5 42.8 8872.3 44.8 8596.7 46.8 6343.9 32.3 9511.4 42.8 9777.8 42.8 8874.1 44.9 8691.6 45.7 6344.2 32.4 9513.9 42.9 9798.0 42.8 8874.5 44.9 8751.5 45.8 6344.5 32.4 9514.2 42.6 9805.1 42.8 8875.2 44.9 8767.5 45.9 6345.1 32.3 9514.9 42.9 9805.5 42.6 8876.7 44.9 8843.3 44.9 6345.5 32.5 9514.9 42.8 9821.9 42.7 8879.0 44.8 8863.9 45.0 6346.2 32.4 9515.4 42.8 9822.6 42.6 8881.5 44.8 8929.4 45.1 6346.5 32.4 9515.5 42.6 9823.8 42.6 8882.2 44.7 8952.4 45.3 6346.6 32.4 9517.6 42.7 9828.8 42.6 8884.9 44.7 9092.3 43.2 6347.6 32.4 9517.6 42.7 9834.0 42.6 8890.0 44.8 9104.5 43.1 6347.7 32.5 9518.6 42.7 9834.1 42.5 8890.5 44.8 9105.8 43.2 6351.9 32.5 9518.7 42.7 9834.3 42.4 8891.5 44.6 9108.5 43.1 6369.5 31.8 9519.6 42.8 9834.5 42.4

58

8892.3 44.8 9113.2 43.0 6375.6 31.9 9520.1 42.6 9835.2 42.5 8894.3 44.9 9119.1 43.1 6385.4 32.0 9520.1 42.7 9835.3 42.5 8894.8 44.7 9120.9 43.0 6394.7 32.0 9520.4 42.7 9835.9 42.5 8897.2 44.7 9130.6 43.0 6417.5 32.0 9521.7 42.8 9836.1 42.6 8898.6 44.8 9137.0 42.9 6430.9 32.0 9522.1 42.7 9836.6 42.4 8900.7 44.9 9139.0 42.9 6446.6 32.0 9522.4 42.6 9837.5 42.5 8901.2 44.7 9146.2 42.9 6462.4 32.0 9522.4 42.9 9838.6 42.5 8909.7 44.8 9153.5 42.8 6474.0 31.9 9524.4 42.7 9840.7 42.5 8910.4 44.7 9153.6 42.9 6485.2 31.9 9524.7 42.8 9840.7 42.5 8915.3 44.5 9165.2 42.9 6502.9 31.9 9525.5 42.7 9840.9 42.6 8915.4 44.7 9171.1 42.9 6511.1 31.9 9525.7 42.7 9841.6 42.5 8932.9 44.6 9173.2 42.8 6521.6 31.9 9526.0 42.6 9841.6 42.6 8945.1 44.5 9173.7 42.8 6532.0 31.8 9530.3 42.7 9842.1 42.5 8951.4 44.4 9175.9 42.8 6549.9 31.9 9530.4 42.6 9843.0 42.3 8966.8 44.4 9185.4 42.8 6558.0 31.9 9530.9 42.8 9843.2 42.4 8979.0 44.4 9187.5 42.8 6568.2 31.8 9531.9 42.9 9843.5 42.5 9001.1 44.5 9189.1 42.8 6586.6 31.9 9532.7 42.7 9843.7 42.4 9009.5 44.4 9191.9 42.8 6603.4 32.0 9533.3 42.7 9844.0 42.6 9023.3 44.4 9194.3 42.8 6608.0 32.0 9536.9 42.7 9844.1 42.4 9034.7 44.4 9195.0 42.8 6625.9 32.1 9538.1 42.7 9845.3 42.5 9049.4 44.4 9196.5 42.7 6637.1 32.0 9538.3 42.8 9846.0 42.5 9063.7 44.4 9199.6 42.7 6638.5 32.1 9539.0 42.7 9846.5 42.5 9081.4 44.5 9204.1 42.7 6638.6 32.0 9539.8 42.7 9846.9 42.4 9082.6 44.4 9206.4 42.7 6642.1 32.0 9540.4 42.4 9849.7 42.4 9096.5 44.5 9212.5 42.6 6642.9 32.2 9540.5 42.7 9850.3 42.4 9101.9 44.4 9220.3 42.5 6653.4 32.4 9544.9 42.7 9850.6 42.4 9106.6 44.5 9239.3 42.5 6656.7 32.4 9546.2 42.7 9851.5 42.3 9117.7 44.4 9250.8 42.4 6658.1 32.4 9551.6 42.8 9852.1 42.5 9119.7 44.4 9262.7 42.4 6668.9 32.4 9551.9 42.7 9852.2 42.4 9120.0 44.4 9293.4 42.4 6669.2 32.5 9561.4 42.4 9852.4 42.4 9128.3 44.2 9328.4 42.4 6674.1 32.5 9566.7 42.5 9852.9 42.3 9128.5 44.3 9346.6 42.5 6680.3 32.6 9587.6 42.4 9853.2 42.4 9136.9 44.3 9355.7 42.5 6683.3 32.6 9600.0 42.4 9853.9 42.5 9138.5 44.2 9371.4 42.6 6685.8 32.6 9612.9 42.3 9854.1 42.4 9146.3 44.3 9386.1 42.5 6688.2 32.6 9626.9 42.3 9854.1 42.5 9152.8 44.1 9394.2 42.5 6690.1 32.7 9639.2 42.3 9854.6 42.5 9154.2 44.2 9404.1 42.5 6693.2 32.6 9640.7 42.2 9855.3 42.6 9162.8 44.1 9412.6 42.5 6693.8 32.6 9649.8 42.1 9856.2 42.1 9164.0 44.1 9419.6 42.5 6694.2 32.7 9654.4 42.0 9856.4 42.5 9164.0 44.1 9432.5 42.5 6708.6 33.0 9662.2 42.2 9856.6 42.5 9164.7 44.2 9436.1 42.4 6865.8 35.0 9669.6 42.0 9857.4 42.6

59

9172.3 44.2 9448.6 42.5 6880.8 34.7 9684.3 42.0 9857.9 42.5 9173.3 44.1 9449.2 42.4 7049.1 36.7 9696.4 41.8 9859.8 42.5 9174.8 44.1 9456.0 42.4 7057.7 37.0 9703.5 41.9 9859.8 42.5 9175.8 44.0 9460.2 42.3 7257.2 38.6 9705.6 41.8 9860.6 42.4 9175.8 44.2 9461.4 42.3 7287.1 39.0 9721.6 41.7 9864.4 42.1 9182.2 44.1 9463.9 42.3 7442.7 40.3 9724.2 41.9 9865.5 42.1 9182.3 44.1 9472.4 42.3 7502.7 40.9 9736.5 41.7 9899.7 42.1 9185.6 44.1 9477.1 42.4 7651.1 41.9 9742.3 41.6 9910.4 42.1 9185.8 44.0 9483.7 42.3 7698.2 42.5 9744.7 41.7 9931.1 42.1 9189.5 44.0 9487.4 42.3 7840.4 43.3 9746.9 41.7 9941.2 42.1 9194.2 44.1 9488.8 42.3 7882.1 43.8 9747.5 41.8 9942.2 42.1 9195.4 44.0 9495.7 42.3 7983.6 44.4 9761.8 41.6 9958.6 42.0 9195.7 44.1 9497.5 42.1 8040.6 44.8 9768.6 41.7 9974.5 42.0 9195.9 44.0 9498.0 42.3 8107.3 45.3 9774.1 41.5 9983.7 41.9 9202.0 44.0 9499.9 42.1 8151.1 45.6 9774.4 41.5 9988.2 41.9 9204.1 43.7 9502.6 42.1 8227.4 45.9 9776.1 41.5 9992.7 42.0 9206.5 44.0 9503.8 42.2 8237.1 46.3 9782.0 41.6 10014.7 41.9 9207.4 44.0 9505.3 42.1 8297.4 46.5 9784.2 41.6 10022.8 41.9 9208.5 44.0 9506.5 42.3 8333.2 46.7 9788.8 41.6 10027.7 41.9 9213.7 44.0 9506.7 42.2 8360.4 46.8 9791.3 41.4 10031.9 41.9 9214.4 44.0 9509.8 42.1 8519.2 47.6 9795.6 41.4 10047.6 41.9 9218.2 43.8 9510.8 42.2 8561.8 47.8 9796.8 41.6 10054.0 41.8 9222.4 43.6 9512.9 42.2 8578.8 47.7 9798.0 41.4 10070.7 41.8 9239.3 43.6 9512.9 42.3 8605.1 47.4 9803.9 41.4 10075.4 41.7 9245.9 43.5 9520.0 42.1 8739.4 47.0 9804.1 41.5 10078.1 41.7 9262.5 43.5 9520.6 42.2 8740.4 46.9 9805.2 41.3 10082.4 41.7 9269.0 43.4 9521.3 42.2 8898.9 46.2 9807.4 41.3 10095.0 41.7 9282.9 43.4 9522.1 42.1 8908.1 46.3 9809.8 41.5 10108.8 41.6 9294.9 43.4 9522.6 42.2 9063.2 45.0 9816.0 41.4 10111.3 41.5 9308.5 43.4 9523.6 42.1 9071.1 45.1 9817.7 41.4 10127.0 41.5 9314.0 43.3 9524.8 42.0 9094.0 44.2 9824.7 41.4 10149.8 41.4 9330.9 43.3 9525.7 42.1 9111.5 43.3 9829.8 41.3 10150.2 41.2 9333.1 43.3 9526.4 42.1 9124.9 43.4 9832.8 41.3 10150.3 41.2 9347.0 43.2 9536.6 42.1 9126.4 43.1 9833.8 41.4 10153.5 41.0 9350.5 43.2 9542.6 42.2 9133.2 43.2 9846.2 40.9 10157.6 41.1 9363.0 43.1 9546.5 41.9 9139.7 43.2 9855.4 40.9 10164.8 41.1 9365.0 43.2 9561.9 41.9 9140.8 43.2 9883.1 40.7 10188.7 40.9 9376.2 43.1 9567.5 42.0 9142.0 43.2 9884.2 40.8 10192.8 40.8 9378.1 43.1 9576.5 41.9 9143.5 43.1 9893.9 40.8 10199.2 40.9 9385.2 42.9 9586.3 41.8 9148.1 43.2 9920.4 40.7 10225.8 40.7 9393.3 43.0 9587.7 42.1 9155.2 43.2 9923.9 40.6 10232.0 40.7

60

9401.4 43.0 9609.9 41.8 9155.7 43.2 9945.3 40.6 10239.4 40.7 9403.5 42.9 9622.2 41.9 9157.3 43.1 9956.5 40.7 10272.2 40.7 9410.4 42.9 9643.7 41.9 9159.4 43.0 9965.6 40.7 10278.7 40.7 9420.2 42.8 9661.9 42.0 9162.7 43.1 9977.7 40.4 10300.3 40.6 9423.4 42.9 9666.7 42.0 9168.7 43.0 9980.3 40.4 10306.0 40.6 9427.5 42.7 9668.4 42.0 9169.0 42.9 9992.4 40.7 10306.3 40.5 9432.3 42.8 9677.0 42.0 9171.0 43.1 9993.7 40.6 10328.2 40.5 9436.4 42.7 9696.2 42.1 9172.5 43.0 10004.9 40.6 10332.3 40.5 9438.9 42.6 9706.9 42.0 9176.1 43.1 10019.4 40.6 10334.8 40.5 9439.9 42.7 9724.2 42.1 9176.9 42.9 10025.8 40.3 10346.7 40.4 9445.4 42.6 9735.1 42.1 9178.0 42.9 10032.9 40.6 10350.5 40.4 9448.7 42.6 9739.1 42.0 9178.4 43.0 10037.8 40.5 10364.4 40.3 9449.3 42.5 9744.5 42.0 9179.0 43.0 10043.1 40.6 10372.3 40.3 9453.1 42.6 9758.3 42.2 9180.8 42.9 10044.4 40.5 10386.5 40.2 9454.8 42.5 9758.8 42.1 9189.3 42.9 10056.4 40.4 10397.2 40.2 9457.2 42.5 9770.0 42.2 9191.2 42.6 10064.1 40.4 10402.3 40.2 9465.1 42.5 9770.6 42.0 9192.7 42.9 10065.2 40.4 10403.8 40.1 9466.4 42.6 9786.1 42.1 9201.9 42.9 10069.0 40.4 10409.3 40.1 9471.0 42.4 9788.8 42.0 9202.1 42.9 10088.1 40.3 10414.6 40.0 9479.1 42.3 9790.5 42.2 9207.0 42.7 10088.2 40.4 10424.6 40.0 9479.7 42.3 9793.0 42.1 9220.4 42.5 10089.3 40.3 10425.1 40.0 9481.1 42.3 9796.8 42.1 9234.2 42.5 10092.3 40.2 10425.7 40.0 9481.9 42.5 9801.4 42.1 9245.5 42.4 10092.8 40.3 10431.8 40.0 9482.2 42.3 9808.3 42.1 9256.5 42.4 10094.7 40.0 10442.7 40.0 9482.3 42.4 9809.0 42.0 9269.0 42.4 10100.6 40.2 10456.1 39.8 9483.4 42.4 9809.2 41.9 9284.6 42.4 10101.4 40.3 10471.1 39.7 9485.4 42.2 9810.4 41.9 9298.7 42.3 10103.4 40.3 10476.3 39.6 9486.3 42.5 9813.4 41.8 9310.5 42.3 10111.4 40.2 10501.8 39.4 9487.5 42.4 9816.0 42.0 9324.9 42.3 10111.7 40.2 10522.3 39.4 9488.7 42.4 9820.2 41.9 9336.7 42.3 10112.7 40.1 10525.3 39.4 9496.7 42.3 9821.7 42.0 9344.3 42.3 10115.4 40.2 10579.3 39.4 9496.8 42.1 9823.0 42.0 9355.1 42.2 10117.4 40.3 10580.9 39.4 9501.8 42.3 9823.4 42.0 9361.8 42.3 10118.4 40.4 10592.0 39.4 9512.9 42.2 9824.5 41.9 9378.7 42.2 10119.0 40.2 10624.1 39.4 9514.3 41.9 9825.0 41.9 9379.0 42.2 10120.4 40.0 10628.7 39.4 9527.8 41.9 9828.1 41.6 9393.7 42.1 10120.6 40.1 10633.6 39.4 9540.8 41.8 9828.8 41.9 9394.5 42.1 10127.8 40.0 10644.3 39.3 9552.7 41.8 9829.2 41.9 9401.7 42.0 10128.8 40.2 10657.2 39.3 9565.1 41.7 9830.8 41.8 9412.7 42.1 10129.7 40.1 10666.0 39.3 9567.9 41.7 9833.6 42.0 9416.4 41.9 10133.5 40.2 10690.0 39.2 9585.2 41.5 9834.0 41.9 9423.1 42.0 10135.2 40.1 10690.1 39.2

61

9595.1 41.6 9835.9 41.8 9424.9 41.9 10137.4 39.9 10690.6 39.2 9604.1 41.5 9836.0 41.9 9428.3 41.9 10140.2 40.0 10696.9 39.2 9615.5 41.4 9839.8 41.9 9435.1 41.8 10140.3 40.1 10703.7 39.1 9629.6 41.5 9840.1 41.9 9436.7 41.9 10151.2 40.0 10707.6 39.1 9630.1 41.3 9840.3 41.8 9443.1 41.8 10713.1 39.1 9648.4 41.3 9840.4 41.7 9448.9 41.8 10718.4 39.1 9660.1 41.3 9843.4 41.8 9460.2 41.8 10728.0 39.0 9668.8 41.2 9847.2 41.8 9464.9 41.8 10729.1 39.0 9675.7 41.1 9849.4 41.8 9466.2 41.7 10738.5 39.0 9679.9 41.2 9852.2 41.8 9466.4 41.6 10749.6 39.0 9682.7 41.2 9852.7 41.5 9467.6 41.7 10754.6 38.9 9689.5 41.0 9854.9 41.9 9470.1 41.7 10756.1 38.9 9707.5 41.0 9860.8 41.5 9471.5 41.8 10757.2 39.0 9710.9 40.9 9869.4 41.4 9476.2 41.7 10770.0 38.9 9711.1 40.8 9883.4 41.3 9486.3 41.7 10774.5 38.8 9713.9 40.9 9888.4 41.4 9486.9 41.7 10775.0 38.8 9718.0 40.8 9918.2 41.4 9495.4 41.7 10775.6 38.8 9731.4 40.8 9922.1 41.3 9498.7 41.6 9733.1 40.9 9925.2 41.3 9498.8 41.7 9748.1 40.8 9942.2 41.3 9499.0 41.6 9750.2 40.7 9946.8 41.8 9499.9 41.6 9751.8 40.6 9954.1 41.3 9500.5 41.6 9753.1 40.8 9956.7 41.6 9504.9 41.6 9753.5 40.7 9960.8 41.3 9506.5 41.6 9759.3 40.6 9984.2 41.3 9513.6 41.7 9766.0 40.4 9984.6 41.4 9521.6 41.5 9768.9 40.4 9990.5 41.2 9532.2 41.3 9771.9 40.4 9990.7 41.2 9541.3 41.4 9772.7 40.7 9992.9 41.1 9551.3 41.2 9773.0 40.4 10010.9 41.4 9560.8 41.2 9775.4 40.5 10014.1 41.2 9587.4 41.0 9778.4 40.6 10017.2 41.0 9591.1 41.2 9782.1 40.4 10021.2 41.1 9611.9 41.1 9786.9 40.4 10023.1 41.0 9631.9 41.2 9789.6 40.3 10034.0 41.0 9633.2 41.1 9791.0 40.4 10042.0 41.4 9651.0 41.1 9794.8 40.3 10045.8 40.9 9664.9 41.1 9796.0 40.4 10046.7 40.9 9673.5 41.0 9813.5 39.9 10051.4 40.9 9686.7 41.0 9823.8 39.9 10052.3 41.2 9701.5 41.0 9844.5 39.8 10062.3 41.1 9710.2 41.0

62

9861.1 39.8 10063.8 40.9 9710.8 40.9 9863.7 39.7 10068.2 40.8 9718.1 40.9 9892.7 39.7 10069.5 40.9 9734.4 41.0 9901.2 39.7 10075.9 40.8 9736.3 41.0 9924.2 39.6 10076.5 40.8 9757.5 40.9 9929.9 39.6 10083.5 40.7 9758.9 40.8 9932.7 39.6 10087.6 40.7 9760.3 40.8 10013.7 39.4 10092.3 40.8 9764.1 41.0 10021.6 39.4 10097.9 40.9 9766.5 40.9 10032.5 39.4 10099.0 40.7 9769.6 40.8 10035.2 39.2 10100.0 40.7 9778.0 40.8 10036.4 39.3 10104.4 40.9 9782.8 40.7 10049.7 39.3 10104.8 40.6 9784.6 40.7 10052.1 39.2 10106.6 40.8 9790.4 40.8 10058.9 39.3 10108.0 40.7 9790.4 40.8 10063.0 39.1 10109.9 40.7 9792.2 40.7 10070.1 39.1 10111.8 40.6 9797.6 40.6 10075.3 39.2 10116.5 40.9 9801.1 40.7 10078.6 39.2 10125.5 40.5 9804.9 40.6 10079.7 39.5 10125.9 40.6 9805.2 40.6 10099.8 39.1 10126.0 40.6 9805.5 40.7 10100.3 39.0 10128.3 40.6 9813.0 40.7 10100.5 39.2 9813.8 40.6 10100.8 38.9 9815.5 40.6 10102.2 39.1 9826.5 40.7 10102.2 39.2 9831.3 40.6 10109.5 38.9 9831.5 40.6 10112.9 39.1 9834.9 40.5 10114.9 38.8 9835.9 40.3 10116.3 39.1 9836.8 40.2 10116.5 38.9 9852.2 40.2 10117.1 38.7 9875.6 40.2 10117.5 39.2 9884.5 40.2 10119.7 38.9 9922.8 40.2 10119.8 38.7 9945.2 40.1 10121.8 38.9 9976.5 40.2 10122.4 38.6 9981.0 40.3 10123.5 38.7 9983.2 40.4 10125.0 38.9 10024.3 40.4 10126.5 38.6 10038.4 40.4 10128.3 38.8 10039.5 40.5

63

10129.6 38.7 10048.5 40.6 10130.5 38.8 10063.1 40.6 10131.7 38.7 10078.2 40.7 10132.1 38.6 10085.9 40.6 10133.1 39.5 10097.5 40.8 10133.2 38.9 10100.7 40.7 10134.6 38.7 10115.7 40.8 10135.8 38.9 10120.3 40.8 10136.4 38.6 10124.3 40.3 10136.5 38.6 10126.6 40.4 10136.6 38.7 10130.6 40.9 10136.7 39.5 10132.9 40.8 10137.2 38.9 10133.4 40.4 10137.5 38.6 10133.8 40.4 10137.7 38.6 10137.2 40.9 10138.2 38.5 10139.5 40.3 10138.5 38.6 10140.2 40.4 10140.2 38.5 10141.0 40.7 10141.0 38.7 10141.4 40.7 10141.3 38.6 10142.0 40.8 10142.0 38.9 10142.4 40.8 10142.5 38.6 10142.8 40.5 10143.1 38.7 10144.6 40.8 10143.7 38.7 10146.5 40.4 10143.7 38.6 10148.0 40.5 10143.8 38.9 10152.5 40.7 10144.9 38.6 10152.5 40.6 10146.3 38.5 10152.9 40.3 10147.7 38.6 10153.4 40.7 10149.2 38.7 10155.3 40.7 10150.4 38.6 10157.1 40.8 10151.2 38.7 10160.1 40.4 10151.5 38.8 10162.6 40.4 10152.0 38.6 10167.1 40.7 10153.6 38.7 10167.2 40.9 10153.9 38.7 10183.8 40.7 10154.7 39.1 10155.2 38.6 10155.4 38.7 10156.1 38.6 10157.6 38.7

64

10158.4 38.6 10159.0 39.1 10159.1 39.2 10159.1 39.3 10159.7 39.3 10159.7 38.6 10160.1 38.6 10160.3 38.6 10160.3 38.5 10160.4 38.8 10160.6 39.1 10161.7 38.8 10161.7 39.1 10163.1 39.2 10163.5 38.6 10163.7 39.2 10163.9 38.8 10164.4 38.9 10165.3 38.9 10165.7 39.2 10166.1 39.1 10167.3 39.1 10167.3 38.8 10168.9 38.7 10170.1 38.8 10170.4 39.0 10172.2 39.3 10172.3 38.8 10172.3 39.4 10172.9 39.1 10173.4 39.2 10175.0 38.7 10175.7 39.1 10176.0 38.9 10176.8 39.0 10176.8 39.3 10177.8 39.2 10177.9 38.8 10179.0 38.8 10179.5 39.2 10180.5 39.2

65

10182.5 39.2 10182.8 39.2 10183.3 39.1 10184.0 39.3 10184.3 38.8 10185.0 39.2 10185.8 39.3 10187.0 39.0 10187.2 38.9 10191.9 39.0 10194.0 39.1 10196.7 39.2 10199.5 39.2 10199.9 39.1 10200.4 39.2 10205.1 39.3

66