ME224 Final Project:

Closed-Loop Rotational Speed Control and

Power Monitoring of Cooling Fan under Varying Conditions

December 7, 2001

Shad Laws Karl Stensvad

Jay Gainer David Choi

Table of Contents Page Summary 3 Introduction 4 Theory 5 Mechanical Setup 6 Electronic Instrumentation 7 Software 16 Data and Analysis 18 Conclusion 25 References 26 Biographical Sketches 27 Appendix 28

Summary The main objective of this project is to design and build a control system for a computer fan. The user inputs a desired angular velocity in RPM into the system, and the computer alters the voltage sent to the fan in order to maintain a constant angular velocity. We then show that this closed-loop control system is functional by inputting different angular velocities, and varying the airflow resistance to the fan. Through all of this, the control system should approximately keep the RPM of the fan constant. We also want to find the power consumption of the computer fan and see if it increases as we add resistance to the airflow. From this power consumption data, we can determine the efficiency of the fan. To accomplish our goal, we built a mechanical setup that could introduce varying levels of resistance to the airflow. We also built a nice homemade encoder using a light and a photoresistor to give two pulses every revolution of the fan. Through some other circuitry, we turned that signal from the photoresistor into a rectified square wave. This then went into a tachometer, basically converting a frequency into a voltage. After some more signal conditioning, this voltage was inputted into the computer via the ADC. After multiplying by a calibrated conversion factor, we find the angular velocity of the fan. In similar ways, the current across the fan is inputted to find the power used, and the voltage outputted by the DAC were both inputted into the ADC. The data in LabVIEW was dumped out into Excel and further analyzed. In the end, our setup and circuits worked beautifully as planned. The encoder setup with the light and photoresistor gave us a very clean square wave, making the frequency easy to find. At times, the minute details of all the circuits and the shear number of wires made things difficult and confusing, but all in all, we were able to work through all of our problems. As expected the efficiency of the fan decreased as we added resistance to the fan and increased the angular velocity. The system did a superb job of maintaining the desired angular velocity as well. Though working on this project we put together all of the knowledge about various circuits and LabVIEW to create a meaningful closed-loop control system.

Introduction The general goal of this experiment is to model a simple spinning fan. To do this, we have designed an electronic circuit interfaced with LabVIEW through a Data Acquisition Card. To accomplish our goal, we first built a circuit with a known resistance in series with the fan. The voltage drop across the resistor was measured to determine the current being sent through the fan. The speed (RPM) of the fan will be controlled by automatically varying the voltage to this series circuit in a closed-loop operation. More specifically, when the desired fan speed is greater than the actual fan speed, a higher voltage will be sent to the fan in order to speed it up. Conversely, when the fan speed is higher than the desired fan speed, a lower voltage is sent to the fan. In order to monitor the fan speed we built another circuit. This circuit consists of an LED and a phototransistor. In short, the phototransistor receives the LED light signal twice every rotation. This raw data was sent to LabVIEW and converted into rotations per minute using a few simple equations. We, then, wrote a program in LabVIEW that takes these data (V, I, and ? ) and exports them into an Excel file where the data can be represented visually. Next, we placed obstructions in front of the fan to block the airflow into the fan. We are looking for a relationship between the desired rpm and the power consumed by the fan. We will also try to find a relationship between fan efficiency and rpm. Since the flow of a fan is roughly linear (if the restrictions in the path of the air are constant) with respect to angular velocity with laminar flow, this can be used to estimate the efficiency of the fan.

Theory After doing some background research on simple fans, we found a few relationships worth noting. First, the airflow out of the fan should be linearly related to its rotational speed. Next, the power used by the fan is related to the square of the rotational speed. So, for every increase in rotational speed, the power of the fan will increase by a factor of the square root of that increase. We also learned that, theoretically, the fan efficiency decreases as the rotational speed increases. This experiment will be conducted six different times. Each time, there will be a different amount of airflow obstruction in front of the fan’s air intake. Different sized plexiglass plates will be placed in front of the fan to act as the airflow obstructions. The plates will force the fan to work harder in order to maintain the desired rotational speed. So, as the plates increase in area, the power of the fan will increase. We also learned, and hope to prove, that as the airflow obstruction increases, the efficiency of the fan should decrease. By running this experiment with the plates of different cross sectional areas, we will try to verify the relationships that we found in our research.

Mechanical Setup The fan portion of the setup was already pre-built for us – a 12 Volt 0.3 Amp fan. The components that had to be designed and built included the airflow resistance device, and the encoder setup. The fan is encased in an aluminum box made out of bent sheet metal and riveted together. There is a slot on the back where different Plexiglas plates can be inserted, cutting down the amount of airflow to the fan. There were several plates with openings of: zero, one, two, three, and nine square inches. The encoder is made up of two aluminum tubes, one with a 15 Volt light bulb, and the other one with a photoresistor. We use aluminum tubes so that the light can be reflected with less of a loss to the environment. The fan also has a hollow tube that spins with itself. At exactly two times per revolution, there is a direct line of sight between the light bulb and the photoresistor. At these times, the voltage across the resistor drops. By measuring the pulses, we can then get the frequency of the fan, and ultimately the angular velocity. The following shows a picture of the front and back of the fan housing:

Below is a picture of the air flow restricting plates:

Electronic Instrumentation In short, the electronic instrumentation has three functions:

?? Use the photoresistor to create an RPM signal for LabVIEW ?? Use a LabVIEW signal to drive a voltage divider consisting of the fan and a

power resistor in a variable manner. ?? Read the voltages supplied both to the fan and power resistor and to the fan alone

and give them to LabVIEW to calculate the power consumption of the fan. The electronic equipment consists of:

?? National Instruments Data Acquisition Card (-10V/+10V range) ?? IBM-compatible computer to control DAQ ?? DC Power Supply (+15VDC, -15VDC, +5VDC, Ground) ?? Actron Automotive Tachometer (designed for +14VDC) ?? Cooling Fan Assembly (DC Fan, Photoresistor, +15V light bulb) ?? Our PC Board

Together, these devices can complete the functions necessary and provide the logic we need. This gives closed-loop control and monitoring as shown:

The DAQ and computer are those found in the Mechatronics Laboratory. LabVIEW was used on the computer to control the DAQ. The DC Power Supply used is from a Protoboard 203A. The Fan Assembly was described above. The Actron Automotive Tachometer is used as a frequency-to-voltage converter. Initial testing showed that while LabVIEW is capable of reading and displaying a square wave signal at up to the required ~150Hz, it is unfortunately incapable of processing this signal fast enough to be accurate. Therefore, an external frequency-to-voltage converter was necessary. Since the signal from the photoresistor can be conditioned (see below) to a +15VDC/0VDC pulsed signal with two pulses per fan revolution (due to mechanical apparatus), this signal can be viewed by an automotive tachometer as the distributor contact points signal for a four-stroke, four-cylinder engine. The Actron Tachometer processes the provided pulsed signal into a constant voltage to be sent to windings in a gauge. Since the windings have a constant resistance, the current though them moves the

windings in a magnetic field against a spring, resulting in an attached needle moving linearly along a scale. A very high-impedence tap was taken from the signal to these windings as not to disturb the readings themselves. The relationship between this output signal and the input frequency (an oscilloscope was used to accurately determine the frequency of this) was determined experimentally to be very linear. Below is a picture of the tachometer that we used:

The PC Board is the component we made to be able to link everything together. The board is layed out as follows:

The PC Board has eleven connections:

?? Power Supply ?? Tachometer In

?? Tachometer Out ?? DAQ ADC0 – Fan RPM monitoring ?? DAQ ADC1 – Fan+Power Resistor supply voltage monitoring ?? DAQ ADC2 – Fan supply voltage monitoring ?? DAQ ADC3 – Fan+Power Resistor power generator monitoring ?? DAQ DAC0 – Fan+Power Resistor power generator regulation ?? Cooling Fan Motor ?? Photoresistor ?? +15V light bulb

Conditioning for these signals is provided by six main loops:

?? Power Supply Loop ?? RPM Pulse Signal Generation Loop ?? RPM Voltage Signal Generation Loop ?? Fan+Power Resistor Power Generation Loop ?? Fan+Power Resistor Voltage Division Loop ?? Fan Power Monitoring Loop

The Power Supply Loop simply provides +15VDC, -15VDC, +5VDC, and a ground to the board and a +15V supply voltage to the light bulb. The RPM Pulse Signal Generation Loop conditions the photoresistor’s signal to be properly used by the tachometer. The photoresistor’s resistance was found to vary from about 750? saturated with the light to over 100k? completely unsaturated with the light. So, a voltage divider with a 1k? resistor and a 5V supply was used to convert this into a usable signal. Another voltage divider using a 1k? resistor and a 1k? potentiometer with a 5V supply was used to create a “cutoff voltage.” This is the point at which we can consider the light being “on” and “off” the sensor. The potentiometer was set using an oscilloscope to get approximately a 90 degree (on a 360 degree scale of the fan’s rotation) pulse. This only has to be accurate enough to give a non-extreme dwell angle (not 0 or 180) so that the tachometer can accurately read the signal. These two voltages are put into a LM741 opamp-based comparator. Testing showed that feedback was necessary; without feedback the signal was dirty. A gain of 1000 was used (2k? and 2M? resistors). The output signal is now a –15VDC/+15VDC pulse – very similar to a square wave. This signal was put through a half-wave rectifier to remove the lower half of it using an IN4 diode and a 47k? resistor. The result is a +15VDC/0VDC pulsed signal at twice the frequency of the fan’s rotational speed. This signal, along with a +15VDC supply, is given to the tachometer.

The RPM Voltage Signal Generation Loop conditions the output of the tachometer into a signal usable to the DAQ. Using the oscilloscope on the “square wave” signal described above, we experimentally found that the ratio between the actual fan RPM and the voltage difference in the two output wires from the tachometer is roughly 10,000:1. We also experimentally found that with a large enough supply voltage, the fan can pass 4,000RPM but not 5,000RPM. So, at 5,000RPM, the voltage difference would be approximately 0.5V. A LM741 opamp-based difference amplifier with a gain of 20 was used. To maintain very high impedance on the tachometer, the resistors used were 100k? and 2M? . The result is a –10VDC/+10VDC signal which is given to DAQ ADC0 for fan speed monitoring.

The Fan+Power Resistor Power Generation Loop takes a signal from the DAQ DAC0 for fan voltage regulation and provides the correct low-impedance voltage supply to the fan and power resistor. It also provides two additional signals. One is a feedback signal to DAQ ADC3 for fan voltage regulation monitoring – it is a direct tap from DAQ DAC0. The other is a signal for the voltage supplied to the fan and power resistor given to the fan power-monitoring loop – it is a direct tap from the generated voltage supply to the fan and power resistor. To provide the correct signal, the –10VDC/+10VDC DAQ DAC0 signal is put through an LM741 opamp-based inverting amplifier with a gain of 1.5 (using 100k? and 150k? resistors). This –15VDC/+15VDC signal was found to be of two high an impedance to be an adequate supply. Therefore, a TIP31 NPN power transistor was used with a +15VDC supply to provide the low impedance necessary. The voltage gain is close to one, although experimentally we found that it is not exactly one and that the relationship is not too easily characterized due to the non-linear nature of a transistor.

The Fan+Power Resistor Voltage Division Loop sets up the voltage divider of the fan and power resistor. This was employed so we could determine the current draw of the fan and therefore calculate the power draw of the fan. Too low a resistance meant that the fan speed could not be adequately controlled or even run at a low RPM. Too high a resistance meant that the fan speed could not get high enough of an RPM. We experimentally selected the resistance just small enough to allow the fan to get a bit over 4,000RPM, which was found to be 50? . A 50? power resistor rated at 10W was selected (actual resistance measured at 49.3? ). The voltage after the resistor was paired with a –15VDC supply and given to the fan. This voltage, like the previous loop, also has a tap on this fan supply voltage which is given to the fan power monitoring loop.

The Fan Power Monitoring Loop simply conditions the signals from the voltage to the fan and the voltage to the fan+power resistor to signals usable by the DAQ. Each signal is put through an LM741 opamp-based inverting amplifier. The gain was set at 0.667 (using 100k? and 150k? resistors) to convert the –15VDC/+15VDC signal to a –10VDC/+10VDC signal. The conditioned fan+power resistor signal is sent to DAQ ADC1 and the fan signal to DAQ ADC2.

Software The LabVIEW program takes care of much of the intelligence of the control system. Basically, the program takes in inputs into the ADC, and sends out a voltage to drive the computer fan out of the DAC. Inputs include: 1) a voltage from the conditioned signal from the tachometer corresponding to the RPM of the fan; 2) the voltage across a 50 ? power resistor that tells us the current across the fan; and 3) the voltage that the DAC is outputting to the fan. These voltage inputs are multiplied by the correct constants to calculate the actual RPM and power through the computer fan. Our LabVIEW is designed to run five trials, each with a different predetermined desired RPM. Each trial runs for 35 seconds. The program compares the desired RPM and the actual RPM from the encoder that we made and adds a factor of the difference to the current voltage being supplied to the fan via the DAC. If the fan is going slower than the desired speed, more voltage is applied; if the fan is going faster than the desired speed, less voltage is applied. Included is a Max & Min function that limits the amount the voltage can change at a time. Without this feature in our code, we found that the voltage supplied to the fan jumps too low when the actual RPM goes beyond the desired RPM. The voltage across the 50 ? power resistor is multiplied by factors that convert it to the current across the fan. From there, LabVIEW can give us the power consumption. The percent error between the desired and actual angular velocities is also recorded. All of the data is outputted into an Excel file.

Data and Analysis The data that we gathered was outputted to Excel files. Please see the appendix for sample data.

Fan Rotational Speed

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The first graph shows both the actual and desired angular velocity of the fan in RPM as a function of time. For this case, the opening in the back of the fan was nine square inches (or fully open). Here we can see the five different trials represented by the thin line. The thick jagged line shows what the actual RPM of the fan is. As the desired RPM is instantly switched, the actual takes a bit of time to catch up. There is a marked overshoot, but the system compensates less and less each time so that at about 10-15 seconds, the RPM of the fan becomes approximately constant. This looks very similar to our temperature controller data and graphs in a previous lab. An interesting thing to note is that it seems to take longer to reach a stable velocity when the fan is decreasing RPM rather than increasing it. This is due to the fact that it is harder for the fan to overshoot a higher RPM than to undershoot a lower one. At higher velocities, air resistance prevents the system from overshooting too much. Basically, this graph shows quite nicely that our closed-loop control system works and can adequately maintain a desired angular velocity.

Power Draw

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0 17.5 35 52.5 70 87.5 105 122.5 140 157.5

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This next graph above is once again for the data collected for the fan without any increased air resistance. It shows the power consumption of the fan superimposed over the actual RPM of the fan. Both of these are graphed as functions of time. Here, we can see that there is more power drawn at higher RPMs. What is more interesting however is that the range of power drawn is greater at higher velocities. This means that the power varies more and has a higher standard deviation for faster velocities. This could be due to the fact that power is proportional to the square of the voltage. This means that at higher voltages (and thus higher angular velocities) the error of the power would be greater than at lower velocities. The power drawn for different air resistances is graphed and analyzed later.

Efficiency

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If we consider efficiency of our system to be defined by angular velocity divided by the power consumed, then we get the graph above. We can observe that the average efficiency is greater for lower angular velocities and lower for higher velocities. This is what we expect because of the air resistance, which becomes a greater factor with increased velocities. We also note that there is more variance in the efficiency at lower velocities because the fan was designed to be run at higher RPMs and is difficult to control in the slower regions. The next graph below shows a simple relationship between the efficiency and the RPM. Here, as we already stated, we can see that those two are inversely proportional. We managed to fit the line quite nicely with a third order polynomial.

Average Efficiency

y = -2E-08x3 + 0.0006x2 - 4.3407x + 10622R2 = 1

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Finally, the error of the desired and observed RPM is graphed below for the nine square inch opening.

Error

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The error is very high at the onset of the switch in desired RPM, but quickly becomes very low. The magnitude of the error is related to the instantaneous change in the desired RPMs. This is there because we limited the amount the voltage could be increased or decreased at once to make the control smoother.

Next, we compare the power curves for all the varying air resistance setups on the same graph:

Power

y = 4E-07x2 - 0.0009x + 1.0062

y = 3E-07x2 - 0.0008x + 0.8191

y = 3E-07x2 - 0.0009x + 0.9306

y = 3E-07x2 - 0.0008x + 0.815

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The graph shows what we would expect. The power drawn by the fan obviously increases as the angular velocity of the fan is increased. This relationship can be fit with a binomial line to a good degree of accuracy. Something else that this data tells us is that the power curve is higher for larger amounts of air resistance. The line that corresponds to the back of the fan being completely blocked off is the greatest, and the line that corresponds to the fan being totally open is the lowest. This is what we would expect because for the same RPM, more power must be used to overcome the air resistance. Another thing to note is that this difference in power is more noticeable as the velocity is increased. In the same way, the total efficiency of the control system can be graphed for all the different resistance setups on the same graph:

Effiency

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The graph above shows in general what we would expect from this system. The efficiency should decrease as more airflow resistance is added. This seems to be the case for most of the plots. The yellow line representing the two square inches is hidden under the black line. The one line that seems a bit out of place is the black one. We would expect this one with the maximum resistance to have the lowest efficiency. One explanation why this isn’t true could be that once all of the air is blocked off in the back, the tolerance between the fan blades and the housing becomes more important. This fan was not designed to be a precision device. Therefore, in the event of a large resistance in the back, air flows in the gap between the fan blades and the housing. This may affect the efficiency. Finally, we plot error for all the varying resistance setups on the same graph:

Error

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This is a very interesting graph. We expect the largest error to be at the two high ends of the fan angular velocities. This is because there is a limit to how fast and slow the fan can go. Beyond this normal functioning window, the error is very high. The curious thing is the two minimums. We can explain this by looking at the way we limited the maximum increase and decrease of the voltage to the fan. We have two separate constants that do this, one for the increase, one for the decrease. One dip may represent the best error conditions for increase, and the other for decrease.

Conclusion This lab was a success. We were able to accomplish our goal of designing a way to control the rotational speed of a fan in a closed-loop monitoring system. The user is able to input a desired rpm value and the fan responds by ultimately spinning very close to that desired rpm. Looking at the graph title “Fan Rotational Speed,” one can see that the fan rotational speed, the thick blue line, closely mirrors the desired rotational speed, in pink. Our data verified that, indeed, the rotational speed is proportional to the square of the power of the fan. We were also able to show that the power of the fan increased when the airflow obstruction increased, as we predicted. Also, the graph titled “Efficiency” shows that the efficiency of the fan is high when the fan is spinning at low speeds and is high when the fan is spinning at high rotational speeds. As the program is running, one can see that the percent error of the actual rotational speed (rpm) and the desired rpm is very low but not quite zero. Since the fan is being sent pulses of voltage, the fan has a tendency to overshoot and undershoot the desired rpm. However, these differences are very low, so the percent error is low, as well. For example, when the fan is spinning at 3000 rpm and the desired speed is 3000 rpm, the percent error is less than 5%. However, when the desired rpm is changed to 2500 rpm, the fan receives a very low voltage until the rotational speed is 2500 rpm. Unfortunately, the fan speed drops below the desired value of 2500 rpm. However, the program identifies this problem and then sends a higher voltage until the fan is spinning at the desired rpm again. This loop goes on and on for the length of the program running time and the rotational speed oscillates close to the desired value. A way to avoid this overshooting tendency would be to use an integrator, which would give a much smoother actual rpm plot. The error in this lab can be attributed to a few factors. First, the seal around the fan is not airtight. This means that even while the impedance to airflow is 100%, air can still be sucked into the fan. Another cause of error came in the early calibration stage of the experiment. We needed to find an equation relating the voltage of the fan and the fan rotational speed. This was done by taking a series of voltage and frequency readings using the oscilloscope while the program was running. We found the relationship to be linear with a nonzero y intercept. This correlation coefficient, R^2 value, for the equation was less than 1, approximately .96. This minor imperfection could cause some error in our rpm readings.

References Mechatronics: Electronic Control Systems in Mechanical and Electrical Engineering, second edition, W. Bolton, Addison Wesley Longman, 1999, ISBN 0-582-35705-5 ME333 – Mechatronics Design Lab Website http://mechatronics.mech.nwu.edu/mechatronics/index.html Electronics and Communications for Scientists and Engineers, first edition, Martin A. Plonus, Harcourt/Academic Press, 2001; ISBN: 0125330847

Biographical Sketches David Choi is a mechanical engineer at Northwestern University with a concentration in biomedical engineering. He is planning to graduate in June of 2003. His experience with sensors and mechatronics include taking the class ME333 – Introduction to Mechatronics where he and his team built a gumball dispensing geography game. David has also taken ME224 – Experimental Engineering where he experienced implementing sensors and LabVIEW to control a system. His other work experience includes working in the robotics lab at the California Institute of Technology in the summer, and working in the Laboratory of Intelligent Mechanical Systems at Northwestern. Going to graduate school in mechanical engineering after graduating is a likely possibility. Ultimately, he would like to integrate mechanical design with medical needs. Jay Gainer is a junior in the McCormick School of Engineering at Northwestern University and will be graduating in the Spring of 2004. He is majoring in Mechanical Engineering with a concentration yet to be decided. Jay graduated from Stevenson High School in the Spring of 1999. While in high school, he got some valuable engineering experience working on a national robot competition. At Northwestern, he worked on a design project to design a better public restroom and also designed a web page through Engineering Design and Communication class. Jay gained mechanical engineering experience working with visco-elastic materials with the goal of making ‘quiet steel’ while working for Materials Science Corporation. This Experimental Engineering course is his first experience working with electronic circuitry. Karl Stensvad is a Student at Northwestern University in his Junior Year. His studies focus on Mechanical Engineering and Psychology. During his two years here, Karl has had many exposures to the design process including two years with the Design Competition (placing second last year) and two complete design projects ending with working prototypes in our required EDC courses. Karl began his Co-Op job this past summer and will be continuing with Northrop Grumman again this spring. He also spends a share of his free time working on projects that use engineering principals such as RC vehicles he builds and modifies. Shad Laws is a Mechanical Engineering student at Northwestern University in his Junior Year. In high school, he received many scholastic awards, including a National Merit Semi-Finalist award. Additionally, he received many awards in Model United Nations and in Music, both classical and jazz. He aided in the development of the world’s first fully automated, safe, and closed-loop large-scale solvent recovery system with DSC Environmental. This has now been proven in the industry to work successfully. He also has a passion for automobiles, which has led him to found LN Engineering, LLC. The small company has already developed revolutionary new products geared toward the aircooled Volkswagen and will continue to make more.

Appendix

Entry

Time Elapsed (sec)

Actual RPM Input Voltage

Desired RPM Allowed Change Fan Voltage Current Power Error Power/RPM Relative Efficiency

0 0 873.835 1.716 3000 -30 2.776 0.036 0.1 71 0.0001144 8738.35

1 0.035 877.893 1.724 3000 -30 2.812 0.038 0.107 71 0.0001219 8204.607477

2 0.07 888.713 1.743 3000 -30 2.882 0.04 0.114 70 0.0001283 7795.72807

3 0.105 896.828 1.758 3000 -30 2.234 0.055 0.124 70 0.0001383 7232.483871

4 0.14 904.943 1.772 3000 -30 3.062 0.041 0.127 70 0.0001403 7125.535433

5 0.175 835.964 1.648 3000 -30 3.16 0.042 0.134 72 0.0001603 6238.537313

6 0.21 853.547 1.68 3000 -30 3.146 0.046 0.143 72 0.0001675 5968.86014

7 0.245 853.547 1.68 3000 -30 2.919 0.053 0.155 72 0.0001816 5506.754839

8 0.28 871.13 1.711 3000 -30 2.571 0.063 0.161 71 0.0001848 5410.745342

9 0.315 850.842 1.675 3000 -30 3.512 0.047 0.164 72 0.0001928 5188.060976

10 0.35 886.008 1.738 3000 -30 3.556 0.049 0.172 70 0.0001941 5151.209302

11 0.385 886.008 1.738 3000 -30 3.68 0.049 0.179 70 0.000202 4949.765363

12 0.42 852.194 1.677 3000 -30 3.589 0.053 0.191 72 0.0002241 4461.748691

13 0.455 911.706 1.785 3000 -30 3.827 0.051 0.196 70 0.000215 4651.561224

14 0.49 927.937 1.814 3000 -30 3.647 0.058 0.21 69 0.0002263 4418.747619

15 0.525 923.879 1.807 3000 -30 3.516 0.063 0.221 69 0.0002392 4180.447964

16 0.56 937.404 1.831 3000 -30 3.915 0.058 0.225 69 0.00024 4166.24

17 0.595 952.282 1.858 3000 -30 3.289 0.073 0.24 68 0.000252 3967.841667

18 0.63 945.52 1.846 3000 -30 4.043 0.06 0.244 68 0.0002581 3875.081967

19 0.665 959.045 1.87 3000 -30 4.241 0.059 0.251 68 0.0002617 3820.896414

20 0.7 891.418 1.748 3000 -30 4.156 0.063 0.264 70 0.0002962 3376.583333

21 0.735 880.598 1.729 3000 -30 3.973 0.07 0.278 71 0.0003157 3167.618705

22 0.77 887.36 1.741 3000 -30 4.677 0.058 0.273 70 0.0003077 3250.40293

23 0.805 896.828 1.758 3000 -30 4.772 0.059 0.282 70 0.0003144 3180.241135

24 0.84 975.275 1.899 3000 -30 4.856 0.06 0.29 67 0.0002974 3363.017241

25 0.875 983.391 1.914 3000 -30 4.585 0.068 0.312 67 0.0003173 3151.894231

26 0.91 990.153 1.926 3000 -30 4.871 0.065 0.316 67 0.0003191 3133.39557

27 0.945 973.923 1.897 3000 -30 5.076 0.063 0.322 68 0.0003306 3024.60559

28 0.98 1064.543 2.061 3000 -30 4.351 0.08 0.35 65 0.0003288 3041.551429

29 1.015 1017.204 1.975 3000 -30 5.153 0.067 0.344 66 0.0003382 2956.988372

30 1.05 1055.075 2.043 3000 -30 4.406 0.084 0.372 65 0.0003526 2836.223118