Abstract:
An apparatus and a method of improving performance characteristics of an internal combustion engine is provided which includes electronically coupling a fuel boost controller to a fuel delivery solenoid of a fuel injector. The boost controller measures a timed release of fuel from an activated fuel delivery valve of the fuel delivery solenoid into a cylinder and activates the fuel delivery valve an extended amount of time over a programmed time for injecting additional fuel over the programmed amount into the cylinder to improve the performance characteristics.

Description:
BACKGROUND 
     Computer technology has been applied to internal combustion engines for quite some time. Microprocessor control circuits have been employed to control real-time computer control of basic engine functions and parameters such as air/fuel ratio and spark ignition timing. These circuits have typically been implemented in gasoline engines. 
     More recently, these techniques have been applied to diesel engines. For example, the volume and timing of fuel injection has been computer controlled for improved mileage and emissions performance. 
     One of the problems associated with the computer control systems implemented today is that they provide no means for the end user to adjust or modify the basic performance characteristics that the manufacturer has programmed into the system. For proprietary and other reasons, the information necessary to modify the control systems is not available to the general public. Furthermore, even if such information were generally available, the technical expertise required to utilize such information would be beyond the scope of most individuals or organizations that would be interested in making such performance modifications. 
     SUMMARY 
     Accordingly, a system enhances performance characteristics of electronically controlled engines. The system may include components that can quickly and easily be installed and used by a novice. In a particular embodiment, a system of improving performance characteristics of an internal combustion engine can include electronically coupling a fuel boost controller to a fuel delivery solenoid of a fuel injector. The boost controller can measure a timed release of fuel from an activated fuel delivery valve of the fuel delivery solenoid into a cylinder. In a particular embodiment, the activated fuel delivery valve occurs when the fuel delivery valve is closed. In another embodiment, the activated fuel delivery valve occurs when the fuel delivery valve is open. 
     The boost controller can activate the fuel delivery valve an extended amount of time, such as holding the valve closed, over a programmed time for injecting additional fuel over the programmed amount into the cylinder to improve the performance characteristics. In a particular embodiment, the programmed amount of time is set by the manufacturer. 
     In one embodiment, the extended amount of time the fuel delivery valve is activated can be determined based on a lookup table. The timing of the extended fuel delivery time can be determined based on a turbo-pressure of the engine. 
     A self-test may be automatically conducted upon a powering up of the fuel boost controller. The self-test may deliver feedback to the operator that the fuel boost controller is installed properly. Feedback may also be delivered to the operator when additional fuel is being injected into the cylinder. The feedback may be delivered to the operator via a light emitting diode. 
     The fuel boost controller may calculate the extended amount of time of fuel injection. The actual rotations per minute of the engine and an approximate amount of fuel being commanded by an engine control module and an injection pump computer can be determined. A throttle position value of the engine can further be determined by computing the ratio of the approximate amount of fuel being commanded by the engine control module and the injection pump computer to the available time for each cylinder, as computed from the rotations per minute of the engine. 
     The throttle position value may be averaged with values of previous throttle position values of other cylinders for removing individual cylinder variations from the averaged value. The total number of averaged values may correspond to an integer multiple of the total number of cylinders of the engine. 
     The desired amount of additional fuel to be delivered to each cylinder may be determined based on a lookup table. The amount of additional fuel to be delivered may be scaled by a scaling value of additional fuel as a function of the computed throttle position value. The extended amount of time to deliver the additional amount of time of fuel delivery may be computed by multiplying the scaled value by the approximate amount of fuel being commanded by the engine control module and the injection pump computer. 
     An average extended time may be calculated to smooth out cylinder-to-cylinder variations in fuel delivery and to delay the introduction of additional fuel during snap acceleration for reducing particulate smoke emissions. 
     A fuel boost controller is also provided for use with an internal combustion engine to improve performance characteristics of the same. An electronic coupler can connect the fuel boost controller to a fuel delivery solenoid of a fuel injector. A measuring routine can measure a timed release of fuel from an activated fuel delivery valve of the fuel delivery solenoid into a cylinder. A fuel delivery routine can activate the fuel delivery valve an extended amount of time over a programmed amount into the cylinder to improve the performance characteristics. 
     A system is further provided for enhancing performance characteristics of an engine. The system can include an engine control module for controlling operation of the engine and a plurality of sensors connectable to the engine control module for supplying engine data to the engine control module. A fuel injection pump can connect to and be driven by the engine control module to deliver a desired amount and timed delivery of fuel to an injector of each cylinder via a fuel delivery solenoid and a fuel delivery valve. A fuel boost controller can connect to the fuel delivery solenoid for measuring a timed release of fuel from an activated fuel delivery valve of the fuel delivery solenoid into a cylinder. A fuel delivery routine can activate the fuel delivery valve an extended amount of time over a programmed amount into the cylinder to improve the performance characteristics. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     The foregoing and other objects, features and advantages of the invention will be apparent from the following more particular description of a performance enhancing system for electronically controlled engines, as illustrated in the accompanying drawings in which like reference characters refer to the same parts throughout the different views. The drawings are not necessarily to scale, emphasis instead being placed upon illustrating the principles of the invention. 
     FIG. 1 is a block diagram of a fuel delivery system that controls the amount of fuel delivered to the internal combustion engine. 
     FIG. 2 is a graph that depicts a normal operating waveform seen at a first terminal of a fuel delivery solenoid that is controlled by the fuel injection pump computer. 
     FIG. 3 is a flowchart of a power up routine. 
     FIG. 4 is a flowchart of an interrupt routine that is performed for edge “A” of FIG.  2 . 
     FIG. 5 is a flowchart of an interrupt routine that is performed for edge “D” of FIG.  2 . 
     FIG. 6 is a flowchart of a subroutine that calculates additional fuel delivery time. 
     FIG. 7 is a graph illustrating throttle response. 
    
    
     DETAILED DESCRIPTION 
     FIG. 1 is a block diagram of a fuel delivery system  10  that controls the amount of fuel delivered to the cylinders of an internal combustion engine. In a particular embodiment, the engine is a Cummins ISB series, 24 valve diesel engine, which is available as original equipment in the 1999 (and earlier) Dodge Pickup Truck. The specific details described herein are described in reference to such a 1999 Dodge Pickup Truck. The use of that environment to describe detailed embodiments is not meant to be, and should not be interpreted as, a limitation of the invention. 
     Generally, an Engine Control Module (ECM)  12  receives and interprets various sensors such as accelerator pedal position  14 , engine rotations per minute (RPM) and rotational position  16 , and intake manifold temperature and pressure  18 . ECM  12  also receives data from a Powertrain Control Module (PCM)  20  which controls body functions of the vehicle, such as air conditioning unit, heater controls, cold start, etc. In a particular embodiment, ECM  12  and PCM  20  include microprocessors for processing the data. The ECM  12  controls injection pump  22  to deliver a desired amount and timed delivery of fuel to the injector of each cylinder via a fuel delivery solenoid  24  and fuel delivery valve  26 . As shown, a low pressure fuel lift pump  21  supplies low pressure fuel to the injection pump  22 . 
     The injection pump  22  can be an electronically controlled injection pump which includes a computer or microprocessor, such as the Bosch VP 44 . Further details of the fuel injection pump, solenoid, and delivery valve can be found in U.S. Pat. No. 5,924,407 to Iwaszkiewicz et al., U.S. Pat. No. 5,769,056 to Geiger et al., U.S. Pat. No. 5,829,413 to Rodriguez-Amaya, U.S. Pat. No. 5,782,619 to Fehlmann, U.S. Pat. No. 5,595,161 to Ott et al., U.S. Pat. No. 5,582,153 to Dutt et al., and U.S. Pat. No. 5,782,620 to Nothdurft et al., the entire teachings of each are incorporated herein by reference in their entirety. 
     As illustrated, a fuel boost controller  28  is retrofitted into a preexisting fuel delivery system to improve performance characteristics of the engine without interfering or modifying any of the manufacturer&#39;s system commands, signal, protocols, or other communications. More particularly, the fuel boost controller  28  is connected to the fuel delivery solenoid  24  of the injection pump  22 . Generally, the fuel boost controller  28  interprets commands being sent from the injection pump computer  22  and determines the amount of fuel programmed by the manufacturer&#39;s system to be delivered in each cylinder. If the fuel boost controller  28  is turned on by switch  30 , it calculates and aids in delivering an increase in the amount of fuel delivered to each cylinder. This increases performance characteristics of the engine, for example, horsepower and torque. 
     The fuel boost controller  28  can be positioned within reach of the vehicle driver. In one embodiment, the fuel boost controller  28  is connected to the fuel delivery system  10  using three wires: a ground wire connecting to injection pump  22 , a wire connecting to the fuel delivery solenoid  24 , and a wire connecting to the power. In a particular embodiment, the power wire connects to fuse # 9  in the fuse panel. Fuel boost controller  28  can include a light emitting diode (LED)  32  which serves numerous functions. First, the LED  32  can be used for self diagnostics to insure the controller has been wired properly. More specifically, when the ignition key is turned “on”, the LED  32  should blink once and stay on. This indicates that the ground and power wires are wired correctly. Once the engine is started, the LED  32  should go out which indicates that the solenoid wire is wired properly. Furthermore, during operation, the brightness of the LED  32  is proportional to the amount of fuel delivery enhancement commanded by the fuel boost controller  28 . Under moderated to heavy load, the LED  32  may be programmed to stay on. 
     In unmodified operation of the engine, the following sequence of events takes place in the fuel injection pump  22  to control fuel injection for each cylinder. The injection pump  22 , which is driven at camshaft speed, receives a timing reference signal from the ECM  12 , which is based upon the crankshaft rotational position sensor  16 . When this signal is received, the fuel injection pump computer  22  commands the fuel delivery solenoid  24  to close a fuel delivery valve  26 . Later, at a point determined by a timing control solenoid  34 , high pressure fuel injection pump  22  begins to build injection pressure. Because the fuel delivery valve  26  is closed, this pressure is directed via a distributor valve arrangement to the injector for the appropriate cylinder. Next, the injector opens and fuel injection starts at this point. When the desired amount of fuel has been delivered to the cylinder, the fuel delivery solenoid  24  is released causing the fuel pressure to the injector to drop as fuel is shunted from the injector, causing the fuel delivery to stop. The amount of fuel delivered is proportional to the amount of pump rotation that occurs between the point when the injection starts and when the fuel delivery solenoid  24  is deactivated. 
     FIG. 2 depicts a normal operating waveform  38  seen at a first terminal of the fuel delivery solenoid  24  which is controlled by the fuel injection pump computer  22 . A second terminal of the solenoid  24  is connected to a high current source of the battery  36 , which in a particular embodiment is nominally 13.8 volts. This time waveform  38  depicts a sequence of electronic events that take place for the delivery of fuel to a single cylinder. This sequence is repeated as each cylinder fires in the engine. The signal from the crankshaft rotation position sensor  16  triggers the start of the sequence of electrical events depicted in FIG.  2 . While portions of the waveform  38  may vary with different throttle positions, the start of the sequence (point “A”) is essentially synchronous with the signal provided by the ELM from the crankshaft position sensor. 
     At time point “A”, the pump  22  turns on a large amount of current to the solenoid  24  which starts moving to close the fuel delivery valve  26 . This large amount of current is maintained until time point “B”, which can be about 400 microseconds. From point “B” until point “D”, a lower amount of current is required and thus supplied by the injection pump computer  22  to hold the solenoid  24  closed. The spike at point “C” is caused by the motion of the valve  26  in the magnetic field of the solenoid and is detected by the injection pump computer  22  to verify that the valve is operating properly. 
     The fuel boost controller  28  includes a microprocessor and a plurality of comparators. A first comparator detects the high current delivery by the injection computer  22  and supplies this as a positive pulse to the boost microprocessor. A second comparator detects the valve motion pulse at time point “C” and supplies as a negative pulse to the boost microprocessor. A third comparator detects the large current flyback pulse (referred to as “back EMF”) at time point “D”, when the injection computer  22  is terminating fuel delivery by cutting off the current in the solenoid  24  allowing the solenoid to open. The opening of valve  26  diverts the high injection pressure from the selected injector and allows it to return to the fuel tank by a return line. 
     The software in the boost microprocessor uses internal counters, running from a fixed clock, to time the duration of these external events, and also to time the extension of the solenoid  24  closure time. The leading edge of the pulse at time point “A” is used as an overall timing reference. By measuring the time interval from one “A” edge to the next “A” edge, the boost microprocessor can compute the actual instantaneous RPM of the engine. By measuring the time interval from the “A” edge to the next “D” edge, the boost microprocessor can compute an approximate estimate of the amount of fuel delivery that is being commanded by the ECM  12  and the injection pump computer  22 . 
     It should be noted that this measurement is not exact due to another timing event which occurs between the injection pump computer  22  and the injection pump. This timing event can be referred to as the fuel injection timing adjustment, which is made by the injection pump computer  22 , using another solenoid controlled valve (not shown). This timing adjustment controls the start of actual high pressure injection. Because the fuel boost controller  28  can measure the end of the fuel delivery period, but not the beginning, it does not determine the exact amount of fuel being delivered. In operation of the boost controller  28 , by estimating the starting point of fuel delivery, a reasonable approximation can be made which is sufficient for the purposes of the boost controller operation. 
     The boost controller  28  measures the “A” edge to “A” edge interval and the “A” edge to “D” edge interval. The ratio of the second interval to the first interval indicates a throttle position measurement which is used to determine an amount of additional fuel delivery that should be applied. This determination can be made by the use of an algorithm or other suitable methods. In a particular embodiment, the amount of additional fuel delivery is determined from a table of values or look-up table stored in the boost controller  28 . 
     When the amount of additional fuel delivery is determined, it must be converted into an amount of time that the boost controller  28  will hold the fuel delivery valve  26  closed after the injection computer  22  has released it. This is accomplished by multiplying the actual delivery time (“A” to “D” interval) by the value obtained from the look-up table. 
     Because of the time required for the boost microprocessor  28  to perform these calculations, the values for additional fuel delivery are not available for use until the following cylinder firing sequence. This is of no consequence, however, as long as new values are available for every cylinder sequence. The one cylinder lag or latency does not have a significant impact on the performance of the boost controller  28 . In a particularerred embodiment, the boost microprocessor  28  is fast enough to perform all of these calculations in less than one cylinder time interval, even at the highest RPM of the engine for which fuel delivery augmentation is desired. 
     Because these events occur asynchronously with the boost microprocessor  22  clock, the measurement and computations are performed by interrupt routines in the software, which allows them to be performed as required and as triggered by the external waveform events. 
     Referring to FIG. 3, upon initial power  40  to the fuel boost controller  28 , the software automatically executes an internal self-test  42 , which provides feedback to the user that the controller is installed properly via LED  32 . After this test has passed, the software enables the interrupt system, and waits for the interrupt events to occur  44 . 
     FIG. 4 depicts the “A” edge interrupt routine, which is triggered by an interrupt in the “A” edge. This routine reads a counter  46  to determine the amount of time since the last “A” edge occurred. This value is stored in memory  48 , and the counter is reset  50  for the subsequent measurement. Next, a subroutine is called that calculates the additional fuel delivery time (described with reference to FIG.  6 ). If the values for these intervals are within acceptable limits, additional fuel delivery is enabled at  54 . If the values are not within acceptable limits, which may be caused by electrical noise interfering with the comparators, or the speed of the engine exceeding predetermined limits, then additional fuel delivery will be disabled. Next, an output from the boost microprocessor  28  is set which enables the hardware to drive the fuel delivery solenoid  24  at the detection of the “D” edge, and initiate another interrupt routine for fuel delivery timing. Finally, an interrupt  56  is enabled to respond to the detection of the “D” edge (see FIG.  5 ). 
     Turning to the “D” edge interrupt routine of FIG. 5, when the “D” edge occurs, the fuel boost controller  28  will automatically draw sufficient current to keep the fuel delivery solenoid  24  closed, if the additional fuel delivery has been enabled. This subroutine, initiated by the “D” edge, determines the proper time to cease the additional fuel delivery. An internal counter to the boost processor  28  is loaded with the calculated extended time value at  58 . When this counter has determined that the calculated extended time value has elapsed at  60 , the additional fuel delivery is ceased at  62 . 
     Referring now to FIG. 6, the subroutine that calculates the additional fuel delivery time first computes the throttle position as defined by the ratio of the “A” to “D” time to the “A” to “A” time. This can be expressed as the ratio of the time of fuel delivery from mthe ELM to the time between successive cylinder firings. Because the ECM  12  and injection pump computer  22  may make cylinder-dependent adjustments for purposes such as efficiency, it is preferred that these compensations not be interfered with by the fuel boost controller  28 . Accordingly, a running average is performed at  66  on the throttle position values for each cylinder. For example, if the engine has six cylinders, the running average is performed for the present throttle position value and the previous five throttle position values. This serves to remove individual cylinder compensations from the averaged value. 
     The average value is used to perform a look-up of the desired additional fuel delivery based on the injection pump computer  22  commanded fuel delivery. An exemplary look-up table is provided in Appendix A. Generally, the look-up table allows for a controlled, gradual augmentation of the stock fuel delivery with an additional fuel delivery controlled by the fuel boost controller  28 . This way, additional fuel delivery can be controlled to occur only at moderate to large throttle positions, and the controller  28  does not affect the fuel economy or emissions performance at low to moderate throttle positions. 
     A particular look-up table includes four columns. The first column is an index number which is an arbitrary unit ranging from 0 to 255. The stroke percentage column indicates the percent of one cylinder&#39;s time that the injection pump computer  22  is delivery fuel. This is used as the measured throttle position. The boost percentage is the amount of additional fuel to be delivered by the fuel boost controller  28 . In a particular embodiment, the boost percentage is normalized, i.e., it runs from 0 to 1. This value is multiplied by an overall scale factor at step  70 , nominally thirty percent in regular production units, to allow different performance levels to be obtained from the controller  28 . This result is multiplied by the actual stock fuel delivery time to give a value of additional time for which the fuel boost controller  28  holds the fuel delivery valve  26  closed. The code column is the boost value, expressed in computer units. 
     Next, an exact additional fuel delivery time is computed from the fuel delivery value by multiplying the scaled value by the “A” to “D” time at  72 . This delivery time is expressed in counter units. The final delivery time is also subjected to a running average at  74  which serves at least two useful functions. First, it additionally smooths out cylinder-to-cylinder variations in fuel delivery, resulting in smoother throttle response (see FIG.  7 ). Second, it serves to introduce an overall delay between when large, fast throttle openings occur and when additional fuel delivery occurs. This delay can be on the order of one half to one second, and serves to allow time for the turbocharger on the engine to build up intake air boost pressure. By delaying fuel delivery relative to the boost pressure, particulate smoke emissions from the engine during snap acceleration are reduced. In an alternative embodiment, the fuel boost controller  28  is electronically coupled to the turbocharger and receives the turbopressure as an input. The controller  28  bases the timing of the fuel delivery on the turbo-pressure to reduce particulate smoke emissions. 
     If the resultant delivery fuel delivery time is within acceptable limits  76 , it is saved for later use by the “D” edge interrupt service routine, in timing the actual additional fuel delivery. 
     In one embodiment, the fuel boost controller  28  can be programmed to cause varying performance levels of the engine. For example, the controller  28  can be programmed to improve horsepower up to about 113 per cent. In a particular embodiment, the fuel boost controller  28  includes jumpers which allow the operator to selectively chose the desired amount of performance increase. In another particular embodiment, jumpers are provided on the controller  28  to selectively delay the addition of fuel to reduce particulate smoke emissions. 
     While the performance enhancing system for electronically controlled engines has been particularly shown and described with references to particular embodiments thereof, it will be understood by those skilled in the art that various changes in form and details may be made therein without departing from the scope of the invention encompassed by the appended claims. 
     
       
         
               
               
               
               
               
             
               
               
               
               
               
               
             
           
               
                   
                 APPENDIX A 
               
               
                   
                   
               
               
                   
                 start i = 
                 90 end i = 
                 120 
                 max = 1 
               
               
                   
                 index 
                 stroke % 
                 boost % 
                 code 
               
               
                   
                   
               
             
             
               
                   
               
             
          
           
               
                   
                  0 
                 0 
                 0 
                 dt 
                  0 
               
               
                   
                  1 
                 0.00196 
                 0 
                 dt 
                  0 
               
               
                   
                  2 
                 0.00392 
                 0 
                 dt 
                  0 
               
               
                   
                  3 
                 0.00588 
                 0 
                 dt 
                  0 
               
               
                   
                  4 
                 0.00784 
                 0 
                 dt 
                  0 
               
               
                   
                  5 
                 0.0098 
                 0 
                 dt 
                  0 
               
               
                   
                  6 
                 0.01176 
                 0 
                 dt 
                  0 
               
               
                   
                  7 
                 0.01373 
                 0 
                 dt 
                  0 
               
               
                   
                  8 
                 0.01569 
                 0 
                 dt 
                  0 
               
               
                   
                  9 
                 0.01765 
                 0 
                 dt 
                  0 
               
               
                   
                  10 
                 0.01961 
                 0 
                 dt 
                  0 
               
               
                   
                  11 
                 0.02157 
                 0 
                 dt 
                  0 
               
               
                   
                  12 
                 0.02353 
                 0 
                 dt 
                  0 
               
               
                   
                  13 
                 0.02549 
                 0 
                 dt 
                  0 
               
               
                   
                  14 
                 0.02745 
                 0 
                 dt 
                  0 
               
               
                   
                  15 
                 0.02941 
                 0 
                 dt 
                  0 
               
               
                   
                  16 
                 0.03137 
                 0 
                 dt 
                  0 
               
               
                   
                  17 
                 0.03333 
                 0 
                 dt 
                  0 
               
               
                   
                  18 
                 0.03529 
                 0 
                 dt 
                  0 
               
               
                   
                  19 
                 0.03725 
                 0 
                 dt 
                  0 
               
               
                   
                  20 
                 0.03922 
                 0 
                 dt 
                  0 
               
               
                   
                  21 
                 0.04118 
                 0 
                 dt 
                  0 
               
               
                   
                  22 
                 0.04314 
                 0 
                 dt 
                  0 
               
               
                   
                  23 
                 0.0451 
                 0 
                 dt 
                  0 
               
               
                   
                  24 
                 0.04706 
                 0 
                 dt 
                  0 
               
               
                   
                  25 
                 0.04902 
                 0 
                 dt 
                  0 
               
               
                   
                  26 
                 0.05098 
                 0 
                 dt 
                  0 
               
               
                   
                  27 
                 0.05294 
                 0 
                 dt 
                  0 
               
               
                   
                  28 
                 0.0549 
                 0 
                 dt 
                  0 
               
               
                   
                  29 
                 0.05686 
                 0 
                 dt 
                  0 
               
               
                   
                  30 
                 0.05882 
                 0 
                 dt 
                  0 
               
               
                   
                  31 
                 0.06078 
                 0 
                 dt 
                  0 
               
               
                   
                  32 
                 0.06275 
                 0 
                 dt 
                  0 
               
               
                   
                  33 
                 0.06471 
                 0 
                 dt 
                  0 
               
               
                   
                  34 
                 0.06667 
                 0 
                 dt 
                  0 
               
               
                   
                  35 
                 0.06863 
                 0 
                 dt 
                  0 
               
               
                   
                  36 
                 0.07059 
                 0 
                 dt 
                  0 
               
               
                   
                  37 
                 0.07255 
                 0 
                 dt 
                  0 
               
               
                   
                  38 
                 0.07451 
                 0 
                 dt 
                  0 
               
               
                   
                  39 
                 0.07647 
                 0 
                 dt 
                  0 
               
               
                   
                  40 
                 0.07843 
                 0 
                 dt 
                  0 
               
               
                   
                  41 
                 0.08039 
                 0 
                 dt 
                  0 
               
               
                   
                  42 
                 0.08235 
                 0 
                 dt 
                  0 
               
               
                   
                  43 
                 0.08431 
                 0 
                 dt 
                  0 
               
               
                   
                  44 
                 0.08627 
                 0 
                 dt 
                  0 
               
               
                   
                  45 
                 0.08824 
                 0 
                 dt 
                  0 
               
               
                   
                  46 
                 0.0902 
                 0 
                 dt 
                  0 
               
               
                   
                  47 
                 0.09216 
                 0 
                 dt 
                  0 
               
               
                   
                  48 
                 0.09412 
                 0 
                 dt 
                  0 
               
               
                   
                  49 
                 0.09608 
                 0 
                 dt 
                  0 
               
               
                   
                  50 
                 0.09804 
                 0 
                 dt 
                  0 
               
               
                   
                  51 
                 0.1 
                 0 
                 dt 
                  0 
               
               
                   
                  52 
                 0.10196 
                 0 
                 dt 
                  0 
               
               
                   
                  53 
                 0.10392 
                 0 
                 dt 
                  0 
               
               
                   
                  54 
                 0.10588 
                 0 
                 dt 
                  0 
               
               
                   
                  55 
                 0.10784 
                 0 
                 dt 
                  0 
               
               
                   
                  56 
                 0.1098 
                 0 
                 dt 
                  0 
               
               
                   
                  57 
                 0.11176 
                 0 
                 dt 
                  0 
               
               
                   
                  58 
                 0.11373 
                 0 
                 dt 
                  0 
               
               
                   
                  59 
                 0.11569 
                 0 
                 dt 
                  0 
               
               
                   
                  60 
                 0.11765 
                 0 
                 dt 
                  0 
               
               
                   
                  61 
                 0.11961 
                 0 
                 dt 
                  0 
               
               
                   
                  62 
                 0.12157 
                 0 
                 dt 
                  0 
               
               
                   
                  63 
                 0.12353 
                 0 
                 dt 
                  0 
               
               
                   
                  64 
                 0.12549 
                 0 
                 dt 
                  0 
               
               
                   
                  65 
                 0.12745 
                 0 
                 dt 
                  0 
               
               
                   
                  66 
                 0.12941 
                 0 
                 dt 
                  0 
               
               
                   
                  67 
                 0.13137 
                 0 
                 dt 
                  0 
               
               
                   
                  68 
                 0.13333 
                 0 
                 dt 
                  0 
               
               
                   
                  69 
                 0.13529 
                 0 
                 dt 
                  0 
               
               
                   
                  70 
                 0.13725 
                 0 
                 dt 
                  0 
               
               
                   
                  71 
                 0.13922 
                 0 
                 dt 
                  0 
               
               
                   
                  72 
                 0.14118 
                 0 
                 dt 
                  0 
               
               
                   
                  73 
                 0.14314 
                 0 
                 dt 
                  0 
               
               
                   
                  74 
                 0.1451 
                 0 
                 dt 
                  0 
               
               
                   
                  75 
                 0.14706 
                 0 
                 dt 
                  0 
               
               
                   
                  76 
                 0.14902 
                 0 
                 dt 
                  0 
               
               
                   
                  77 
                 0.15098 
                 0 
                 dt 
                  0 
               
               
                   
                  78 
                 0.15294 
                 0 
                 dt 
                  0 
               
               
                   
                  79 
                 0.1549 
                 0 
                 dt 
                  0 
               
               
                   
                  80 
                 0.15686 
                 0 
                 dt 
                  0 
               
               
                   
                  81 
                 0.15882 
                 0.004 
                 dt 
                  1 
               
               
                   
                  82 
                 0.16078 
                 0.005 
                 dt 
                  1 
               
               
                   
                  83 
                 0.16275 
                 0.007 
                 dt 
                  1 
               
               
                   
                  84 
                 0.16471 
                 0.009 
                 dt 
                  2 
               
               
                   
                  85 
                 0.16667 
                 0.012 
                 dt 
                  3 
               
               
                   
                  86 
                 0.16863 
                 0.014 
                 dt 
                  3 
               
               
                   
                  87 
                 0.17059 
                 0.018 
                 dt 
                  4 
               
               
                   
                  88 
                 0.17255 
                 0.024 
                 dt 
                  6 
               
               
                   
                  89 
                 0.17451 
                 0.028 
                 dt 
                  7 
               
               
                   
                  90 
                 0.17647 
                 0.033 
                 dt 
                  8 
               
               
                   
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