[ieee 2009 international conference on engineering education (iceed) - kuala lumpur, malaysia...

2009 International Conference on Engineering Education (ICEED 2009), December 7-8, 2009, Kuala Lumpur, Malaysia

An EV -Simulator for Electric Vehicle Education G. N. Reddy

Drayer Department of Electrical Engineering, Lamar University Beaumont, TX, USA

[email protected]

Abstract-This paper presents an Electric Vehicle simulator to aid in Electric Vehicle Education. There has been an exponential surge in demand for developing new generation of vehicles using electric-technology. That has caused rapid shift in design paradigm from mechanical to electrical. Such a paradigm shift requires developing new technology educational programs in electric vehicles. The EV-simulator presented in this paper will be helpful for such programs. The simulator is written in Visual C++IMS Visual Studio .NET 2007. It is called LAMAR-EVSiml after Lamar's first Electric Vehicle Lamar-EVI. The tool is primarily tailored for educational use. Input data to the simulator is presented through a set of input data files including specifications of: the vehicle, the electric-elements, and the environment. The simulator estimates output parameters hierarchically from the tire, gear-box, motor, battery-pack, and finally at vehicle-level. The estimated output parameters include: various drag forces, torques, currents, voltages, RPMs, powers, top speeds, and mileages. Unlike other ev-simulators, this simulator embeds dynamic equations & algorithms contextsensitively so that the output simulation trace are selfinstructive.

Keywords-Electric Vehicle Education; EV-Simulator; EV Design Software; Lamar-EVSiml

I. BASIC EV -HARDWARE

"Fig. I" shows a basic configuration of an Electric Vehicle (EV). It essentially consists of standard drive-train with electric propulsion replacing an internal combustion engine. It requires a tailor made adapter-set to couple the electric traction motor to a vehicle-specific drive-train. Specific elements used with our Lamar-EVI are:

1. Vehicle: VW-Rabbit 1980; 2. Motor: advanced DC-motor: 203-06-4001; 3. Controller: dc-motor controller: Curtis-pmc 1221 4. Batteries: 9 pba, 12-volt, 60 lb, series-connected, Interstate

batteries, one 12-volt auxiliary battery for main contact 5. Charger: 96-120 vdc charger: evc40lc to run from 115 vac 6. sr-adapter-set: to couple adv-dc-motor to vw-rabbit-1980 7. Throttle: foot-pedal-5k pot wi micro-switch to cutoff in idle Familiarity with EV -hardware is essential to better understand the simulation results.

978-1-4244-4844-9/09/$25.00 ©2009 IEEE 131

II. VEHICLE-SIMULATORS

There are several vehicle simulators in the market today, these can be divided into the following three categories:

1. Mechanical vehicle simulators [1-2] 2. HEV (Hybrid Electric Vehicle) simulators [3-6] 3. EV (Electric Vehicle) simulators [7]

Left-TIre

wheel-assembly ""--"-",--'

Left-drive-axel "" cv-joint

.-'-tt----7'1 u-joint

To couple motor & gearbox differential break pedal )-----------------HI Feed-backward EV-simulation: <= Pm, Vm, 1m, Rm: Motor <= (Nd, Gk) Drive_train <= Pt, Tt, F, W: Tire

(Nc, Nm) => Battery: Vbp, Ibp, Pbp: => Vehicle: Umax, Mileage ,-..LL-'----, Right-Tire

Figure I. Basic Electric Vehicle Configuration: Lamar-EV I.

The first category of tools includes CarSim [I] and Cartest 2000 [2]. CarSim is used to study the mechanical stability of a vehicle in response to braking, steering, and acceleration. Cartest on the other hand, is used to compare such things as acceleration-profiles of different existing-vehicles.

The second category tools are essentially used to do performance analysis of hybrid-power-trains for optimal fuel economy and minimal pollution. That is, to determine percentage of power-share between mechanical-propulsion to the electrical propulsion. It also involves in determining optimal control strategies for HEV operation. Some of these HEV simulators are written by themselves [3]. The other tools are already developed include: PSAT 6.1 [4] developed and sponsored by DOE's Vehicle Technologies Program. The most complex of HEV-simulators is the Advisor [5]. It is currently maintained and distributed by A VL. Majority of the current HEV -simulators are written in Matlab/Simulink.

The third category of tools [6-7] is pure EV -simulators. The EV -simulator presented in this paper is similar to [6-7]. It is, however, heavily tailored for educational use. Here the entire set of dynamic equations and algorithms used are

2009 International Conference on Engineering Education (lCEED 2009), December 7-8, 2009, Kuala Lumpur, Malaysia

context-sensitively embedded into the output simulation trace 3.2 OUTPUT SIMULA TION TRACE so one can fully understand how an individual output The output simulation trace is generated using "feed-parameter is estimated. In an educational setting one want backward" simulation executive. The computed output know what the outputs are but more importantly to want to parameters can be divided into the following categories: know how those outputs are computed. Furthermore, this paper in itself comprehensively covers entire EV-simulation Part-A: Computing Overall Vehicle Net Weight in one place. The combination of this document with the Part-B: Computing Static Drag Forces simulator should provide good material for EV -education. Part-C: Computing Tire-Torque Multiplication Factor

Vehicle simulators can also be categorized as "feedforward" and "feed-backward" based where computation starts and where it ends. The feed-forward-simulators simulate real-life scenarios: here computations start with the driver's pedal position and ends with computing torque delivered at the wheels. In the feed-backward simulators, it starts with the required torque at the tire and ends with in finding driver's pedal position (the amount of fuel or potthrottle position for EVs). Some of the feed-forward simulators are: CarSim, Cartest-2000, and the ADVISOR; whereas Uve's and Halstead's EV-Calculators are feedbackward simulators. The EV -simulator presented in this paper, Lamar-EVSiml, is a feed-backward simulator. The following sections describe Lamar-EVSiml.

III. LAMAR ELETRIC VEHICLE SIMULATOR 1

The output listing of this simulator, Lamar-EVSiml, can be divided into two sections: Listing of Input Data & Listing of the computed values.

3.1 INPUT DA TA: Input to the simulator is specified using three input data files: a. vehicle-data; b. electric-elements-data; and c. environmentdata.

A. Vehicle Data Input File The frrst input file includes: al - vehicle information such as: drag-coefficient, frontal area, drive efficiency, and gear ratios of the gear box; a2 - the tire specification: width, aspect ratio, and rim-diameter; a3 - other vehicle parameters such as: rolling resistance, break and steering, weight removed and weight added when converted into an electric vehicle.

B. Electric Elements Input Data File The second input file contains: bI - Electric motor's specs such as: its max volts, max weight, hp, and motor constants -a, b, c, d, k, and n; b2 - Battery pack specs such as: individual battery - voltage, weight, Puekert number, Peukert amps, dcresistance, number of batteries connected in series and number of such strings connected in parallel; b3 - Motor controller specs: minimax voltages, max current, its weight, and overall efficiency; b4 - the charger specs: minimax voltages, max current, and its weight.

C. Environment Input Data File The third input file contains environment in which vehicle is going to be driven such as: c1 - percentage of incline; c2 -wind-speed and relative-wind-factor; and c3 - the tireinflation-factor.

132

Part-D: Computing Dynamic Drag-forces, Torques, Powers Part-E: Computing Gear Results Part-F: Computing Top-Speeds in Different Gears Top-Speed

Algorithm For the formulas used in this simulation refer to [8].

Part-A: Computing Overall Vehicle Net Weight

In this section, overall vehicle weight is determined from the known ev-element-weights. This includes the weight of: vehicle, battery-pack, motor, controller, and charger. It also accounts for overall weight removed and any miscellaneous weight added. Overall net weight of the vehicle is given by

(1)

where Wcw is the original vehicle curb weight; Wa and Wr are the weights added and removed while converting the vehicle into electric. The weights added is given by

(2)

where W bp is the battery pack weight, W m is the motor weight, We is the controller weight, Weh is the charger weight, and W ms is any miscellaneous weight added to the vehicle. The battery pack weight Wbp depends on n-number of batteries connected in series and m-number of such battery-strings connected in parallel. The battery pack weight is given by

(3)

where Wb is the weight of an individual battery. The weights removed Wr is given by

where Weng is the weight of the ice, Wfs is the weight of the fuel system, Wex-ec is the combined weight of the exhaust and emission control systems, W sl is the weight of the starter system, and WeI-hI is the combined weight of the cooling and heating systems. All weights used in this simulator are in lbs.

Part-B: Computing Static Drag Forces ?????

Here the simulator estimates the static drag-forces encountered by the EV which are independent of the vehicle speed. This includes weight-drag-force, incline-drag-force, hill-climb-drag-force. The weight-drag-force is due to the overall net weight of the vehicle and incline-drag-force is due to road's percentage of incline. The static drag force due to vehicle weight is given by


where Cr is the coefficient of rolling resistance, Cb is the coefficient of breaking and steering resistance of the vehicle, and h is the percentage of incline or hill climbing in the drivecycle. The static drag force due to hill is given by

Part-C: Computing Tire-Torque Constant Cite The tire torque multiplication factor T t1mf is used to

compute torque at the tire from the drag-force as:

T = Cttc * F (7)

where T is the torque at the tire in ft-Ibs, Ctte is in ft, and F is the overall static-drag-force in lbs. Cttc is a constant for a given vehicle and is computed from the vehicle's tire specifications as shown in Appendix A and B. It's value is given by:

(8) where Rl is the vehicle tire's revolutions per mile. It is computed from the tire-size specifications as shown in Appendix B. To some extent it varies with tire-inflationcoefficient Clif•

Part-D: Dynamic Drag-forces, Torques, powers Dynamic-drag Forces:

In this section, dynamic drag-forces are computed for varying vehicle speeds. Dynamic drag forces involved are area-drag-forces and wind-drag-forces. The area-drag-force is a function of vehicle drag-coefficient, vehicle frontal area, and the vehicle speed and is given by:

(9) where Cd is the drag coefficient, A is the frontal area of the car in sq-ft, Vi is the vehicle speed in mph. The drag coefficient of the vehicle depends on the aero-dynamic-shape of the vehicle. Its value may varye from 0.25 for a best shaped sedan to 0.45 for a worst dynamic vehicle such as a truck.

The wind-dynamic-drag-force is function of wind-speed and vehicle speed ratio. It is computed as the product of the area-drag force and a wind-factor. The wind factor in turn is proportional to the wind-speed and inversely proportional to the vehicle speed in a very complex way. It's effect will be highest at lower vehicle speeds and becomes minimal at higher vehicle speeds. The dynamic-wind-drag-force is given by:

(10)

Where Cwfi is the wind-factor at wind-speed Wi and vehicle speed Vi. The relative wind factor Cwfi is given by

133

Cwfj = {0.98 (�:)2 + 0.63 (�:)} Crw - 0.40 (�:) (11)

where Wi is the average wind speed in mph, Vi is the vehicle speed in mph, Crw is the relative wind factor. The relative wind factor depends on the atmospheric humidity, temperature, and how vehicles are driven such as driving with open windows. Its value varies between 1.2 to 1.6 depending on the vehicle type and how it is driven. As it can be seen from (11), the effect wind-speed decreases at higher vehicle speeds. The total sum of all the drag forces Fti at vehicle speed Vi and wind speed Wi is given by:

Ftotl = Fw + Fh + Fal + FWI (12)

where Fw is the drag force due to vehicle weight, Fh is the drag force due to hill-climbing, Fa; is the dynamic area drag force, and FWi is the dynamic wind drag force.

Dynamic torques:

Knowing the cumulative drag forces Ftoti at varying vehicle speeds, the corresponding rotational torques, at the tire, are then computed using the vehicle's torque multiplication factor as

Ttirel = Tttmf * Ftotl (13)

where Tttmf is the tire torque multiplication factor given by (8), Ftot is the total static and dynamic drag forces on the vehicle given by (12).

Dynamic power: The power requirements are then estimated from the

known torques. The factors involved in computing the power are: the tire torque, the vehicle speed, tire's rotations per mile, and overall drive-train-efficiency.

(Ttirel * VI * R1) Ptirel =

(5252 * 60) (14)

where Ptirei is the power at the tire in hp, Ttirei is torque at the tire in ft-Ibs, Vi is the vehicle speed in mph, and revPerMile is the tires's revolutions per mile.

Part-E: Computing Gear Results

In this section, the dynamic performance requirements of the motor and the battery are computed; which are then used in predicting the overall vehicle performance in different gears.

To supply the required torque and power at the tire, the motor requirements are computed including: torque, rpm, amps, volts, and power; the requirements at the battery-pack are then computed including: power, amps, volts; and fmally, the overall vehicle performance in terms of its expected mileage and the attainable top-speeds in each gear are estimated. The top-speed algorithm is listed in part F.

Computation of Motor Requirements: The required motor torque Tmotorj, in ft-Ibs, is given by:


(15)

where Ttirei is the tire-torque at i-mph, Gi is the gear-ratio, and TJd is the overall drive-train efficiency.

The required motor rpm R.m, in rpm, is given by: (Ui * Gk * Rl)

Rmi = 60

(16)

where Ui is the vehicle speed in mph, Gk is the gear-ratio, Rl is the tire's revolutions per mile.

The required motor amps Imh in amps, is given by:

1 _ (Tmi )N I· - -ml K

(17)

where Tmi is the required motor torque at vehicle speed of imph, K and N are motor constants.

The required motor volts Vmotorh in volts, is given by:

(Rmi * D) Vmi = {

A } = - + C

TmlB

(18)

where Tmi is the required motor torque, in ft-Ibs, and Rmi is the motor rpm at vehicle speed of i-mph; and fmally A, B, C, D are motor constants.

The required motor power P mi, in kw, is given by:

(19)

where lmi is the motor current at vehicle speed of i-mph, V mi is the corresponding motor volts.

Computation of Battery-Pack Requirements: The required battery-pack Pbph in kw, is given by:

Pb - Pml PI -

(l1c >l1m) (20)

where P mi is the motor power at vehicle speed of i-mph. The TJm is the overall efficiency of the motor in converting electrical energy into mechanical energy; and fmally, TJc is the overall controller efficiency in converting the DC battery pack voltage into Pulse Width Modulated PWM-signal to the DCmotor in case of a DC-drive; and into 3-phase Variable Frequency Drive VFD-signal to the AC-motor in case of an AC-Drive.

The required battery-pack Ibph in amps, is given by:

I - Pbpl bpi -

(Vbpl > m ) (21)

where Pbph Pbpi are the battery pack power and voltage at vehicle speed of i-mph; m is the number of series-connected battery strings configured in parallel.

The battery-pack voltage Vbph in volts, is then given by:

134

Vbpi = Vbpmax - (Ibpi * Rbp) (22)

where V bpmax battery-pack voltage, in volts; Rbp is the batterypack resistance, in ohms. �p in turn is computed as, (� * n)/m; where � is the individual battery resistance, n the number of batteries connected in-series, and m the number of such series connected battery strings connected in parallel.

Computing vehicle parameters: The vehicle range in miles, at different vehicle speeds, Rvrl, in miles, is given by:

(23)

where IbPk is the individual battery Peukert amps, in amps; Ibpk is the battery-pack current, in amps, at vehicle speed imph; n is the individual battery's Peukert-exponent.

Part-F: Computing Top-Speeds - in Different Gears The Top-speed Algorithm

The top-speeds, in each gear, that the vehicle can attain is limited by: a. the capabilities of the battery-pack - if it can provide sufficient voltage and current required for the motor; and if the motor in itself can rotate at the rpm required at the top-speed. The procedure used to compute the top-speed in the form a psedo-code listed in Part-F of the output simulation trace. It is top-speed algorithm. To determine the top-speed and corresponding limiting factor in each gear: First find the required motor voltages, amps, and the RPMs for the entire speed-range at an interval of one mile. The top-speed is the minimal speed at which one of the following three limiting factors is reached: battery-pack max voltage, battery-pack max current, or the max of motor RPM.

IV. THE LAMAR-EVSiml SOFTWARE

The software is implemented in Visual C++ under MS Visual Studio .NET 2005. The executable is stand-alone. It has three input files and generates one output file. Appendix C shows a small section of the output simulation trace. The software is available for interested readers.

V. CONCLUSIONS

This software was to teach a graduate course on "Modeling and simulation of Electric Vehicles" and found to very valuable. It is essential that the EE-programs recognize this huge paradigm shift in the auto design and alter their curriculum to include the study, design, and simulation of electric vehicles & hybrid-electric vehicles. Current version of the EV -simulation software that we have developed, LamarEVsiml, is text-based; the next version, which is currently in progress, is a GUI-based.

ACKNOWLEDGMENTS

This work in part funded through the project: Lamar-EVl, Green Foundation, Port Arthur, Texas, 2006-2007.

2009 International Conference on Engineering Education (lCEED 2009), December 7-8,2009, Kuala Lumpur, Malaysia

REFERENCES

[ I] CarSim (2009), carsim.com.

[2] CarTest software (2009), cartestsoftware.com

[3] Center for Automotive Research (2009). Modeling, Simulation & Control of HEV, Ohio State University, Columbus, Ohio 43212; http://elearn.eng.ohio-state.edu.

[4] NREL, PSAT 6.llMatlabI4: Power_train Systems Analysis Toolkit, 2009, transportation.anl.govl modeling_simulationlPSAT/index.html.

[5] Department of Energy DOE (2004). ADVISOR Simulation Tool for Vehicle Evaluation and Testing, http://wwwl.eere.energy.gov/vehiclesandfuels/pdfs/ success/ advisor_simulation _tool.pdf

[6] Uve Rick, Uve's Electric Vehicle Calculator, 1997-2004, http://www.geocities.comlCapeCanaverai/ lab/ 8679/ evcalc.html.

[7] Jerry Halstead, EV-Calculator, 2005-2009, http://www.evconvert.comltools/evcalc/

[8] Seth Leitman and Bob Grant, Build Your own Electric Vehicle, 2nd ed., McGraw-Hill: New York, NY.

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2009 International Conference on Engineering Education (lCEED 2009), December 7-8,2009, Kuala Lumpur, Malaysia

APPENDIX A: Computing Tire Torque Multiplication Constant: Cttc

Cttc is needed to compute torques from the drag forces. It is expressed as function of revPerMile, number of revolutions a vehicle's tire rotates per mile, as follows:

Power = Torque * Speed = Force * Velocity (AI)

where the "Power" is in ft-Ibs/sec, the "Torque" in ft-Ibs, the "Speed" in radians per second, drag-force "Force" is in lbs, and fmally the "Velocity" is in ftlsec.

Torque = (Velocity / Speed) * Force = Cttc * Force (A2)

For a given vehicle Cttc is a constant; and how it is computed is shown in the following section. The equation (a2) with units is given by:

P(ft-Ib/sec) = T(ft-Ibs)*S(radians/sec) = F(lbs)*V(ftlsec) or

T(ft-Ibs)={V(ftlsec)/S(radians/sec)} *F(lbs)=Cttc * F(lbs) (A3)

From (a3),

Cttc = {V(ftlsec)/S(radians/sec)}

jt/sec = {(60*60)/(1760*3)} mileslhr

(A4)

(A5)

Since, 1 revolution = 2 7t radians; 1 radian = (1I27t) revolution;

radians/sec = (1I27t) revs/sec = (60*60/27t) revslhour (A6)

Substituting (a5) and (a6) into (a4) gives: Cttc = V(ftlsec)/S(radians/sec) = {(60*60)/(1760*3) mileslhour} 1 {(60*60/27t) revlhour} = 27t/(1760*3) miles/rev = (5280/27t) 1 revPerMile = 840.76 1 R1.

Cttc = 840.761 Rl (A7)

APPENDIXB: Computing Tire's Revolutions Per Mile (RI) & Tire Size Specification

In (A 7), if Rl is known then Cttc can be computed. This section describes how to compute this parameter revPerMile of a tire for a given vehicle's tire specification.

Tire size specification: The tire size in North America is specified by three parameters: 1. Tire-width in mm; 2. tire-side-wall-height specified as a percentage of the tire-width; and 3. tire-rimdiameter in inches. For example, 190-60-14R tire has a tire width of 190 mm; the tire-side-wall-height is 60% of the tirewidth (190 * 0.6 = 114 mm = 4.49 inches); and finally, the tire-rim diameter is 14 inches. The total wheel diameter will then be 14 + (2 * 4.49) = 22.98 inches. The construction of the fabric tire is Radial type. Here, first the side wall height of the tire is determined using the tire's aspect ratio as:

136

. . (tireAR) (

1 ) tireswH = tireWi dth * -- * --100 10'2.54 (Bl)

where tireSWH is the side wall height in inches, tirewidth is the width of tire in mm, tireAR is the tire aspect ratio expressed as:

tire = ( tire SWH )

* 100 AR tire width

Computing revPerMile RI: Wheel diameter is given by

wheeleDi a = tireRlmDi a + (2 * tireSWH)

(B2)

(B3)

Distance traveled, in inches, by the wheel in one revolution is:

disPerRev = p i * wheeleDi a (B4)

revPerMile, number of revolutions this wheel rotates in one mile, with tire inflation coefficient Ctif is given by:

revPerMile = {(1760 * 3 * 12/ disPerRev)} / etif (B5)

where Ctif is the tire inflation coefficient typically varying from 0.8 to 1.0 corresponding to 80% to 100% tire inflation.

APPENDIXC: Lamar-EVSim1 : Output Simulation Trace

LAMAR-EVSim1: OUTPUT SIMULATION TRACE G. N. Reddy Drayer Department of Electrical Engineering Lamar University, Beaumont, TX 77710 Update 2.0, 03/24/2009

A: READING INPUT DATA Reading data from: in1_vehic1e.txt Vehicle Information: Reading input data 1: End Reading data from: in2 e1ectricE1ements.txt Electric Elements: Reading input data 2: End Reading data from: in3_environmental.txt Environmental Data: Reading input data 3: End

INPUT DATA 1: in1 vehicle.txt a1. Vehicle Information: Cd, Drag coefficient A, Frontal area, sq-ft Wvcw, Vehicle curb weight, lbs =

Nd, Overall drive efficiency =

gl, Gear ratio 1 g2, Gear ratio 2

INPUT DATA 3: in3 environmental. txt c1. Environmental Conditions: h, Percentage of hill-climb =

windSpeed, mph Crw, Relative wind factor Ctif, Tire inflation factor rimDia, inches

0.30 18.00

2500.00 0.91

12.01 7.82

5.00 15.00

1. 60 0.9639

14.00


PART D: DYNAMIC DRAG FORCES, TORQUES, POWERS FOR VARYING SPEEDS AT THE TIRE: VehSpeed mph 10 20 30 40 50

a. Fwt 1bs 172 172 172 172 172 b. Fh 1bs 191 191 191 191 191 c. Fa 1bs 1.4 5.5 12.4 22.1 34.5

windFactor 4.4 1.3 0.7 0.4 0.3 d. Fw lbs 6.0 7.2 8.4 9.5 10.7 e. Ft lbs 370 375 383 394 408 f. tireTorque ft-lbs 345 350 357 367 380 g. tirePower hp 9.9 20.0 30.7 42.0 54.4

DYNAMIC EQUATIONS: Fa [i] =Cd*A*pow (vehSpeed[i] , 2)/391; windFactor[i]=(0.98*r1sq+0.6*r1)*Crw-0.40*r1;where,

Ft[i] = Fwt + Fh + Fa[i] + Fw[i]; tireTorque[i] = Tttmf * Ft[i];

60 70 80 172 172 172 191 191 191

49.7 67.7 88.4 0.2 0.2 0.2

11.8 13.0 14.2 424 443 465 395 413 433

67.8 82.7 99.2

tirePower[i] = (tireTorque[i] * vehSpeed[i] * revPerMile) / (5252 * 60);

90 172 191

111. 9 0.1

15.3 490 456

117.5

E: GEAR RESULTS: MOTOR, BATTERY_PACK, VEHICLE: PERFORMANCE IN DIFFERENT GEARS: Motor: torque-rpm-amps-volts-power Battery_Pack: power-amps-volts Vehicle: mileage, top speed

GEAR 1 RESULTS: VehSpeed mph 10 20 30

a. tireTorque ft-lbs 345 350 357 b. reqMotorTorque ft-lbs 32 32 33 c. reqMotorRpm rpm 1805 3610 5416 d. reqMotorAmps amps 249 251 255 e. reqMotorVolts volts 40 81 123 f. reqMotorPower kw 10 20 31 g. batteryPackPower kw 11 23 35 h. batteryPackAmps amps 93 189 289 i. batteryPackVolts volts 113 105 97 j. vehRange miles 12 9 8 TOP SPEED: 29 mph; Limitation: Battery voltage; reqMototVolts

DYNAMIC EQUATIONS:

40 50 60 70 367 380 395 413

34 35 36 38 7221 9026 10831 12636

260 266 273 282 166 210 255 303

43 56 70 85 48 62 77 94

397 515 644 787 88 79 68 57 7 6 6 5

@ this speed 119

reqMotorTorque[i] = tireTorque[i] / (geaCratio[n] * Nd); reqMotorRpm[i] = (vehSpeed[i] * geaCratio[n] * revPerMile) / 60;

80 433

40 14441

291 352 103 114 947

44 5

batteryPackAmps[i]=(batteryPackPower[i]/batteryPackVolts)/numOfStrings; vehRange[i] = vehSpeed[i] * puekertAmps / r4; where r4 = pow(batteryPackAmps[i], puekertExp);

GEAR 5 RESULTS: VehSpeed mph 10 20 30 40 50 60 70

a. tireTorque ft-lbs 345 350 357 367 380 395 413

j. vehRange miles 9 7 6 5 5 TOP SPEED: 60 mph; Limitation: Battery voltage; reqMototVolts @ this speed

F: COMPUTING TOP SPEEDS, IN DIFFERENT GEARS TOP-SPEED ALGORITHM: for (i = 1; i <= 90; i++) { if (reqMotorVolts[i] > batteryMaxVolts)

topSpeed = i-1, vLimit = reqMotorVolts[i-1], vflag 1; if (reqMotorAmps[i] > batteryMaxAmps)

topSpeed = i-1, aLimit = reqMotorAmps[i-1], aflag 1; if (reqMotorRpm[i] > motorMaxRpm)

4

119

topSpeed = i-1, rpmsLimit = reqMotorRpm[i-1], rpmflag = 1; } Note: reqMotorVolts[i], reqMotorAmps[i], and reqMotorRpm[i]

are already computed for all i (i = 1 .. 90)

END OF OUTPUT SIMULATION TRACE: LAMAR-EVSim1

137

4

80 433

3

90 456

42 16247

302 404 122 135

1126 30 4

90 456

3

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