Assignment 2

Interoffice Memorandum

TO : Dr. Antonio Gauchia

FROM : Joy Pandya

DATE : 10 – 10 – 2016

Subject: HW-2. Power Requirement, Introduction to Matlab and Model Based Design

In this report, analysis of the race vehicle through the data collected from DAQ (Data

Acquisition System) has been shown. Simulink model has been generated for calculations.

Process

When the vehicle is moving, it experiences mainly 2 resistances; drag resistance, rolling resistance and slope resistance. Drag resistance depends on vehicle speed, air speed and vehicle aerodynamic profile. For very slow speed, we can ignore the drag resistance. Rolling resistance is the resistance between vehicle tires and the pavement and slope resistance is due to the road profile on which vehicle is moving. If the slope is more, the vehicle has to overcome more gravitational force and thus, more slope resistance.

Finding

The equations have been generated using Simulink and data for vehicle acceleration profile,

tractive force profile, vehicle resistance profile and vehicle speed and slope profile has been

plotted and discussed.

MEEM/EE 4295

Introduction to Propulsion Systems for Hybrid Electric

Vehicles

Michigan Tech

HW-2. Power Requirement, Introduction to Matlab and

Model Based Design

Date: 10 – 10 – 2016

Student name: Joy Pandya

HW-2. Power Requirement, Introduction to Matlab and Model Based Design

P a g e 2 | 16

1 Introduction

In part 1 of HW, time, velocity and slope data is given. I have made arrays of that data into

Matlab. I have also used derivative block into Simulink to find out the acceleration. Finally, I

used callback function to fetch acceleration to the Matlab. In part 2 of HW, I have prepared

Simulink model for vehicle tractive forces (drag resistance, rolling resistance and slope

resistance). I have also calculated total resistance vehicle is facing. I have used callback function

to call all the calculated parameters to the Matlab Then I have prepared plots of tractive force

profile, vehicle acceleration profile, vehicle resistance profile and vehicle speed and slope

profile and I also presented discussion on that.

2 Calculations, plotting and discussion

We have data obtained from DAQ as shown in table 1.

Table 1: Vehicle parameters (obtained from DAQ)

Time (s) [0 13 145 148 160 165.5 180 183 300 300.001 349.999 350 390 390.001 493.6 500]

Vehicle speed (mph) [0 60 60 40 40 70 70 55 55 55 55 55 55 55 55 0]

Slope (deg) [0 0 0 0 0 0 0 0 0 4 4 -4.5 -4.5 0 0 0]

Vehicle weight (Lbf) 4100

Rolling resistance coefficient f0=0.008; fs=0.002

Drag coefficient 0.4

Vehicle front area (m2) 2.7

Feeding these data into Matlab, we can generate plot for vehicle speed and slope profile.

Matlab code for getting time, vehicle speed and slope in array form is shown as Figure: 6 in

Appendix. Figure: 1 denotes vehicle speed (mph) and terrain slope (deg) vs time.

2

Figure 1: Vehicle speed and slope profile

3

Acceleration calculation:

Calculation for acceleration has been done using Simulink. Simulink model is shown as Figure: 7

in Appendix We can get acceleration as shown in Figure: 2.

Figure 2: Vehicle acceleration profile

From Figure: 1, we can say that maximum value of vehicle acceleration is 2.5 m/s2 at

162 s and maximum value for vehicle de-acceleration is 3.85 m/s2 at 490 s.

Between 0 s to 15 s, velocity increases and thus acceleration also increases.

Between 15 s to 145 s, velocity is constant so acceleration is 0.

Between 145 s to 493 s, velocity first decreases, then it remains constant, then it

increases, then it remains constant for some time, then again it decreases and finally it

remains constant till 493 s. Same trend can be seen in acceleration plot. Acceleration is

0 between 185 s and 493 s as velocity is constant.

Between 493 s and 500 s, velocity decreases as so acceleration also decreases.


4

Resistance calculation:

I have developed the Simulink model for calculating rolling resistance, drag resistance

and slope resistance. Model is shown in appendix (Figure: 8 and Figure: 9). Matlab code

for plotting results is shown as Figure: 10, Figure: 11, Figure: 12 and Figure: 13 in

appendix.

It is important to know how the values of resistance changes with time and which

resistance is more dominant than another. To compare these two things, I have plotted

drag resistance, rolling resistance, slope resistance and total resistance in single graph,

which can be seen in Figure: 3.

Formulas used:

1. Drag resistance (N) = 0.5 * Cd * A * v2 * ῥa

Where, Cd = Aerodynamic drag coefficient

A = Vehicle front area (m2)

v = Vehicle speed (m/s)

ῥa = density of air (kg/m3)

2. Slope resistance (N) = w*sineΘ

Where, w = mass of vehicle (kg)

Θ = Pavement angle with horizontal

3. Rolling resistance (N) = w*fr*cosΘ

Where, fr = fo + fs (𝑣

100)2.5

fo & fs = Rolling resistance coefficient

v = speed of vehicle (km/h)

w = mass of vehicle (kg)

Θ = Pavement angle with horizontal

4. Total resistance (R) = Drag resistance + Slope resistance + Rolling resistance

5

Figure 3: Vehicle resistances profile

6

Discussion:

1. Between 0 – 15 s:

From Figure: 3, we can say that resistances increase from 200N to 775 N

between 0 s to 25 s. We can justify this by observing Figure:1 and Figure:2. From

Figure: 1, we can see that vehicle velocity increases from 0 mph to 60 mph in 0 –

15 s. So Rolling resistance and aerodynamic drag resistance should also increase

between this time frame. From Figure: 3, we can see that, during this time

period, these both resistances are increasing from 200 N to 300 N and 0 N to 490

N respectively. As terrain slope is 0 deg., slope resistance value is 0 N.

Total resistance increases from 200 N to 790 N.

Rolling resistance will not be 0 N even if vehicle is not moving because of static

rolling resistance coefficient, fo.

2. Between 15 – 145 s:

From Figure: 1 and Figure:2 we can see that driving conditions do not change in

this time frame. So, value for resistances should not change. We can see the

same thing in Figure: 3.

3. Between 145 – 185 s:

From Figure: 1, we can see that in this time period, vehicle speed first decreases

from 60 mph to 40 mph, then it remains constant at 40 mph for 12.5 s, then it

increases from 40 mph to 70 mph, then it remains constant at 70 mph for 15 s

and then it decreases to 55 mph. As we know aerodynamic drag and rolling

resistance is directly proportional to vehicle speed, we should expect the same

changing pattern for these 2 resistances. From Figure: 3, we are able to see the

exact same pattern for these 2 reactive forces. Aerodynamic drag force reduces

from 490 N to 200 N, remains 200 N for 12.5 s, shoots up to 650 N, remains 650

N for 15 s and comes down to 400 N. Rolling resistance reduces from 300 N to

250 N, remains 250 N for 12.5 s, shoots up to 300 N, remains

300 N for 15 s and comes down to 250 N. As terrain slope is 0 deg., slope

resistance value is 0 N.

Total resistance also decreases from 790 N to 450 N, remains 450 N for 12.5 s,

increases to 950 N, remains 950 N for 15 s and then decreases to 650 N.

4. Between 185 – 300 s:

From Figure: 1 and Figure:2 we can see that driving conditions do not change in

this time frame. So, value for resistances should not change. We can see the

same thing in Figure: 3.


5. Between 300 – 390 s:

From Figure: 1, we can see that velocity remains constant during this time frame

but terrain slope increases from 0° to 4° at 300 s, remains 4° for 50 s, come down

to -4.5° at 350 s and remains at -4.5° for 40 s. So, only slop resistance value

should change. From Figure: 3, we can see slope resistance increases from 0 N to

1280 N at 300 s, remains at 1280 N for 50 s, drops down to -1450 N at 350 s and

remains at -1450 N for 40 s.

Total resistance value changes from 650 N to 1930 N, remains 1930 N for 50 s,

come down to -800 N at 350 s and remains -800 for 40 s.

Negative value for total resistances shows that car can move without any

external force.

6. Between 390 – 500 s:

From Figure: 1, we can see that at 390 s, slope increases from -4.5° to 0° then it

remains constant till 500 s. Between 493 s to 500 s, speed decreases from 55

mph to 0 mph. So, at 390 s, slope resistance should increase and then till 500 s, it

should be constant. And drag resistance and rolling resistance should decrease

between 493 s to 500 s. From Figure: 3 we can see that, at 390 s, slope

resistance increases from -1450 N to 0 N and it remains constant till 500 s.

Total resistance value increases to 650 N at 390 s and then it remains constant

up to 493 s.

Between 493 s and 500 s, value for drag resistance and rolling resistance

decrease from 400 N to 0 N and 250 N to 200 N respectively.

Total resistance value changes from 650 N to 200 N between 493 s and 500 s.

At 300 s, total resistance value shoots up because vehicle starts climbing 4° slope at

constant speed and constant acceleration. If the vehicle is climbing up, weight

component of vehicle also needs to be counted in calculating total resistance value. So,

we require more force to be applied on vehicle to maintain its constant speed. Vehicle is

climbing slope for 50 s, so during that time, total resistance value will be maximum.

At 350 s, vehicle starts down hilling -4.5° slope and thus weight component of the car

acts in the direction of vehicle motion and it helps car to move forward. That reduces

overall resistance value. For 40 s, vehicle is climbing down. So between 350 s and 390 s,

total resistance value is lowest.


Tractive force calculation:

Traction needed to maintain given speed of vehicle can be calculated by adding total resistance

value to the mass times acceleration. So, F = R + m*a

Figure: 4 shows the plot for tractive force profile. Figure: 10 shows the Matlab code for the

same.

From Figure: 2 and Figure: 4, we can say that till 300 s, tractive force profile resembles

with the acceleration profile. Reason behind this is between 125 s and 200 s, value for

acceleration is between 2.5 m/s2 to -3 m/s2. And in the same time interval, value for

total resistance is between 950 N and 450 N, which is low with comparison to highest

total resistance values. Now, for calculating traction force, we are multiplying

acceleration to mass and then add them to total resistance. So, high acceleration values

will lead to higher value of mass times acceleration term and adding total resistance

value will not make any significant change in that. So the tractive force graph will closely

follow the acceleration curve profile. Same thing can be explained for the portion of the

graph after 493 s.

Between 300 s and 390 s, value of acceleration is 0 m/s2. So during this time mass times

acceleration term will also be 0 and tractive force plot will follow total resistance profile.

Tractive force value is highest and lowest at 162 s and 490 s respectively (i.e. 5500 N and

-7000 N). At these exact times, acceleration values are also highest and lowest.

Figure 4: Tractive force profile


Power needed:

We can calculate power by following formula:

P = F * v

Where, F = Traction force

v = Vehicle speed

I have write code in Matlab to determine power and plot it with time. Code is shown in

appendix (Figure: 14) Plot is shown in Figure: 5.

As power is the product of traction force and speed, power curve should follow same

path as traction curve. From Figure: 4 and Figure: 5, we can say that profile for both the

curves are similar.

Figure 5: Vehicle power profile


3 Appendix

Figure 6: Converting time, speed and slope data into array form using Matlab

Figure 7: Simulink model for calculating acceleration using derivative block


Figure 8: Simulink model to determine drag resistance, slope resistance and rolling resistance

Figure 9: Total vehicle resistances


Figure 10: Matlab code for plotting Tractive force profile, speed profile and slope profile

Figure 11: Matlab code for plotting vehicle acceleration profile


Figure 12: Matlab code for plotting vehicle resistance profile

Figure 13: Matlab code for plotting power vs time


Figure 14: Power calculation

Assignment 2

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