Excel Spreadsheet for Battery Calculations6.pdf

About Global Documents

Global Documents provides you with documents from around the globe on a variety of topics for your enjoyment.
Global Documents utilizes edocr for all its document needs due to edocr's wonderful content features. Thousands of professionals and businesses around the globe publish marketing, sales, operations, customer service and financial documents making it easier for prospects and customers to find content.
rpm Forward accelerate ICE ICE rpm Angular speed Power
 
1 
CAN-View Data Collection and Analysis for a 2005 Prius 
L. David Roper, roperld@vt.edu 
 
Introduction..................................................................................................................................................2 
Data Collected .............................................................................................................................................2 
Data Analysis ...............................................................................................................................................3 
Stationary............................................................................................................................................3 
Tight Circle .........................................................................................................................................3 
Counterclockwise Tight Circle ..................................................................................................3 
Clockwise Tight Circle ..............................................................................................................5 
Motormile Speedway..........................................................................................................................7 
Counterclockwise 20 mph .........................................................................................................7 
Counterclockwise 40 mph .........................................................................................................9 
Clockwise 20 mph ...................................................................................................................11 
Clockwise 40 mph ...................................................................................................................14 
Brush Mountain Trip ........................................................................................................................16 
Steering, Gas Pedal and Brake Pedal.......................................................................................16 
ICE rpm, MG1 rpm and MG2 rpm (rolling wheel radius of 11.5”) ........................................17 
ICE rpm and VVTi ..................................................................................................................17 
Battery Current and Fuel Flow................................................................................................18 
ICE Power, Battery Power and Total Power ...........................................................................18 
Forward Acceleration ..............................................................................................................19 
Road Angle ..............................................................................................................................19 
Radius of Curvature .................................................................................................................20 
Template Excel Spreadsheet for CAN Data Analysis ...............................................................................21 
Other articles by L. David Roper about Hybrid Vehicles .........................................................................21 
Appendix 1: List of CAN Parameters Recorded .......................................................................................22 
Appendix 2: Maps of the Brush Mountain Trip ........................................................................................23 
Two-Dimensional Map .....................................................................................................................23 
Topographic Maps ............................................................................................................................24 
Appendix 3. Equations ...............................................................................................................................28 
Power Split Device ...........................................................................................................................28 
Power and Energy.............................................................................................................................28 
Air-Friction Drag Force ....................................................................................................................29 
Road angle ........................................................................................................................................29 
Centripetal acceleration ....................................................................................................................29 
Radius of Curvature ..........................................................................................................................29 
 
 
2 
Introduction 
 
The availability of the CAN-View add-on (http://www.hybridinterfaces.ca) for the Prius II enables the 
driver to see many parameters of the car change with time as it is driven. The CAN-View box is attached 
to the MFD (Multi-Function Display) and the OBD (On-Board Diagnostics plug under the steering 
wheel) to collect data from the OBD to display on the MFD. 
 
For a Prius with factory- installed navigation the CAN-View device is easy to install 
(http://www.roperld.com/science/prius/CanViewInstall.pdf). 
 
CAN-View has a serial port for collecting data on a portable computer 
(http://www.roperld.com/Science/Prius/CAN-ViewCapture.htm). 
 
A Microsoft Windows program has been written by Gary Morris for analyzing the data 
(http://mggm.net/prius/candecoder.html). He used the CAN coding information supplied by Attila Vass 
(http://www.vassfamily.net/ToyotaPrius/CAN/PriusCodes.xls ) plus some he discovered himself. 
 
Gary Morris provided many of the ideas used in this work. 
Data Collected 
 
The purpose of this web page is to give some examples of collected data and some analysis of the data. 
The types of data collected are given in Appendix 1. 
 
The examples are: 
1. Stationary : Readings with the car pointing in the four primary directions in my reasonably 
flat driveway. 
2. Tight Circle : Clockwise and counterclockwise movement in the smallest possible circle 
(tight circle). See appendix 3 for the mathematics of the turning radius. 
3. Motormile Speedway: Clockwise and counterclockwise laps around the Motormile 
Speedway (http://www.motormilespeedway.com) Dimensions: Straights are 506 feet long, 
55 feet wide, and banked seven degrees. Turns are 550 feet long, 70 feet wide, and banked 15 
degrees. (Thanks to Mr. Al Shelor and Mr. David Hagen for permission to use the Motormile 
Speedway.) Laps were run at speeds of approximately 20 mph and 40 mph. 
4. Brush Mountain Trip: A trip from my home at 1001 Auburn Drive, Blacksburg VA to the 
top of Brush Mountain on Rt. 460 toward West Virginia, a distance of 9.1 miles, and return. 
Appendix 2 contains maps of the trip. The trip lasted about 17 minutes (1025 seconds). The 
average speed was 32.1 mph (including stops). 
 
3 
Data Analysis 
There are four quantities that are measured that required considerable effort to figure out exactly what 
they are. Attila Vass: (http://www.vassfamily.net/ToyotaPrius/CAN/PriusCodes.xls ) calls two of them 
“sideway acceleration” and “acceleration”; there are two of each discovered by Morris. 
 
They are Side Angular Speed1 (S1), Side Angular Speed2 (S2), Forward Acceleration1 (A1) and 
Forward Acceleration2 (A2). It will be show below for reasonably controlled specific vehicle runs that 
the following equations hold to a high degree of approximation: 
 
1
2
1
2
 and 
 where 
forward acceleration  and 
angular speed.
14.5
2(72.1)
f
f
A A
S
S
a
a
ω
ω
−
+
=
=
=
=
 
Stationary 
Here are the stationary readings for the four primary directions at location (37.209ºN 80.452ºW = 
reasonably level driveway of LDR): 
 
Direction 
SideAccel1 
SideAccel2 
Accel1 
Accel2 
East 
0 
-3 
5 
13 
West 
0 
-3 
2 
-6 
North 
0 
-3 
17 
12 
South 
0 
-3 
-6 
-3 
 
So, the two "side accelerations" do not change with direction, but differ by 3. 
And the two "accelerations" vary with direction. Why do these parameters have values for a stationary 
vehicle? 
Tight Circle 
Counterclockwise Tight Circle 
ICE rpm, MG2 rpm & MG1 rpm: 
 
 
4 
Front-Left, Front-Right, Rear-Left & Rear-Right wheels rpm: 
 
 
Angular-speed parameters: 
 
 
Forward-acceleration parameters: 
 
 
 
5 
It appears that (S1+S2)/2 is the angular speed, ω : 
 
This is a least-squares fit of (
)
1
2 /
S
S
C
+
 to the angular speed 
(
/
 where 
turn radius=12.6 feet.
v r
r
ω =
=
). C is 192.9 for the best fit. 
Clockwise Tight Circle 
ICE rpm, MG2 rpm & MG1 rpm: 
 
Front-Left, Front-Right, Rear-Left & Rear-Right wheels rpm: 
 
Angular-speed parameters: 
 
6 
 
 
Forward-acceleration parameters: 
 
 
It appears that (S1+S2)/2 is the angular speed, ω : 
 
This is a least-squares fit of (
)
1
2 /
S
S
C
+
 to the angular speed 
(
/
 where 
turn radius=12.6 feet.
v r
r
ω =
=
). C is 198.4 for the best fit. 
 
The average value of C for both counterclockwise and clockwise motion is 195.7 . 
 
7 
Motormile Speedway 
Counterclockwise 20 mph 
ICE rpm, MG2 rpm & MG1 rpm: 
 
Angular-speed parameters: 
 
Forward-acceleration parameters: 
 
 
8 
Front-Left, Front-Right, Rear-Left & Rear-Right wheels rpm: 
 
Battery current & fuel flow: 
 
ICE, battery & total power: 
 
 
 
9 
It appears that A1-A2 is approximately the forward acceleration: 
 
This is a least-squares fit of (A1-A2)/C to the forward acceleration in miles/hr/sec. (The best fit is for C 
= 15.9 .) 
Counterclockwise 40 mph 
ICE rpm, MG2 rpm & MG1 rpm: 
 
Angular-speed parameters: 
 
 
10 
Forward-acceleration parameters: 
 
 
Front-Left, Front-Right, Rear-Left & Rear-Right wheels rpm: 
 
Battery current & fuel flow: 
 
 
11 
ICE, battery & total power: 
 
 
It appears that A1-A2 is proportional to the forward acceleration: 
 
This is a least-squares fit of (A1-A2)/C to the forward acceleration. (The best fit is for C = 14.0 .) 
Clockwise 20 mph 
ICE rpm, MG2 rpm & MG1 rpm: 
 
 
12 
Angular-speed parameters: 
 
Forward-acceleration parameters: 
 
 
Front-Left, Front-Right, Rear-Left & Rear-Right wheels rpm: 
 
 
13 
Battery current & fuel flow: 
 
ICE, battery & total power: 
 
 
It appears that A1-A2 is proportional to the forward acceleration: 
 
This is a least-squares fit of (A1-A2)/C to the forward acceleration. (The best fit is for C = 15.3 .) 
 
 
14 
Clockwise 40 mph 
ICE rpm, MG2 rpm & MG1 rpm: 
 
Angular-speed parameters: 
 
Forward-acceleration parameters: 
 
 
15 
Front-Left, Front-Right, Rear-Left & Rear-Right wheels rpm: 
 
Battery current & fuel flow: 
 
ICE, battery & total power: 
 
 
16 
It appears that A1-A2 is proportional to the forward acceleration: 
 
This is a least-squares fit of (A1-A2)/C to the forward acceleration. (The best fit is for C = 12.8 .) 
 
The average value for the four case is C = 14.5 . 
 
Brush Mountain Trip 
Steering, Gas Pedal and Brake Pedal 
 
• Steering is about 100 for straight ahead travel and note the large value (over 500) at the 360 degree turn 
around at the top of the mountain. 
• Gas Pedal is high going up the mountain just before the 360 degrees turn around. Just before that there 
was a short decline, so Gas Pedal was zero. And, of course, the Gas Pedal is zero and there is some 
Brake Pedal coming down the mountain after the turn around. 
• Note the symmetrical stops at four stop lights and stop signs on the outgoing and ingoing legs of the trip. 
There was an extra stop sign near the beginning of the outgoing leg. 
 
 
17 
ICE rpm, MG1 rpm and MG2 rpm (rolling wheel radius of 11.5”) 
 
• All rpms are zero at the stop signs and lights. 
• 
ICE rpm is high and MG1 rpm is high positive going up the mountain just before the 360 degrees turn 
around and ICE rpm is low (freely spinning) and MG1 rpm is high negative just before that on a decline. 
And, of course, the ICE spins freely with high negative MG1 rpm coming down the mountain after the 
turn around. 
 
ICE rpm and VVTi 
 
 
 
18 
Battery Current and Fuel Flow 
 
 
ICE Power, Battery Power and Total Power 
 
ICE (Internal Combustion Engine) power is calculated as prescribed by Norm Dick, the inventor of 
CAN-View, ascribing 58 kW to 238 in the CAN output for fuel flow and assuming linearity. Of course, 
battery power is voltage times current, and it is positive going into the battery. So, total power going out 
of the vehicle is ICE power minus battery power. 
 
19 
Forward Acceleration 
One can take the average of the four factors (14.5) used to relate forward acceleration to A1-A2 for the 
four Motormile Speedway runs to calculate forward acceleration for this Brush Mountain trip: 
 
It calculates close to the acceleration except for the times when the Prius is going down and up slopes; 
then the gravitational acceleration, g,  has a component along or opposite the forward direction, 
respectively. The accelerometers cannot tell the difference between vehicle and gravitational 
acceleration. 
Road Angle 
One can use (A1-A2)/14.5 to calculate the road angle: 
{
}
(
)
1
2
14.5
arcsin
/
.
A A
a g
θ
−


=
−

  (See Appendix 3.) 
The result is: 
 
The red curve is a 10-second moving average to smooth out the obvious measurement noise. 
 
 
20 
Radius of Curvature 
One can use the angular speed (S1+S2/2/225 to calculate the radius of curvature
v
ω
 with 
[=IF(ABS(5280v/?/3600)>2000,0,5280v/? /3600) in Excel for v in mph. This eliminates very large radii 
of curvature (2000 ft) due to small deviations in the vehicle path.]: 
  
The red curve is a 10-second moving average to smooth out the obvious measurement noise. 
 
A similar graph can be calculated from the steering angle as outlined in the section on tight circles: 
 
The two graphs directly above are similar, but not exactly the same. 
 
 
21 
Template Excel Spreadsheet for CAN Data Analysis 
A template Excel Spreadsheet can be downloaded at http://www.roperld.com/science/prius/template.xls 
and used according to the following instructions: 
1. Use the cancoder.exe program (http://mggm.net/prius/candecoder.html) to create a CSV file for a 
set of recorded CAN data. 
2. Load the CSV file into Excel and copy the data excluding the titles row at the top to the 
clipboard. 
3. Open the template.xls file and paste the copied data into the file beginning at position (row 2, 
column 1). That is, leave the top titles row and the right-hand colored columns as they are in the 
template. 
4. Then some calculations will be automatically done to the right in the colored columns. 
5. Some graphs of the data and calculations will automatically be done on the worksheet graphics. 
6. The template spreadsheet is set up for 30 minutes of driving (1800 rows = 1800 seconds). It can 
be extended to longer times by copying the last colored row-columns on the right to more rows. 
Each row is 1 second of driving. 
Other articles by L. David Roper about Hybrid Vehicles 
http://www.roperld.com/Science/Prius/HybridVehicles.htm 
 
22 
 Appendix 1: List of CAN Parameters Recorded 
 
• Voltage 
• State of Charge (SOC) 
• Battery Current 
• Maximum Charge Current 
• Maximum Discharge Current 
• Minimum Battery Temp (ºC) 
• Maximum Battery Temp (ºC) 
• Speed (kph) | Speedometer 
• Speed Related 
• Front Left Wheel 
• Front Right Wheel 
• Rear Left Wheel 
• Rear Right Wheel 
• 
ICE rpm (See graph directly below for a possible way to find a non- linear relationship between 
ICE rpm and ICE power.) 
• 
ICE Temp (ºC) 
• Coolant Temp (ºC) 
• Side Angular Speed1 (S1) 
• Side Angular Speed2 
• Forward Acceleration1 (A1) 
• Forward Acceleration2 (A2) 
• Steering (Gary Morris discovered a calibration offset that is subtracted from positive steering 
values and added to negative steering values.) 
• Go Pedal 
• Brake Pedal 
• Brake Pressed 
• EV Mode 
• Cruise Control 
• Lights 
• Fuel Injection [Used to calculate mpg = mph*1100/(fuel inj)] 
• Fuel Flow (ICE power can be calculated by multiplying fuel flow by 58 kW and dividing by 238, 
assuming linearity of ICE power with fuel flow. See graph directly below for a possible way to 
find a non- linear relationship between ICE rpm and ICE power.) 
• VVTi (Variable Valve Timing-Intelligent) 
• Gas Gauge 
 
23 
Appendix 2: Maps of the Brush Mountain Trip 
Two-Dimensional Map 
 
7.1 miles each way. 
 
 
24 
Topographic Maps 
The times for specific locations on the out trip are indicated below each map: 
 
 
9 = 425 seconds  (downhill, beginning of left curve), 10 = 440-460 seconds (uphill, end of 
curve), 11 = 510-520 seconds (turn around). 
 
25 
 
8 = 320-340 seconds , (stop light) 
 
26 
 
6 = 215 seconds  (stop light slow down), 7 = 245 seconds  (turn onto US460 bypass), 
8 = 320-340 seconds , (stop light) 
 
27 
 
1 = 20 seconds  (stop sign right turn), 2 = 35 seconds  (stop sign right turn), 3 = 105 seconds  
(downhill, then left turn), 4 = 135 seconds  (stop sign right turn), 5 = 170-180 seconds (stop 
light), 6 = 215 seconds  (stop light slow down) 
 
28 
Appendix 3. Equations 
Power Split Device 
From http://www.ecrostech.com/prius/original/PriusFrames.htm and 
http://www.engin.umd.umich.edu/vi/w4_workshops/Miller_W04.pdf : 
 
Let 
• S = rpm of small generator/motor (MG1) 
• L = rpm of large motor/generator (MG2) 
• E = rpm of Internal Combustion Engine (ICE) 
• V = vehicle speed in mph 
• Nr  = number of gears in outer (ring) gear (= 78) 
• Ns = number of gears in inter (sun) gear (= 30) 
 
 
Then  (S - E)/(L - E) =  -Nr/Ns  or  S = (1 + 78/30)E - (78/30)L . 
 
But
ft
in
ft
mile
min
hr
4.113(12 )(5280
)
60.1
2 (11.5 in)(60
)
L
V
V
π
=
=
, where V is in mph, 4.113 is 
the gear ratio between the ring gear and the wheels for the Prius II and 
11.5 in is the rolling radius of the wheels (depends on the tires). 
 
 
 
Power and Energy 
• Battery power for current I (Amperes) and potential V (Volts) is BP
IV
=
in kW. 
• ICE power is assumed to be 58(fuel flow)/238 in kW. 
• Kinetic energy of vehicle of mass m and speed v: 
2
1
2
kE
mv
=
. 
 
 
29 
Air-Friction Drag Force 
Assume that the only external frictional force of consequence is the air- friction drag due to the velocity 
v of the vehicle. (For high speeds this is a good approximation for the external frictional forces.) Then 
the air-friction drag force is to a good approximation 
2
2
1
2
d
F
c A v
mCv
ρ
= −
≡ −
 (http://en.wikipedia.org/wiki/Drag_equation) where 
• 
dc = drag coefficient (unitless) (0.26 for 2004-5 Toyota Prius II) 
• 
A = projected area perpendicular to the velocity (~2.52 meter² for Toyota Prius II) 
• 
ρ =  air density 
3
kg
meter
1.2
≈
. (Depends on the temperature, air pressure and the amount of water 
vapor in the air.) 
• 
m = mass of the vehicle (1311 kg  for Toyota Prius II) (The mass is only needed in the equation 
directly below; it will cancel out in the final equations of interest.) 
• 
4
1
1
2
meter
/
3.0 10
d
C
c A m
ρ
−
=
=
×
∼
 for Toyota Prius II. 
 
(Force in Newtons, mass in kg, velocity in m/sec and acceleration in m/sec2.) 
 
Thus, the total force acting on a vehicle moving up a hill of angle ? is 
2
4
1
meter
sin
 where 
6 10
d
F F mg
mCv
C
θ
−
=
−
−
= ×
 for the Prius II. 
The second term is the gravitational force and third term is due to air friction.
dF  is the force that propels 
the vehicle of mass m to accelerate it or keep it moving at a constant speed opposing air friction and the 
component of gravity. Friction always opposed the direction of motion; so, its sign must be adjusted 
accordingly. 
 
Road angle 
(
)
arcsin
/
 
A a g
θ


=
−

 for the 2003-6 Prius, where A  is the accelerometer measurement. 
If one uses v  in miles/hr, a  in miles/hr/sec (true acceleration) and g = 32.2 ft/sec2, then one must 
multiply ag  by (5380 ft/mile)/(3600 sec/hr) 
 
Centripetal acceleration 
The CAN gives 
[
]
1
 and 
 (angular speed in 
)
1
2
v
s
S
S
ω
− ∝
+
. One can use them to calculate the radius of 
curvature: 
/
 .
r
v ω
=
For r in feet and v  in miles/hr one must multiply 
/
 .
v ω
 by (3600 sec/hr)/(5380 
ft/mile). 
For speed v  and a circle of radius r  with bank angle ϕ : centripetal acceleration is 
2
sin
c
v
a
g
r
ϕ
=
+
. 
This can be used to calculate the bank angle
2
arcsin
/
c
v
a
g
r
ϕ


=
−




. 
Radius of Curvature 
The specifications of the Prius II give the turning circle as 34.1 feet, which refers to the outside of the 
car. For physics analysis the turning circle of the center of mass is what is needed, which is, according to 
 
30 
the published 2005 Prius specifications (34.1 – 4.86) feet = 29.24 feet. Thus, the turning radius  of the 
center of mass is 14.62 feet. 
 
However, for my Prius the turning circle (between outer edges of back wheels) is 30 ft for 
counterclockwise motion and 29.1 feet for clockwise motion. The distance between the centers of the 
back tires is 4.86 feet. Thus, (30-4.86) feet = 25.1 feet and (29.1-4.86) feet = 24.2 feet and the turning 
radii are 12.6 feet for counterclockwise motion and 12.1 feet for clockwise motion. The steering CAN 
value (after applying the calibration offset) is 432 for counterclockwise motion and -444 for clockwise 
motion. 
 
The mathematics of the radius of curvature for a vehicle is given by 
http://planning.cs.uiuc.edu/node658.html. The following diagram is taken from that web page: 
 
 
The radius of curvature is represented by 
 and the wheel base is 
8.86 feet
L
ρ
=
for the 2005 Prius. The 
equation for the radius of curvature is 
/tan
cot
 where 
steering angle.
L
L
ρ
φ
φ
φ
=
=
=
 If the CAN 
steering parameter, s, is proportional to the steering angle, then 
(
)
/tan
/
 where  is the proportionality constant.
L
s a
a
ρ =
Solving this equation for the proportionality 
constant yields 
(
)
/ arctan
/
.
a
s
L ρ


=

  For counterclockwise motion 
705.5
a =
 and for clockwise 
motion 
703.1.
a =
 Use the average 704.3.