|
Quantifying Coastdown Measurements |
| An
article by John Tetz - 1/15/07 |
|
I have been doing coastdown
measurements for a few years. In 2005 I published a
report
on Crr Vs Temperature. Since that report I have been using a datalogger that was built by Kit Wolf from the UK.
This has seriously improved the accuracy and ease of data
taking. Another change was Paul Sims of Greenspeed added a
system of user improvements to the TCoastf3 spreadsheet that
seriously reduces the time to calculate the results. With
both of these changes I can take a lot more data in much
less time giving me the ability to see patterns. And I am
seeing some strange things. I’m publishing this report in
hopes that by sharing this information there will be some
answers from the HPV community.
Before I get into the specifics I want to correct a
statement I made in my 2005 report saying trikes have higher
Crrs than bikes. This was totally wrong information. Trikes
have similar Crrs to bikes.
By using the coast system to make toe vs Crr measurements I
eventually found that the cross tube supporting the front
wheels on my trike was bending with rider weight more than I
thought. Because I have head tube suspension, the tie rods
have to be perpendicular to the head tube angle to minimize
toe vs suspension travel. But at the time I didn’t think the
cross tube was bending enough to significantly change toe,
so to correct for this I changed the tie rod angle plus
added a couple of layers of carbon over my thin wall steel
cross tube bringing the Crr to a level about the same as a
bike.
|
 |
Here is a plot showing a
typical Crr vs Toe change on a commercial trike. This shows
how the Toe adjustment on a trike effects Rolling Resistance
(Crr). Note that the rate of change with toe in is less than
the toe out suggesting that final settings should be biased
towards the toe in direction.
You can click on any of these
images to see a higher resolution picture.
|
The rate of toe change on my trike is less than some
commercial trikes. I believe this is due to the small amount
of end play in my tie rod ball joints which seems to allow
the front wheels to seek a more neutral toe. To explain this
theory I had a tie rod end come off at the steering center
(not the wheel end) during a ride (luckily at slow speed).
The wheel immediately turned partially sideways stopping the
vehicle. I was on the side of the crowned road
.
The problem was how to get the vehicle home about 1.5 miles
away. I couldn’t walk the vehicle with a loose wheel. So I
got on it and held the tie rod in my hand thinking I might
have the strength to hold the wheel straight. As I gingerly
got started I was surprised that there was practically no
pressure on the tie rod. The wheel was able to seek its
proper heading. And if I turned the handlebars the loose
wheel automatically turned. However I did have to hold the
tie rod when hitting a bump because the wheel would go into
an oscillation – damped out by my hand. This strange event
turned out to be very informative.
CdA ESTIMATION
Another error that led me to believe trikes had higher Crrs
was in estimating CdA. The Spreadsheet system I am using
requires at least an estimated CdA value while calculating
Crr measurements (and a Crr value for CdA measurements). I
had estimated trikes CdAs by comparing the typical on road
cruising speeds I got with my trike (T7 - version 7) against
the speeds on my Low Front Wheel Drive bike (LFWD). I
typically saw 15 mph on the trike vs 17 mph on the LFWD. I
had previously made steep grade CdA measurements on the LFWD
which is around 2.3 sq ft, (.21 sqm). Using the
PDG
spreadsheet for comparisons, the speed difference between
the two vehicles gives a CdA for the trike around 2.8 sq ft
(.26sqm). Later when I got the chance I did measure the
steep hill CdA and it indeed is around the 2.8 value.
When I borrowed two standard commercial trikes I mistakenly
used the 2.8 for their estimated CdAs. Because the TCoastF3
spreadsheet calculates the combined Crr CdA drag, this means
if the estimated CdA value is low the Crr value will be high
(and visa versa). The overall measurement system is set up
to reduce this cross influence by doing the Crrs at a low
speeds and the CdA at high speeds, but the influences are
still there even as weak as they are.
By using a low value CdA of 2.8 for the commercial trikes
this then gave a correspondingly high Crr which happen to be
fairly close to what I was getting on my trike. So by not
being careful with all the above errors I got lulled into
thinking that trikes have higher Crrs.
Eventually doing steep hill CdA measurements I found the
standard trikes CdAs were more like 3.5 sq ft (.33sqm). The
higher aero drag I believe comes from the under seat
handlebars. The arms being alongside the body results in an
increase in frontal area. Plus the air being forced to go
around the arms creates a larger turbulent wake also adding
to an increase in drag.
Here is a table showing the effect of CdA on calculated
terminal speed down a 6.4% grade
|
CdA |
Crr |
Terminal
speed |
| 2.3 |
.0055
|
42 |
| 2.5 |
.0055
|
40 |
| 2.8 |
.0055 |
40 |
| 3.5
|
.0055 |
35.8 |
CdA diff 3.5/2.3 = 66%
Speed difference = 42/35.8 = 17.3 %
The effect of Crr differences on terminal speed is
|
CdA |
Crr |
Terminal
speed |
| 2.3 |
.0055 |
43 |
| 2.3 |
.0070 |
42.2 |
| 2.3 |
.0080 |
41.8 |
.008/.0055 = 45 %
Speed difference 43/41.8 = 2.9 %
A fairly large Crr difference of 45% only produces a 2.9%
speed difference.
|
| Here are plots of the actual
coasts runs on for the ICE Q Trike down a relatively linear slope
of 6.4%, over a distance of 1450 feet.
Transient means starting from
zero speed. Note the speed is leveling off but that does not
mean the vehicle obtained Terminal speed. After 1500 feet
the grade begins to slowly flatten. |
ICE Q trike coastdown from 0 MPH |
|
ICE Q trike coastdown from 31.3
MPH |
Vinitial runs means crossing
the coast start at some velocity. TCoastF1 calculates the
Terminal speed for the ICE Q trike to be 38 mph (61 kph) and for my
T7 trike to be 41.8 mph (67.3 kph). Kinetic energy being as weak
as it is it would take a much longer hill to obtain those
optimal terminal speeds (and long enough linear grades are
very difficult to find). |
| Here are
Transient and Vinitail plots of my T7 (Version 7 of my trike).
|
T7 trike coastdown from 0 MPH |
|
T7 trike coastdown from 35.4 MPH |
Yes I braked at 1500 feet.
Note that on this T7 trike Vinitial plot the initial speed is
higher than the ICE Q trike plot, therefore the speed crossing the
finish line will be higher. However the TCoastF1 spreadsheet
will still correctly calculate the CdA. Without such
spreadsheets doing the calculations to account for speed and
time, comparisons of vehicles would be difficult.
But note the different transient speeds on both vehicles as
they cross the finish at 1450 feet.
Both runs were at essentially the same temperature and
weights within 5 pounds (2.3kg) of each other. Transient
testing may have some merit providing they are done at the
same temperature, weights, rider, and rider clothing.
|
These runs are done on a fairly
busy 4 lane highway but with a decent amount of linear slope
and room on the shoulders with relatively smooth black top.
Luckily there is a traffic light at the top of the hill
about 1800 feet before my coast trap. So I wait for a rush
of cars to go by that had collected at the light. Then wait
about the time the light turns red and the last of the cars
to pass, then wait a few more seconds longer for the wind
they generated to die down a bit (cant wait until its all
gone) and then let the brakes go and hope no cars catch me
before my run is over. Not all runs are successful which
means there is a lot more climbing to be done. And of course
there cannot be any natural wind. So I have to wait many
days for low wind and time of day where there is hope of
less traffic.
Crr vs TEMPERATURE
Another in the long list of variables is that Crr changes
quite drastically with temperature. If you’re trying to
reproduce results from day to day or week to week, then the
tests need to be done at close to the same temperature.
When trying to compare results over a wide temperature
variation a Crr vs temperature plot would be needed. This plot is a bit difficult to
make because the test vehicle has to remain the same over
many months – no changes to affect CdA, Crr, toe, or weight.
Because of this I use my 8 year old LFWD (low front wheel
drive bike) as my standard. Also as it gets
colder I have to use more clothes, which of course changes CdA,
so I add a tenth or so to the CdA value.
|
| This plot shows a slight
curve. As expected, as the temperature climbs above 70 F
(21C), Crr does not continue to drop but flattens out.
I was
busy with other projects during the summer so I do not have
the high temperature plots. I will upgrade this data next
summer.
VM = Faired velomobile trike
with T7 chassis
LFWD = Unfaired low front wheel drive bike
T7 = Unfaired Tetz trike |
 |
 |
Crr vs SPEED
Over a period of time while making a series of Crr
measurements I began to notice that at higher coast speeds
the Crr values were correspondingly higher. So I began to do
a set of ever increasing speed measurements. Plot 5 shows
two separate coast tests done on different days. These are
LFWD tests. As you can see the angle of both are the same.
Note that the difference in Crr values between the two
curves are from the difference in air temperature.
However when measuring the
Crr on my Velomobile the change in Crr vs speed is much
less. |
| Here is a plot showing three
vehicles. The dashed line at the slow end of the VM run is
done on a shorter coast course.
Here are a T7 run, a VM run and a LFWD run. Note the resulting angle of
the bare trike is steeper even than the LFWD bike and the VM
is flatter. If this is predominantly a Crr change, that
change should show up as an identical angle slope on all
three vehicles. But it doesn’t. |
 |
 |
So something else is
happening here. What this indicates to me is the
possibility that the CdA is changing. So I held Crr constant
on TCoastF3 and varied CdA to get the same overall drag on
the following plot. That is the horizontal line thru the Oct
10th run. This gives a range of CdA values from 1.9 sq ft
(.18sqm) at low speeds to 2.5 sq ft (.23 sqm) at high speed.
The 2.5 is the same value for an all out high speed flat ground CdA.
(Note: All out for the run up distance I have...) The speeds are in
the mid 20 mph (32kph) range.
However 2.5 is higher than
the steep hill CdAs which are consistently around 2.1 to 2.2
sq ft.
As shown previously in the
CdA vs Speed table, with
a value of 2.5 the downhill coast speeds would not be as
high. |
So where is the difference coming from? Is there an error in
the basic physics and math inside the spreadsheets use to
calculate the combined drag of Crr and CdA? So I did a
spreadsheet comparison by using the published data from the
ICE Crr coastdowns and plugging their values into my
TCoastF3. ICE uses a Vinitial speed and a final speed value
over a measured distance.
TCoastF3 uses Vinitial speed and time over a measured
distance. TCoastF3 does have a detailed calculation table
where I can determine end of coast distance/speeds. The Crr
results were very close which indicated the physics and math
are the same. I could see a small grade of around.0.03% on
the ICE indoor data. |
Here are steep hill VM CdA
runs. I do a distance calibration run on the climb up the
hill. It is 1445.3 feet . The transient max speed is 42.97
mph for a time of 38.55 seconds. TCoastF1 gives a CdA value
of 1.3 sqft and a grade of 6.5%. Calculated terminal speed
if the grade was long enough would be 60.3 mph
I did brake after the finish line.
|
 |
 |
Here is run 2 . Calibration
up is for a longer distance of 1806.6 feet. Transient speed
is 48.3 mph at a time of 45.9 seconds on a grade of 6.5%.
Calculated Terminal speed is 58.14 mph.
I didn’t do Vinitial speed runs
because the speeds would be uncomfortably high.
|
FLAT GROUND VM CdA
MEASUREMENTS
I also did flat ground CdAs with the VM which is similar to
steep hill results.
|
Start Crr
pole
to Black pole
|
Distance
648 feet
|
north
direction
|
south
direction
|
|
run
|
% grade
|
Crr
|
CdA
|
spd/time
|
spd/time
|
|
1
|
0.137
|
0.00555
|
1.35
|
21.09/25.17
|
21.23/23.19
|
|
2
|
0.146
|
“
|
1.34
|
21.67/24.36 |
22.12/22.77
|
|
3
|
0.156
|
“
|
1.31
|
21.85/24.10 |
21.78/23.12
|
|
|
|
Avg
|
1.33
|
|
|
So why is the flat ground VM
CdAs similar to the steep grade while the LFWD CdA is
consistently higher then the steep hill?
So is it possible the CdA is low on the LFWD at low speeds,
then climbs to 2.5 and then at speeds typical of steep down
hills drops? So I did some normal low speed to as high speed
as I could get on my test road with the LFWD. But did not
see any rounding off of the curve with speeds as high as 22
mph.
I can almost believe the air flows more easily around the
LFWD at low speeds. I can also believe a similar thing
happens with the VM and then changes at a higher speed
(possibly decreasing or increasing vs speed) depending on
the quality of flow over the shell.
|
I also did some very slow
speed Crr test and indeed it shows a flattening as the speed
drops.
A complication of very slow speed tests the grade percent
has to be quite low, well below .3 %. If much greater the
vehicle will not make to the finish line on the up grade.
Also the speed near the end of the coast could be so slow
that the spreadsheet will have difficulty giving solid
results. One could increase the speed but then we get into
the speed problem as discussed above. One could reduce the
distance of the coast trap but this results in short coast
times. That puts an accuracy demand on the Datalogger
system. Typical short coast speeds/times can be 5.5 mph (8.9
kph) and times of around 6 to 8 seconds over a distance of
54 feet (1646 cm), and less time for speeds at 8 mph. For a
more ideal time accuracy, times need to be in the 15 second
and above range. So I did both short course and long course
runs. |
 |
At this point I do not know what causes the slant to the
above curves.
FINAL SPEEDs
During these tests I had the impression the VM wasn’t
losing as much speed as the LFWD during the Crr tests which
possibly could mean that even with a low CdA of the VM it is
still working down there. So I compared the speeds crossing
the finish line over a 178.2 foot (5431 cm) course with 15.8
and 15.84 seconds run on the up grade direction
(aproximately.14% grade). I chose the up grade for
comparisons thinking this may show the greatest differences.
Both runs were done during the same evening at the same
temperature of 40 F.
|
VM
|
LFWD
|
|
Vinitial
mph/kph
|
Finish Speed
Mph/kph
|
Vinitial Speed
Mph/kph
|
Finish Speed
Mph/kph
|
|
9.51/ 15.3
|
5.92/9.5
|
9.46/15.2
|
5.95/9.57
|
|
Crr .00713
|
CdA 1.3
|
Crr .00718
|
CdA 2.3
|
|
Weight 47 lbs
|
|
Weight 27 lbs
|
|
No real difference in finish
speeds given the Crr values are bit different, the weights
are different, and the CdAs are different - all sort of
balancing out. So much for perceptions.
ROAD SHAPE
I had hoped that these tests could be done on a wide variety
of road shapes.
But while doing tests on different sections of my road I
began to see a difference in Crrs from my Normal coast
course.
Here are results from 4
different roads sections. LFWDCrr4
|
Pole
across from Company to Black pole
|
|
|
|
|
run
|
grade
|
Crr
|
dist
|
speed/times
up/dwn
|
|
|
1
|
0.0011
|
0.00682
|
212.4
|
9.24/19.86,9.76/18.36
|
|
2
|
0.017
|
0.00708
|
“
|
9.49/19.3,9.39/19.33
|
|
|
3
|
0.001
|
0.00686
|
“
|
9.58/18.79,8.95/20.53
|
|
|
Avg
|
0.00692
|
Why is
this higher?
|
|
|
|
|
|
|
|
|
|
|
|
Black
pole to Studeny pole
|
|
|
|
|
|
4
|
0.111
|
0.0059
|
207.5
|
9.91/17.45,10.15/16.03
|
|
5
|
0.127
|
0.00577
|
212.4
|
9.87/18.09,10.23/16.22
|
|
5
|
134
|
0.00571
|
“
|
9.52/19.07,9.76/17.11
|
|
|
Avg
|
0.00579
|
Bumps on
road
|
|
|
|
|
|
|
|
|
|
|
|
Normal course
|
|
|
|
|
|
|
6
|
0.167
|
0.00544
|
177.8
|
8.61/17.57,8.91/15.33
|
|
7
|
0.142
|
0.00542
|
“
|
8.85/16.75,8.27/16.79
|
|
8
|
0.131
|
0.0056
|
“
|
8.95/16.50,8.86/15.6
|
|
|
|
Avg
|
0.00549
|
“
|
|
|
|
|
|
|
|
|
|
|
|
|
Mid pole
to Company pole Temp dropped to 58 F
|
|
9
|
0.279
|
0.00612
|
118.6
|
10.54/8.59,9.92/8.65
|
|
|
10
|
0.309
|
0.00584
|
123.5
|
9.11/10.79,8.86/10.14
|
|
11
|
0.279
|
0.00554
|
“
|
8.59/11.54,8.66/10.41
|
|
12
|
0.299
|
0.00535
|
“
|
8.32/12.06,8.65/10.35
|
|
13
|
0.301
|
0.00558
|
“
|
8.95/10.99,9.16/9.76
|
|
|
|
Avg
|
0.00569
|
|
|
|
|
The first set shows a higher Crr, while runs 4 thru 13 show
a consistent Crr. The road for section 1 appears to have a
portion that has a concave shape. Ian Sims got involved with
doing coast downs and he too had problems with a concave
test courses. Here it may be that during conditions of very
low speed we may be getting into Function 4 conditions.
There are 4 coast functions. F1 (TCoastF1) is down grade
with increasing in speed. F2 is up hill decreasing in speed.
F3 (TCoastF3) is flat ground decreasing in speed. F4 is
slight grade with the vehicle moving slowly but at a
constant but low speed – a sort of low speed terminal speed.
It could be that on a concave road, enough percentage of the
coast is in the F4 condition squiring the results. A Bell
Labs friend generated the math and physics for TCoast F1 and
F2. I do not know the math or physics required for F4.
The thing is the overall physics and math used for these
calculators are based on idealized linear road shapes which
are unlike the variations on an actual roads. A possible
limitation to spreadsheets ability. I suppose when setting
up for choosing a test road section the ideal process is to
do tests on several sections of road and eliminate the one
that is an outliner.
SAME ROAD SECTION
Riding over the same left right path way on the road in both
directions is important in an attempt to cancel out road
variations. I have not painted a line on my road so part of
the data variations are from not riding over the identical
paths.
|
 |
Another issue is collecting data
over the same physical length of road in both downhill and
uphill directions. I
have two telephone poles used as reference that are spaced
177.6 feet apart for my Normal coast course. I have a short
perpendicular painted line 10 feet (304.8 cm) before each
pole as a mark to turn on the Datalogger. This allows the
Datalogger to get a stabilized Vinitial speed reading by the
time it gets to the pole. The spreadsheet is set up to
choose how many wheel revolutions it uses before reading the
Vinitial speed.
This plot shows the coast
down in both directions. |
ROAD SURFACE
Another variable is road surface textures. Here I haven’t
done enough testing to show the results of different
surfaces.
TIRE PRESSURE
Another variable is tire pressure. This plot is an average
of three runs at each pressure.
I choose fat tires on my
vehicles and pressures at 60 psi for ride quality so I do
all my tests at that pressure. I simply don’t have the time
to insert tire pressure in all the variables I have to deal
with at this time. |
 |
TIRE CIRCUMFERENCE
Tire circumference calibration at a know pressure is very
important so the Up-Load from the Datalogger will calculate
the correct distances, speeds and times. I use a 100 foot
steel tape measure to calibrate circumference. Easy to do on
a trike - much harder to do on a bike. For a bike I roll out
say 20 revolutions to find out about where the wheel will
end up. Then ride the bike and stop about where 20
revolutions would be. Then after coming to a stop and
putting my feet down I roll the wheel either forward or back
generally a quarter a revolution or so until the calibration
mark (generally the valve stem) comes down to the road.
Putting the feet down un-weights the tire but is such a
small percentage of the overall distance.
TEST EQUIPMENT
Equipment capability - don’t know enough about the
temperature stability of the datalogger.
WIND
If there is anything above a breadth of air don’t waste your
time and energy taking data. The time to do a series of
several runs can take 20 minutes, and time to convert
datalogger output to the SS results and storing the data is
around an hour. I generally do tests in the summer near the
end of day before the sun goes down because the wind often
dies. I could do them in early morning except I am a late
night person. Later in the year I do much of the tests at
night. I have small LEDs to mark the start/end of the coast
trap. Though I cant see the speedometer, I have done so much
testing that I have a pretty good feel for speed.
|
TIRE WARMING
Note in this case a slowly decreasing Crr. This may be due
to the tires warming up. Ian Syms also sees this reduction
on his drum tire testing machine. Yet another variable. |
|
LWWDCrr1 60psi at 68F |
|
Run
|
Crr
|
grade
|
|
1
|
0.00662
|
0.119%
|
|
2
|
0.00665
|
0.196
|
|
3
|
0.00601
|
0.164
|
|
4
|
0.00553
|
0.217
|
|
5
|
0.00551
|
0.163
|
|
6
|
0.00572
|
0.182
|
|
7
|
0.00555
|
0.163
|
|
8
|
0.00553
|
0.166
|
|
9
|
0.00509
|
0.167
|
|
10
|
0.00497
|
0.172
|
|
11
|
0.00503
|
0.173
|
|
12
|
0.00503
|
0.163
|
|
AVG
|
.00560
|
|
|
CONCLUSION
I have shown a range of data, some with questionable
results.
- What is happening with
the speed effect?
- Also the shape of the
road ?
- What am I missing here?
The shape of the road
affecting results bothers me. I thought I could at least
trust the results from almost any part of a reasonable test
road.
I would like to hear from others as to what your experiences
have been and hopefully find out what may be going on here.
.
With all the variables it’s easy to see why there are
differences in values from other methods of measuring Crrs
and CdAs.
I was hoping to contribute a low cost system where anyone
anywhere in the world can take data and compare results with
others but there are so many variables that I am beginning
to wonder if this is possible.
John Tetz
Contact John at jgtetz #at#
msn.com (replace #at# in email address with @)
Related Documents
CdA measurement document by
John Tetz
Grade document by John Tetz
Measurements document by John
Tetz
Coastdown document by John
Lafford
TCoastF1 spreadsheet by John
Tetz
TCoastF3_flatground
spreadsheet by John Tetz
|
