John Tetz Coast Measurements
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