Tire Crr Testing on Rollers - The Chart..and a "how to"

In my last post I outlined the "math behind the madness" of testing the rolling resistance of bike tires on home rollers. In this one, I'll be showing the results of some of that testing I've personally done over the past year or so. I'll also go through a few tips and tricks I've learned in doing this sort of testing...just in case anyone else is crazy enough to try some of this potentially mind numbing testing.

OK, I know a few of you are out there are "champing at the bit" to see the results, so without any further ado, here's a chart showing my estimates for the power to roll a pair of various tires I've tested (on a "real road" and for an 85kg bike plus rider mass):

Here's the same chart, but showing the estimated "on road" Crr values:

As can be seen, that's a fairly wide range of power requirements.  The wrong tire choice can easily "cost" a rider 10-15W of power to go a given speed.  When choosing tires, I commonly think of a scene from "Indiana Jones and the Last Crusade" where the Templar Knight guarding the Holy Grail says "...you must choose, but choose wisely...".  After all, when you're done with a race and you lose by seconds, or inches...you would hate to have the following be said about your tire choice:

The Setup:

OK, now that we've got that all out of the way, I thought I'd describe a bit about the setup I use for doing this sort of testing.  As you can see in the pic at the top of this blog post, it's a fairly simple affair consisting of a set of 4.5" diameter Kreitler rollers, a front fork stand, and a bike equipped with a power meter (and a power meter head unit).  That's really basically it.  A couple of other pieces of equipment that are crucial for getting consistent results, in my experience, are:

• A means to measure ambient temperature
• A means to measure rear wheel load
• A separate speed sensor and magnet (NOT on the wheel, but on the roller - see below)
• A notebook and pen

For measuring the ambient air temps during the test, I use my trusty Brunton ADC Summit, which I place at about axle level somewhere near the side of the rear wheel of the bike during the testing.

To measure the rear wheel load of the setup, I actually just use a digital bathroom scale which I've checked against known weights and typically is within 0.5 lbs of the actual weight.  In order to make that rear wheel load measurement, I mount the fork in the fork stand, and in stead of placing the rear wheel on the rollers, I stack the scale on top of some wood scraps and place the rear tire on the scale.  I stack it so that the rear axle is the same height off the ground as it would be on the rollers.  As it turns out, a couple of scrap pieces of 3" square wooden post and the thickness of my scale put that measurement to within 1/4" of what it is on the rollers.  Perfect.

Now then, let's talk about the speed sensor I mentioned above.  One of the most important things to get an accurate measure of in this testing is the actual "ground speed" during the test.  This can be done with a wheel mounted magnet and speed sensor, BUT that requires determining and changing the wheel rollout number for EACH tire tested.  In my experience, that can be a bit problematic...especially due to the curved contact patch that is present on the rollers.  It's very hard to get an accurate and consistent measure of wheel rollout that way.  To solve that problem, I realized that instead of triggering a speed sensor on the wheel, I could instead attach a magnet to the end of one of the rear drums and then use a speed sensor triggering off of the drum.  All I needed to do was to carefully measure the diameter of the metal drum (which will NOT be changing from test to test) and use THAT as the ground speed measurement for the testing.  Here's what that looks like:

That's just a small rare-earth magnet attached to the end cap of the roller with double-sided tape, and a Garmin ANT+ speed/cadence sensor taped to the roller frame.

Lastly, the notebook and pen are where I write down the date, what tire I'm testing, the size, the ambient temps during the testing, the power meter zero offset numbers, and the actual measured tire width as mounted.


The Protocol:

Alright, so everything is set up and we've gathered all the stuff needed.  What's next?  How do I do this? Well, here's a quick rundown of how I go about doing a tire Crr test (in "10 easy steps"!) This isn't the only way to do it, but it's how I've settled on things after doing this testing for a while:

1. Mount the tire on the test wheel - Most of my testing is done with my old yellow-cap PT wheel with a Mavic Open Pro rim.  I started out testing with this wheel in order to get both a hub and crank power to determine the level of typical drivetrain losses in the setup.  I wanted to know that for the occasions when I would be testing tires (such as tubulars) which I couldn't mount to the clincher PT wheel. Since I'm mainly interested in tires for time trials and road racing, I'll test them using a latex inner tube.  Testing by others has shown that using a butyl tube can cause 10-15% higher Crr than with latex.
2. Pump the tire to the test pressure - What pressure to use is really up to you.  I chose to do all of my testing with 120psi.  The reason I chose that value was mainly so that I could compare my results more easily to the results of others, most notably the testing done by Al Morrison.  Understand that on a perfectly smooth surface, the higher the pressure you pump tire up to, the lower the measured power requirements will be...however, that will only be true on the rollers, or on flat surfaces that are just as smooth.  On "real roads", i.e. roads with typical roughness, that isn't necessarily the case and there will tend to be a pressure above which higher pressures actually will make you slower overall.  Anyway, the key here is to pick a pressure and stick with it through your testing so that you are comparing tires on an equivalent basis.  
3. Place the wheel in the test bike - Install the rear wheel in the test bike and place the chain in the chosen gear for the testing.  I do my testing in a 53x13 gear for consistency. If it's not in there already, install the fork into the fork mount.
4. Measure the rear wheel load - This is done how I described above.  I'll usually only do this once during a session, and for me I've found it's typically within a pound or two each time (my body weight tends to be fairly stable).  This doesn't seem to be a super-critical measurement either, since a 1 or 2 lb. difference will only result in ~1-2% error in the final calculation.
5. Place rollers under rear wheel - At this point, move the scale out from under the rear wheel and slide in the rollers. To get a consistent placement of the rear wheel on the rollers, I'll lift the fork mount slightly off the ground while I allow the rear wheel to spin as it touches the 2 rollers and then I carefully place the fork mount on the ground.
6. Climb on board - It's now time to saddle up.  I usually approach the bike from the non-drive side and put my left foot on the pedal and then carefully swing my right leg over taking care not to disturb anything in the setup.  I'll then spin the cranks to make sure the PM is awake and the speed reading is working, at which point I'll clip out and zero the PM through the head unit.  I'll note the offset value (from my Quarq) in the notebook along with the ambient temperature.
7. Tire warmup - Now it's time to warm up the tire to working temperature.  Since my tests are done at 90 rpm (I find it's easier to hold a consistent rpm rather than focusing on the wheel speed) I'll warm up the tire at 95 rpm for 5 minutes.  At the end of the 5 minutes, I'll stop and quickly check the PM zero offset and write the value down in my notebook along with the ambient temperature reading.
8. The Test - Now it's time for the test.  I'll bring the cadence up to 90 rpms and once that is steady, I'll start a 4 minute interval in the PM head unit.  I'll concentrate on keeping a steady cadence through the whole interval, trying to be especially steady through the final 2 minutes since that is the section of the data I take the average power and ground speed from.  At the end of the 4 minute test interval, I'll again note the PM offset (to make sure it hasn't moved appreciably during the test for some reason) and write down the ambient test.  That's it.  Test over...either I stop there, or if I have more to tires to test, I'll start back at step one (skipping the load measurement for repeat tests) and on through the remaining steps.
9. Download Data - Now it's time to get the average power and ground speed values from the head unit.  I'll typically load the file into Golden Cheetah and then highlight the final 2 minutes of each test session and read off the averages as calculated.
10. Calculate the Crr - The final step is to take the average power and speed values, along with the wheel load and ambient temperature taken at the end of the test interval into a spreadsheet I've written to quickly do the calculations.  I've loaded the spreadsheet onto Google Drive and it can be accessed here: Crr Spreadsheet

Other Notes:

• After doing a number of runs using both the crank-based power meter and the PT wheel, I was consistently finding that for the gearing chosen and the lower power levels (typically 50-100W) seen on the 4.5" rollers, the drivetrain losses were on the order of 5%.  That's the value I enter in the spreadsheet.
• I did a fair number of runs with the exact same tire and at different ambient temperatures to determine what I should use as the temperature compensation value.  In my case, I found it to be ~1.36% change per deg C (lower Crr with higher temperatures).  Here's the plot of those tests:

• I normalize the Crr values to 20C.  If you want to know what the Crr would be at various temperatures, you can just enter those temperatures into the appropriate cell on the first sheet of the spreadsheet.
• Added 2/19/12 - I realized I forgot to point out that I use a "smooth to real road" factor of 1.5X to account for the higher energy dissipation requirements of typical road roughness.  This value is based on comparisons of roller based Crr measurements ("translated" to flat surface) and actual "on road" Crr derived from field tests and other means (i.e. iAero coast down values) for the same tires.

Well...that's about all I can think of for now.  Hopefully that will help encourage others to give this a try.  It's really not that difficult to do and is a good way to help you to "choose wisely" when it comes to tires for your "go fast" bike setup.

Tire Crr testing on Rollers - The Math

I've been doing a little bit of tire testing lately.  But, before I reveal any results, I thought it would be good to go over some math.  I know, I know...(I can hear the groans already), but I think it's important to review so people understand why it's reasonable to equate power to move a tire on a roller to power on flat ground.  

It's long been known that bicycle rollers act as a sort of rolling resistance "amplifier".  In other words, the differences in the rolling resistance between tires is magnified when riding on the rollers.  It's usually a fairly subtle thing to try to "feel" the difference in rolling resistance in tires when riding outside, but it's pretty easy to tell the fast tires from the slow tires on rollers just by the exaggerated effort it takes.  But, the question has long been "how much" of an amplifier are they? Well, back in 2006 I was discussing this with a few folks and realized that the equations to make that comparison between rollers and a flat surface Crr (Coefficient of rolling resistance) were already available...they just needed to be combined.  Then, it was pointed out to me that the particular geometry of a typical roller setup needed to be accounted for as well.  The normal "dual roller" setup on the rear of a roller set results in a geometric effect that actually increases the normal force on each roller.  In other words, you can't just take the rear wheel load as if it was a single roller. So, I added that to the equations as well.

Anyway, what you see below is the short "paper" I sketched up back then on the subject:

Flat Surface RR from Roller Testing – Tom Anhalt – 5/2/06

The power required to turn a wheel on a drum at a specific speed is governed by the equation:

P_Drum = Crr_Drum x V_Drum x M x g (a)

Where,

P_Drum = Power required to turn drum (Watts)

Crr_Drum = Coefficient of Rolling Resistance of the tire on the drum (unitless)

V_Drum = The tangential velocity of the drum (m/s)

M = The mass load of the wheel on the drum (kg)

g = gravitational constant = 9.81 m/s²

Rearranging equation (a) to solve for the Crr of the tire on the drum results in:

Crr_Drum = P_Drum / (V_Drum x M x g) (b)

Then the contact patch deformation of a tire of a specific diameter and a roller of a specific diameter can be equated to the deformation of an equivalent diameter tire on a flat surface using the following equation [Bicycling Science, 3^rd edition, pg 211]:

1/r_eq = 1/r₁ + 1/r₂ (c)

Where,

r_eq = equivalent wheel radius

r₁ = tested wheel radius

r₂ = tested drum radius

For convenience purposes, this equation can be rewritten using the appropriate diameters (r x 2) and is then:

1/D_eq = 1/D_wheel + 1/D_Drum (d)

For a tire of a given construction, it has been shown that the Crr varies inversely proportionally to the wheel radius, and thus the wheel diameter, in the range of D_wheel^0.66 to D_wheel^0.75 [Bicycling Science, 3^rd edition, pg. 226]. To simplify for this purpose, the assumption is made that the Crr varies inversely proportionally to D_wheel^0.7

From this, it can be then written that:

Crr_flat / Crr_Drum = D_eq^0.7 / D_wheel^0.7 (e)

Equation (e) can be combined with (d) and rearranged to give:

Crr_flat = Crr_Drum x [ 1 / (1 + D_wheel/D_Drum)]^0.7 (f)

Substituting equation (b) for Crr_Drum in equation (f) results in:

Crr_flat = [P_Drum / (V_Drum x M x g)] x [ 1 / (1 + D_wheel/D_Drum)]^0.7 (g)

Mass Correction Factor:

When doing Crr testing on rollers, the mass loading of the wheel or wheels will need to be corrected due to front-rear loading ratio and the fact that 2 offset rollers contact the rear wheel, thereby increasing the normal force on the rollers due to geometry effects.

Rear Wheel Only Case - When the test is done using a front fork mount and only the rear wheel contacting the rear rollers of the test setup, the following “effective mass” (M_eff) needs to be calculated and substituted for M in equation (g) :

M_eff = M_rear / cos [arcsin (X/(D_wheel + D_Drum))] (h)

Where:

X = separation distance of rear roller axles (consistent units with D_wheel and D_Drum)

M_rear = vertical mass load on rear wheel (kg)

Front and Rear Rollers - When the test is performed using both the front and rear rollers, the following Meff needs to be calculated and substituted for M in equation (g) :

M_eff = M_front + M_rear / cos [arcsin (X/(D_wheel + D_Drum))] (i)

Where:

M_front = vertical mass load on the front wheel (kg)

Power Correction:

Depending on the method of power measurement, the following offsets can be used to account for drivetrain and drum rotation losses in the calculation of P_Drum for use in equation (g):

For Powertap - P_Drum = P_Powertap – 5W (accounts for drum bearing losses) (j)

For SRM - P_Drum = P_SRM – 15W (accounts for drum bearings and driveline losses) (k)

Where:

P_Powertap and P_SRM are the power readouts (W) from the appropriate power meters.

These power offsets are somewhat arbitrary and should be modified if better data is known about the particular test setup.

That's basically it.  I'd like to note a couple things about the last section on "Power Correction".  First, after doing a bunch of testing since then, I don't bother accounting for the drum bearing losses.  Also, when using a crank-based power meter, like an SRM or a Quarq Cinqo, I've found (after using a PT in conjunction for quite a few tests) that it makes more sense to account for the drivetrain friction with just a straight percentage.  A typical value taken for drivetrain losses on bicycles is ~2.5%, but that is typical at higher power levels (i.e. higher chain tensions).  For the lower power levels I usually see in tire testing with a rear only roller setup (usually ~100W or less, with the better tires closer to ~50W) I typically see ~5% drivetrain losses, so that's the figure I use.

It's important to remember that the point of this is to get a "ballpark" feel for the difference between tires, not necessarily an absolutely accurate value.  It's been shown that percent difference in power requirements on the rollers equate very well to percent differences on the road.  What we're really looking for is a sort of "scaling factor" to put the differences seen on the rollers in perspective as to what to expect on the road.

There you go...equation (g) is easily written into a spreadsheet.  After that, it just takes a few measurements of the roller setup, weighing the rear wheel load, and some time on the rollers with a power meter equipped bike and nearly anyone can "test tires".

LeMond Power Pilot - Does it give good numbers?

Considering that it was announced today that Greg LeMond had formed a new venture to sell the Revolution trainer, and that my last post had dealt with the Revolution, I thought it would be a good time to also talk about the Power Pilot device that LeMond sells for use with the trainer.  If someone already has a non-wheel based power meter on their bike, then the Power Pilot would be a bit redundant.  But, for those who use a PT wheel primarily, or don't have another form of power measurement, the Power Pilot could be a good alternative for determining the "load" during a trainer workout.  The following is a brief look at the power reporting and recording performance of the LeMond Power Pilot. In particular, it is compared to the output of a “known good” Quarq CinQo crank-based power meter.  "Known good" in this sense is a power meter which has had it's torque slope checked and adjusted and has a zero offset that is stable.

BACKGROUND

The LeMond Power Pilot is a device designed to be used in conjunction with the LeMond Revolution trainer to primarily monitor and record the training efforts of the rider. The Revolution trainer is a high inertia wind trainer with the somewhat unique configuration whereby the rear wheel of the attached bike is removed and is not a part of the driven assembly. The chain of the bike drives a rear cassette which is attached to a relatively high mass flywheel through a belt drive gear reduction system. In my last blog post ("What's the Virtual CdA and Crr of the LeMond Revolution Trainer"), it was shown that this system “mimics” the aero drag of a typical sized rider on a road bike (CdA = ~0.35 m^2) and the rolling resistance of average tires (Crr = ~ .005). The inertial mass was also found to be equivalent to a rider mass of ~45kg, which although it is less than the mass of a typical rider, it is far higher than the much lower inertial masses of most indoor trainers on the market today. This accounts for the often reported excellent “road feel” of the Revolution trainer.

The Power Pilot uses an ANT+ sensor to read the drive pulley rotational velocity, and by extension, the flywheel speed during operation. Along with the known aero properties of the flywheel fan, the aero drag power is calculated using that speed measurement and an estimate of the air density (based upon the user entered altitude, an internal temperature sensor, and an internal humidity sensor.) The speed sensor is also used to determine the acceleration/deceleration of the flywheel mass to account for that in the power reporting. Additionally, the Power Pilot firmware allows for a coastdown calibration to be performed which then accounts for any unit to unit variation in the “fixed” losses of the mechanism.

THE TEST AND RESULTS

In order to determine how well the Power Pilot performs these calculations, it was decided to compare the Power Pilot output to the power values measured using a Quarq CinQo crank-based power meter. The particular CinQo used in this testing is a “known good” unit which has been recently calibrated for torque slope and demonstrates a very stable zero offset. To make the comparison, a ride was undertaken whereby a “cassette sweep” was performed. The ride started with the bike in a gear selection of 53/25 and then progressed down the cassette every ~1.5 minutes until a gear selection of 53/12 was used, all the while keeping a constant 60 rpm cadence. Then, the chainring was shifted to a 39T and the progression was repeated partially up the cassette. Finally, two additional runs were taken at a higher cadence (and thus power). A plot of both power traces vs. time is shown below:

Looking closely, one can see that aside from a slight offset, the values reported by each power meter “track” very closely to each other. This can further be seen if the power values relative to each other are plotted on a point-by-point basis. The plot below shows the power reported at each point in time with the CinQo power values on the x-axis and the Power Pilot values on the y-axis.

Typically, due to factors such as variations in recording rates, calculation algorithms, etc. the sort of plot above doesn't turn out very well as a comparison tool for power meters. However, in this case, the point-by-point power reporting is fairly good and it appears that the Power Pilot reports ~94% of the power reported by the CinQo. Considering that the Power Pilot estimate is taking place “downstream” of the bicycle drivetrain losses (much like a PowerTap wheel) in comparison to the crank-based location of the CinQo, a ~6% drivetrain power loss is reasonable, and typical of an average drivetrain.

Rather than looking at the point-by-point plot and it's curve fit, often it's more useful to look at a plot of the averages reported by the power meters over constant power sections. The plot below is the same as the previous plot, but the averages over each of the “intervals” of the cassette sweep are plotted and a curve is fit to them. As can be seen the fit is fairly “tight” to the data and the slope of the fit (i.e. the drivetrain loss) is similar to that reported above, albeit slightly lower. This appears to point out that the correlation between the 2 devices may be slightly better during constant power efforts. Alternatively, it could reveal that the time correlation of the point-by-point data looked at above may be slightly “off”.

However, understanding where the power meters don't agree can sometimes be much more enlightening in that it can reveal systemic difference between the devices. One tool for doing this is something called a “Mean – Difference” Plot. This plot shows the difference between the power values reported by the 2 devices plotted against their average. The Mean-Difference plot of this ride is shown below:

The things to look for in this type of plot that reveal systemic “issues” are characteristics like the spread of the points getting larger or smaller with the mean power values or the difference not trending in a monotonic fashion. Neither of these types of issues appear to be present above, implying that the Power Pilot “agrees” with the CinQo output in a consistent and predictable manner.

Another area of interest for comparisons of this type is how the 2 devices respond to sprint type efforts. An additional ride was undertaken where a pair of short sprints were performed in order to see if there were any anomalies between how each device reported these efforts. As can be seen below, the shapes of the curves are very similar with the peak values also being very close to each other.

CONCLUSIONS

This brief examination of the power output of a LeMond Power Pilot on a Revolution trainer shows that it does an acceptable job at determining and recording the rider's power output when compared to a “known good” crank-based power meter. The power output is similar to what one would expect to see from a hub-based power meter, which is favorable for the likely customer base for this product, namely users with no other power meter or Power Tap owners who want to train indoors with and/or by power.