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John Tetz: Crr vs Temperature, p.1
Did you know that Crr [Coefficient of Rolling Resistance] changes drastically with temperature changes? I didn’t. And I don’t remember seeing any data to this effect in any of the bicycle literature. I believe I have sufficient data to show that indeed it does change.
In November 2004 I finished building a prototype trike designed to go inside a velomobile body eventually. I did the typical debugging and testing, including coastdown tests to determine Crr. However, when I typed the coastdown data into the TCoastF3 spreadsheet, it couldn’t calculate the Crr value. I thought there might be a bug in the program so I dug out the backup copy, and the copy gave the same can’t-calculate response.
Then, as a last resort, I typed in ever-increasing Crr values. I started with what I thought to be a typical value of around .005, and increased it to .008, which I thought was high. No good. So I increased it more, and when I got to .01 the calculator started working. Eventually the Crr value was .012. I thought, this is impossible, it can’t be this high! This was more than double what I have been seeing on my bikes. Yet I remembered that when I did the coasting, the trike did not make it to the end of the coast distance, not until I upped the speed coming into the test trap. The trike was indeed slow. Something was up.
So I got my LFWD (Low Front Wheel Drive, weight 25 lbs/11.3 kg, rider weight 158 lbs/71.7 kg) bike out and did several coastdown runs. The spreadsheet said the Crr was .0065. Another shock. I have been taking Crr tests over the last couple of years, and have been seeing numbers down in the .004 range. What gives?
I continued to do coastdown tests, waiting for days when there was little or no wind, and with further data, I spotted a pattern. As it got colder, the Crr values went up; on warmer days, it went back down. The Crr vs Temp graph shows a plot of the data collected so far. Vt3 is Velomobile Trike version 3, weight 35 lbs/15.9 kg. Yes, it took me 3 versions to get the proper layout changes so it will fit inside a streamliner shell (shell still in construction as of 01/17/05).
We all know our HPVs are slower in winter, perhaps because the air is denser? But here we see that the major cause is the Crr. Projecting the slope on the trike data to warmer temps, it looks like the Crr would be around .009 at 75F. That is high. Why?
This clearly shows the effect of temperature. David Wilson (one of the authors of Bicycling Science) sent me a quote by Jim Papadopoulos from the 3rd edition:
"Preliminary PowerTap measurements on the road and on a home ‘wind’ trainer have suggested significant effects on tire rolling resistance of temperature (with Crr dropping roughly one percent for each degree Celsius of temperature rise) and speed (with Crr doubling when wind-trainer speed reaches 5 m/s)."
If I use the LFWD data from 32 degrees F (0 C) to 75 F (23.8 C), the Crr decreases from .009 to .004. My data shows a per degree change larger than Jim's.
I do not have summer temperature data yet on the trike, but I am posting this now in January to share with the HPV community so we can try to figure out what is happening. Hopefully others will learn how to do testing on their vehicles, particularly with different tires. There is enough winter left to get a range of additional data. I will upgrade this plot as the weather warms up.
What can be causing such high readings on the trike? The theory is there is 1/3 the weight on each wheel, meaning the total drag should be not much different than on a bike. But it’s way higher than on the bike. Can’t be aero drag. The top coastdown speeds are in the 9 mph down to 3 mph range.
Tire pressure? I set the pressure to 85 lbs. for all tests. This is the pressure I use on the road for ride comfort and handling on rough surfaces. I am using Primo Comets on both vehicles. Vt3 has the fat 1.75s on all three wheels, and the LFWD has a 1.75 up front and a 1.35 on the back. These tires on the LFWD have given me consistent Crrs in the .004 range during the summer. And at 100 lbs. they are down in the .0038 range. I don’t have access to different tires, and it’s a lot of work to change tires.
Toe-in/out errors? I did some coastdown tests to find out. I physically set the toe by measuring across from the front and then the rear of the wheels at an equal height off the ground. The top of my wheels lean in with camber, so this height measurement is critical. I set it with a slight toe-in because my tie rods are in front of the king pins, and as the cross tube is bending in from rider weight and bumps, the toe will head towards a toe-out direction.
I did two tests on different days. For each test the first step was to do runs at that reference setting. Then I unbolted one of the tie rod ends and turned it in one turn, then another (10-32 thread). Then I turned the tie rod out one turn and then one more, followed by a final reference run. On the second test, I only did two turns in and two turns out and the reference runs. The data shows that where I physically set the toe results in the lowest Crr.
What about wheel bearing drag? It was reported in Bicycling Science that wheel bearings have a Crr of around .011 (p. 144, 2nd edition), and that the effective resistance is very low because of the large ratio of wheel diameter to bearing diameter. For my 20 inch wheels and a 1.25 diameter bearing, the Crr is around .001.
I jacked the bikes up and spun the wheel that has the bike computer magnet, then measured the run-down time from 9 mph to 3 mph at different temperatures. The LFWD data is from the front wheel, which includes the drag of the freewheel hub. The Trike data is from one of the front wheels, which have sealed bearings. The LFWD has ball and cone bearings, plus the freewheel pawls.
The times for the LFWD wheel coastdown from 39 F to 69 F increased from 15 to 25 seconds - a big change, and this is on an unloaded wheel. This has to affect total Crr, but by how much? I do not have the physics or math background to calculate out the bearing losses from the tire losses. Is there someone in the HPV community that can do this?
With one extra wheel, this may explain why the trike has a higher rolling resistance, regardless of temperature, as the two plots have similar angles. I would really like to see Crr measurements on a range of commercial trikes and different tires.
My Coastdown System
The method of coasting to obtain Crr data is difficult and requires a detailed discipline. If it was easy, everyone would be using Crr/CdA information rather than guessing - hey, it’s the 21st century, no more guessing. In the past, it took expensive laboratory equipment to collect this information, but we now have easily available tools in the form of your computer, bicycle wheel, bicycle speedometer, hand-held digital stop watch, and spreadsheets. Here are the basic techniques, including links to more detailed information, so that anyone can make these measurements.
The basic technique is to read the initial speed - not an exact speed but a known speed at the start of the coast trap - and record the time over a carefully measured coast distance. Do this in both directions, and get several pairs (up/down pairs) to average out errors.
Next, take any one pair and times and enter the data into the coast spreadsheet. Then manipulate the variables of grade and Crr values until the coast calculator is close to zero difference. The method is detailed on the first sheet on the spreadsheet. I recommend not averaging the speeds and times. It is more accurate (but more work) to do individual pairs.
Initial speeds are purposely low, in the range of 9 mph for the Vt3 and 8 mph for the LFWD. The speeds at the end of the run should be high enough on the bike to prevent wobble, which no doubt would affect results. On the trike, if the speeds near the end of the trap are very low, the spreadsheet calculator doesn’t like this, and large errors can occur. Keep the end speeds at least 2 mph. These initial speeds are chosen to be low enough to reduce the effects of CdA.
The spreadsheet does need a CdA (Coefficient of aerodynamic Drag times frontal Area) value that can be estimated until it is measured. I have enough experience over the last four years of doing tests that I can now estimate CdAs. Also I know what the LFWD CdA actually is and can estimate for the Vt3, which I feel is around 2.8 sq ft. It could possibly be 2.7, but I doubt if it is down to 2.5. I easily out-coast trikes on the LFWD. As a comparison: Bacchetta Aero approx 2.4, RANS Rocket 2.5, Tour Easy with a sock 2+, Lightning P-38 2.9, Tour Easy 2.9, Optima Baron 2.4, Challenge Jester 2.4
Here are examples of changing CdA on the spreadsheet and its effects on Crr results:
CdA 2.6 Crr = .0131
CdA 2.8 Crr = .0129
CdA 3.0 Crr = .0128
As you can see, not much effect. This is exactly why I like doing Crr at low speeds and CdA at high speeds. Because Crr affects results at higher speeds, always do Crr measurements first. To clearly see the effect of Crr, plug in some numbers into the PDG (Power/Distribution/Gearing, including mid drives) spreadsheet:
Vary the speed, and on the distribution chart you will see how far up in speed Crr is sucking up power, particularly with low CdA vehicles. PDG is a work horse spreadsheet. I use it a lot for measuring my power capabilities and estimating other vehicles’ CdA or Crrs. Between the three spreadsheets, we have very informative tools with which you can play “what if” games, which can affect new designs, help tailor record attempts, or used to check manufactured vehicles. Having actual numbers, rather than guessing, gives us a better understanding of possibilities.
There are four possible coast functions:
F1: coasting down a grade at increasing speed, used to determine CdA
F2: coasting up a grade decreasing speed; don’t need this
F3: coasting on flat ground decreasing speed, used mainly for Crr and also flat ground CdA measurements
F4: an odd one, coasting down a very low grade, such as 0.5%, at a steady but low speed, 3 mph a kind of low speed terminal speed
The spreadsheets for TCoastF1.xls and TCoastF3.xls that do the necessary complicated calculations can be downloaded from the IHPVA website:
Both spreadsheets have instructional text on the first sheet. These spreadsheets took a long time and effort to generate by a friend at Bell Labs. I did the on-road testing and asked for various features. He did the physics and math. There is lots of physics involved. This makes information available to people that do not have the detailed physics and math backgrounds.
The first thing to do is to find a proper section of road - this can be difficult. Read the text Grade.doc available on the IHPVA web site for more details:
The grade needs to be flat, but there is no such thing as flat. Nature builds in slope for drainage. A grade of less than 0.3% is acceptable. On steeper grades the vehicle may have problems coasting up past the finish line. Upping the speed by 1 mph may work, but be careful to stay away from the influence of CdA. The coast trap can also be shorter. Ideally it needs to be about 150-200 ft. long in order to give a decently long coast time (also to reduce % timing errors).
Once the requirements are understood, you can then look for the appropriate road. I have a smooth macadam road very near my home with minimal traffic; passing cars create wind and errors. Next, accurately measure this coast trap distance. Read Measure.doc, available on the IHPVA web site for more detail:
A quick measure summary: lay out a long tape measure on the ground, the longer the better, about 50 - 100 ft. Using a bike as a measuring device, walk the bike and count the revolutions of the wheel. Divide the distance by the revolutions to get the wheel circumference. Do this at a known tire pressure. Then, using that calibrated bike wheel, walk the coast distance counting the wheel revolutions to get an accurate coast distance. I paint small unobtrusive start stop lines on the side of the road.
You also need to accurately calibrate the bike’s odometer/speedometer. Walk your calibrated wheel bike over, for example, a 0.4 mile distance counting the revolutions. Counting out loud helps. Calculate the distance. Then ride the bike and calibrate the odometer. I assume the speed is then also calibrated. We use it for the critical Initial Speed readings. The speedometer needs to read in tenths.
Now here’s the tricky part. Give yourself about 50 ft. or more to get up to a nice uniform speed, and then stop pedaling about 30 ft. from the trap so the bike is coasting at a stable speed. As you come towards the start, observe the rate of speed change on the tenths readout. This is updated one per second, so it typically drops around 0.2 to 0.3 mph. The reading may update before, during, or after the start. I prefer the later reading because the update is reading what has just happened. Get a reading and estimate what the speed is at crossing. Say it out loud to help put it in memory (yours). The rate of dropping is higher on steeper up grades, another reason to choose flatter grades.
The challenge at the start is that you are staring at the speedometer, reading the numbers to get a feel for where they are, picking up the start line out of the peripheral vision, and then reading a speed while simultaneously starting the coast trap stop watch. This sounds like a total overload, doesn’t it? It helps to put yourself in a zone, a Zen state, so you can take in all this information. The human is quite a sensory capable machine. Kind of blank stare at the speed changes, the rest comes. Practice, practice, practice.
It helps immensely to have a bright tall object at the start, such as a traffic cone, well within you peripheral vision. It’s also hard to read the speed number after the passing of the start and push the stop watch button at the actual start. The reaction is to tie the two together. I make a perceptional note as to how far beyond the start I collected the information, and at the finish line I stop the watch in the same relative position. I don’t look directly at the finish line cone, so this relates to the start line position.
Does this system work? Here is a typical sheet of data. Look at the variation in Crr down the list. The variations are well within reasonable values. Wind will create more variations. If the wind is above 4 mph, forget testing. I tried using other techniques before I had these spreadsheets, and this system shines above some others.
Speed sensitivity tests (I varied the data 9S and 10N):
Reducing both times by 0.1 mph, Cr = .0125 (originally .0129)
Reducing both times by 0.2 mph, Cr = .0120
Time sensitivity tests:
Reducing both up and down times by 1 second, Cr = .0115
Reducing only up time by 1 second, Cr = .0125
Both speed and time are a part the data spread on the plot. This is reasonable, given the lack of precision measuring equipment. Speed and time variations cause much less change than do temperature variations. So, for data spread we have: initial speed variations, time variations, and wind effects. By paying attention to details, we can reduce or eliminate errors from coast distance, odometer calibration, weights, and tire pressure errors.
To reduce timing errors, I tried using two timing tapes straddling the start line, tripping a digital stop watch. The tapes worked well as a timing device, but bumping over the tapes slowed the vehicle by about 8 %. The upside down triangle on the Crr vs Temp graph is LFWD data running over those tapes. This bump data would probably be different with different tires sizes, tire pressures, and weights of vehicles. I also thought of photoelectric timers. This means that part of the device (reflectors) would have to be way out on the road, very possibly being hit by a car.
What we need is a small, portable, low cost, data logger that can be clipped onto any vehicle, picking up a signal off a wheel magnet (maybe two magnets), with a push button to indicate the start and finish lines, ideally downloadable to a computer to read the initial speed and coast times. If any one knows of such a device please let me know.
While I am asking for favors, is there an expert that could write sub routines for the TCoast spreadsheets ones that can automatically zero the difference errors in cells N8 and N9? This would really help reduce the tediousness of hunting and pecking to get the results, making the spreadsheet much more user-friendly.
We have published coastdown Crr data with various tires (John Lafford) using a 3-wheeled test vehicle. The results are consistently higher than bike data. And some organization in England used a trike vehicle, and their Crrs are also higher. Now I can see why.
I am still wondering why trike Crrs are so much higher than bikes. What about 4-wheeled vehicles? Variations of tires on trikes? Rough road Crrs? Wet surface Crrs? Delta vs tadpole? More questions than answers. And only a few people are doing Crr measurements, which limits the range of variations.
If a number of HPV members were to learn how to make accurate Crr measurements on their own vehicles, this pool would be a tremendous information potential yielding a wider range of possibilities. I would be willing to assist anyone who serious wants to learn how to make these measurements.
See page 2 for September 2005 update with summer temperature results .