I found this posting over at "Prius Technical Stuff" (Thanks Dick!) and I strongly suspect it applies to our tires too: The Recumbent Bicycle and Human Powered Vehicle Information Center Bob Wilson
Aha! So while rr is basically a constant relative to speed, it changes with temp - therefore the "cold weather hit" is worse at highway speeds because BOTH aerodynamics AND rolling resistance are negatively affected by the cold. It would be interesting to plot this against tire psi to see if harder tires have a greater beneficial effect in cold temps than in warm - but it sounds like the first prescription for bad cold-weather mileage is firmer tires.
Hi everyone My 2010 european specs Prius has 195/65 R15 Bridgestone Ecopia EP100 tires. In the news article about these tires www.bridgestone.com/corporate/news/2007102303.html it is written that the rolling resistance coefficient is 0.0074. The test temperature is corrected to 25ºC using the formula Fr25=Fr[1+K(tamb-25)] where K is 0.008 for passenger car tires (pg21 of NHTSA document 575.106 http://www.nhtsa.gov/staticfiles/rulemaking/pdf/Rolling_Resistance_FRIA.pdf) The correction given by the linear formula is valid for the temperature range of 20-30ºC Although it seems that the real formula should be a polynomic of second order as shown in the figure 6.3 of the paper "Heavy Truck Modeling for Fuel Consumption Simulations and Measurements" (http://130.236.48.54/en/Publications/Lic/01_LIC_924_TS.pdf) still we can estimate the difference in fuel mileage for the temperature drop using the linear equation. Given a fuel mileage of 50mpg (4.73l/100Km) at 25ºC (77ºF) in my Prius estimated 1550Kg (3420lb) mass, the energy spent in the tires in 100Km (metric units) is 0.0074*1550Kg*9.8m/sec2*100000m = 11.24MJ If the temperature drops to 0ºC (32ºF) the new rolling resistance coefficient is 0.0074/(1-0.008*25) = 0.00925 or 25% higher. The energy spent in the tires in 100Km at 0ºC (32ºF) is 14.05MJ which is 2.81MJ more than at 25ºC (77ºF) To convert those 2.81MJ to gasoline burnt volume, I use the average ICE efficiency in my usual 16Km (10miles) trips which is 32.5% and the gasoline energy by volume which is 34.78MJ/liter. The calculation is 2.81/34.78/32.5% = 0.249liters/100Km increase in fuel economy, which is equivalent to 2.5mpg less to arrive to 47.5mpg. In short, the cold effect on tires in my 2010 Prius is: In metric. If fuel economy is 4.73l/100Km at 25ºC, at 0ºC the fuel economy is 4.98l/100Km In US units. If fuel economy is 50mpg at 77ºF, at 32ºF the fuel economy is 47.5mpg. Big hugs from Frank
The math went over my head but this is potentially very useful information. Does this sound right to our resident math gurus?
It is common to replace a complex curve with piecewise linear sections. That is what is being done here. It can be done to any degree of required accuracy by using more and smaller linear sections. Tom
Frank T-- I take it that you are trying to compare the same amount (i.e., mass) of similar fuel, which is why you do not adjust the energy/litre for temperature (which would change things a bit, no?) and why you don't adjust for summer vs. winter gas. Am I right, or crazy? Or both? [Or even neither?]
Thanks kgall. Interesting issue. Well, I tried to put fuel economy numbers to the difference in theoretical tire friction due to ambient temperature. That is, if you make the same trip the same day with the same gas tank, but early morning at 0ºC (32ºF) and in the afternoon at 25ºC (77ºF) you can expect a 2.5mpg difference in those trips (for a 50mpg reference fuel economy) due to the tire resistance effect. But if those trips are make during winter at 0ºC (32ºF) and during spring/summer at 25ºC (77ºF) with different gas tanks filled with winter / summer gas, then you should take into account what you suggest. But probably there are other correlated effects like gas price, because I think we pay the same number of dollars for the same amount of chemical energy (Joules or BTU) given the difference of density during winter/summer. But anyhow I am not an specialist in retail gas distribution. So if anyone has better information, is invited to share it with us. Big hugs from Frank
Interestingly, I was noticing that I was having a hard time maintaining speed when traveling down familiar slopes while in warp stealth mode yesterday. In areas when I can normally hold a specific speed for long periods I noticed I was slowly losing speed. This happened in nearly every place I try and glide. The car just felt heavy or something. Then I realized that the temperature was 50F-55F. I normally travel these areas, lately, at 75F-98F and gliding (warp stealth) is so much easier.
