Dartmouth 2010
Join Date: Nov 2007
Location: Hanover, NH
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Calculating Rolling Resistance
About two years ago I got an email from a man named Ernie Rogers describing his method of determining rolling resistance. Here's the meat of it:
Quote:
The opposing force against a moving car is the sum of the rolling resistance and the aerodynamic drag:
F = Crr M g + Cd A 1/2 rho V^2
In words, the rolling resistance is the rolling resistance coefficient times the total mass of the car in kilograms times the gravity constant (9.81). The aerodynamic drag is the drag coefficient times the frontal area of the car times onehalf the air density (1.22 at sea level) times V squared. V is the velocity of the car if there's no wind.
Otherwise, add headwind /subtract tailwind. This is tricky because any side wind in effect changes the drag coefficient. This side wind effect is important for a person designing a car. For you, trying to get the rolling resistance for your tires, it means avoid wind as well as you can. At least, measure the coastdown in both directions and average. This also helps to cancel out any slope effect. Yes, we had assumed the road is flat and level.
If you multiply the force above by the car's velocity on the road in meters per second (mph x 0.447), you have the power needed at the road. If you divide the force by M, then you have the acceleration:
a = Crr g + (Cd A rho V^2) / 2M
Get M by taking your car to a truck scale and weigh it with you and the fuel, etc. You need to know A and Cd unless you are measuring that too. There are places all over the internet that will give you Cd and A. Do a google search for "[your car] drag coefficient" Or, try "drag area" which gives you Cd A together.
Okay, now all we need are some numbers for the acceleration (actually, deceleration) and you can start calculating.
Find the flattest, smoothest road you can. Get up to a good speed (80?), put the car in neutral, and time the speedometer through 70, 60, 50, 40, 30, 20 mph with a stopwatch. Find out what the speedometer error is and correct the speeds. A GPS is really handy for the corrections but you can do a pretty good job by timing your car between highway mile markers. Ideally, you will get the correction at several speeds because the speedometer is not linear. (Hmm, I forgot that when I did my test.)
Now, make a graph of your speed (in meters /sec) versus time. Find the slope of a tangent line at a high speed, and again at a slow speed. Now, you have the acceleration at two points. The rolling resistance is the bigger term for the slow speed and the aero drag is the bigger term at high speed.
Look up the Cd A for your car, put it into the equation at slow speed, and solve for Crr. You should have your answer. To be sure you used the right Cd A, put your Crr into the equation for high speed and solve for Cd A. If you don't get the same value, put the new calculated value into the slowspeed equation and calculate again. Eventually, they will check together.
A little note: this process is assuming that Cd and Crr are both really constants. Some people will argue that it isn't true. I think we shouldn't worry about it to do so makes things way too complicated for a coastdown test, my opinion. Another caution is that we are really measuring all of the friction in the bearings, etc., back to the shaft disconnect along with the rolling resistance. Again, I think it's too much trouble to worry about it. Anyway, the correction should be small, I think your true rolling resistance may be a little less than what you calculate.
Ah, done. See if you have any questions.
Ernie Rogers

