Measure tire rolling resistance with a bounce test
 

Hello, folks,

One of the big problems in getting the best mileage is to know what tires will give the lowest rolling resistance. I have an idea for a quick test to evaluate tires. A low-cost test setup would have to be designed. I am presenting the math results here without deriving them. Let me know if you want to dig deeper. Anybody interested in trying this? /Ernie Rogers

Bounce Method for Rolling Resistance Measurement of Tires

The rolling resistance coefficient of a tire can be measured by simply bouncing the tire on a hard surface. To get the correct result the contact patch in the bounce test must be the same size as the contact patch during normal use. This can be done by experiment, or found analytically by using the following relationship:

Mg x = mg h

Mg is the load on the tire in normal use
and x is the associated deflection (forming the contact patch),
mg is the weight of the tire and wheel during the bounce test
and h is the drop height that the tire is dropped in the test.

The tire deflection can be calculated with the following approximate relationship:

x = (1/8r)(Mg/Pw)^2

It was assumed that Mg = PwL,
L is the length of the contact patch
P is the tire pressure
w is the width of the load-bearing tread
r is the radius of the tire

In the bounce test, the height of bounce is divided by the drop height. The energy absorbed in the bounce is:

ΔW = mg (h – hb)

where hb is the height of bounce. The ratio of the heights will be defined as η (eta):

η = hb/ h

With the above information, a relationship can be found between the rolling resistance coefficient, Crr, and η. Two equivalent forms are given:

Crr = Mg (1- η)/(8Pwr)
Crr = L (1- η)/8r

The required drop is found to be only a few inches for passenger tires. The drop could be straight down to a solid floor or the tire could be suspended to swing and bounce against a vertical surface.

Wouldn't you need to factor in the weight of the rim?

Wouldn't that be estimating the Crr, since you are deriving Crr from a bounce test, and not directly measuring RR?

The only valid way I can think of to properly test this is to conduct both bounce tests and proper Crr testing and see if there is a correlation in the results.

Really, what is the Crr$
 

Excellent comment, Tas. Really, what is the Crr?

For me, it's a parameter I need to calculate fuel economy. For everyone, we use it to decide which tires give the best mpg, and these two are really the same thing. But, does the standard measurement for Crr fill the need? The fuel economy of a car is highly dependent on the interaction between the road surface and the tire, AND the suspension. There is a lot of bouncing going on in the real situation.

Okay, Tas, back to your point-- validation is very important. I would say, someone should be checking BOTH the accepted method and the bounce test to see how well they correlate with actual fuel economy.

Ernie Rogers

The rim probably does affect Crr
 

Hmmm, THAT is an interesting question-- how does the weight of the wheel (or rim) affect the efficiency of a tire? It does of course. Neither my proposed test or the standard test would account for that.

Good observation.

Ernie Rogers

Steel-on-steel is too harsh for me; make mine Superball tires! :thumbup:

I suspect the bounce test could work to a certain degree, by this I mean there probably would be a correlation, but it might never be verified. Even with a very simple bouncing test, there is still a lot of variables to control.

We all know hysteresis is the major factor influencing rolling resistance, but I suspect hysteresis in a rolling tire is different than from a bouncing one as hysteresis changes with the speed of the loading-unloading cycle, which may be analog, but is different between a rolling and a bouncing tire.

Crr is such a complex principle, not only does it changes with every tire size, it also changes at every speed it is tested...

The one factor not taken into account is the tread pattern which can also influence the RR of the tyre although it would probably not show up in a simple bounce test.

A given load on a rolling surface like a chassis dynomometer would be a better test and not that difficult to arrange either.

Pete.