[Ernie Rogers]

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.