I said that soft rubber gives lower rolling resistance.
Then, Clark said,
Quote:
Originally Posted by ConnClark
If there was any truth to this then why do steel belted radial tires have a lower rolling resistance than than an ordinary radial tire?
Also note that the soft or hardness of a rubber has nothing to do with its internal friction.
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Well, I think I will start with a disclaimer-- While I have designed many structures over the years, I have never designed a tire. I will be giving my impressions, based on engineering principles and sometimes I might get it wrong. Now, here goes.
In my view, the pneumatic tire is one of the greatest inventions of all time. (Along with bar soap.) Here's why an air-filled tire is such a great invention. First, having some give in the tire is essential to protecting other car parts from jarring loads. Essentially, we want the tire to act as a spring. There are lots of springy materials a person could use in a tire, and they all have a weakness, except one. The weakness is that when you flex a solid material, you never get all the energy back when you let it unflex. Air is the wonderful exception. When you compress air in a short time (adiabatically-no heat loss), and then let it go back, no energy is lost. So, except for whatever energy is lost in the tire shell, a pneumatic tire has perfect efficiency.
Now, let's deal with the shell. The ideal shell material holds the air pressure but has the least involvement in the spring action. It needs to have good flexibiliy, no stretch in the tread area (but flexible), and the right give in the side walls (with minimum stretch) to form the contact patch.
Bending is the desired type of shell deformation. When a sheet of material bends, energy is absorbed as strain energy, by a formula like this--
S = a K T^4
Which says that the strain energy S is proportional to the stiffness K times the thinkness of the material raised to the fourth power. Each time the material flexes, energy is lost. The energy returned is proportional to the coefficient of restitution, let's call it R, and for the energy lost, it's 1-R:
Energy lost = (1-R) S
You should notice that the energy lost is proportional to the stiffness, K. In some ways at least, the thickness of the shell is set by the strength needed to contain the pressure. Steel wire in the tire provides great strength, allowing the shell to be much thinner and thereby reduce the strain energy in the rubber, which is where the energy loss occurs. The steel cord has very low internal friction (1-R) and lies on the neutral axis in bending, so almost no energy is lost in the steel.
So, contrary to intuition, steel cord has the effect of improving flexibility in the rubber layers and reducing stretch, and thus improves efficiency.
Now, as to whether or not hardness (stiffness) of the rubber is related to the internal friction, I admit there is some uncertainty there. But, the formula directly above suggests that the energy lost is proportional to the strain energy (for a given value of 1-R) and that in turn was proportional to the stiffness. It seems that silica is often added to the rubber to lower internal friction, and I'm sure that doesn't make the rubber softer.
Ernie Rogers
Today
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