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WFalicoff

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We recently replaced our Nokian WRG2 185/60R15 with Nokian WRG3 185/65R15 tires. Both had the asymmetrical pattern. We went with the larger size at the recommendations of "Ed" of Ed's Tire in Medford Oregon. I was quite surprised how much time he spent with me on this. The ride was noticeably smoother and the handling more neutral. The latter change was not expected given that the old tires had a lower profile. So I was pleased with the improved performance. But then I got to thinking whether the bigger diameter tire might hurt acceleration and have an impact on actual mpg. I decided to do some calculations comparing the OEM Dunlop tire to the new Nokian tire.

First I looked up the weight, diameter and revs per mile of the two tires. For the Dunlop we have the weight 16lb, the diameter 24.0 inch and the revs per mile 871. (The diameter is the nominal value and is lower when the vehicle is at speed. ) For the Nokian tire the values are 15lb, 24.4 and 850. So the Nokian is lighter than the Dunlop but slightly larger in diameter. I did a quick calculation of the revs per mile using the nominal diameter of the tires and realized the values did not match those of the manufacturer. I did a search and found out that this is the case and that the nominal diameter is always larger than the diameter associated with the revs per mile. This is due to various factors including the pressure in the tire. The "rolling circumference" is typically 3% lower than that of the nominal circumference. With this info I calculated the rolling diameter of the two tires from the revs per mile of the manufacturers. For the Dunlop the diameter is 23.155" and for the Nokian it is 23.727". Note the the Nokian is in line with the 3% formula.

I decided to do a calculation of the kinetic energy and inertia of the wheel with the two different tires at 60mph. I found a flywheel calculator app on the internet. At 60mph the revs per minute are the same as the revs per mile. This simplified the numbers. I assumed the wheel was 16 pounds and had a diameter of 15". So I calculated the kinetic energy and inertia of the wheel at the two different revs per minute, 971 and 950. I assumed that the mass of the wheel was in a ring. At 871 rpm we get Ke in joules of 1096.161 and an inertia kg.mA^2 of 0.263. At 850 rpm we have 1043.941 and 0.263, the latter being the same value for both. Next I calculated these two values for both tires using their rolling diameters and assuming the mass was in a ring. For the Dunlop we have at 871 rpm Ke 2612.050 with an inertia of .627. For the Nokian the values are 2448.784 and .618. If we add the wheel and tire values together you can see that this only improves the advantage of the Nokian, which ends up with a lower inertia, because of its lighter weight. Also the centrifugal force is lower for the Nokian setup. I guess the higher Ke and centrifugal force would be advantageous for maintaining speed in which case the advantage would go to the smaller heavier tire.
Actually the ring assumption is not realistic as the material for the wheel and tires are spread out nonlinearly in space. In reality the difference in weight and diameter is fairly small and probably would have a minimal effect on acceleration and braking. The edge definitely goes to the Nokian tires for ride comfort and handling.

As I never did this type of analysis before perhaps I made mistakes. I look forward to comments and corrections.

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