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During the lifecycle of tires, when do they have the best performance :

  • When they are new
  • Few weeks afer buying
  • Mid-life
  • Near the end-life

Performance I mean fuel economy.

  • when they are close to the end of their life, they will have the smallest diameter... so mpg will be worse... – Solar Mike Jul 8 '19 at 8:31
  • @SolarMike thank you good tip. That is also why high pressure on tires is more eco ? – DesignerAnalyst Jul 8 '19 at 8:57
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    @SolarMike Can you guarantee that the mpg will be worse just because the diameter is smaller? The engine will have a higher RPM for the same road speed, but there will also be less load on the engine. Surely it depends on the design of the engine and the speed being driven. – HandyHowie Jul 8 '19 at 9:16
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    No, pressure increasing fuel economy doesn't mean the tire diameter becomes larger. It just means tire deformation when driving is less, so rotational resistance will be smaller as well. – juhist Jul 8 '19 at 10:22
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    Realistically, any difference in fuel economy due to tyre wear is going to be so tiny as to be lost in the noise - driving style, traffic conditions etc make far more difference – Nick C Jul 8 '19 at 14:36
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The answer is, fuel economy is best:

  • Near the end-life

...which is opposite to what Solar Mike claimed in the comment.

The reason for this is that near the end-life, tire has the least amount of rubber deforming when being driven. Thus, there is less rubber to cause rotational resistance.

However, the effect is small and likely outshadowed by tire pressure. So, if you never fill your tires with air, their performance can due to a small air leak actually decrease over time. What I claimed (better fuel economy when old) applies only if you keep constant pressure in the tires.

The effect noted by Solar Mike, speed and thus fuel economy decreasing with decreasing diameter, is there but I assume it is significantly smaller than the effect of less rubber causing less rotational resistance. Not only that, but also a modern CVT just adjusts the gear ratio accordingly, whereas a modern electric car works equally well at all motor speeds.

Note, however, that rolling resistance is only 15%-25% of total resistive forces in a car. So, if you improve it by let's say 10% by using worn tires (as Solar Mike noted, sidewall deformation is significant and sidewall doesn't wear), you get only about 2% improvement in fuel economy with worn tires.

Sources:

  • https://swsu.ru/sbornik-statey/pdf/sr286.pdf says "Reductions in tread thickness, volume, and mass are among the means available to reduce rolling resistance, but they may be undesirable if they lead to shorter tire lives and larger numbers of scrap tires"
  • https://www.tirerack.com/tires/tiretech/techpage.jsp?techid=29 says "During stop-and-go city driving, it's estimated that overcoming inertia is responsible for about 35% of the vehicle's resistance. Driveline friction is about 45%, air drag is about 5% and tire rolling resistance is about 15%. -- Overcoming inertia no longer plays an appreciable role in the vehicle's resistance during steady speed highway driving. For those conditions it is estimated that driveline friction is about 15%; air drag is about 60% and tire rolling resistance represent about 25%."
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  • not all cars are cvt... The sidewall is what deforms while it is the tread pattern that gets worn through use. Any real figures for your answer (which is partly why I only made a comment...) Also, if "old" tires are so good, why aren't they used for racing? – Solar Mike Jul 8 '19 at 11:27
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    @SolarMike I guess traction is the consideration for racing. – juhist Jul 8 '19 at 11:36

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