Hopefully you don't take me the wrong way. I'm not picking on you, but I disagree that the advantage is meaningful.
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Originally Posted by Jawnathin
There is no rounding errors for engine speed, mechanically the engine will be turning over at a higher RPM. That 50RPM at 3800rpm is almost 100rpm at 7000rpm. The car with the shorter tire will have a higher average RPM. The car makes more power at higher RPM resulting in higher average horsepower on course.
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Can you quantify this? Show me a dyno plot where there is a meaningful difference at any 100 RPM gap above our 3800 RPM baseline. That's pretty generous given that it's only a 100 RPM gap from 7000-7500 RPM. You should be able to, say, use an integral (or hell, even a Riemann sum) to get the area under the curve from 30-55 MPH for both a 24.4" tire and a 24.7" tire. Then make a statement along the lines of "Tire A delivers X% more horsepower from 30-55 MPH than Tire B." We can then perform a similar thought experiment assuming we installed a new air filter that provides a 2HP improvement across the entire dyno plot and see what percentage improvement that is. That will tell you something very good about the magnitude of your result.
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Originally Posted by Jawnathin
You haven't added the more advantageous torque multiplier the shorter tire gives you. Yes, that is small too, but compounded with the higher RPM/power output, the car will apply more power to the ground compared to a taller geared car. Even a little more power is still more power.
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Can you quantify how much extra torque multiplier you get? A number talks. Math talks.
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Originally Posted by Jawnathin
In an autocross you're on the throttle like 80+% of the time. Given the choice between a car that accelerates slower or faster, what would you take?
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We can go look at someone's datalog to get a real number instead of 80%. But whatever that means, it's now a multiplier against whatever result you got from your Riemann sums - i.e. you only get that advantage 80% (or whatever that multiplier is) of the time, which reduces its impact.
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Originally Posted by Jawnathin
Thousandths add up to hundredths. Hundredths add up to tenths. This can be the difference between a win and a loss. No one who takes autocrossing seriously would turn down an opportunity to off some time.
I'm not saying 235/40 is better than 245/40, they both have their pros and cons, but to say that an acceleration advantage doesn't matter or is of no benefit is nonsensical.
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No disagreement here on thousandths being important. I missed contingency last year by .069 one event. I missed a trophy by .006 another event. What I disagree on is that 0.3" of tire diameter is a more significant effect than extra grip from a wider tire. I can carry more speed through a turn (which I then carry down the straight), I can power out of the turn sooner, and I can brake later.
Even just carrying 1MPH more through a turn would put my 245/40 tire higher up on the revs than a 235/40. Ok, the torque multiplication is different - is it enough to make up the 1MPH gap I will carry for the whole straight plus the fact that my motor is pushing more HP at corner exit? You can calculate this all out. I'll eat my words if the math says I'm wrong.