That isn't how this works and your math wasn't even correct even if you were comparing the correct things. You used diameter when you should have used radius there and yes that would have made your second number even lower. In addition your units of measure for that 1,250 number aren't actually Joules. That is Joules per second. You have to multiply that by 3.2 seconds to get Joules. Next, you need to accountant for all four wheels and tires and the weight difference is 10 lbs not 5 lbs. Finally, you used 5 lbs as the force there. That is the weight difference of the wheel not a force or torque being applied to the wheel. That makes no sense at all to use the weight there. You would need to use the torque being applied to the wheel there. However, none of that matters because your second number doesn't represent anything relevant to what we are talking about.
Didn't even bother to check my math here, just told me I was wrong, eh?
1 HP is 745 J/s because 1 HP is 745W. So 5 HP is 3730 J/s, times 3.2 seconds. That's 12,000J. Exactly what I said, and not off by 3.2.
That's the total energy you gain from 5HP. Which you, in your first post indicated was an amount so small to be ignored.
And no, I did not use radius in calculating the MMOI of a 5lb torus. Nor did I use 5LB as a force.
A 5lb MASS torus with an inner RADIUS of 10" and outer of 13" has a MMOI of 8.472 lb*ft^2.
This is a very conservative estimate, because I am assigning ALL of the mass to the tire which is at the maximum radius.
That torus spinning at 800 RPM is 60MPH. 800 RPM for that MMOI takes 1,250J to achieve.
Sure, you need 4 tires. So that's 5,000J. Now you claim it's 10LBS not 5. Ok, 10,000J.
It literally takes less than 5HP to accelerate 4, 10LB lighter wheels to 60 MPH. Yet you say 5HP is what you gain from a 1% change in diameter (or radius, funny how math works that way), and is irrelevant.
Let's not forget that a 4,200LB car at 60 MPH has about 685,000J of KE, just to show how little a 10KJ change makes. It's literally <0.002%.
And let's just prove to ourselves that this works. 685KJ over 3.2s is 214KJ/s. 214KJ/s is 290HP, delivered continuously over that 3.2 seconds. Sounds basicity exactly right for a M3P which has to limit power at lower speeds and falls off up top.
It appears that you are trying to calculate the energy at at constant speed for the wheel in that second part. I am not sure why you think that is relevant? That isn't going to tell you anything about acceleration. Your analogy just isn't correct at all.
Yes, because the only thing that matters is the energy it took to get to that speed. Outside of wheel spin, gear ratios, etc, all that matters is the rate of energy put into the system and total energy needed. The total energy needed to get 10 lb lighter wheel to 60 MPH is 2,500J. You have 3.2 seconds to do that. That's 781 J/s. That's exactly 1 HP per wheel that 10 lbs per wheel saves you.
I have shown you exactly why rotational mass is so important with both the equations and with actual data from controlled tests. I am not sure what else I can do to convince you that changing to smaller and lighter wheels works.
No, you have completely screwed up the equations, and done uncontrolled tests with different diameter and mass wheels and tires. So you haven't proven that the wheel size matters at all, and you've dismissed diameter completely even though it has a larger impact to the equation by your own admission than the mass change.
If you're gonna refute this run the actual math, with numbers, don't just tell me I did it wrong or that "rotational mass matters more."