[CanAutM3]

Originally Posted by swamp2

CanAutM3: One major problem with your attachment with the math is the following: We are discussing two hypothetical vehicles identical except for Iw thus minimally you need Iw1 and Iw2 and they are not equal.

Please have another look at the math, I still believe it is sound. The math is to find the optimal shift point for a given hypothetical vehicle; solving for the intersection point between two "tractive force" equations. It is not to compare two different vehicle conditions. Since the wheels are not changed during a gear change, Iw in a given gear equals Iw in the next gear, hence Iw1=Iw2.

As I stated in my post, acceleration is still part of the equation though; and acceleration varies with Iw. So I concede that shift points will vary with wheel inertia. But it also implies shift points would vary depending on mass, incline, towing, etc... Which is becoming much more complex than I anticipated.

Next step for me is to introduce the equation of acceleration in the formula and see where I can reduce it to... just need to find some free time to doodle more with the math

Originally Posted by swamp2

Also in regards to your statement,

"While I underestimated the impact of drivetrain inertia on optimal shift points, I still think that Cartest overestimates the impact by using the mass factor rather than the actual inertia."

CarTest, according to direct correspondence with the author, does not use mass factors. The software makes the assumption that all cars have the same I's for various drivetrain components and explicitly calculates the inertial terms.

Thanks for this clarification. I should not speculate on CarTest without seeing the code. From here though, it should be an easy step for the author of CarTest to add the various moments of inertia as input parameters. This could make the software even more powerful.

Any clue if CarTest uses fixed values of I or values of I that are proportional to the weight of the car?

Originally Posted by swamp2

Although this assumption clearly is not strictly correct, it certainly appears to be a suitable approximation so as not to cause significant errors in its predictive capability. However, in the other extreme, the error of entirely leaving out the inertial terms, is very significant. Again for a car like the M3, easily equal to 20% of a cars weight in 1st gear.

While I agree that the impact is significant in the lower gears, it is much less so in the higher gears. I figure about a 4% difference in torque for the 3-4 shift and less than 1% for the 6 to 7 shift.

Most (not to say all) of the shift point calculations I have made in the past always yielded very obvious red line shifts in the lower gear. Since the error is much smaller in the higher gears, despite my calculations being off, they were close enough not to see a difference in real life. This is most likely why I never realized my error of ignoring engine inertia.

I am still confused as to why CarTest comes up with very similar shift points (7200RPM) in all gears in the simulation in post #195. If the impact of engine inertia gets lower in the higher gears, shouldn't the shift points be progressively closer to red line with higher gears (equal ratio between ratios here)?

If I can understand it properly, I could recalculate gear ratios that would yield redline shifts while optimizing the power plateau. Which is where this whole discussion started .