Quote:
Originally Posted by Mangler
Tech engineer here so physics are not the strong suit.
Don't you want to change gears so that the gear you go into can accelerate faster than the gear you shifted from? For instance shift so that the rpms fall to max torque of the next gear? I guess this means are you shifting manual or dct? Will change this due to lag of gear engagement.
T

Give the entire thread a reread and look at the graphs, "Drive Power in Gears" and Torque Curve in my OP. I'll discuss with a bit more detail below.
With any normal gear box you always accelerate significantly worse with each successive shift (see Time to Acceleration graph or perhaps better titles Acceleration vs. Time...). There is simply no way around that. But as is obvious, you can't stay in any gear indefinitely. When concerned with maximum performance, the ideal shift point is one simply that maximizes the acceleration across the gear change (at each point in time individually). Shift too early and you lose out on more time at a much higher acceleration in your current gear. Shift too late and the next gear chosen earlier would have provided more thrust. Again the simplest way to explain how to calculate this is to shift either at redline or at the rpm/speed at which curves of vehicle thrust vs. speed, gear by gear, intersect. If they do not intersect the shift will be at redline. Some cars like the E92 M3 should be shifted at redline in all gears. Some vehicles should always be shifted before redline and others are a mix. The key components to the calculation and that affect ideal shift points are the drive force vs. speed curves. You get the drive force from the crank torque (rated engine torque vs. rpm  converted to vs. speed) minus parasitic and gearbox inertial "losses" as well as the gear ratios, final drive ratio and drive wheel radius. However, generally speaking, the shape of these drive force curves will mirror the engines crank torque curve. Drastically falling torque curves at higher rpm generally will lead to ideal shifts before redline since the curves will be more likely to cross.
There will some corrections to this "algorithm" based on shift times. Strictly speaking this algorithm assumes "DCT like" instantaneous shifts. Actual rpms/speeds for ideal shifts would become slightly higher when accounting for speed losses due to drag loss when no power is being applied when the clutch is disengaged during a shift.
This is really more engineering than physics, perhaps one would say applied physics...