Quote:
Originally Posted by swamp2
Torque, power, redline shift points, etc. A reply to many who asked various questions.
I think the easiest way to think about shift points and whether they are at redline or not is the shape of the torque curve. If it is more flat and flatter closer to redline the car will be a redline shifter. Another way to say this is that engine has a linear power curve (and the E92 M3 is epically linear in this particular regard). For power and torque curves typical of a turbo BMW or say many Corvettes with a flat or knee shaped and declining power at high rpm, these cars will need to be shifted before redline for maximum performance.
The simplest way to determine exact shift points is as follows. Plot on a single graph force at the drive wheels vs. vehicle speed (torque would do as well, but we clearly are not/can not use crank torque nor a plot vs. rpm) for all of the gears. If any two of these curves intersect that means one has better acceleration (simply more force can be applied) by shifting to the next gear rather than holding higher or to redline. In particular note the green to blue change, i.e. 2nd to 3rd shift in the first plot for the M4.
When you look at these curves and play with the gear ratios making sure you not done something absurd like a 30 mph top speed in 1st gear at redline, that you have closely spaced gears and that top speed issues are sorted out, the falling torque curve simply haunts you not allowing all of the curves to fit together without the intersections. When the cars has a linear power curves it becomes trivial to have non-intersecting curves. Make sense? Make some of your own spreadsheets will really help if you care about the details...
See the attached plots for more, the first with my assumed gears for the F82 M4 (but actual torque and power curves) and the second for the E92 M3 M-DCT. Sure my gears for the M4 are bound to be off a bit, heck even the final drive I predicted may be off, but that does not change the essence of the cars power delivery - the entire shape of its torque curve. The 1M and the new M5 both should be shifted prior to redline in many of its gears to obtain maximum possible acceleration, period. Similarly I can guarantee the new M4 will be the same given a 7500+ rpm redline.
Sorry for the very bold traces in the plots, I suspect a java bug has made many graphs from my CarTest software nearly invisible without the very bold traces. You'll still clearly get the idea.
It is worth noting that these curves also tell one a lot about the feel and experience of the car. They show how the M4 will really hit a quick and dramatic wall in the upper rpms whereas the M4 tapers off much less dramatically. This gives the very "linear" feel to the M3 along the lines of its linear power curve. Not so much for the M4.
Lastly when a cars torque falls dramatically at high rpm it is essentially turning into a poor air pump and hence a poor "breather". This is the nature of the beast with most production turbo systems compared to a high performance NA engine which is designed to be as free flowing as possible from intake to exhaust at very high flow rates (rpm).
|
A decent analysis, aside from one big issue. Torque does not perform work, it doesn't propel the car forward. This torque roll off you are speaking of might be inconsequential only because the fall off seems slower than the corresponding increase in engine speed. The slope of the torque curve is greater than -1, up to a point. The result is that the power either continues to climb or remains flat, until the curve inflects and it no longer does.
You should be concerning yourself with the shape of the power curve, only. Your own analysis demonstrates this because you've plotted tractive effort versus wheel speed. With some units manipulation (change the abscissa units from km/h to m/s and the ordinate values to newtons without the multiplier), that becomes power, not torque.
The intersection of those curves you plotted occurs at the point where the power (not torque) available with engine speed increases is less than that available with an upshift. Since induction performance is not gear dependent, this point occurs at the same engine speed, no matter how fast or slow you are going. And it isnt necessarily at the point when power begins to drop off, either. It all depends on how wide or narrow the next gear is. To use hyperbole to demonstrate; If second gear drops engine speeds to 1500 RPM after a sprint to 65mph and 6800rpms, it's always better to keep going to ~7750rpms than upshift. But, of course, you know that since thats what the intersections demonstrates.
Now, if I am to be specific and talk about the S55, I'll have to wait and see when that horsepower curve inflects, and what the actual ratios look like. However, I'm confident that BMW is far more aware of the math behind picking shift points than you and I. As such, the car will favor higher shift points than is currently believed. After all, short shifting is not in keeping with the ///M aesthetic. That's reserved for the N series drivers.