Shift Points
There are two ways to consider shift points, and it helps to look at the math behind it.
Without having exact gear ratios on hand, lets work with some easy numbers to make a good example (and because I don't have the numbers in front of me and I am too lazy to go get them):
1st gear 2.92:1
2nd gear 1.90:1
3rd gear 1.33:1
4th gear 1.00:1
5th gear 0.80:1
The ideal shift for acceleration *should be* made such that the engine "lands" at the torque peak. In a 1997 M3, that is at 3800RPM. So, you need to figure the ratios of the gears to one-another. Divide each gear ratio by the gear ratio of the next gear, so you get:
1st:2nd = 1.53
2nd:3rd = 1.42
3rd:4th = 1.33
4th:5th = 1.25
(Remember, these are with my sample numbers!).
Then multiply this set of ratios by the torque-peak RPM to show the shift points for gear to gear. You get:
1st:2nd = 1.53 x 3800RPM = 5814RPM to shift
2nd:3rd = 1.42 x 3800RPM = 5396RPM to shift
3rd:4th = 1.33 x 3800RPM = 5054RPM to shift
4th:5th = 1.25 x 3800RPM = 4750RPM to shift
This is generally the ideal calculation for shift points for acceleration, but it is hampered by the fact that a quick gear change takes about 1/2 second. (BTW: Given the gear-ratios, torque-peak and HP-peak numbers, this info works for any engine. So, if you are looking for a high speed over a short distance, avoiding shifting because of the 1/2 second loss, you should shift at the horsepower peak (240 of 'em @ 6400 RPM), which will bring you back into the power-band for what will still be good acceleration. Ideally, you want to keep the engine between max. torque and max. HP.
While this theory works, it does not work under all situations. If you have a long straight, and could use all five gears (if you shifted at the ideal shift points), but by redlining it (or at least coming close), you could get away with only three or four, the time savings from *not* shifting gears will generally outweigh the advantages of optimum shifts. In other words, the longer the straight, the more useful the optimum points are.
This calculation works for any automobile, including turbo/SC/rotary (etc.) engine cars. Under perfectly ideal conditions (gear changes do not take any time), then the calculated shift-points would be the ideal acceleration. Typically, however, in a shootout to the next stoplight, the shift should occur at max. HP in order to delay the gear change.
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