Ok, with all this talk about gearing and drag racing...It's now time to turn our attention to OPTIMAL SHIFT POINTS!
The idea here is to "maximize area" under the hp curve...(an integral for calculus types!)
Ideally, this means hp before and after the shift is EQUAL!
This is not always practical because:
the spacing between gears may be too large AND the rev limiter does not allow the engine to reach the optimal shift point!
Based on our earlier discussion we realized that maximizing acceleration meant MAXIMIZING HORSEPOWER sent to the wheels...
So what this mean? Let's look at the horsepower chart again....(540i non Vanos and M5)
HP peaks at 6600 rpm for the M5 and is basically flat until the rev limiter kicks in at 7000 rpm.
Ideally, if we had custom super close ratio gearing we would shift at 7000 rpm and the rpm in the next gear would be 6600 rpm.
This way we would maximize the available horsepower.
I've done a spreadsheet on the M5s speed vs. rpm for each gear...
From what I can tell...the optimal shift points for each gear is 7000 rpm for stock s/w.
With Dinan S/w letting it out to 7300 rpm is a good idea except for the 5-6 shift.
Since, the motor cuts out at the rev limiter you really don't want to hit it because you interrupt the power...
Let's test this out...
Consider the 1-2 shift. 1st gear is a low 4.23 gear and 2nd is 2.53.
If we shift at 7000 rpm = 40 mph, the new rpm after the shift is 4200 rpm.
This means hp at the wheels goes from about 330hp to 255hp before and after the shift, respectively!
Since hp drop before and after shift is so big it means that the gear spacing is too wide to be optimal OR the rev limiter kicks in too early!
Let's consider "short shifting" ie. shifting early. Now let's shift at 5000 rpm. HP at 5000 rpm is 300 at the wheels = 29mph. After the shift we'd be at 3000rpm or only 170 hp at the wheels.
By short shifting...We never use all the horsepower available in 1st gear AND HP after we shift is also lower!
In a HONDA S-2000 with a 8900 rpm redline and peak hp at 8200 rpm...Short shifting at 5000 rpm results in a 0-60 time of 11 seconds up from about 5.5 doing it right!
Let's look at Ben Treynor's dyno chart with Dinan s/w at: http://www.treynor.com/M5_Mods.htm
Looks like Ben's Car makes about 325hp AT 7300 rpm.
If we shift at 7300 rpm from 1-2 we're at 42mph and 325hp.
After the shift we're doing 42mph at 4200 rpm or about 265 hp.
Note that this is slightly better than shifting at 7000rpm!
Below: I detail optimal shift points for 7000 rpm cutoff and 7300 rpm cutoff.
Assumptions: Gears 1-6: 4.23, 2.53, 1.67, 1.23, 1.00, 0.83, 3.15 Rear End.
7000 rpm Shift Point (40mph) HP Before: 330
HP After 255 at 4200 rpm.
7300 rpm shift point (42mph) HP Before: 325
HP After: 265 at 4400 rpm.
7300 rpm shift pt is better as we pick up 10 hp after the shift!
7000 rpm Shift Point (67mph) HP Before: 330
HP After: 275 at 4600 rpm.
7300 rpm shift point (70 mph) HP Before: 325
HP After: 290 at 4800 rpm.
7000 rpm: 101 mph, HP Before 330, HP After 305 at 5100 rpm.
7300 rpm: 106 mph, hp before 325, HP after 315 at 5400 rpm.
NOTE: How the hp drop after shifting is narrowing AS Gear SPACING GETS CLOSER!!
7000 rpm: 137 mph, hp before 330hp, HP After:
317 hp at 5700 rpm.
7300 rpm: 143 mph, hp before 325, HP after: 320 hp at 5900 rpm.
5-6 shift: (I assume engine has hp to achieve these speeds, Big IF!)
7000 rpm: 169mph, hp before 330 hp, HP After: 328 at 5800 rpm.
7300 rpm: 176mph, hp before 325hp, HP after 330 at 6050 rpm.
For the 5-6 shift 7300 is NOT more optimal because hp is greater after shift than before.
The 5-6 gear spread is the narrowest in the gear set...And basically would allow us to keep the engine in the flattest portion of the hp curve!!! Too bad wee need to be going SUPER GONZO SPEEDS to test this!!!