Tim,
here is why a shift at 4200 rpm is best.
Take an 84 XF Falcon EFI S-pack. First schedule or table is the EFI 2.77:1 diff, and the later wide ratio single rail BW 3.47, 2:1, 1.43:1, and 1:1 ratio gear box. The second is with an XB GT 351 close ratio single rail BW gear box
That gives us shift points to change at. As SR said, as long as its still pulling towards the peak power level from the torque peak side of the curve, then you'll gain in acceleration. If you have wrung its neck in second, and then fallen right on to the peak power level with an upchange to third, the engine will be over its peak power, and won't give its all. Since torque peek to power peak is often 1.25 to 1.4 different in revs, the gear ratios are set at intervals of 1.4:1 or more.
The torque curve is the only thing used, but I've included Hp here as well. I scaled these off the metric DIN 70020 (net flywheel figures, corrected to 760 mm Hg at 20 degrees) sheet Ford supplies for ADR compliance. Care of Wheels, Page 45, November 1984. All were looking at is the potential accelleration due to the twisting force at the out put shaft of the gear box. Later on, we'll look at Potential Acceleration.
The figures are:-
1984 XF EFI (SCALED, NOT exactly THE SAME AS ADVERTISED)
|0750 rpm|210 lb-ft|030 bhp|
|1000 rpm|215 lb-ft|041 bhp|
|1250 rpm|224 lb-ft|053 bhp|
|1500 rpm|228 lb-ft|065 bhp|
|1750 rpm|234 lb-ft|078 bhp|
|2000 rpm|239 lb-ft|091 bhp|
|2250 rpm|244 lb-ft|105 bhp|
|2500 rpm|245 lb-ft|117 bhp|
|2750 rpm|245 lb-ft|128 bhp|
|3000 rpm|
246 lb-ft|140 bhp|
|3250 rpm|244 lb-ft|151 bhp|
|3500 rpm|242 lb-ft|161 bhp|
|3750 rpm|229 lb-ft|
163 bhp|
|4000 rpm|199 lb-ft|152 bhp|
|4250 rpm|186 lb-ft|150 bhp|
|4500 rpm|169 lb-ft|145 bhp|
TABLE ONE:
Example. There are seven columns. First is engine rpm before gear change, second is engine torque before gear change, third is shaft torque before gear change, fourth is new engine rpm after gear change up to new gear, fifth is the torque at that new rpm, sixth is the shaft torque in this new gear, seventh is the amount of torque lost or gained. The idea is to minimise the loss or gain. Ideal change up rpm is the one that yields a nice fat zero! The best selection is marked with a red S for shift, and the rpm before shifting is made red too. Rocket scientists can interpolate upshift rpm to the nearest rpm.
Shift from 3.47:1 Ist gear, into 2.00:1 second gear. Loss of 3.47/2.00= 1.735:1. Lower gear ratio multiplies torque.
|Revs/min|Torque_|Shaft T_|RPM fall_-|Torque_|Shaft T_|Loss/Gain|
|3750 rpm|229 lb-ft|795 lb-ft|2161 rpm|244 lb-ft|488 lb-ft|-307 lb-ft|
|4000 rpm|199 lb-ft|691 lb-ft|2305 rpm|244 lb-ft|488 lb-ft|-203 lb-ft|
|
4250 rpm|186 lb-ft|642 lb-ft|2450 rpm|245 lb-ft|488 lb-ft|
-154 lb-ft|S
|4500 rpm|169 lb-ft|765 lb-ft|2594 rpm|245 lb-ft|488 lb-ft|-277 lb-ft|
Shift from 2.00:1 2nd gear, into 1.43:1 third gear. Loss of 2.00/1.43= 1.399:1. Lower gear ratio multiplies torque.
|Revs/min|Torque_|Shaft T_|RPM fall_-|Torque_|Shaft T_|Loss/Gain|
|3750 rpm|229 lb-ft|458 lb-ft|2681 rpm|245 lb-ft|350 lb-ft|-100 lb-ft|
|4000 rpm|199 lb-ft|398 lb-ft|2860 rpm|245 lb-ft|350 lb-ft|-48 lb-ft_|
|4250 rpm|186 lb-ft|370 lb-ft|3039 rpm|246 lb-ft|352 lb-ft|-18 lb-ft_|
|
4500 rpm|169 lb-ft|340 lb-ft|3218 rpm|244 lb-ft|349 lb-ft
|+9 lb-ft_-|S
Shift from 1.43:1 3rd gear, into 1.00:1 top gear. Loss of 1.43/1.00= 1.430:1. Lower gear ratio multiplies torque.
|Revs/min|Torque_|Shaft T_|RPM fall_-|Torque_|Shaft T_|Loss/Gain|
|3750 rpm|229 lb-ft|327 lb-ft|2622 rpm|245 lb-ft|245 lb-ft|-82 lb-ft|
|4000 rpm|199 lb-ft|285 lb-ft|2797 rpm|245 lb-ft|245 lb-ft|-40 lb-ft|
|4250 rpm|186 lb-ft|265 lb-ft|2972 rpm|246 lb-ft|246 lb-ft|-19 lb-ft|
|
4500 rpm|169 lb-ft|243 lb-ft|3147 rpm|244 lb-ft|244 lb-ft
|+1 lb-ft|S
Summary: The change up positions ranges from 4250 rpm in 1- 2nd second to 4500 rpm in 2-3 rd, and 3 rd to 4th. The maximum power comes in at 3750 rpm, so the change-up is
20 % beyond the peak power rpm.
TABLE TWO:
As above, but with a close ratio 4-speed gearbox. The aim is to see what it does to the change-up rpm. Ratios 2.42:1, 1.78:1, 1.26:1, 1:1 top
Shift from 2.42:1 Ist gear, into 1.78:1 second gear. Loss of 2.42/1.78= 1.360:1. Lower gear ratio multiplies torque.
|Revs/min|Torque_|Shaft T_|RPM fall_-|Torque_|Shaft T_|Loss/Gain|
|3750 rpm|229 lb-ft|554 lb-ft|2758 rpm|245 lb-ft|436 lb-ft|-118 lb-ft|
|4000 rpm|199 lb-ft|482 lb-ft|2942 rpm|245 lb-ft|436 lb-ft|-46 lb-ft|
|
4250 rpm|186 lb-ft|448 lb-ft|3126 rpm|245 lb-ft|436 lb-ft
|-12 lb-ft|S
|4500 rpm|169 lb-ft|411 lb-ft|3310 rpm|244 lb-ft|484 lb-ft|-23 lb-ft|
Shift from 1.78:1 2nd gear, into 1.26:1 third gear. Loss of 1.78/1.26= 1.413:1. Lower gear ratio multiplies torque.
|Revs/min|Torque_|Shaft T_|RPM fall_-|Torque_|Shaft T_|Loss/Gain|
|3750 rpm|229 lb-ft|408 lb-ft|2654 rpm|245 lb-ft|309 lb-ft|-99 lb-ft|
|4000 rpm|199 lb-ft|354 lb-ft|2831 rpm|245 lb-ft|309 lb-ft|-45 lb-ft_|
|4250 rpm|186 lb-ft|329 lb-ft|3008 rpm|246 lb-ft|310 lb-ft|-19 lb-ft_|
|
4500 rpm|169 lb-ft|303 lb-ft|3185 rpm|244 lb-ft|307 lb-ft
|+4 lb-ft_-|S
Shift from 1.26:1 3rd gear, into 1.00:1 top gear. Loss of 1.26/1.00= 1.26:1. Lower gear ratio multiplies torque.
|Revs/min|Torque_|Shaft T_|RPM fall_-|Torque_|Shaft T_|Loss/Gain|
|3750 rpm|229 lb-ft|388 lb-ft|2976 rpm|245 lb-ft|245 lb-ft|-43 lb-ft|
|
4000 rpm|199 lb-ft|251 lb-ft|3175 rpm|244 lb-ft|244 lb-ft
|-7 lb-ft|S
|4250 rpm|186 lb-ft|233 lb-ft|3373 rpm|244 lb-ft|244 lb-ft|-11 lb-ft|
|4500 rpm|169 lb-ft|214 lb-ft|3571 rpm|235 lb-ft|235 lb-ft|+21 lb-ft|
Summary: The change up positions ranges from 4375 rpm in 1- 2nd second to 4500 rpm in 2-3 rd, and 3 rd to 4th. The maximum power comes in at 4125 rpm, so the change-up is
10-17 % beyond the peak power rpm.