Optimal Shift Point

Skip the BS and go to the calculator.
Calculates the optimal upshift rpm and road speed for each gear of your car to acheive maximum acceleration. (except for the highest, of course!) You provide torque vs. flywheel rpm data, transmission and differential (final) gear ratio data, and drive wheel diameter for your car. Once you have input the data and click on the Calculate button, the optimal upshift rpm for each gear at what road speed is displayed.

Optimal shift point is defined as the flywheel rpm for which the difference in transmission output torques between two gears is near zero for the same output shaft speed (and same road speed). If the difference never approaches 0, the optimal shift point is at redline.

Simplified Example: Which is a better shift point from 2nd to 3rd gear, 4000 rpm or 5000 rpm?
Data: Torque --- 296 ----- 310 ---- 290 ----- 280
- rpm x1000 ---- 2.6 ----- 3.3 ---- 4.0 ----- 5.0

Gear -- 1 --- 2 --- 3 --- 4 --- 5 --- 6
Ratio - 4 -- 2.3 - 1.5 - 1.2 - 1.0 - 0.85

Calculation:
2nd gear Output Shaft Torque @ 4000 flywheel rpm = 290*2.3=667  Output Shaft Speed = 4000/2.3=1739
3rd gear flywheel rpm @ 1739 output shaft speed = 1739*1.5=2600 Output shaft torque = 296*1.5=444
Torque drop=667-444=223 @ 4000 rpm

2nd gear Output Shaft Torque @ 5000 flywheel rpm = 280*2.3=644  Output Shaft Speed = 5000/2.3=2174
3rd gear flywheel rpm @ 2174 output shaft speed = 2174*1.5=3300 Output shaft torque = 310*1.5=465
Torque drop=644-465=179 @ 5000 rpm

Since the drop in torque is less at 5000 rpm, this is a better shift point than 4000 rpm

This utility does this calculation for every 50 rpm step within the range of data you provide, using straight line interpolation between data points. It returns the rpm in each gear which yields a torque drop to the next gear as close to zero as possible. In a output torque vs road speed graph, this would be where the torque curve lines for two adjacent gears intersect. In a car with a flat-ish torque curve and optimal street gearing, the gear-torque curves do not intersect. This means the optimal shift points will be redline in each gear.

This calculator is a bit simplistic, it assumes a fairly regular torque curve (not necessarily flat) with only modest bumps and drops along it, in which a gear-torque curve will only intersect it's neighbor once, if at all. For complex torque curves with major peaks and valleys, where the gear-torque curve may intersect it's neighbor more than once, a more rigorous analysis is required. This is best done by entering the above data in a spreadsheet, along with final drive (differential) ratio and diameter at tire tread (not wheel diameter).

The final drive and tire info isn't strictly required, but plotting the graph using actual road speed instead of output shaft speed yields a more meaningful chart. Your spreadsheet should calculate the actual torque to the wheels (engine torque * gear ratio * final drive ratio) and the car's road speed in each gear for the full range of engine rpms. Plot the results as a torque@wheel vs. road speed chart, a separate torque line for each gear. By examining how each gear curve intersects it's neighbor, you can reasonably determine the best shift point by locating which gear yields the highest torque at any given speed.

RPMs entered below must be listed in order lowest to highest, any values beyond the highest that remain set to 0 will be ignored. Any torque units can be used as long as all values use the same unit of measure. You only have 10 points available to define the torque curve. Enter points that would best define the curve using stright line segments. List any rpms you do not need or gear ratios you do not have at the end as 0. The sample data shown is for a 2011 BMW 1M Coupé from an independent dyno test. Note the max. torque is well above the value of 332 quoted by BMW. One's inclination would be that the optimal shift point is 5300 rpm where the torque starts falling off significantly. This is not the case, the optimal upshift is around 6900 from gears 1 and 2 and around 6000 for the other gears. Even though the torque is falling off, you are still getting more torque in the lower gear, giving more acceleration. This is an example why this calculator is useful.

Torque & HP Curves

   Data

Torque
rpm(x1000)

Gears 1 2 3 4 5 6 Final Tire Dia (in)
Ratio

Results

Shift @
rpm(x1000)
XX

Speed
(mph)
XX




How is this the correct method? For any point in time, the highest acceleration is acheived with the highest torque at the wheels. Gears multiply torque, so generally, the lowest gear provides the highest acceleration. The problem is, you can't go very fast in 1st gear, so you need to upshift to go faster, even though it means lower torque output. As long as the output torque in 1st gear is higher than output torque in 2nd for a given road speed, you should stay in 1st. Of course, you will soon run out of rpms and be forced to upshift.

The same holds true for 2nd. As long as the output torque in 2nd is greater than what you would get from 3rd for any given road speed, you should continue to accelerate in 2nd. Depending on your car's torque curve and gearing, there may be a point where, for a given road speed, you can get the same torque in 3rd as you are getting in 2nd. This is where you would want to shift, as the torque curve is falling, and because of the multplying effect of gears, the output torque in second is falling faster than it would be in 3rd. In this case, more torque is acheived in 3rd gear, so you should use it.

But once again, if 3rd gear torque never approaches what you are getting in 2nd, you will eventually hit redline and be forced to upshift. So in this case, redline would be the optimmal shift point because you can get more torque at any speed in 2nd than you would in 3rd. And so on through all the gears...



Copyright © 2012 Glenn Messersmith
Creative Commons License This calculator is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License. Full code is available in this page's source code. View with Shift-F12 in IE, or Ctrl-U in most other browsers. Option+Apple+U for Mac Safari.