Calculating Shift Points March 31, 2016 03:53 1 Comment

A question we get asked nearly every time we dyno a car is  "where should i be shifting at?"   This question is actually quite easy to determine and i will use a couple of our good customers cars as reference points.  Before we start going through the math of calculating the shift point, we will look at the three cars we are going to compare.  

 

First up, is a road race car we built and support.

The car: 

 The car is a 2.3L stroker motor, with a stock evo 9 turbo, and a short ratio 5 speed (JDM 5th gear).   the car also runs 275x35x18 tires.  This car dynoed 397whp.

The dyno sheet:

Next on the list is a local drag race/street car.

this car is sporting the stock 2.0L motor, with a 4.11 final drive and stock 8 gear ratio setup, with a FP red equivalent turbo, making 533 whp.   Hes running a 255x40x17 tire setup.

The dyno sheet:

The last car we will compare is a well known car affectionately known as "Ricebox".

  Ricebox is also a 2.0L motor, with a precision 6466 turbo, shep ultimate ratio transmission also with a 4.11 final drive.   This car makes 722whp at full boost.

The dyno sheet:

 

The first step of determining the shift points is to understand the gear ratios and tire size of each car and how that translates to the actual torque applied to the ground.   i have put the data into a small table below:

 

gear Road Race Car  Red Car Ricebox
1st gear 2.785 2.928 2.785
2nd gear 1.95 1.95 1.95
3rd gear 1.444 1.407 1.407
4th gear 1.096 1.031 1.031
5th gear 0.825 0.72 0.761
final drive 4.53 4.11 4.11
tire diameter (in) 25.6 25 25.5

 

With the ratios in hand, we next want to break down the dyno sheets for each car.  for simplicity sake, we will use 250 rpm increments, and we want to look at the torque value.

rpm Road Race Car  Red Car Ricebox
3500 430 183 96
3750 467 224 96
4000 465 273 99
4250 451 315 134
4500 432 394 172
4750 423 425 211
5000 412 432 271
5250 398 440 331
5500 375 444 417
5750 361 442 463
6000 340 439 508
6250 322 433 526
6500 300 419 531
6750 285 406 532
7000 268 397 524
7250 253 385 512
7500 241 365 497
7750 230 353 488
8000 219 342 474

 

 

There are two things to understand when looking at the dyno results from a chassis dyno.  We are using a Dynojet 424x inertia dyno.  First, the dyno by its nature takes into consideration all driveline losses.  The power is measured by what the tires puts down on the roller.  Second, the dyno does NOT measure what is commonly called "wtq" or "wheel torque".   I honestly don't know where that "measurement" came from as it is not correct.  a better term would be "driveline loss corrected brake torque" where the brake torque is commonly known as the torque at the engine.  And since the dyno reads the horsepower after the driveline losses and calculates the torque from that based on engine speed, the dynos displayed torque is simply what is seen at the engine taking into consideration those driveline losses.  If that doesnt make sense, we can look at the following tables to help make this more clear.

The transmission of the car multiplies the torque the engine generates by reducing the speed.   For example, in first gear the car moves very slowly, but it has a tremendous amount of torque at the tire.  In 5th gear, the car will go really fast, but it has so little torque at the tire it cant even accelerate from a stop.  We can visualize this for each car by plotting the vehicle speed vs the engine speed in each gear, and we create whats commonly known as a speed by gear chart.

Road Race Car:

Red Car:

Ricebox:

 

With the torque chart we can next use the torque multiplier of the transmission to calculate the torque at the tire in each gear.  This is done by taking the torque number at each of our rpm increments and multiply it by the gear ratio and again by the final drive ratio.

Road Race Car:

Red Car:

and the Ricebox:

Our last step is to take the data from the torque vs rpm graph, and the relationship between rpm and speed for each gear to determine the torque vs vehicle speed for each gear:

Road Race Car:

Red Car:

and Ricebox:

 

The results of the torque vs speed graph tell us exactly at what speeds we should be shifting.   Maximum acceleration for the car will always be when the highest torque is applied at the axle.   so we want to follow the highest point in the graph at each speed.

 

Looking Closely at the road race cars chart, when the colored lines intersect is when the driver should shift.  This ensures that he is riding the curve of maximum torque at the axle.  I have indicated those intersect points on this graph:

Its pretty obvious that revving the 2.3 stroker motor out to redline is in fact slower then shifting early.   The data shows he should be shifting from 1st to 2nd at 6750rpm (roughly 40mph), from 2nd to 3rd at 6500rpm (roughly 55mph), from 3rd to 4th at 6250rpm (roughly 75mph), and from 4th to 5th at also 6250rpm (roughly 97mph).  My next study will be to do this same data set instead with a 4.11 final drive to see how it improves the torque across the speed range.  We collect track data at all the local tracks and can analyze what speed ranges each track sees, so we can determine what final drive will be optimal.

 

For the Red Car, the curve looks a little different.   there aren't any intersection points for the graphs, which means it makes sense to always run it out to at least the 8000 rpm our dataset goes to.  I have drawn a red line to show what happens through a 1st-5th gear run:

There are two rather steep drop off points, the first being on the 1-2 shift, and the second on the 2-3 shift.   the torque drops considerably at those points, so it would make sense to rev the engine out a little longer to maintain the gearing torque advantage.   By the time this car gets through 3rd gear at 8000rpm, the torque is nearly identical to the torque in 4th gear @5900rpm,  and likewise when winding out 4th gear to 8000rpm, when you shift the rpm will drop to ~5600rpm. Looking at these plots I would rev out to about 8500 in 1st and 2nd, and shift around 8200 in 3rd and 4th.

 

The last car is Ricebox.   The graph for Ricebox has large drops between every shift.  This means the larger turbo really needs to be revved out to 9000+rpm to maintain a consistent torque output at the axle.  I have drawn a red line on the path of shifting at 8000rpm would land it.   

Its obvious that the big turbo in Ricebox has a significant advantage vs both the road race car and the red car once it gets above 40mph.