:o Please move on if you aren’t interested in keyboard racing, this thread will serve as an attempt to answer the question: “How much does short shifting really hurt 1/4 mile performance on a B8.5 S4”
The main motivation for this came from dparms thread on thrust curves for the facelift vs pre-facelift DSG cars here http://www.audizine.com/forum/showthread.php/510547-2013-DSG-has-different-gear-ratios-than-2012-DSG?p=8120455&viewfull=1#post8120455. He was nice enough to supply me with source data from some dyno pulls he had. I believe it was stasis stg 1 flash.
The key to this argument is to understand the RELATIVE changes in performance, not to match/predict real-world performance.
Assumptions (there are going to be a shit load of them)
- Constant rolling friction with coefficient of friction 0.017;
- Approximate air drag, parameters are taken from here: http://www.carfolio.com/specifications/models/car/?car=268598
- Dyno figures will be supplied with each simulation and assumed to be torque at the wheels;
- Transmission is forced to keep min 4000 RPM (configurable actually), prevents motor from “bogging” down at launch;
- The launch is shitty, there is no tire model here, so this aspect is easily the weakness.
- Car weighs 4150 lbs with driver (rest of physical parameters can be seen in simulation code).
Methodology
Using newtons laws to compute total longitudinal forces, and simulate until reaching 1/4 mile distance. Compute the gear shifts based on ratios provided by dparm, have the option for including the short shifting. Here is a basic list of the functions
gear = checkShiftMap(currentGear, RPM);
powertrainTorque = engineTorque(RPM) * TransRatio(gear) * FD_ratio;
totalForce = powertrainTorque * tireRadius - rollingFriction - airDrag;
Keep in mind that the accuracy of this is also a function of the dyno I have, which after plotting some HP figures, seems a little strange on the top end. Would be nice to get better data if anyone has it.
Here’s what I get if I assume a dyno of this
https://farm4.staticflickr.com/3894/15160385015_5644421057_b.jpg
Short Shifting DSG = 11.86@116.37 with 60 ft 1.84 sec
https://farm4.staticflickr.com/3900/15159997792_1f7f2b4326_b.jpg
Shifting at 7200 RPM = 11.58@118.66 with 60 ft 1.83 sec
https://farm4.staticflickr.com/3867/14973808187_ea5811f424_b.jpg
This gives an idea of the thrust curve at the wheels (where the dotted green includes drag and rolling friction)
https://farm4.staticflickr.com/3923/15157406841_992a3f98b3_o.jpg
So according to this math, the DSG short shifting is costing a stg 2 car (most likely running a race tune) .3 seconds in the 1/4 mile and 2.4 MPH in trap speed. Seems reasonable to me. Might be better if we have better dyno source data, I asked Arin but he didn’t reply to my PM.
TL:DR There is no shortened version, this is AR ;D
I will include the code below so anyone else can run it in MATLAB, there are absolutely bugs to be found. I place the functions in separate files, you’ll need the signal processing toolbox to call the statistical spline function csaps.
Edit - adding this
But here is easily the most important comparison of the powertrain force at the road, the blue signal is the normal shifting, while the red is from the short shifting trans. The short shifting means that you are sooner in a higher gear, and thus even though the torque at the flywheel might be greater, the taller gear means you have less force at the road. Taking the integral of the difference in these two traces should correspond to the difference in speed, modulo the difference in drag force.
https://farm4.staticflickr.com/3881/15138048616_f92c32676b_b.jpg