# Transient Response 2

In the earlier post I wrote that “in the Street classes a car’s peak lateral-G capability is of zero importance in determining speed through a slalom.” What?

The analysis was done a while back (see J-Rho covering it in part 5 of his series Comparative Vehicle Dynamics) that all the techno-nerdy autocrossers (like me) know about where someone (I won’t mention his name) derived the time around cones in a slalom using basic physics. In his derivation it came down to how much the car must move left and right and the peak grip (lateral-G capability) of the car. Using his formula you can calculate the time lost by leaving more space around the cones, for instance, and you can compare one car to another based on width and peak lateral acceleration capability.

The only problem is that it doesn’t work.

Am I saying that the math (for sinusoidal curves) was wrong? No. What I am saying is that it is a useless, misleading, nonsensical simplification that totally missed and therefore obscured what really matters since it was done over 15 years ago. Let me prove it. With data.

Soon after acquiring a GPS data device I noticed something weird. I will illustrate it with values from recent runs, but it was clear from the very first run I ever took with data.

In my last autocross in the Corvette the course contained both slaloms and sweepers, as usual. In five different sweepers the data shows the car pulling sustained lateral acceleration values of 1.250, 1.083. 1.084, 1.125 and 1.260 Gs. In various slalom sections the car pulled peak levels of 0.676, 0.774 and 0.552 Gs.

In my most recent autocross I co-drove a 2008 Cayman and in various sweepers achieved 1.299, 1.080 and 1.276 Gs. In the slaloms the car pulled 0.720, 0.435, 0.469 and 0.627 Gs.

[Update: I’ve come to realize that my data device was missing the momentary peaks of lateral G. Those peaks were still less than the steady-state capability however. As we will learn later, it takes Street Touring preparation level for most cars to even momentarily achieve peak steady-state lateral-G in a slalom, so the point stands.]

See the pattern?

For a long time I thought I was just pitiful at driving slaloms. It made me work really hard to improve. I got faster! The pattern didn’t change, however. I’m so stupid!

If a car can’t achieve it’s peak lateral acceleration capability within a slalom then peak lateral acceleration capability is not important and is no predictor of slalom speed. Any mathematical formula that claims to be able to predict the time from cone to cone in a slalom that uses peak lateral acceleration capability is just. plain. wrong.

We need to start over and rethink it. I’ll do that in the next installment.

## 4 thoughts on “Transient Response 2”

1. Are you logging steering angle vs g’s? I suspect that the large difference between slalom and steady state g’s has to do with a combination of car width, length, slalom length, and suspension compliance. In a kart I’d say you probably always hit steady state g’s. This is a case where all of these variables are taken to an extreme, but it does show that a blanket statement is probably not completely accurate. Based upon the experience with my Miata (which has a steering angle sensor) certain slaloms definitely approximate steady state for brief moments. When driving larger cars the slalom is just too tight to reach this state. Additionally, making a car wider increases it’s lateral grip (all other things being equal) which would widen this gap.

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• Chuck: Thanks for the comment. I’m not logging steering angle. I agree that all those things you mention affect how close a car can get to max steady-state lat-G in a particular slalom, if a car can hit max Lat-Gs, or whether it can spend any significant time there. So think about this: let’s say we have a vehicle (Kart, FSAE car, F1 car) that can easily hit max lat-G for an extended time between some set of slalom cones. That means a big portion of the time the arc is circular. But there is no constant radius section in a sinusoidal curve. Once again, this shows that assuming a sinusoid is not a good model for what actually happens.

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2. Pax

I would question the accuracy of the data. How granular is the lateral g data? Is it even capable of capturing the true peak g in a slalom with such quick transitions? I look at throttle position on my solo storm but factor in its being captured by a Bluetooth obd-II reader on a 20 year old car.

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• I use 20Hz GPS data ported to Circuit Tools which I think is reasonably accurate, but not as good as an accelerometer. The peak values are very dependent upon how much smoothing is applied. For instance, I looked at some data from Nats. With no smoothing the jagged Lat-G trace has peaks of 1.4g in the corners before and after a slalom and peak of about 0.9 in the slalom. But, nobody believes such numbers. With significant smoothing applied the numbers are more like 1.2G in the corners and .65 in the slalom. This was a multi-time national champion driving the car with a broken sway bar, so poor transient response. (We had the shocks cranked up to max trying to compensate for the problem we knew we had, but didn’t know what was actually wrong.) Granted, an accelerometer might very well catch a higher peak in the shorter duration events in the slalom. I would very much like to see data that shows a Street-class car consistently achieving 1.2G in a 55′ to 85′ slalom. If any cars can do it I’d bet on the ES Miata or MR2.

Of course this data, from the broken 944, would represent the low end of transient response. The Corvette is better, but still does not achieve full lateral-G in any slalom I’ve ever taken data on. It is possible to achieve full lateral-G in a slalom by “over-driving” of course, but this is really slow and normally only occurs when someone gets really late and is trying to miss the cone.

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