Raceing line analysis (very basic study)

[Outsider]

I had wondered for the longest time how much different the racing line was between holding a certain steering input around a corner, and constantly increasing the steering input up to apex, then constantly unwinding. Well since I got bored at work the other day, and decided to put together a study of just that.

This in nothing new. Just puts two driving styles in perspective.

The two scenarios are:
Scenario one (constant rad); driver comes to turn-in point, and inputs (instantaneously) a certain steering angle which is maintained through out the turn up until the track-out point (where the 90deg turn is complete). This creates a perfect circular arc through the 3 points (turn-in, apex, track-out points)

Scenario two (changing rad); driver comes up to the turn-in point (different point then from scenario one) where they start to incrementally give more and more steering angle up until the apex, at which point they incrementally take away steering angle (straightening out the wheel) until they reach the track-out point, where the 90deg turn is complete.

Assumptions I've made for this exercise: vehicle is moving at the limit of lateral grip throughout the turn (in both scenario one and two). In scenatio one, the speed is constant through the turn, since the turning radius is constant throughout the turn, however in scenario 2, the speed varies, since the turning radius is always changing.
The actual numbers are meaningless in and of themselves. They only make sense when compared to another scenario using similar assumptions, which is why the data is compared.

Conclusions:
I've looked at this data in 2 ways.
Spreadsheet "Racing Line -test B.xls" starts and ends both racing lines at the same point. You can see that the apex can be pushed much further onto the track, yet the time taken to complete both arcs is pretty much the same.
But there's more; The entry and exit speed from scenario 2 are about 3 times larger then scenario 1. So you can enter and exit the same turn 3 times faster. That's significant!

http://www.onsendesigns.com/stuff/Racing%20Line%20-Test%20B.png

Spreadsheet "Racing Line -test A.xls" places the apex of both arcs at the same point, and lets the turn-in and track-out point move accordingly.
To keep the measurements normalized, the time around the bend was taken for the same distance traveled (data between the green rows in the spreadsheet) by both arcs, which means the time taken from the start of the blue arc to the start of the pink ark was ignore, as was the time from the end of the pink arc to the end of the blue arc.
The time was for all intents and purposes the same for both paths, however again the entry and exit speed was higher for the blue arc(scenario two).

http://www.onsendesigns.com/stuff/Racing_Line-Test%20A.png

Here's a link to the spreadsheets I made if you want to look at the gritty details.
Racing line -test A.xls (http://www.onsendesigns.com/stuff/Racing%20line%20-test%20A.xls)
Racing line -test B.xls (http://www.onsendesigns.com/stuff/Racing%20line%20-test%20B.xls)
Let me know if you think I've made any mistakes, or if the results don't make sense, or of course, if you have any questions.
Also, share your thoughts!

[thgear]

did you factor in the fact that most vehicles have suspensions geometries that affect grip and weight transfer variables depending on steering angle?

[malcolm]

There was an excellent article about this in Racecar Engineering a few years ago.

:)

[MazdaMatt]

Obviously a car's grip is dynamic depending on both the constant G-force load and the delta-G-force, but for a comparitive study this is great :)

What factor is equal between the two lines? Maximum g-force, or time taken to complete, distance travelled or something else?

Methinks you need to get your wheels back on the track... it has been a long winter, hasn't it?

[malcolm]

http://ca.youtube.com/watch?v=lmWq56GUK-0

^^excellent example of the parabolic line technique, where you coast into the corner and let the car naturally scrub off speed.

Basically, if you have to get on the throttle before the apex, you entered the corner too slow! :cool:

[MazdaMatt]

"This video has been removed by the user".

Does anybody driving a low-power car wait till the apex to hit the gas?

[Outsider]

Obviously a car's grip is dynamic depending on both the constant G-force load and the delta-G-force, but for a comparitive study this is great :)

What factor is equal between the two lines? Maximum g-force, or time taken to complete, distance travelled or something else?

Methinks you need to get your wheels back on the track... it has been a long winter, hasn't it?
As mentioned, this is a very basic, (read simplified) version of the real world, but it can still provide some insight.
No suspension geometry was considered/used. Just simple physics.

Matt, the variable that is constant between the two lines is g-force. Time taken to complete, distance traveled and velocity were back calculated from that.

[malcolm]

http://ca.youtube.com/watch?v=ZieROgA5Hvc

try that one.

I've used the technique in both the 520 bhp Corvette, 240 bhp S2000, as well as a 140 bhp Formula BMW and my 112 bhp Toyota MR2, all to great effect. :)

[Marsh]

The flaw in the analysis is Longitudinal acceleration. If the constant radius car is travelling at the limit of lateral acceleration then it's longitudinal speed is the same at the exit as it was at the apex. The car that is changing steering input can accellerate through the exit of the corner achieving a higher exit speed, not to mention they have a higher entry speed for the same reason. Thus the changing radius car will be much faster on the straights, which accounts for more overal track length and are much more important when factoring lap times. Also the higher entry speed of the changine radius car makes it impossible for a constant radius car to pass it.

[MazdaMatt]

Now, knowing that a parabolic line is of greater entry and exit speed... is a driver better off to use a constantly-changing steering input, or use a set-and-forget steering input and create a parabolic line by trail braking and washing out to exit via throttle?

Possibly the optimum line uses both: stable turning radius in the section closest to the apex, but with a parabolic entry and exit portions...

All those cars are rwd, what about throttle before the apex in a fwd car?

[Marsh]

Now, knowing that a parabolic line is of greater entry and exit speed... is a driver better off to use a constantly-changing steering input, or use a set-and-forget steering input and create a parabolic line by trail braking and washing out to exit via throttle?

Possibly the optimum line uses both: stable turning radius in the section closest to the apex, but with a parabolic entry and exit portions...


I would assume both. The answer lies in slip angle. The tires achieve their maximum grip an some optimal slip angle. You want all four tires working at that slip angle. Whether that requires x amount of steering or not will depend on the car.

[Outsider]

I would think it's far easier to constantly be adjusting the steering, the it would be to modulate the brakes.
Besides, once you break the limit of grip on the tire (as you would by using the brakes, and throttle to turn a constant radius into a changing radius) the grip is actually less then the max drip the tire can give you before it's slipping.
Dynamic friction is alway lower then static friction.

Besides, changing the steering input at a constant rate is much easier then trying to linearly modulate the acceleration/deceleration of the vehicle (which may not be linearly related to the travel of the pedals) at least not to the same degree of linearity as the steering can give you, since the amount of travel of the arms/hands on the wheel is much more then the few inches you have to modulate the throttle/brakes.

[RETROCRX]

The point is moot......a tire will not accept an instantaneous input to a constant steering angle without losing grip.

A slow turn-in and parabolic steering input allows the tire to maintain grip.

Try it.....enter the same corner at the same speed and try the 2 different input techniques.

Not to mention how abrubt inputs affect contact patch loads and how that all translates into suspension movement and chassis pitch/roll.

Just my take on it for what it's worth......

Rob

[Marsh]

Besides, once you break the limit of grip on the tire (as you would by using the brakes, and throttle to turn a constant radius into a changing radius) the grip is actually less then the max drip the tire can give you before it's slipping.

Don't confuse tire "slip" with tire "slide". Because rubber is very flexible a tire with a side load on it will not travel in the direction it is pointed it will crab or "slip" at another direction as it's pushed by the side load. The difference between the direction a tire is pointed and the direction it's actually traveling is called the "slip angle". The more flexible a tire is the higher this angle is before the tire breaks into full slide. At all times some part of the contact patch is moving across the ground. Slide only occurs when the ENTIRE contact patch is moving across the ground.

The amount of grip available depends on the flexibillity of the tire (stiff racing tires work at much lower slip angles than street tires do) and the prevelance of the grip mechanism. Straight mechanical grip (what Newtons laws account for) are much lower sliding than static. So is adhesive grip. Hysterisous grip, however, doesn't work without slip and continous to work well at very high degrees of slip. So a tire utilizing more hysterisous should work better at higher slip angles.

BTW I used to make adjustements with the steering wheel mid corner. Now I make adjustments with the pedals mid corner (and I'm a lot faster than I used to be). I think if you go for some ride alongs you'll find the faster and more experienced drivers do the same. The reason is that the steering wheel can only adjust two wheels. It is always a combination and the correct result should look (to an outside observer) like a very stable steering wheel dispite a changing turn radius.