Damon, I get your point, but just using made up numbers doesn't work for such a situation, because they may not match reality. Taking a super tight turn is likely to require half the speed of the long one, not just a 15% reduction, because the G force in a turn varies directly as a function of the radius of the turn.

 

G force does not vary only as a function of radius. It varies as a combination of straight line velocity AND radius. For a given velocity a tighter radius gives more g, a wider radius less g. This why is no matter how much power you car has you can use up the entire traction budget in every corner.

You can figure out EXACTLY what the difference is for the differing radi: Compute the angular velocities of each. Does a radius twice as tight require a 50% reduction in velocity? (Do the math). After computing that look at the parabolic line again. It only operates at that tight radius for a very short period of time. On the way in and out it's operating at a much wider radius and thus carrying more speed in those areas...

As for the numbers they were not made up. I've been using a chassis datalogger for some time now and have quite a bit of data for my car. The g force, apex speeds and time down the straight are very similar for situations may car has seen. You can use faster speeds or more/less time and follow the trends yourself. There will certainly be a point where the parabolic line is slower, but it's in very, very slow corners.



Fritz, it's simiar to a double apex in the path traveled but very different as well. A double apex has two apexes. That means you turn in, slow for the first apex, get a squirt of throttle in while coming out wide a little and then slowing again for another apex. The parabolic line only slows once, only makes one apex and only accelerates once. The double apex does each of those twice.

...not to say that the double apex is not going to be faster in some situations. Again the entire point is not that the parabolic line is always fastest, it's that in many situations it is faster than the classic "widest radius possible" way of cornering. The point is to consider other options that may make the car faster in some corners.

My example with numbers can certainly be changed to make the parabolic line slower in some situation. All you guys with track experience and data should spend some time with pencil to paper. You might find yourself suprised. If it works at only one corner at a track you spend a lot of time on you just went faster than you could before with no changes to the car, just your technique. How is that a bad thing?

 

Guys, guys, let's settle this with some good old fashioned fun on the track

 

Maxing out your friction circle is a vector quantity. The parabolic path requires your acceleration to be a specific vector. A NA Rx7 simply cannot break straight line traction at 35 MPH unless it's raining. Therefore in a straight line you cannot max your friction circle at 35 MPH.

If you are getting .7G longitudinal acceleration at 35 MPH then you are getting .35G longitudinal acceleration at 70 MPH. If you are cornering at anything less then .9G lateral acceleration at 70 MPH you are probably not using all of your available friction circle. If you change your entry speed and use a different line to max your friction circle, you are no longer using the parabolic path.

The parabolic path is strictly defined up to the point that your longitudinal acceleration (or braking) can no longer max the friction circle (otherwise the path would expand to infinity - that's a really big racetrack). Once your max longitudinal acceleration + cornering acceleration falls below the friction circle you are free to turn in more. For braking you should always be able to max your friction circle but for acceleration it depends on your HP/weight ratio. At that speed/cornering load your path is free to change to the more circular (classic) path.

At higher speeds (probably anything >70 MPH in a production based NA car) that breakpoint will probably be inside the corner. At some higher speed that breakpoint will be at the vertex of the parabola (classic line with trailbraking).

ed

 

The parabolic line is basically "squaring off the corner" in motorcycle racing parlance, and some use the term "double apex" because of its apparent trajectory that hits two apexes in the corner. That is not always the case, however, and you are usually using the techniques described for the parabolic line; i.e., you come in hard and fast, get the bike/car slowed and turned, and then get on the throttle hard to blast out of the corner. There is no "slowing twice" for two apexes; you come into the corner, get to your "turning point" and accomplish that with braking/steering, and then get on the throttle early and hard-- the line may encompass two apexes, it may not. This is what I think Fritz was referring to.

It's become more commonplace to use this technique in motorcycle racing as horsepower levels and overall traction (the tire sizes now dwarf what they used to be even 10 years ago) have increased, and momentum doesn't play as much of role as it did in the past. But for many of the lower-hp classes, the "classic" racing line that conserves as much momentum as possible, still holds many advantages in certain situations.

 

As I said before, it's dependent on the section of the track you're in, and what's ahead of you.

If we're talking about the current corner and then a long straight, exit speed (or acceleration) is king.
Am I off in this?

If you're connecting into another turn, then other factors come into play.

We can debate all we want about what is "ideal" and what is more "efficient", but I think it still has to do with what you are more comfortable with.
I've seen weird datalogs on vehicle on-track position, and even fast drivers do not take any of the typical racing lines.
I read in an old RCE about Jackie Stewart versus one of the editors climbing into the same Formula open-wheel racer, and while the RCE editor stuck to typical racing lines, Stewart consistently drove faster and quicker at all parts of the track.
Checking out the vehicle on-track position datalog showed some really odd racing lines from Stewart...


-Ted

 

Absoutely. If you're linking several corners than your exit out of the first isn't so much about speed, it's about positioning the car correctly for the best entry into the following corner. I'm not trying to claim this is the end all technique. I'm agreeing with the article that in most instances where people would use a classic line the parabolic line will be faster.

It's not squaring off the corner at all; look at the diagram. Squaring off the corner is still turning in, relaxing the steering for a moment across the middle of the corner and then turning in again. The parabolic line only uses one turn to rotate the car around the corner, it just does it over a much smaller area of the turn compared to a classic line.


Yes. I already showed an example of that above. One car gave up a lot of speed around the corner and therefore came out of the corner much slower. However that "slow" car was able to get on the gas earlier in the corner than the "fast" car and in doing so he caught the car in front on the straightaway, even though the car in front had greater exit speed from the corner and accelerated at the same rate as the "slow" car.

 

It's not that simple. The "friction circle" is never a perfect circle, it generally squashed on top and bottom and the reason is simple. During cornering you have 4 tires doing the work (granted two of them do most of it but all four contribute). During braking you also have four tires doing the work (but weight transfer to the front leaves less and less for the rears to contribute). During acceleration (assuming 2wd) you only have 2 tires at all times capable of speeding up the car. Because of this most every 2wd car is capable of cornering and braking at higher g than it can accelerating in a straight line. No matter what the horsepower of the car this will be true. This explains why 4wd cars are said to "put the power down" better: In a straight line the 4wd car has four tires putting its power down and thus if it has the power it can out grip the 2wd car under acceleration all else equal.

My car for instance routinely shows 1.3 g in cornering, 1 g in braking and .72 in acceleration. Those are all traction limited numbers; best the car can presently do. My car's friction circle (and nearly every other car) is more of an ellipse with the bottom fatter than the top. Most all cars are capable of turning and braking harder than they can accelerate, no matter what the horsepower because the tires dictate what the car can do.

Here is an actual friction circle my car produced during one lap 2 weeks ago. The extreme outer edge represents about 1.3 g as that was the highest recorded value. The top of the circle is forward acceleration, it's roughly half of 1.3g. The bottom of the circle is braking and it's roughly 3/4 of 1.3 g.

 

Well, this is getting a little too involved with semantics here for me. All I was saying is the basic premise of the cornering technique is the same. Squaring off the corner to me means coming in fast (instead of getting everything set up with a wide entry, etc.), getting the machine slowed and turned (in one motion), and then powering out with a minimum of fuss. The absolute trajectory and steering inputs are really irrelevant in my opinion (sorry, no offense intended, Damon ). The advantages are the same: more ground covered with higher overall speed, and the ability to get on the throttle earlier and harder than the "classic" racing line.

 

I'm glad you're following me I consider a double apex braking late turning in early past the first apex under braking then pivoting with the brake to point the car then peg the gas you don't need to ease into it because the line to the second apex is a straighter line. So if you do it correctly you should go from heavy braking to heavy gas which has to be a good thing Bottomline the more stress you can put on the car without loosing control over the shortest distance will result in the fastest lap time. HP shouldn't matter.

 

Agreed. Good "in a nutshell" statement

 

The part everyone is missing is that the "super tight turn" is done over a very, very short distance of the corner. A classic line through a 180 degree turn will essentially be cornering at max g for nearly the entire 180 degrees through the corner. While cornering at max g the car has no grip left to accelerate or brake. The parabolic line with its "super tight turn" will only be super tight through about 30 degrees of the corner. The parabolic line is much slower across the apex but it's only through about 30 or so degrees of the turn, that's 1/6 the length of the classic line! The other 150 degrees or so of the turn the parabolic car is driving at a much higher average velocity than the classic car. That's the tradeoff the parabolic line makes: It gives up a high apex speed for more speed before and after the apex. Added up this gives a higher average speed through the segment than the classic line does.

Look at the diagram for the parabolic line again and study how huge the arcs before and after the apex are; they are much bigger than the classic line can do so the parabolic line has greater speed here. Certainly at the apex the radius is very tight but this very tight distance is over a very short length of time compared to the classic line. This is the key. The parabolic car only spends a very short time going slow around the apex. The rest of the time it's carrying much more speed. The classic line carries max cornering g (and thus can't accelerate or brake) through nearly 100% of the corner. The parabolic line carries max cornering g roughly 20% of the time it's in the corner. The rest of the time the parabolic car has the ability to out brake and out accelerate the classic car.

 

For what it's worth, my fastest autocross times (by far) have been when I've been as gentle on the gas and brakes as possible with most of the time spent in high lateral acceleration. Although, there are occasional straights or sweepers where I can get the car up to speed and then brake hard before the corner.

I generally like to brake late and turn early, then accelerate forward with a gentle post apex sweeping line. I try to copy the lines of the fastest drivers.

 

Damon, thanks for responding to my message twice When I said G force varies directly with radius I meant at a given speed, of course velocity matters quite a lot. G force actually varies as a square of the speed.

Anyway, it looks like this, as with many things in racing, is highly variable depending on a lot of conditions, especially the type of car. I'd love to try it out myself but my poor RX-7 is out of commission until next season due to blown engine. I may be doing a kart day soon though, so I'll definately check it out.

 

Ok, I read the article and I mostly agree with it but nowhere does it address the points I have been trying to make.

The article is based on a theoretical car that can accelerate at 1G to 225 MPH. Amature level cars simply do not do that. If you can maintain 1G acceleration past the entrance to the outgoing straight it doesn't really matter. However the acceleration you can maintain is directly related to your HP (Power=Mass*Acceleration*Velocity). Double your speed and you only have half the acceleration ability, triple it and you only have one third.

Yes, your friction circle is not as big to the front as to the sides or rear but you don't have enough HP to reach it anyway. If you cannot spin your tires in a straight line at 20 MPH (without dumping the clutch), then you have less than .25G available at 80 MPH. (ok, you don't have gearing to put max HP at 20 MPH but you get my concept)

You can keep your acceleration vector pointed in the right direction at the edge of your traction circle only if you alter your path to a more circular path.

The concept of the article is totally true but if you don't have professional HP/weight levels you cannot keep the vectors pointing the right way by following a parabolic path.

Any corner above 60 MPH in a street based racecar will probably need a compromise between "classic" and "parabolic".

Still it's an excelent article, it made me think hard about exactly what I'm trying to do on the track.

ed

 

Thanks for the reference Damon. I picked up a copy yesterday, and the magazine's definitely an interesting read.

 

The article is not based on that at all; that was an example (I gave an example earlier but mine was declared "made up" and so didn't apply. This one however is also "made up" and does apply?). Try plugging in some of your own numbers that your car is capable of and see what happens. Page 56, third column is where that example of "1g acceleration" is. Even if the math isn't understood any number you want can be placed in the equations since it explains word for word how to compute the velocities and sector times.

Nobody like math? The article is based on a straight forward mathematical model and the rebuttals all seem to be based on "that can't be right". Nobody have a sharp pencil?

Which way the vectors are pointing has nothing to do with horsepower. You can make the vectors point anywhere you like by using the steering wheel. That's the entire premise of the article.

Anybody actually tried it or maybe even come up with examples where the parabolic line is slower with some reasoning other than "it's not right"?

 

I haven't read the article, but if anyone is interested a car accelerating at 1G runs the 1/4 mile in around 9.1 seconds.

Carry on,

-bill

 

I agree.

Instead of talking about high HP cars, you should consider how much G's (0.2, 0.5, 0.9 or more) you can pull out of the corner (having also the friction circle in mind) with your car on that specific corner. Surely I take some corners differently, depending on the HP they have. With FD I take T10 on the track we go to with parabolic line, knowing I have enough power to accelerate nicely down the straight. In a 160hp Honda you just dont have enough power to fully utilize the friction circle going in with the parabolic line so I choose the normal line. But this is done automatically, I dont really have to think much about about it....

Sooo... if you dont have to power to backup your full utilization of the friction circle exiting the corner better stick to the classic racing line.

Fangio or Ascari used this parabolic line with great success decades ago.
But then again, they were also using engine to slow down

 

If my previous post was a bit unclear, Ed obviously read my mind and put it down on the forum, lol.

This is what I had in mind.

Thinking about it, with lower HP car I take that T10 corner as a combination of parabolic and classic racing line - i.e. dive in further with slower speed, then aggresively turn the car and accelerate towards late apex. This keeps me on the edge of the friction circle througout the corner. I was fastest that day for about 0,5sec (on 80sec lap) among 50 cars

 

Don't take this the wrong way because I include myself in my statement, but just because you beat everyone doesn't mean you drove the car to the limit of its ability or the limits of the track that day; it just means you were faster than everyone else. There's a big difference.

 

Damon is right. However, if you are faster than everyone else, you are doing something pretty well. Especially when there are 50 others.

 

Or that they were all really bad drivers.

Kidding! Kidding!

 

That was on stock Honda delSol (with bad chasis twisting because of targa roof and stock suspension) with 150k miles on the car. Many other cars were modded, including one Integra Type-R.

I just wanted to point out I had to be doing something better then others and to give myself some credibility over the stuff I talk about