I thought you had to be 16 (or under) to use one of these icons. You were trying to gain credibility right??

Classic line, parabolic line, double-apex-with-half-twist-and-cherry-on-top, it's all the same. What counts is we like going as fast as possible.

Looks like Damon has mathematically proven that the parabolic line is faster in situations with few other variables. It is up to all of us to apply this in real-world testing where there is no shortage of crazy variables - like how much rubber is there already on the day's favorite line and debis off from it? That one always gets people.

I am going to plot some curves and will post later.

This is the best thread I've followed on the RX-7 Forum in years.

I didn't prove sh*t. I just read an interesting article that I agree with and can understand because of some of my past school and study experiences. I knew it would be an arguable and "sore" topic but thought people might like to investigate for themselves.

Now I know how the first guy who claimed the world was round felt. Everyone just knew the world was flat. How'd they know that? They can't tell you. It just is ;)

Ok, you got me. When I saw that the article was working off the example of constant acceleration, I knew that there was a loophole in there somewhere. The HP levels of professional racecars allow them to accelerate at the limit of traction inside most corners. Once you are onto the outgoing straight, it doesn't matter. You are already quicker and faster than an equal car that took the wrong line.

After thinking this through for a long time (because I am not willing to remember any Calculus) I finally realize the only car that will do better on a classic line is a car with so little HP (or a corner with such a high speed) that the X component of the acceleration on the parabolic path falls faster than the Cosine of the radial component of the Classic line.

Essentially your corner exit speed would have to be about equal to your terminal velocity. Then the classic line is best for you.

There's going to be a medium sized middle ground where the parabolic line is faster but not by much. (my brain hurts I'm not going to figure it out)

And any real racecar should be following the parabolic path.

ed

Oh... so at the age of 26 you're no longer allowed to joke around ?

C'mon... relax :)

I'd agree that is the most common case.

Not by much is all it takes to outrun the other guy who was just as fast as you :) The beauty of it is that you didn't do anything but drive your car differently. If this technique works in only one corner on the entire track you still dropped lap time you may not have been able to before. The point is to always be faster than the other guys, right? :cool:


I didn't go that far. I just spent a lot of time studying the graphs on p 57 ;)

Excellent
 

Greatest topic I've read on the site! Hell, it even helped me with some of my Dynamics work. One of the turns leading up to my job is an uphill ~70 degree turn. In my stock worn suspension FB with bad tires I can exit the turn around 3-5 kms faster with the parabolic line(use a lamp post coming up the hill to start accelerating and another post at the exit of the turn as a marker). I think the parabolic line also works best when corner exit space(width of track or road) is too little to allow the vehicle to "drift" out to the point where it uses all its available traction. Please correct me if my logic is flawed.

but then theres Grip and drift style racing/driving that has to be taken into thought also theres 2 totaly diffrent lines and at that drifting can seem slower to the eye in a turn but engine stays in its powerband so your faster going in and exiting the turn and yes this is a great discussion we need more like it

The engine being in its powerband doesn't mean sh*t when you're spinning the tires on the pavement. If the tires are wildly spinning or sliding you're not going anywhere as quickly as you could be, no matter how much power you have.

Anyone think the fastest way down the 1/4 mile is to spin the tires the length of the track? Then why do people continue to insist doing it around a corner is fast? :confused:

Because InitialD said it was. :D

Come on Umrswimr, your z06 vs my AE86 of DOOM!!! Down Akina!!!

I actually owned an AE86, which is why I can feel confident that I will be victorious. :D

Minor correction: my car is not a Z06. :(

Watched the F1 spa race this weekend. Turn 1 is like a U-turn, with a very long wot section that follows. From what I studied on tape, none of the drivers used an elliptical cornering method ... all used the classic radius. That magazine is not available here, I would have enjoyed digging into the write-up. Seems like there is a disconnect between theory and reality.

During prerace coverage, they displayed a 1-lap datalog for M Shumacher, including rpm, speed (gear can be extracted), brakes, and TPS. Would be great if someone recorded it on dvd, and could post it here. Looked like about 2.3g braking from 200 to 75 mph.

I bet it's actually more than that. From highspeed with all the downforce initial braking g's are phenominal.

Kevin, the F1 cars have a fairly large turning radius, which is probably why they don't run that line on any track. In fact, the teams have to make suspension changes to even make the hairpin at Monaco.

Additionally, the parabolic line might not be humanly possible to achieve with any consistency, given the brutal abilities of F1 cars.

F1 cars suffer 1G of deceleration from ~200 mph by just lifting off the throttle. I'm guessing they regularly experience well over 2G braking and accelerating, and 4G cornering. Rough stuff....:) That Le Rouge turn at Spa looks terrifying at speed....

The main assumption, as stated in the article, is that this car has equal(1G) acceleration in all directions(meaning a perfectly round friction circle). I'm sure this was done to simplify the math, however, this assumption isn't realistic at all. I don't know of any real-world car that meets the assumption. A typical friction circle looks like one shown earlier in this thread. There is more available G-force under braking and cornering(all 4 tires contributing) than acceleration(only 2 tires contributing unless 4WD). I have a feeling using these realistic G-force figures may lead to a different conclusion, and the fastest line would vary between car to car.

The 1g assumption is used to simplify the math. As for cornering g being higher than accel g this will be true for nearly every car, but that doesn't really factor into the equation because If we are looking at two straights with a 180 degree corner connecting them acceleration in a straight line is still what determines how quickly we can cover the distance. The actual g ability of the car in each direction doesn't matter much. The entire intent of the parabolic line is to spend your time accelerating down the straight at whatever rate you're capable of rather than spending a lot of time using your grip in pure cornering. Regardless of your acceleration potential if you spend more time accelerating and less time cornering your average lap speeds will still be higher. It doesn't matter if the car can corner at 3 times the g at which it can accelerate. The fastest way for that car to travel around a racecourse is to spend as much time as possible with the throttle to the floor.

Imagine you're the guy with binoculars on the left of this pic: pic. What you see is the car speeding from right to left, pause while it changes direction in the corner and then speed out from left to right. The time the car is in the corner will appear to you as a pause in the car's motion because of your viewpoint. The car that gets through your field of vision the fastest will carry the most speed down each straightaway and spend the least amount of time "going no where" while in the corner. Ideally this means the car would travel right to left at its highest speed, freeze in place while instantly changing direction, then speed back out from right to left. Obviously freezing in place is impossible but the point is that the car will only be in the field of view of your binoculars for a certain period of time. If you spend more of that time with your acceleration vector actually pointing up and down the straightaways you will cover that distance in the shortest time possible. Using the classic line insists that your "pause" as viewed through the binoculars be longer. The fastest way to cover the section is to get up and down the straights while spending the least amount of time with the steering turned changing the car's direction. The classic line will always insist you spend greater time changing direction and less time slowing/accelerating up and down the two straights compared to the elliptical line.

cheap go-cart theory?
 

Based on Spa, I suspect a flaw in Mr Z's assumptions, vs how he is being interpreted. Since I can only see the posted pics, one point that caught my eye was that upon exit, terminal velocity is reached (a=0) while still under traction limited by combined acceleration and cornering vectors on the parabolic line. This would be more realistic for a cheap single speed go-cart on that Spa corner, vs an F1 car. If possible, could you send me a copy of the article be email or snail? That mag ain't around here, I checked.

That goes back to an argument brought up earlier, the corner speed vs. ability to get on the throttle. But I think that the rally vs. pavement points have been brought up before. Also, even though we can think of mass as a point where the center of gravity is, there has never been any studies of a car turning in an arc, versus a car sliding in an arc, if there is an optimal way to guide a car around a corner. Though intuitively, I would think it's the same. Just my two cents.

EDIT: Whoops, I gotta stop bringing back old topics.

static friction will always be higher than kinetic friction. however on certain surfaces, the difference becomes small enough that sliding the car doesn't lose as much speed. in rallying it can also allow you to change your line at any point in the corner more easily, allowing you to make small corrections to the corner you haven't lapped continuously as with circuit racing.

Great thread Damon - Thanks for posting. The forum needs more threads/topics like this.

Unfortunately, I doubt that I'll be able to get the magazine around here.