It's still motor-racing, but... ..."catenary".

[alangbaker]

It's not specific to Formula cars so I wasn't sure where to put this question:

I'm having a bit of a debate with someone about the optimal line through a corner and the shape of the curve that results, and he insists that it's a catenary curve.

For this who might not know, a catenary curve is the curve that a rope (or chain—that's where the word actually comes from: the latin word for chain was "catena").

This guy is a bit of a pill and he insists that I can't have possibly gone through 4 different racing schools (1 Skip Barber 3-day basic, 2 SB 2-day advanced, and my clubs 2-day basic) and become a race driving instructor without the word "catenary" having come up may times. He said (and I quote):

“That's why I brought up the word "catenary" which _every_ (real) racer knows all about, as it's one of the most important words in racing schools.”

So... ...has anyone EVER heard the racing line described as a catenary?

I've got my one thoughts on what curve is made and I'd like to have that discussion with someone sometime, but let's start with this.

[hdsporty1988]

I had never heard the term before your post. Having now looked it up I know why, it's clearly not the optimal racing line through any curve I'm aware of!

[E1pix]

The only use of the term I’m aware of is in fabric manufacturing, like tents and awnings. How that relates to corner lines, I have some ideas all equalling a valued total of Zip.

Let the guy think whatever the H he wants, sounds like he will either way — and perhaps *especially* when you prove him wrong.

I finally, recently rid myself of a “friend” like this. He insisted since sunset comes earlier in the winter, doesn’t that mean it drops faster relative to summer?

I explained this is a constant determined by silly stuff like orbits and other things unrelated to having a flat earth (LOL), but on he went…

[stonebridge20]

38 years in this game and never have I heard that word used by anyone.

I bet your "friend" reads a lot of books.

[mmi16]

Been racing since 1988 and have never heard the term CATENARY used to describe any aspect of a turn.

Was a railroader for 51+ years until I retired and and the word CATENARY applied to the system that supplied a overhead electrical wire to supply power to electric locomotives and cars.

[t walgamuth]

Been racing since 1988 and have never heard the term CATENARY used to describe any aspect of a turn.

Was a railroader for 51+ years until I retired and and the word CATENARY applied to the system that supplied a overhead electrical wire to supply power to electric locomotives and cars.

I know the word but never heard it as a line in a corner. I believe it is the strongest shape for a suspension bridge.

[DaveW]

I know the word but never heard it as a line in a corner. I believe it is the strongest shape for a suspension bridge.

Catenary, as stated previously, is defined by the shape a rope or cable, etc., with equal load applied vertically (if the ends are at equal height, like gravity pulling on an empty clothesline or a suspension bridge main cable) at every point in its length.

An optimal cornering trajectory in racing is defined by many things, but one thing is certain - the G-load vector is never continuously aimed perpendicular to the straight line between the corner's endpoints.

So, IMO, catenary has little relationship to the "best" line in racing.

I can understand the analogy - equal load at every point along its length, but the literal definition just doesn't apply to cornering load.

And to again answer the original question - I've never before heard of its being applied that way.

[TimH]

I spent enough time in St. Louis to know the arch is designed as a reversed catenary rather than a less-esthetic parabola.

To say that EVERY turn should be one shape is as absurd as saying your cornering speed should always be constant.

[Peter Olivola]

Is he perhaps mistaking a parabola for a catenary?

[DaveW]

Is he perhaps mistaking a parabola for a catenary?

A parabola is closer, but still doesn't fit every corner for every type of car.

[alangbaker]

A parabola is closer, but still doesn't fit every corner for every type of car.

I can make a very strong case that the first 45 degrees of any corner you enter off a straight should be a parabola.

As a teaser, think about a simple 90 degree corner, the friction circle and in which direction the acceleration of the car should be at all times.

[DaveW]

I can make a very strong case that the first 45 degrees of any corner you enter off a straight should be a parabola...

To minimize lap time, a FVee is likely to brake early and carry full throttle almost all the way through almost any type of corner. The HP is so low that full throttle (at least back when I was running a Vee) rotated the rear footprint force vector in almost any corner so it was aimed close to the center of the turn, maximizing cornering AND exit speed. So the parabolic portion is likely to be later in the turn.

Of course all bets are off if someone is contesting the turn.

Edit: If the Vee is able to be trail-braked w/o sacrificing corner exit speed, then Alan may be right about the parabolic character of the entry segment. Back when I ran my Vee, I was not able to trail brake it w/o losing time and exit speed.

[alangbaker]

To minimize lap time, a FVee is likely to brake early and carry full throttle almost all the way through almost any type of corner. The HP is so low that full throttle (at least back when I was running a Vee) rotated the rear footprint force vector in almost any corner so it was aimed close to the center of the turn, maximizing cornering AND exit speed. So the parabolic portion is likely to be the latter portion of the turn.

Of course all bets are off if someone is contesting the turn.

Even with an FV, the initial part of any corner should be a parabola. I promise you: I've looked at the physics of the situation. And those same physics dictate the the acceleration phase of a turn is not a parabola.

Think about breaking the velocity vectors of a 45 degree corner (entry and exit) into two component vectors: one in the axis that bisects the 90 degrees and one perpendicular to that. Now consider the friction circle concept.

[FVRacer21]

I just watched a video on how they came up with the formula for a catenary.

Now I know how much I don't know about a catenary and how much Calculus I have totally forgotten since college.

Niki Lauda used to say there are no diagrams on how to drive corners in his book, as any driver that was any good would already know how to drive fast...

He is right in that each turn in each car is unique. West Bend at Lime Rock in a FV is very different than a GT1 car.

To get back to the initial question, I would have to get out Going Faster - but I cannot remember Carl, Bruce, Bill, Mike, or Skip, ever use that word.....

ChrisZ

[Offcamber1]

So... ...has anyone EVER heard the racing line described as a catenary?

When I was in college I had a freshman English Literature course and had to read "The Catenary Tales."

Chaucer, I think...

[E1pix]

… a FVee… The HP is so low...

I’m utterly shocked with the above news.
(Must I add a wink, Haha)

Merry Christmas to all the great people here.

Best in 2024.

[DaveW]

Even with an FV, the initial part of any corner should be a parabola. I promise you: I've looked at the physics of the situation. And those same physics dictate the the acceleration phase of a turn is not a parabola.

Think about breaking the velocity vectors of a 45 degree corner (entry and exit) into two component vectors: one in the axis that bisects the 90 degrees and one perpendicular to that. Now consider the friction circle concept.

I automatically break corners into sectors when I think about handling. And I thoroughly understand the friction circle. Plus it's not the same for the front and rear tires. All I can say with absolute confidence about this is that theoretical physics has to be empirically validated.

Enjoy the holidays, everyone !!

Alan, see my edit to post 12 - I may, at least partially, agree with you.

[TimH]

All I can say about this is that theoretical physics has to be empirically validated.

Enjoy the holidays, everyone !!

"A physicist can perfectly describe a spherical chicken on a frictionless nest."

[FVRacer21]

When I was in college I had a freshman English Literature course and had to read "The Catenary Tales."

Chaucer, I think...

Wasn't Chaucer in Sha Na Na?

[alangbaker]

I automatically break corners into sectors when I think about handling. And I thoroughly understand the friction circle. Plus it's not the same for the front and rear tires. All I can say with absolute confidence about this is that theoretical physics has to be empirically validated.

Enjoy the holidays, everyone !!

Alan, see my edit to post 12 - I may, at least partially, agree with you.

No worries, Dave. Spoken like a gentleman!

This is all just so much filler until we can start racing again.

And it's all only because I read an e-book about "THE" racing line that started very novelly by saying "imagine you're an astronaut" in space.

I read the conceptualization of the line we should use and the way we should be applying forces (or more correctly, those things in the reverse order), and it lead me to what I THINK is an epiphany about the racing line...

...and trail braking...

...and where we apex and how and why that should be different for cars with different acceleration potential.

But much more importantly:

Merry Christmas to you and all my fellow racers!

[alangbaker]

Edit: If the Vee is able to be trail-braked w/o sacrificing corner exit speed, then Alan may be right about the parabolic character of the entry segment. Back when I ran my Vee, I was not able to trail brake it w/o losing time and exit speed.

I think the heart of the issue is that the most efficient way to accelerate from one velocity vector to another is to do so with a vector that "splits" the input and output velocities.

If a car can brake and corner with the same maximum acceleration (friction circle), then the for first half of a corner (after you've done threshold braking to the maximum entry speed—TBD later), you can then choose an amount of longitudinal and lateral acceleration that in combination accelerates the car in that perfect direction I just talked about: back in the direction of the bisector of any corner up to 90 degrees.

That is changing the car's velocity vector in the most efficient way, and has you trail braking all the way to the middle of a 90 degree corner.

Now: imagine a car that had no forward acceleration possible. Say a "car" designed for a race down a hill.

If the exit of the corner was perfectly level, the best you could do for the second "half" of the corner would be to run the largest circular arc you could make.

The other extreme is a car that can accelerate as hard as it brakes and corners (so... ..no real car), and in that case, the corner becomes a perfect parabola (subject to the driver's ability to achieve it) with the acceleration vector always pointing precisely back along the bisector of the entry and exit angle. A combination of brake and cornering all the way to mid-corner and then you'd immediately be adding throttle from there until track-out.

If the corner is MORE than 90°, I still haven't worked everything out, but it obviously degenerates to the case of a 360° bend, in which case the acceleration vector always points to the turn's centre, so I suspect that any corner of greater than 90 degrees involves a segment of pure lateral acceleration between the long trail braking entry and getting back on the throttle.

Long-winded I know, but I'd value any thoughts anyone has.

[Larry H]

Would the corner apex then move forward in the turn with less HP and move back with more HP?

The other factor that screws with a nice parabola is downforce for cars that have aero down force.

[DaveW]

Would the corner apex then move forward in the turn with less HP and move back with more HP?

The other factor that screws with a nice parabola is downforce for cars that have aero down force.

Earlier apex with less HP, later apex with more so you can accelerate with maximum possible throttle from or before the apex until the next braking zone. At speeds below 50 MPH or so, aero has a relatively small effect on cornering trajectory. Of course that depends on amount of downforce relative to weight and HP. Some solo karts have so much wing that the effect of downforce is apparent as low as 20 MPH.

[E1pix]

^^^ This is really interesting…

I can’t speak to cars directly — but can say in karting anyway that overall, the lines of directional travel are the same regardless of power.

What’s different is slip angle of the entire chassis, from slide-in braking all the way to full power-on — at which point 100% bite and barely any further steering input is preferred, whether having 5 hp or 50.

In karts anyway, steering once on power sucks the life out of the next straight. I presume Vees are the same but only when finally pointed the right way.

[pacratt]

Whenever a non-racer spews their "knowledge" at me, and implies I should know what they know, I open myself to being educated.
"Here...I know a spot...we'll take MY car and you can show me..."
Then comes the smirk & huff, followed by some classic excuses.
Glenn
P.S. Some of my best shut-downs are when I meet a new "Mr. Racing-Know-It-All". I just let them go on and then show them pictures of me racing.

[E1pix]

This all reminds me of the era where the Missus and I were attempting to climb the 100 highest points in the Lower 48.

We met a guy who watched a friend and I crushing a ping-pong ball. He jeered and pointed, we played a game, think he got five points and mostly out of grace. ;-)

Then my friend and I admitted we’d never seen Rainier. He interjected that the best, known route up the peak was the “Spiral Method.”

I think we said nothing, but have referenced it for nearly 40 years since. He got bored, and sauntered off.

I don’t recall if he was spinning in circles to walk away in a straight line.

[Larry H]

Earlier apex with less HP, later apex with more so you can accelerate with maximum possible throttle from the apex until the next braking zone. At speeds below 50 MPH or so, aero has a relatively small effect on cornering trajectory. Of course that depends on amount of downforce relative to weight and HP. Some solo karts have so much wing that the effect of downforce is apparent as low as 20 MPH.

That make sense. I got it backwards.