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How badly Arlen/Maria gets it wrong: the catenary curve and road racing.

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  How badly Arlen/Maria gets it wrong: the catenary curve and road racing. Alan <nuh-uh@nope.com> - 2026-10-23 13:00 -0700
    Re: How badly Arlen/Maria gets it wrong: the catenary curve and road racing. Jörg Lorenz <hugybear@gmx.net> - 2026-10-25 09:11 +0100
      Re: How badly Arlen/Maria gets it wrong: the catenary curve and road racing. Alan <nuh-uh@nope.com> - 2026-10-25 11:05 -0700
        Re: How badly Arlen/Maria gets it wrong: the catenary curve and road racing. Jörg Lorenz <hugybear@gmx.net> - 2026-10-25 22:19 +0100
          Re: How badly Arlen/Maria gets it wrong: the catenary curve and road racing. Alan <nuh-uh@nope.com> - 2026-10-25 14:38 -0700
    Re: How badly Arlen/Maria gets it wrong: the catenary curve and road racing. Tom Elam <thomas.e.elam@gmail.com> - 2026-10-26 07:38 -0400
      Re: How badly Arlen/Maria gets it wrong: the catenary curve and road racing. Alan <nuh-uh@nope.com> - 2026-10-26 11:55 -0700
        Re: How badly Arlen/Maria gets it wrong: the catenary curve and road racing. Tom Elam <thomas.e.elam@gmail.com> - 2026-10-28 09:19 -0400
          Re: How badly Arlen/Maria gets it wrong: the catenary curve and road racing. -hh <recscuba_google@huntzinger.com> - 2026-10-28 11:37 -0400
    Re: How badly Arlen/Maria gets it wrong: the catenary curve and road racing. Tom Elam <thomas.e.elam@gmail.com> - 2026-10-26 11:49 -0400
      Re: How badly Arlen/Maria gets it wrong: the catenary curve and road racing. Alan <nuh-uh@nope.com> - 2026-10-26 11:34 -0700
        Re: How badly Arlen/Maria gets it wrong: the catenary curve and road racing. Tom Elam <thomas.e.elam@gmail.com> - 2026-10-28 09:58 -0400
          Re: How badly Arlen/Maria gets it wrong: the catenary curve and road racing. Alan <nuh-uh@nope.com> - 2026-10-28 11:57 -0700
            Re: How badly Arlen/Maria gets it wrong: the catenary curve and road racing. Tom Elam <thomas.e.elam@gmail.com> - 2026-10-28 17:38 -0400
              Re: How badly Arlen/Maria gets it wrong: the catenary curve and road racing. Alan <nuh-uh@nope.com> - 2026-10-28 14:43 -0700
                Re: How badly Arlen/Maria gets it wrong: the catenary curve and road racing. Tom Elam <thomas.e.elam@gmail.com> - 2026-10-29 07:46 -0400
                  Re: How badly Arlen/Maria gets it wrong: the catenary curve and road racing. Alan <nuh-uh@nope.com> - 2026-10-29 10:35 -0700
                    Re: How badly Arlen/Maria gets it wrong: the catenary curve and road racing. Tom Elam <thomas.e.elam@gmail.com> - 2026-10-29 14:17 -0400
                      Re: How badly Arlen/Maria gets it wrong: the catenary curve and road racing. Alan <nuh-uh@nope.com> - 2026-10-29 11:40 -0700
                        Re: How badly Arlen/Maria gets it wrong: the catenary curve and road racing. Tom Elam <thomas.e.elam@gmail.com> - 2026-10-30 10:41 -0400
                          Re: How badly Arlen/Maria gets it wrong: the catenary curve and road racing. Alan <nuh-uh@nope.com> - 2026-10-30 10:24 -0700
                            Re: How badly Arlen/Maria gets it wrong: the catenary curve and road racing. Tom Elam <thomas.e.elam@gmail.com> - 2026-10-30 14:39 -0400
                              Re: How badly Arlen/Maria gets it wrong: the catenary curve and road racing. Alan <nuh-uh@nope.com> - 2026-10-30 11:57 -0700
                  Re: How badly Arlen/Maria gets it wrong: the catenary curve and road racing. Alan <nuh-uh@nope.com> - 2026-10-29 11:14 -0700
                    OT: And the coward ducked out of this one... (was Re: How badly Arlen/Maria gets it wrong: the catenary curve and road racing. Alan <nuh-uh@nope.com> - 2026-10-30 10:26 -0700
              Re: How badly Arlen/Maria gets it wrong: the catenary curve and road racing. Jörg Lorenz <hugybear@gmx.net> - 2026-10-29 07:46 +0100
                Re: How badly Arlen/Maria gets it wrong: the catenary curve and road racing. Alan <nuh-uh@nope.com> - 2026-10-29 01:26 -0700
                  Re: How badly Arlen/Maria gets it wrong: the catenary curve and road racing. Jörg Lorenz <hugybear@gmx.net> - 2026-10-29 11:17 +0100
                    Re: How badly Arlen/Maria gets it wrong: the catenary curve and road racing. Alan <nuh-uh@nope.com> - 2026-10-29 11:09 -0700
                      Re: How badly Arlen/Maria gets it wrong: the catenary curve and road racing. News <News@Group.Name> - 2026-10-29 16:04 -0400
                        Re: How badly Arlen/Maria gets it wrong: the catenary curve and road racing. Alan <nuh-uh@nope.com> - 2026-10-29 13:13 -0700
                          Re: How badly Arlen/Maria gets it wrong: the catenary curve and road racing. News <News@Group.Name> - 2026-10-30 09:59 -0400
    Re: How badly Arlen/Maria gets it wrong: the catenary curve and road racing. "Joel W. Crump" <joelcrump@gmail.com> - 2026-10-27 18:15 -0400
      Re: How badly Arlen/Maria gets it wrong: the catenary curve and road racing. Brock McNuggets <brock.mcnuggets@gmail.com> - 2026-10-27 15:56 -0700
    Re: How badly Arlen/Maria gets it wrong: the catenary curve and road racing. Chris <ithinkiam@gmail.com> - 2026-10-28 08:08 +0000

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#146550 — How badly Arlen/Maria gets it wrong: the catenary curve and road racing.

For quite some while, we've seen that once Arlen/Andy/Wally 
J/Maria/(other numerous posting nyms) gets an idea fixed in his/her 
head, almost no demonstrations of facts will sway him/her.

For instance!

I'm a road racing driver and instructor. I've been racing since 2013.

But for Arlen (I knew him first by that nym, IIRC) he became convinced 
that I couldn't possibly be those things...

...despite lots of conclusive evidence of the fact.

And it boiled down to only a couple of things.

First, I drive a BMW 135i, and Arlen insisted that if I didn't know 
which nicknames were used for BMW's cars and motorcyles, then I couldn't 
possibly be a racing driver. Mar 9, 2023

'If Alan claims to race beemers, he's a moron for not even knowing the 
first thing about his fabrications since the term came about in racing 
circles.

Jesus Christ.
What kind of idiot 'racer' doesn't know that?

Hence, I wish you wouldn't quote that moron Alan Baker, Jolly Roger, but
now that you have, if he doesn't even know the difference between a 
bimmer and a beemer, there's zero chance of his track fabrication being 
true.'

And on December 20, 2023, he brought up the "catenary" curve.:

'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.'

And now (of course) he's taken to using AI LLMs to try and "prove" his 
"facts"...

...so I did the same:

I asked Gemini:

"Can you find any reference online that refers to the shape of the curve 
a road racing car takes through a corner as being a catenary curve?"

And the response was:

"No, online references and vehicle dynamics literature do not refer to 
the curve a racing car takes through a corner as a catenary curve."

But let's not stop there!

I asked ChatGPT the same question, and it answered:

'I searched for references that explicitly describe a road-racing car's 
path through a corner as a catenary curve, rather than merely discussing 
the geometry of the racing line.

So far, I haven't found a convincing reference that makes that exact 
identification. I did find some useful sources discussing the 
mathematical shape of a racing line, which help distinguish a catenary 
from other curves that might look similar.'

But my laughing at him over this led to him putting me in his kill file!

And after scouring the internet, the only place he could find a 
reference to a "catenary" curve in racing...

...was the curve that one programmer chose to use...

...in a simulation...

...of a track for racing model wooden race cars...

...that were about one foot long!

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#146551

On 23.10.26 22:00, Alan wrote:
> For quite some while, we've seen that once Arlen/Andy/Wally 
> J/Maria/(other numerous posting nyms) gets an idea fixed in his/her 
> head, almost no demonstrations of facts will sway him/her.
> 
> For instance!

It took you a while to come to this conclusion.
I think it is pathological. The best thing for *your* wellbeing would be
to ignore him and killfile this Troll.

-- 
Ave Caesar! Morituri te salutant!

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#146552

On 2026-10-25 01:11, Jörg Lorenz wrote:
> On 23.10.26 22:00, Alan wrote:
>> For quite some while, we've seen that once Arlen/Andy/Wally
>> J/Maria/(other numerous posting nyms) gets an idea fixed in his/her
>> head, almost no demonstrations of facts will sway him/her.
>>
>> For instance!
> 
> It took you a while to come to this conclusion.
> I think it is pathological. The best thing for *your* wellbeing would be
> to ignore him and killfile this Troll.
> 

On the contrary!

Such people are NOT going away.

So for my wellbeing, it's best I am amused by them.

:-)

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#146553

On 25.10.26 19:05, Alan wrote:
> On 2026-10-25 01:11, Jörg Lorenz wrote:
>> On 23.10.26 22:00, Alan wrote:
>>> For quite some while, we've seen that once Arlen/Andy/Wally
>>> J/Maria/(other numerous posting nyms) gets an idea fixed in his/her
>>> head, almost no demonstrations of facts will sway him/her.
>>>
>>> For instance!
>>
>> It took you a while to come to this conclusion.
>> I think it is pathological. The best thing for *your* wellbeing would be
>> to ignore him and killfile this Troll.
>>
> 
> On the contrary!
> 
> Such people are NOT going away.
> 
> So for my wellbeing, it's best I am amused by them.
> 
> :-)

Your choice, Don Quichotte.


-- 
"Roma locuta, causa finita" (Augustinus)

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#146554

On 2026-10-25 14:19, Jörg Lorenz wrote:
> On 25.10.26 19:05, Alan wrote:
>> On 2026-10-25 01:11, Jörg Lorenz wrote:
>>> On 23.10.26 22:00, Alan wrote:
>>>> For quite some while, we've seen that once Arlen/Andy/Wally
>>>> J/Maria/(other numerous posting nyms) gets an idea fixed in his/her
>>>> head, almost no demonstrations of facts will sway him/her.
>>>>
>>>> For instance!
>>>
>>> It took you a while to come to this conclusion.
>>> I think it is pathological. The best thing for *your* wellbeing would be
>>> to ignore him and killfile this Troll.
>>>
>>
>> On the contrary!
>>
>> Such people are NOT going away.
>>
>> So for my wellbeing, it's best I am amused by them.
>>
>> :-)
> 
> Your choice, Don Quichotte.
> 
> 

Hey...nothing wrong with tilting at windmills for the fun of it!

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#146555

On 10/23/26 4:00 PM, Alan wrote:
> I'm a road racing driver and instructor. I've been racing since 2013.

Alan, you are not currently racing. The last time that you raced with 
SCCBC was Sept 14, 2024. I was the only appearance that year. So you 
have not been racing, at least via SCCBC (or BHCMR too), for two years.

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#146558

On 2026-10-26 04:38, Tom Elam wrote:
> On 10/23/26 4:00 PM, Alan wrote:
>> I'm a road racing driver and instructor. I've been racing since 2013.
> 
> Alan, you are not currently racing. The last time that you raced with 
> SCCBC was Sept 14, 2024. I was the only appearance that year. So you 
> have not been racing, at least via SCCBC (or BHCMR too), for two years.

I didn't ski last year either...

...doesn't mean I'm not a skier.

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#146565

On 10/26/26 2:55 PM, Alan wrote:
> On 2026-10-26 04:38, Tom Elam wrote:
>> On 10/23/26 4:00 PM, Alan wrote:
>>> I'm a road racing driver and instructor. I've been racing since 2013.
>>
>> Alan, you are not currently racing. The last time that you raced with 
>> SCCBC was Sept 14, 2024. I was the only appearance that year. So you 
>> have not been racing, at least via SCCBC (or BHCMR too), for two years.
> 
> I didn't ski last year either...
> 
> ...doesn't mean I'm not a skier.

That is not the point. You are a race car driver but you have not been 
racing since 2013. You raced from 2013 to 2014 with at least one year 
off. You statement implies you are still active.

This is the strictly truthful standard you apply to others, Fakerboy.

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#146567

On 10/28/26 09:19, Tom Elam wrote:
> On 10/26/26 2:55 PM, Alan wrote:
>> On 2026-10-26 04:38, Tom Elam wrote:
>>> On 10/23/26 4:00 PM, Alan wrote:
>>>> I'm a road racing driver and instructor. I've been racing since 2013.
>>>
>>> Alan, you are not currently racing. The last time that you raced with 
>>> SCCBC was Sept 14, 2024. I was the only appearance that year. So you 
>>> have not been racing, at least via SCCBC (or BHCMR too), for two years.
>>
>> I didn't ski last year either...
>>
>> ...doesn't mean I'm not a skier.
> 
> That is not the point. You are a race car driver but you have not been 
> racing since 2013. You raced from 2013 to 2014 with at least one year 
> off. You statement implies you are still active.

So?  Who's the authority that determines how long of an idle stretch one 
is 'allowed' to have, before one changes from current to former?


> This is the strictly truthful standard you apply to others, Fakerboy.


So if someone stated this past spring that they were continuing to be 
vacation traveler, such as intending to go to Nova Scotia in August, but 
as of 2-3 months later, there's still no word that they actually did...

...is that long enough to 'prove' that their traveling days are over?


-hh

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#146556

On 10/23/26 4:00 PM, Alan wrote:
> So far, I haven't found a convincing reference that makes that exact 
> identification. I did find some useful sources discussing the 
> mathematical shape of a racing line, which help distinguish a catenary 
> from other curves that might look similar.'


Just Google "catenary curve in road racing" guys

The Misconception vs. The Reality

In racing, drivers strive to find the line of maximum radius (the 
geometric apex) or the line of maximum exit speed (the late apex).

• The Misconception: Some automotive enthusiasts use "catenary" to 
describe a smooth, naturally flowing, variable-radius curve that 
transitions seamlessly into and out of a corner.

• The Reality: True racing lines do not follow a catenary formula (\(y = 
a \cdot \cosh(x/a)\)). Instead, they are composed of clothoids (Euler 
spirals) for entering and exiting a turn, and circular arcs at the apex.

And this


Why Track Designers Use Spirals (Not Catenaries)

When a race car transitions from a straightaway into a corner, it cannot 
instantly switch from zero steering angle to a sharp turning angle. 
Doing so would upset the chassis and break tire traction.

• Linear Steering Input: Designers use clothoid spirals because they 
mirror human physiology and physics. As a driver turns the steering 
wheel at a constant speed while driving forward, the car naturally 
traces a clothoid.

• Load Transfer: This gradual increase in curvature allows the weight of 
the vehicle to shift smoothly to the outside tires, maximizing grip.

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#146557

On 2026-10-26 08:49, Tom Elam wrote:
> On 10/23/26 4:00 PM, Alan wrote:
>> So far, I haven't found a convincing reference that makes that exact 
>> identification. I did find some useful sources discussing the 
>> mathematical shape of a racing line, which help distinguish a catenary 
>> from other curves that might look similar.'
> 
> 
> Just Google "catenary curve in road racing" guys
> 
> The Misconception vs. The Reality
> 
> In racing, drivers strive to find the line of maximum radius (the 
> geometric apex) or the line of maximum exit speed (the late apex).
> 
> • The Misconception: Some automotive enthusiasts use "catenary" to 
> describe a smooth, naturally flowing, variable-radius curve that 
> transitions seamlessly into and out of a corner.
> 
> • The Reality: True racing lines do not follow a catenary formula (\(y = 
> a \cdot \cosh(x/a)\)). Instead, they are composed of clothoids (Euler 
> spirals) for entering and exiting a turn, and circular arcs at the apex.
> 
> And this
> 
> 
> Why Track Designers Use Spirals (Not Catenaries)
> 
> When a race car transitions from a straightaway into a corner, it cannot 
> instantly switch from zero steering angle to a sharp turning angle. 
> Doing so would upset the chassis and break tire traction.
> 
> • Linear Steering Input: Designers use clothoid spirals because they 
> mirror human physiology and physics. As a driver turns the steering 
> wheel at a constant speed while driving forward, the car naturally 
> traces a clothoid.
> 
> • Load Transfer: This gradual increase in curvature allows the weight of 
> the vehicle to shift smoothly to the outside tires, maximizing grip.

You should quit while you're behind.

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#146566

On 10/26/26 2:34 PM, Alan wrote:
> On 2026-10-26 08:49, Tom Elam wrote:
>> On 10/23/26 4:00 PM, Alan wrote:
>>> So far, I haven't found a convincing reference that makes that exact 
>>> identification. I did find some useful sources discussing the 
>>> mathematical shape of a racing line, which help distinguish a 
>>> catenary from other curves that might look similar.'
>>
>>
>> Just Google "catenary curve in road racing" guys
>>
>> The Misconception vs. The Reality
>>
>> In racing, drivers strive to find the line of maximum radius (the 
>> geometric apex) or the line of maximum exit speed (the late apex).
>>
>> • The Misconception: Some automotive enthusiasts use "catenary" to 
>> describe a smooth, naturally flowing, variable-radius curve that 
>> transitions seamlessly into and out of a corner.
>>
>> • The Reality: True racing lines do not follow a catenary formula (\(y 
>> = a \cdot \cosh(x/a)\)). Instead, they are composed of clothoids 
>> (Euler spirals) for entering and exiting a turn, and circular arcs at 
>> the apex.
>>
>> And this
>>
>>
>> Why Track Designers Use Spirals (Not Catenaries)
>>
>> When a race car transitions from a straightaway into a corner, it 
>> cannot instantly switch from zero steering angle to a sharp turning 
>> angle. Doing so would upset the chassis and break tire traction.
>>
>> • Linear Steering Input: Designers use clothoid spirals because they 
>> mirror human physiology and physics. As a driver turns the steering 
>> wheel at a constant speed while driving forward, the car naturally 
>> traces a clothoid.
>>
>> • Load Transfer: This gradual increase in curvature allows the weight 
>> of the vehicle to shift smoothly to the outside tires, maximizing grip.
> 
> You should quit while you're behind.

Yet another example of Fakerboy acting like his insulting behavior 
model, Donald Trump.

So, what exactly is wrong with the statements above that are not mine, 
but were found on the web? You will not answer, you will deflect with 
another insult.

A catenary line implies you would tangentially touch the apex at a 
single point halfway through a constant radius curve. That is far from 
ideal.

The quote below applies to single curves. Chicanes get a lot more 
complicated depending on how tight they are. Also, curves are not always 
constant radius.

Reference: Google "clothoid racing line" to find:

quote:

What is a Clothoid Racing Line?

• Smooth Transition: Instead of a driver abruptly steering into a sharp, 
fixed-radius circular arc, a clothoid-based entry and exit smoothly 
blend the straightaway into the corner.

• Control of Lateral Force: It ramps up lateral (centripetal) 
acceleration gradually rather than instantaneously, preventing sudden 
tire slip or chassis shock.

• Optimization in Path Planning: Autonomous vehicle controllers and 
automated racing algorithms use clothoid segments or splines to 
mathematically map the ideal, continuous path between straight and 
curved track segments.

Why Not Just Use a Standard Circle?

• A True Circle is Suboptimal: A pure circular racing line forces a 
constant speed or awkward trail-braking transition if you are driving at 
the limit.

• Jerk and Grip Management: Real-world racing lines use variable-radius 
approaches (resembling Euler spirals or oval/droop-snoot trajectories) 
to delay braking, maximize the apex speed, and get the car pointing 
straight toward the exit sooner.

end quote

PS: I learned this years ago racing go karts. The truth is that the 
ideal racing line is different for every race course and cannot be a 
single simple symmetrical curve for every corner.

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#146568

On 2026-10-28 06:58, Tom Elam wrote:
> On 10/26/26 2:34 PM, Alan wrote:
>> On 2026-10-26 08:49, Tom Elam wrote:
>>> On 10/23/26 4:00 PM, Alan wrote:
>>>> So far, I haven't found a convincing reference that makes that exact 
>>>> identification. I did find some useful sources discussing the 
>>>> mathematical shape of a racing line, which help distinguish a 
>>>> catenary from other curves that might look similar.'
>>>
>>>
>>> Just Google "catenary curve in road racing" guys
>>>
>>> The Misconception vs. The Reality
>>>
>>> In racing, drivers strive to find the line of maximum radius (the 
>>> geometric apex) or the line of maximum exit speed (the late apex).
>>>
>>> • The Misconception: Some automotive enthusiasts use "catenary" to 
>>> describe a smooth, naturally flowing, variable-radius curve that 
>>> transitions seamlessly into and out of a corner.
>>>
>>> • The Reality: True racing lines do not follow a catenary formula 
>>> (\(y = a \cdot \cosh(x/a)\)). Instead, they are composed of clothoids 
>>> (Euler spirals) for entering and exiting a turn, and circular arcs at 
>>> the apex.
>>>
>>> And this
>>>
>>>
>>> Why Track Designers Use Spirals (Not Catenaries)
>>>
>>> When a race car transitions from a straightaway into a corner, it 
>>> cannot instantly switch from zero steering angle to a sharp turning 
>>> angle. Doing so would upset the chassis and break tire traction.
>>>
>>> • Linear Steering Input: Designers use clothoid spirals because they 
>>> mirror human physiology and physics. As a driver turns the steering 
>>> wheel at a constant speed while driving forward, the car naturally 
>>> traces a clothoid.
>>>
>>> • Load Transfer: This gradual increase in curvature allows the weight 
>>> of the vehicle to shift smoothly to the outside tires, maximizing grip.
>>
>> You should quit while you're behind.
> 
> Yet another example of Fakerboy acting like his insulting behavior 
> model, Donald Trump.
> 
> So, what exactly is wrong with the statements above that are not mine, 
> but were found on the web? You will not answer, you will deflect with 
> another insult.
> 
> A catenary line implies you would tangentially touch the apex at a 
> single point halfway through a constant radius curve. That is far from 
> ideal.
> 
> The quote below applies to single curves. Chicanes get a lot more 
> complicated depending on how tight they are. Also, curves are not always 
> constant radius.
> 
> Reference: Google "clothoid racing line" to find:
> 
> quote:
> 
> What is a Clothoid Racing Line?
> 
> • Smooth Transition: Instead of a driver abruptly steering into a sharp, 
> fixed-radius circular arc, a clothoid-based entry and exit smoothly 
> blend the straightaway into the corner.
> 
> • Control of Lateral Force: It ramps up lateral (centripetal) 
> acceleration gradually rather than instantaneously, preventing sudden 
> tire slip or chassis shock.
> 
> • Optimization in Path Planning: Autonomous vehicle controllers and 
> automated racing algorithms use clothoid segments or splines to 
> mathematically map the ideal, continuous path between straight and 
> curved track segments.
> 
> Why Not Just Use a Standard Circle?
> 
> • A True Circle is Suboptimal: A pure circular racing line forces a 
> constant speed or awkward trail-braking transition if you are driving at 
> the limit.
> 
> • Jerk and Grip Management: Real-world racing lines use variable-radius 
> approaches (resembling Euler spirals or oval/droop-snoot trajectories) 
> to delay braking, maximize the apex speed, and get the car pointing 
> straight toward the exit sooner.
> 
> end quote
> 
> PS: I learned this years ago racing go karts. The truth is that the 
> ideal racing line is different for every race course and cannot be a 
> single simple symmetrical curve for every corner.

Your "analysis" is as shallow as the argument you made when you first 
declared that Honda-powered Formula F cars weren't legal at Mission.

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#146569

On 10/28/26 2:57 PM, Alan wrote:
> On 2026-10-28 06:58, Tom Elam wrote:
>> On 10/26/26 2:34 PM, Alan wrote:
>>> On 2026-10-26 08:49, Tom Elam wrote:
>>>> On 10/23/26 4:00 PM, Alan wrote:
>>>>> So far, I haven't found a convincing reference that makes that 
>>>>> exact identification. I did find some useful sources discussing the 
>>>>> mathematical shape of a racing line, which help distinguish a 
>>>>> catenary from other curves that might look similar.'
>>>>
>>>>
>>>> Just Google "catenary curve in road racing" guys
>>>>
>>>> The Misconception vs. The Reality
>>>>
>>>> In racing, drivers strive to find the line of maximum radius (the 
>>>> geometric apex) or the line of maximum exit speed (the late apex).
>>>>
>>>> • The Misconception: Some automotive enthusiasts use "catenary" to 
>>>> describe a smooth, naturally flowing, variable-radius curve that 
>>>> transitions seamlessly into and out of a corner.
>>>>
>>>> • The Reality: True racing lines do not follow a catenary formula 
>>>> (\(y = a \cdot \cosh(x/a)\)). Instead, they are composed of 
>>>> clothoids (Euler spirals) for entering and exiting a turn, and 
>>>> circular arcs at the apex.
>>>>
>>>> And this
>>>>
>>>>
>>>> Why Track Designers Use Spirals (Not Catenaries)
>>>>
>>>> When a race car transitions from a straightaway into a corner, it 
>>>> cannot instantly switch from zero steering angle to a sharp turning 
>>>> angle. Doing so would upset the chassis and break tire traction.
>>>>
>>>> • Linear Steering Input: Designers use clothoid spirals because they 
>>>> mirror human physiology and physics. As a driver turns the steering 
>>>> wheel at a constant speed while driving forward, the car naturally 
>>>> traces a clothoid.
>>>>
>>>> • Load Transfer: This gradual increase in curvature allows the 
>>>> weight of the vehicle to shift smoothly to the outside tires, 
>>>> maximizing grip.
>>>
>>> You should quit while you're behind.
>>
>> Yet another example of Fakerboy acting like his insulting behavior 
>> model, Donald Trump.
>>
>> So, what exactly is wrong with the statements above that are not mine, 
>> but were found on the web? You will not answer, you will deflect with 
>> another insult.
>>
>> A catenary line implies you would tangentially touch the apex at a 
>> single point halfway through a constant radius curve. That is far from 
>> ideal.
>>
>> The quote below applies to single curves. Chicanes get a lot more 
>> complicated depending on how tight they are. Also, curves are not 
>> always constant radius.
>>
>> Reference: Google "clothoid racing line" to find:
>>
>> quote:
>>
>> What is a Clothoid Racing Line?
>>
>> • Smooth Transition: Instead of a driver abruptly steering into a 
>> sharp, fixed-radius circular arc, a clothoid-based entry and exit 
>> smoothly blend the straightaway into the corner.
>>
>> • Control of Lateral Force: It ramps up lateral (centripetal) 
>> acceleration gradually rather than instantaneously, preventing sudden 
>> tire slip or chassis shock.
>>
>> • Optimization in Path Planning: Autonomous vehicle controllers and 
>> automated racing algorithms use clothoid segments or splines to 
>> mathematically map the ideal, continuous path between straight and 
>> curved track segments.
>>
>> Why Not Just Use a Standard Circle?
>>
>> • A True Circle is Suboptimal: A pure circular racing line forces a 
>> constant speed or awkward trail-braking transition if you are driving 
>> at the limit.
>>
>> • Jerk and Grip Management: Real-world racing lines use variable- 
>> radius approaches (resembling Euler spirals or oval/droop-snoot 
>> trajectories) to delay braking, maximize the apex speed, and get the 
>> car pointing straight toward the exit sooner.
>>
>> end quote
>>
>> PS: I learned this years ago racing go karts. The truth is that the 
>> ideal racing line is different for every race course and cannot be a 
>> single simple symmetrical curve for every corner.
> 
> Your "analysis" is as shallow as the argument you made when you first 
> declared that Honda-powered Formula F cars weren't legal at Mission.

Total BS. Just another Trump-like knee-jerk response.

I learned racing lines following faster go kart drivers many years ago. 
The above makes total sense to me. If you disagree feel free to share 
your knowledge. Until then shut up.

You corrected me on the local rules and I accepted and respected your reply.

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#146570

On 2026-10-28 14:38, Tom Elam wrote:
> On 10/28/26 2:57 PM, Alan wrote:
>> On 2026-10-28 06:58, Tom Elam wrote:
>>> On 10/26/26 2:34 PM, Alan wrote:
>>>> On 2026-10-26 08:49, Tom Elam wrote:
>>>>> On 10/23/26 4:00 PM, Alan wrote:
>>>>>> So far, I haven't found a convincing reference that makes that 
>>>>>> exact identification. I did find some useful sources discussing 
>>>>>> the mathematical shape of a racing line, which help distinguish a 
>>>>>> catenary from other curves that might look similar.'
>>>>>
>>>>>
>>>>> Just Google "catenary curve in road racing" guys
>>>>>
>>>>> The Misconception vs. The Reality
>>>>>
>>>>> In racing, drivers strive to find the line of maximum radius (the 
>>>>> geometric apex) or the line of maximum exit speed (the late apex).
>>>>>
>>>>> • The Misconception: Some automotive enthusiasts use "catenary" to 
>>>>> describe a smooth, naturally flowing, variable-radius curve that 
>>>>> transitions seamlessly into and out of a corner.
>>>>>
>>>>> • The Reality: True racing lines do not follow a catenary formula 
>>>>> (\(y = a \cdot \cosh(x/a)\)). Instead, they are composed of 
>>>>> clothoids (Euler spirals) for entering and exiting a turn, and 
>>>>> circular arcs at the apex.
>>>>>
>>>>> And this
>>>>>
>>>>>
>>>>> Why Track Designers Use Spirals (Not Catenaries)
>>>>>
>>>>> When a race car transitions from a straightaway into a corner, it 
>>>>> cannot instantly switch from zero steering angle to a sharp turning 
>>>>> angle. Doing so would upset the chassis and break tire traction.
>>>>>
>>>>> • Linear Steering Input: Designers use clothoid spirals because 
>>>>> they mirror human physiology and physics. As a driver turns the 
>>>>> steering wheel at a constant speed while driving forward, the car 
>>>>> naturally traces a clothoid.
>>>>>
>>>>> • Load Transfer: This gradual increase in curvature allows the 
>>>>> weight of the vehicle to shift smoothly to the outside tires, 
>>>>> maximizing grip.
>>>>
>>>> You should quit while you're behind.
>>>
>>> Yet another example of Fakerboy acting like his insulting behavior 
>>> model, Donald Trump.
>>>
>>> So, what exactly is wrong with the statements above that are not 
>>> mine, but were found on the web? You will not answer, you will 
>>> deflect with another insult.
>>>
>>> A catenary line implies you would tangentially touch the apex at a 
>>> single point halfway through a constant radius curve. That is far 
>>> from ideal.
>>>
>>> The quote below applies to single curves. Chicanes get a lot more 
>>> complicated depending on how tight they are. Also, curves are not 
>>> always constant radius.
>>>
>>> Reference: Google "clothoid racing line" to find:
>>>
>>> quote:
>>>
>>> What is a Clothoid Racing Line?
>>>
>>> • Smooth Transition: Instead of a driver abruptly steering into a 
>>> sharp, fixed-radius circular arc, a clothoid-based entry and exit 
>>> smoothly blend the straightaway into the corner.
>>>
>>> • Control of Lateral Force: It ramps up lateral (centripetal) 
>>> acceleration gradually rather than instantaneously, preventing sudden 
>>> tire slip or chassis shock.
>>>
>>> • Optimization in Path Planning: Autonomous vehicle controllers and 
>>> automated racing algorithms use clothoid segments or splines to 
>>> mathematically map the ideal, continuous path between straight and 
>>> curved track segments.
>>>
>>> Why Not Just Use a Standard Circle?
>>>
>>> • A True Circle is Suboptimal: A pure circular racing line forces a 
>>> constant speed or awkward trail-braking transition if you are driving 
>>> at the limit.
>>>
>>> • Jerk and Grip Management: Real-world racing lines use variable- 
>>> radius approaches (resembling Euler spirals or oval/droop-snoot 
>>> trajectories) to delay braking, maximize the apex speed, and get the 
>>> car pointing straight toward the exit sooner.
>>>
>>> end quote
>>>
>>> PS: I learned this years ago racing go karts. The truth is that the 
>>> ideal racing line is different for every race course and cannot be a 
>>> single simple symmetrical curve for every corner.
>>
>> Your "analysis" is as shallow as the argument you made when you first 
>> declared that Honda-powered Formula F cars weren't legal at Mission.
> 
> Total BS. Just another Trump-like knee-jerk response.
> 
> I learned racing lines following faster go kart drivers many years ago. 
> The above makes total sense to me. If you disagree feel free to share 
> your knowledge. Until then shut up.
> 
> You corrected me on the local rules and I accepted and respected your 
> reply.
Only after arguing it ENDLESSLY.

I'll tell you one little thing:

The line IN to the middle of a corner...

...from braking to speed necessary to simply negotiate it...

...forms a parabola...

...for any corner up to 90 degrees.

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#146577

On 10/28/26 5:43 PM, Alan wrote:
>> You corrected me on the local rules and I accepted and respected your 
>> reply.
> Only after arguing it ENDLESSLY.
> 
> I'll tell you one little thing:
> 
> The line IN to the middle of a corner...
> 
> ...from braking to speed necessary to simply negotiate it...
> 
> ...forms a parabola...
> 
> ...for any corner up to 90 degrees.

NO! It's a lot mope complicated. Google "is a parabola always fastest 
racing line" please. But you won't, so I will save you the trouble:

Quote:

No, a parabola is not always the fastest racing line.
While a symmetric parabolic line (often associated with trail braking 
into a pinched corner and an early throttle-out) works well for certain 
isolated or specific turn types, the absolute fastest racing line 
depends heavily on the context of the track.

Why a Parabola Isn't Always Fastest

• Corner Isolation vs. Sequences: A geometric or parabolic line assumes 
a corner exists in complete isolation. On a real track, corners connect 
to other corners, hairpins, or straights, meaning you must compromise 
entry or mid-corner speed to maximize acceleration onto the most 
important or longest straight.

• Car Performance and Power: For low-power cars, prioritizing a late 
apex to get on the throttle earlier outweighs maintaining a smooth 
parabolic mid-corner speed. For high-power or heavy cars, the physics of 
weight transfer and tire grip change the ideal curve.

• Alternative Mathematical Curves: True mathematical optimizations for 
race tracks frequently use Euler spirals (clothoids) or compound curves 
rather than a simple parabola to transition smoothly between 
straight-line braking, steady turning radius, and full-throttle exit.

• Defensive Driving and Traffic: Real-world racing requires adjusting 
lines to block competitors, avoid marbles/debris off-line, or manage wet 
weather grip, overriding pure theoretical geometry.

End quote

Hmmmm

Maybe your mistaken belief in parabolic racing lines helps explain how 
McKay, McColl and Floer beat you so often.

[toc] | [prev] | [next] | [standalone]

#146579

On 2026-10-29 04:46, Tom Elam wrote:
> On 10/28/26 5:43 PM, Alan wrote:
>>> You corrected me on the local rules and I accepted and respected your 
>>> reply.
>> Only after arguing it ENDLESSLY.
>>
>> I'll tell you one little thing:
>>
>> The line IN to the middle of a corner...
>>
>> ...from braking to speed necessary to simply negotiate it...
>>
>> ...forms a parabola...
>>
>> ...for any corner up to 90 degrees.
> 
> NO! It's a lot mope complicated. Google "is a parabola always fastest 
> racing line" please. But you won't, so I will save you the trouble:

1. So you think AI is right.

As I said: you should quite when you're behind.

> 
> Quote:
> 
> No, a parabola is not always the fastest racing line.
> While a symmetric parabolic line (often associated with trail braking 
> into a pinched corner and an early throttle-out) works well for certain 
> isolated or specific turn types, the absolute fastest racing line 
> depends heavily on the context of the track.

Ummmm....nope.

> 
> Why a Parabola Isn't Always Fastest
> 
> • Corner Isolation vs. Sequences: A geometric or parabolic line assumes 
> a corner exists in complete isolation. On a real track, corners connect 
> to other corners, hairpins, or straights, meaning you must compromise 
> entry or mid-corner speed to maximize acceleration onto the most 
> important or longest straight.

Whether or not you need to compromise entry changes many things, but for 
the braking phase of a corner, the object is to change the vector of the 
car's velocity in the most efficient way possible.

> 
> • Car Performance and Power: For low-power cars, prioritizing a late 
> apex to get on the throttle earlier outweighs maintaining a smooth 
> parabolic mid-corner speed. For high-power or heavy cars, the physics of 
> weight transfer and tire grip change the ideal curve.

Not during the braking phase.

It changes what the precise VALUES are, but the shape is still parabolic.

> 
> • Alternative Mathematical Curves: True mathematical optimizations for 
> race tracks frequently use Euler spirals (clothoids) or compound curves 
> rather than a simple parabola to transition smoothly between straight- 
> line braking, steady turning radius, and full-throttle exit.

And that's going back to what was already wrong.

> 
> • Defensive Driving and Traffic: Real-world racing requires adjusting 
> lines to block competitors, avoid marbles/debris off-line, or manage wet 
> weather grip, overriding pure theoretical geometry.

And that's outside the scope of the discussion.

> 
> End quote
> 
> Hmmmm
> 
> Maybe your mistaken belief in parabolic racing lines helps explain how 
> McKay, McColl and Floer beat you so often.

LOL!

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#146582

On 10/29/26 1:35 PM, Alan wrote:
> On 2026-10-29 04:46, Tom Elam wrote:
>> On 10/28/26 5:43 PM, Alan wrote:
>>>> You corrected me on the local rules and I accepted and respected 
>>>> your reply.
>>> Only after arguing it ENDLESSLY.
>>>
>>> I'll tell you one little thing:
>>>
>>> The line IN to the middle of a corner...
>>>
>>> ...from braking to speed necessary to simply negotiate it...
>>>
>>> ...forms a parabola...
>>>
>>> ...for any corner up to 90 degrees.
>>
>> NO! It's a lot mope complicated. Google "is a parabola always fastest 
>> racing line" please. But you won't, so I will save you the trouble:
> 
> 1. So you think AI is right.
> 
> As I said: you should quite when you're behind.
> 
>>
>> Quote:
>>
>> No, a parabola is not always the fastest racing line.
>> While a symmetric parabolic line (often associated with trail braking 
>> into a pinched corner and an early throttle-out) works well for 
>> certain isolated or specific turn types, the absolute fastest racing 
>> line depends heavily on the context of the track.
> 
> Ummmm....nope.
> 
>>
>> Why a Parabola Isn't Always Fastest
>>
>> • Corner Isolation vs. Sequences: A geometric or parabolic line 
>> assumes a corner exists in complete isolation. On a real track, 
>> corners connect to other corners, hairpins, or straights, meaning you 
>> must compromise entry or mid-corner speed to maximize acceleration 
>> onto the most important or longest straight.
> 
> Whether or not you need to compromise entry changes many things, but for 
> the braking phase of a corner, the object is to change the vector of the 
> car's velocity in the most efficient way possible.
> 
>>
>> • Car Performance and Power: For low-power cars, prioritizing a late 
>> apex to get on the throttle earlier outweighs maintaining a smooth 
>> parabolic mid-corner speed. For high-power or heavy cars, the physics 
>> of weight transfer and tire grip change the ideal curve.
> 
> Not during the braking phase.
> 
> It changes what the precise VALUES are, but the shape is still parabolic.
> 
>>
>> • Alternative Mathematical Curves: True mathematical optimizations for 
>> race tracks frequently use Euler spirals (clothoids) or compound 
>> curves rather than a simple parabola to transition smoothly between 
>> straight- line braking, steady turning radius, and full-throttle exit.
> 
> And that's going back to what was already wrong.
> 
>>
>> • Defensive Driving and Traffic: Real-world racing requires adjusting 
>> lines to block competitors, avoid marbles/debris off-line, or manage 
>> wet weather grip, overriding pure theoretical geometry.
> 
> And that's outside the scope of the discussion.

OMG Fakerboy. We are talking about the racing line, not the practice or 
qualifying line.

> 
>>
>> End quote
>>
>> Hmmmm
>>
>> Maybe your mistaken belief in parabolic racing lines helps explain how 
>> McKay, McColl and Floer beat you so often.
> 
> LOL!

Quoting you:

 >>> The line IN to the middle of a corner...
 >>>
 >>> ...from braking to speed necessary to simply negotiate it...
 >>>
 >>> ...forms a parabola...
 >>>
 >>> ...for any corner up to 90 degrees.

End quote.

A parabola is a functional form for a line that can be precisely 
graphed. No race car driver EVER drove a precise parabola. In Geometry 1 
I learned a line has length and 0 width. That's right, 0, not an atom, 
not an electron, 0. A parabola is a theoretical geometric construct that 
can be approximated in the real world. As is a circle, a square, a 
hexagon, etc.

A parabolic-like SHAPE may be correct in some special cases. For 
example, your restriction to less than 90 degrees as a special case. 
Even then real world differences in the car and the track (especially if 
curves involve elevation and banking changes) will dictate other racing 
lines.

So do you contend that a parabolic shape is the best racing line in all 
situations for all track curves? if so, prove me wrong.

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#146583

On 2026-10-29 11:17, Tom Elam wrote:
> On 10/29/26 1:35 PM, Alan wrote:
>> On 2026-10-29 04:46, Tom Elam wrote:
>>> On 10/28/26 5:43 PM, Alan wrote:
>>>>> You corrected me on the local rules and I accepted and respected 
>>>>> your reply.
>>>> Only after arguing it ENDLESSLY.
>>>>
>>>> I'll tell you one little thing:
>>>>
>>>> The line IN to the middle of a corner...
>>>>
>>>> ...from braking to speed necessary to simply negotiate it...
>>>>
>>>> ...forms a parabola...
>>>>
>>>> ...for any corner up to 90 degrees.
>>>
>>> NO! It's a lot mope complicated. Google "is a parabola always fastest 
>>> racing line" please. But you won't, so I will save you the trouble:
>>
>> 1. So you think AI is right.
>>
>> As I said: you should quite when you're behind.
>>
>>>
>>> Quote:
>>>
>>> No, a parabola is not always the fastest racing line.
>>> While a symmetric parabolic line (often associated with trail braking 
>>> into a pinched corner and an early throttle-out) works well for 
>>> certain isolated or specific turn types, the absolute fastest racing 
>>> line depends heavily on the context of the track.
>>
>> Ummmm....nope.
>>
>>>
>>> Why a Parabola Isn't Always Fastest
>>>
>>> • Corner Isolation vs. Sequences: A geometric or parabolic line 
>>> assumes a corner exists in complete isolation. On a real track, 
>>> corners connect to other corners, hairpins, or straights, meaning you 
>>> must compromise entry or mid-corner speed to maximize acceleration 
>>> onto the most important or longest straight.
>>
>> Whether or not you need to compromise entry changes many things, but 
>> for the braking phase of a corner, the object is to change the vector 
>> of the car's velocity in the most efficient way possible.
>>
>>>
>>> • Car Performance and Power: For low-power cars, prioritizing a late 
>>> apex to get on the throttle earlier outweighs maintaining a smooth 
>>> parabolic mid-corner speed. For high-power or heavy cars, the physics 
>>> of weight transfer and tire grip change the ideal curve.
>>
>> Not during the braking phase.
>>
>> It changes what the precise VALUES are, but the shape is still parabolic.
>>
>>>
>>> • Alternative Mathematical Curves: True mathematical optimizations 
>>> for race tracks frequently use Euler spirals (clothoids) or compound 
>>> curves rather than a simple parabola to transition smoothly between 
>>> straight- line braking, steady turning radius, and full-throttle exit.
>>
>> And that's going back to what was already wrong.
>>
>>>
>>> • Defensive Driving and Traffic: Real-world racing requires adjusting 
>>> lines to block competitors, avoid marbles/debris off-line, or manage 
>>> wet weather grip, overriding pure theoretical geometry.
>>
>> And that's outside the scope of the discussion.
> 
> OMG Fakerboy. We are talking about the racing line, not the practice or 
> qualifying line.
> 
>>
>>>
>>> End quote
>>>
>>> Hmmmm
>>>
>>> Maybe your mistaken belief in parabolic racing lines helps explain 
>>> how McKay, McColl and Floer beat you so often.
>>
>> LOL!
> 
> Quoting you:
> 
>  >>> The line IN to the middle of a corner...
>  >>>
>  >>> ...from braking to speed necessary to simply negotiate it...
>  >>>
>  >>> ...forms a parabola...
>  >>>
>  >>> ...for any corner up to 90 degrees.
> 
> End quote.
> 
> A parabola is a functional form for a line that can be precisely 
> graphed. No race car driver EVER drove a precise parabola. In Geometry 1 
> I learned a line has length and 0 width. That's right, 0, not an atom, 
> not an electron, 0. A parabola is a theoretical geometric construct that 
> can be approximated in the real world. As is a circle, a square, a 
> hexagon, etc.
> 
> A parabolic-like SHAPE may be correct in some special cases. For 
> example, your restriction to less than 90 degrees as a special case. 
> Even then real world differences in the car and the track (especially if 
> curves involve elevation and banking changes) will dictate other racing 
> lines.
> 
> So do you contend that a parabolic shape is the best racing line in all 
> situations for all track curves? if so, prove me wrong.

You just two posts ago claimed the clothoid was the "best racing line" 
without caveats...

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#146597

On 10/29/26 2:40 PM, Alan wrote:
>> So do you contend that a parabolic shape is the best racing line in 
>> all situations for all track curves? if so, prove me wrong.
> 
> You just two posts ago claimed the clothoid was the "best racing line" 
> without caveats...

Oh my, another Fakerboy deflection! What are the chances? 99.999%!

A parabolic line is a subset of a clothoid with a unique set of 
coefficients. Anyway, see the proof of your error below.

Here is a non-AI explanation of why a parabolic shape racing line 
touching the apex at 45 degrees into a 90 degree turn is often not the 
ideal racing line, and a later apex is.

https://www.drivingfast.net/racing-line/

Quote:

Common mistake:

It's very common for drivers to apex too early due to nerves about the 
approaching corner and eagerness to take the turn. The racing line apex 
which is often out of view at the point of turn in, or further round the 
corner than you expect (see Diagram 3 below). This is where experience 
and track knowledge come in.

End Quote

I'm thinking that you simply lacked the nerve to follow the fastest 
racing line. What the heck did they teach you at that fancy racing school?

Your shocking lack of basic racing techniques makes me more certain than 
ever that you could never be considered an exceptional driver in the 
SCCBC world.

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