# Wrecks from racing track singularities

Do most wrecks in automobile racing start at the singularities of the track - e.g., where the straight path becomes circular? Might this likewise be true of road driving?

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S_Happens
Gold Member
It depends on what type of racing. For example, it would certainly not be the case for figure 8 racing (or 1/4 mile racing, but that is quite obvious). I think it would have much more to do with each specific turn and what type of racing. There are turns where it is easier to make a move on someone, or if the points system includes "laps led", the final turn or two are therefore very important places to try and make a move.

So, really we need to specify. Do you mean to include multiple vehicles or simply one driver losing control/wrecking all by themself? Are they to be influenced by actually winning the racing/accumulating points?

Road driving includes many things that racing does not, such as stop lights/signs, pedestrians, other drivers who are texting on a cell phone, etc.

Since my questions involve tracks with singularities, one could more easily isolate the position of singular influence on, say, slippage of tires from sudden (hypothetically infinite) changes in acceleration, or track condition resulting from such wear near the point of singularity.

The "singularity" would pose the most dangerous place of a circular/straightaway track for a driver to drive, especially accelerate.

A banked circular or elliptical track, having smooth changes in trajectory, would avoid those problems of unwieldy acceleration.

S_Happens
Gold Member
I don't think I understand what you're asking.

I read your first post as "Do most wrecks in automobile racing start..." at the beginning of a turn? I was wondering what you really meant at first by singularity, but then you seemed to simply describe it as the start of a turn.

In your second post, I'm again confused by "singularities" and "hypothetically infinite." Are we talking about the real world or a hypothetical turn that cannot exist (or something else altogether)?

Either we're talking about something real and I am not understanding, we're talking about something that doesn't exist in the real world (especially in auto racing) and I don't see the point of the question (especially trying to apply it to "road driving" ), or we're talking about something in between and you're both asking if the singularity poses the greatest danger to driving AND actually stating that it is the place of greatest danger.

At this point, I think you mean singularity in the mathematical sense, which wouldn't be a transition from straight to circular, and we could never seen in the real world.

The mathematical singularity of acceleration I refer to occurs at the transition between a straight line and a semicircle. To justify this in the real world, that most common racetrack shape transforms (in the simple case) a race car from a constant linear velocity (i.e., zero acceleration) to a constant orbital velocity (finite radial acceleration, ar). The point like change in acceleration, lim[t--> 0] ar/t, approaches infinity.

If there is a physical effect on the racetrack for this shift in acceleration, consider the change between the inertia of the race car when transitioning from the straightaway to the semicircle. There might be more skid marks at that point, eventually track wear there, and other changes. These conditions, I offer, might be conducive to car wrecks, spin outs, etc. In any case, there should be some measurable effect on the (race or family) car, its tires or pavement at the singularity. Any deviation from linear motion to curvilinear motion involves a singularity of acceleration impracticable for actual driving.

Office_Shredder
Staff Emeritus
Gold Member
Any deviation from linear motion to curvilinear motion involves a singularity of acceleration impracticable for actual driving.
So are you suggesting that cars can't actually turn?

russ_watters
Mentor
Do most wrecks in automobile racing start at the singularities of the track - e.g., where the straight path becomes circular? Might this likewise be true of road driving?
How exactly would that look? Would the cars go straight instead of turning? In that case, I'd have to say almost none.

S_Happens
Gold Member
I think you're just looking at this like a version of Zeno's paradox.

In reality, there is a finite change in acceleration in a finite amount of time. You can probably also consider that even though you could make the track go directly from straight to perfectly semi-circular, the track itself is wider than the cars travelling on it, so the cars would not have to be able to navigate this "singularity." Surely you can also imagine that in order to transition from straight to circular, the cars must travel in a non circular path for a finite distance.

I think the singularity does not exist.

So are you suggesting that cars can't actually turn?
No, I'm saying that cars cannot negotiate a singularity of acceleration.

How exactly would that look? Would the cars go straight instead of turning? In that case, I'd have to say almost none.
I am saying that either a car which maintains a straight trajectory, or one which maintains a circular (generally, elliptical and banked) trajectory, has better traction than it would at a transition point between the two.

The singularity might be "smeared out" from straightaway to circle (or vice versa) by the track design, but would still suffer a region of intensified acceleration.

S_Happens
Gold Member
There IS no singularity. The acceleration will depend on the radius of the turn (considering constant velocity). At the earliest point in the turn, the radius will be very large (if you want to consider that it approaches infinity as t would tend to 0 from the positive to add more confusion, then fine) with the raidus decreasing until it reached whatever semi-circle you want the track to be. As the radius decreases (with constant velocity), the acceleration increases, so there concern is never at the very beginning of the turn.

I think you're just looking at this like a version of Zeno's paradox.

In reality, there is a finite change in acceleration in a finite amount of time. You can probably also consider that even though you could make the track go directly from straight to perfectly semi-circular, the track itself is wider than the cars travelling on it, so the cars would not have to be able to navigate this "singularity." Surely you can also imagine that in order to transition from straight to circular, the cars must travel in a non circular path for a finite distance.

I think the singularity does not exist.
I agree with you now in large part. By "smearing" the singularity, I believe one can somewhat moderate but not eliminate aberrant acceleration -- even by using banks.

Without a physical singularity, the phenomenon still exists. I wonder whether actual racetracks take the mathematical spread-out singularity into consideration. When dealing with 200+ mph speeds and likewise vying cars, errors are indeed critical.

S_Happens
Gold Member
OK, I'll try again.

There is no smearing of a singularity and no singularity period. There is NO issue at the transition point from straight to turning. The issue of this singularity stems from trying to imagine the motion of a mathematical point particle, which is not something that is applicable to the real world in any way. Imagning this singularity is useless and incorrect.

The only acceleration (centripetal) is caused by the car turning, which is = v2 / radius. Not that a straight line is a cirlce of infinite radius, but you can see that if you take the limit of the acceleration as the radius goes to infinity (approximating our straight section of track), the acceleration goes to zero. This would be the reverse of the transition you are imagning, so either imagine it backwards or consider the car finishing the semi-circle and returning to another straight away. This shows a perfect continuity rather than a singularity and matches exactly what we see in the real world. The singularity is simply the result of a poor visualisation.

AlephZero
Homework Helper
Roads are not designed as straight line and circles segments joined end to end. There are standard transisiton curves used to give a smooth change of accleration into and out of the curve. Google for clothoids or Cornu spirals for the "optimum" shape, but other shapes are also used.

A typical design guideline is that the time needed to turn the steering wheel smoothly at the transition into and out of a curve should be at least 2 seconds at the driiving speed for which the road is designed.

This applies even more to railway tracks than to roads, because trains don't have any freedom to choose their own path round a curve.

For race tracks, you need to consider the "racing line" round the corner, not the geometrical shape of the track.

Alfi
Do most wrecks in automobile racing start at the singularities of the track ?

naw ... hehehe
from this NASCAR fan point of view....

Most wrecks are caused by Kyle Busch

:rofl:

russ_watters
Mentor
I am saying that either a car which maintains a straight trajectory, or one which maintains a circular (generally, elliptical and banked) trajectory, has better traction than it would at a transition point between the two.

The singularity might be "smeared out" from straightaway to circle (or vice versa) by the track design, but would still suffer a region of intensified acceleration.[emphasis added]
It seems fairly obvious to me that that isn't true. I think you're confusing the concepts of jerk and acceleration. Jerk is a rapid change in acceleration and if a racetrack were to have a straight with a circular curve attached, there would be a step change in acceleration from zero to the acceleration of the curve. That's infinite jerk, but it is not "a region of intensified acceleration".

In any case, the reality is that a car can't instantly go from no acceleration to the acceleration of a turn: it has a steering wheel that must be turned in order to provide that acceleration and you can't turn the wheel instantly.

russ_watters
Mentor
For race tracks, you need to consider the "racing line" round the corner, not the geometrical shape of the track.
Very good point - the actual shape of the track isn't really relvant as drivers will cut their own curves.

The singularity terminology is unfortunate.

If you had a circular track or a long strait track there would be no issues. The circular track has constantly changing acceleration and is the hardest on the adhesion of tire to road, much more than a curve that straitens out.

I suggest that if accidents are concentrated there it has little to do with the physics of the road and everything to do with human judgement since the relationships between the relative motions of the cars are most in flux there.

farukz3
automobile service garage help

can anybody here help me on auto service garage design?

Alfi
Do most wrecks in automobile racing start at the singularities of the track - e.g., where the straight path becomes circular?
The problem can be eliminated.

Make the race track to these proportions .

(x/3 )^2.5 + (y/2)^2.5 = 1

Not circular but with no straight sections. :)

( it has a name, but I can't recall it. ..sorry.. I only remember the equation, the book is back at the library )

edit ...
I'm sure I saw it in this book ....
Here's Looking at Euclid: A Surprising Excursion Through the Astonishing World of Math [Hardcover]
Alex Bellos (Author)

ah ...found it ..
Piet Heins curve.

I would very much like to see a track laid out like this and then let's see what the drivers and car adjusters could make happen.

http://www.oberonplace.com/products/plotter/tutor/lesson2.htm

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No, I'm saying that cars cannot negotiate a singularity of acceleration.
Oh, I'm quite sure acceleration can change instantaneously from one value to another without destroying the car. It's velocity which cannot change instantaneously, as that would require infinite acceleration.