AdamBrouillard

This thought experiment is mostly about getting someone to think about how a racing line is about wasting as little force as possible. Let's look at it another way. Imagine we are in a giant open parking lot and we're going along at full speed. Now we want to turn around and head backwards as quickly as possible. In our rocketship vehicle we would simply reverse thrusters to stop and head back in a straight line. We would have 100 percent force helping us go backwards.

In our super powerful 4 wheel drive car we have to do a 180 though. Would we start doing a big arc or would we slow down in a straight line first and then do a smaller arc? What would give us the greatest total force pushing us backwards while wasting as little as possible doing our 180?

The corner entry path is typically a Euler spiral simply because it's a path of linearly decreasing radius. Most cars brake and turn with very similar force so that's what you end up with. The golden egg arc looks like the radius tightens much quicker as you reach the top of the egg. A car might do a corner entry arc like that if it brakes much better than it turns. Maybe something like a bus. Or if it loses a lot of grip as it decelerates. A car with a massive amount of aero downforce for example.

996tnz

Thanks Adam. At least that's helped me stop obsessing about eggs.

Ideally I'd want to start by thinking about ensuring that while the car must reach its lowest speed only at the very apex, for any given trajectory that same speed must still be fast enough to ensure that ALL of its grip is devoted to providing lateral (or put differently 'centripetal') force, that the car must always be generating max combined possible G (on the limit of its traction circle) throughout the manoever, while always maximising the amplitude of the G vector acting in the opposite direction to the intended one (ie the opposing reactive thrust vector in the direction of intended travel is always as big as it can be.

Provided those base requirements are all adhered to, then going by your clues, the shape and size of the cars GG plot (and maybe its initial speed?) make for the biggest determinant of the resulting optimal path. Crazy hours of the morning here so will leave it there for now, other than to note that trailbraking in and acelerating out at the traction limit appear to be natural consequences of those requirements.

AdamBrouillard

Yeah, assuming the car is driven perfectly at the limit, it's all about the shape of a car's overall traction circle. For the super powerful 4 wheel drive car we would want the tightest arc the car could do while maintaining the limit.

KJM9

Yeah! That's just what I was going to write!!

Great stuff, Adam. Thank you!!

AdamBrouillard

No problem, glad it helped. I've always liked that one.

T&T Racing

What would be the Euler spiral for a Porsche 944 2.5LNA at Watkins Glen Corner 1 which is at the end of the front straight and is slightly less than a 90 degree corner. Would you turn in early for a low hp car with braking capability 3X the acceleration g. What I mean by turning in early is turn 20 ft before the theoretical optimum turn in point. The turn in is on the downhill and you trail brake after turn in.
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AdamBrouillard

You can get a decent idea by getting an overhead map of the track and overlaying the spiral so it meets up at a decent apex, but that's not really a great way to work up a corner. The only way to work up a corner is to do it in the car so here is some general advice. Not worrying about your line initially, first make sure you are able to reach full throttle at the apex and are at the limit through the whole exit. Then make sure you are at the limit during the whole entry. If you get that far see if your steering is constantly tightening from entrance to apex. To get beyond that point you really need to start paying attention to the whole overall track movement and force direction stuff I'm always going on about.

Once all that is squared away your corner entry line is going to be in the shape of a spiral and you should be able to picture in your head what it looks like on the track as you drive. But it's generally not a good idea to start with the spiral, it's more of a result.

Manifold

IMO, this is especially the case for this corner, because of the large camber and the way the camber varies through the corner.

It's a nice corner for experimenting, since there's so much paved runoff in case you make a big mistake.

T&T Racing

A procoach drove my race car at WGI and all the laps were video recorded with a GoPro Hero 2. The FOV captured steering orientation. I reviewed the fastest lap video at 1/2 recording speed.

I stopped the video at each change of steering angle from corner entry to corner exit. For each frame, I did a print screen saver and then printed the frame on low photographic paper using a color ink jet printer

For each corner, the procoach continuously increased the steering angle as the car approached the apex, with no or only very minor increase within X feet of the apex. The car was a full throttle at the apex.

Depending on the angle of the corner, banking after the apex, etc. the unwinding of steering wheel from apex to corner exit varied. In most cases, the procoach did not starting unwinding the steering wheel until the car was at least 50 - 75% to from apex to corner exit, ie the spiral was tight for a considerable time before the spiral radius increased to a large diameter.

I could post the frames for corner 1.

959fan

hey raptor remember this little guy? i was suppose to drive to TWS and we were to do the GCC2007... then it blew its motor at Willow Springs and i never made the trip. it has been sitting ever since. however i'm finally putting it back together now. get ready for GCC2017? can't believe 10 years has passed. better late than never right? instead of driving to you how about you fly out to have some fun at Sears Point?

Veloce Raptor

GerbilRaper? is that you?

Sears is one of my favorite tracks.

959fan

So you will come out then? Sounds good.

trebien

OK, I'll throw it out there.

Sawing the wheel.

Slow back and forth makes sense while balancing adhesion in a carousel or sweeping corner situation.

But I was looking at this video, and the amount of sawing the wheel was drastic - seems like the on/off again nature of the inputs wouldn't be doing any favors to lap times... it's exactly NOT smooth.

Obviously, he's at the limit of adhesion and needs to unwind the wheel a good bit... but it seems extreme.


Thoughts?

Veloce Raptor

Early ClubSports had the original suspension which was a real hair ball on Pirellis...

winders

You saw as much as you have too. What looks like a busy mess from inside the car looks smooth and fast from outside.....and that is what matters!