I'm not a racing driver, nor do I have an engineering degree, but I think your friend is misunderstanding either what Rob Wilson is saying, or what he himself is saying. Because from where I'm sitting, what he's saying has no direct bearing on any of the points you've raised from Rob Wilson in this thread.
While there are of course physics reasons for why certain lines are better than others, I think your friend is too
concerned with the mathematical side of things. For example, the slant in the surface road is for all intents and purposes irrelevant, because it's there in all situations, accelerating or braking with or without steering lock and regardless of how much steering lock you put on. So I'm not quite sure why he felt the need to mention it. And while I'm sure most drivers will try to avoid crossing the crown in the track's surface in a corner (if there is one) because of the inherent bumpiness and additional instability that would induce while already suffering lateral load, I don't think it has any bearing on the racingline otherwise unless we are talking significant camber and then only in the additional speed it allows.
Rob Wilson's point, if I understand him correctly, is that a higher apex speed will not necessarily result in a higher average speed on the following straight. This is true, because while the speed measured is in a forward direction from inside the car, from an observer's point of view a not insignificant vector of that speed is not forward in the direction of the track
, as a result of centrifugal force commonly mentioned as the g-forces experienced by the driver. Like so.
So what Rob Wilson says is to make sure you have to worry about the vector that would take you off-track for as short a time as possible, ie. shorten the corner by making sure you do the actual turning as quickly as possible.
"Warning the car" is something Jacky Stewart also says. As I understand it, you basically load up the tyres by turning a little bit before you want to start the actual turn, so you feel where the limit of grip is beforehand
. This makes the car's behaviour during
the turn predictable which means you have confidence in what's going to happen which means you will be able to commit to the turn which means you'll be faster than if you had to guess roughly what your car can put up with in that particular corner in the particular conditions when you arrive at that turn.
I would say that, while all of this is eminently sensible from a pure numbers perspective following the laws of physics, there are a couple of problems approaching this from a purely mathematical perspective like raymondu999's friend seems to try to do (and apologies if I misunderstood, which is entirely possible). One is the ever present conundrum of the spherical chicken in a vacuum
and the other is the driver. Humans aren't perfect, input processing takes time as does (re)action output. Add mental factors like confidence on the day, in the car and the tyres, the weather and all of that together will mean that basically, while there might be a perfect line for any given car for any given corner, the fastest way through that corner with that car with a particular driver in a particular instant in particular conditions, might not follow that exact line. The numbers will tell you it never can be, and that is of course true, but if you made that driver follow the mathematically perfect line, he might be slower than following his (natural) line. Not necessarily because he can't drive that line, but it might be that he can't modulate the throttle well enough on the exit so he is either taking too long to accelerate or he is getting excess oversteer. Or he might have problems with the trail-braking required to follow the perfect entry line to the apex. Or there might be dust, or marbles on that line. In essence, the act of driving itself isn't a science even though there are scientific guidelines one can follow to make it better overall
. If it was perfectly scientific, we'd only have overtaking between vastly different speed cars (didn't the working group say it was 3s a lap or so speed difference required to overtake a car when they started fiddling with adjustable front wings and KERS and DRS?). If it was, robots would be able to race one another around a track faster than humans.