In 2017 I wrote about my perception of keeping a car in its lane. I repeat here a portion that applies to slowing on curves, as well as to why we hug the inside of curves.
On a straightaway, I am controlling my line of motion relative to the road margins a considerable distance ahead. Visual features seem to approach relatively slowly at that distance, and I have plenty of time to correct deviations. I remember that when I was learning to drive, I controlled distance between the edges of the car and points much closer to the car on the edges of the road. At that distance, visual features seem to approach quite fast. [I remember that this felt disconcertingly close to the margins of control, and I remember oversteering back and forth.] On a curve to the left I am constrained to see visual features which are much closer than those that I control on a straightaway. I have less leisure to correct deviations, and subjectively I feel less securely in control.
Conversely, when I go around a curve to the right, the center line on the outside of the curve is comparatively much more visible than the right edge was in the above case, because I’m sitting on the left side of the car. I tend to hug the inside of that curve too, but not so closely as I hug the inside of a left-hand curve.
You may suppose that people ‘cut corners’ because it’s shorter and faster. Behavior is not significantly different when the driver is going slowly to e.g. an appointment that he dreads, and therefore is not controlling “get there faster”.
There is a reason that roads are equipped with a center line that divides the two lanes. It sets a boundary. Oncoming cars belong on the other side of that boundary, and I belong on this side. Now imagine that you are driving in a country where there is no dividing line. Instead, there is a center line in each lane. Your task as a driver is to keep your car centered on that line, and oncoming cars are to do the same. Between you and oncoming traffic, with a combined speed over 100 mph, is unmarked blacktop. Are you comfortable with that? I’m not. I want that boundary.
I think these anecdotes support my perception that we control avoidance of lane margins in the same way that we control avoidance of obstacles, and that the appearance of ‘car in center of lane’ (true only on a straightaway, mind you) is a consequence of that.
I think this is why the pheromone trails followed by ants straighten over time. The ants sense the pheromone ahead of them, not under them, and so they head straight for a point ahead of them along the curve, ‘hugging the inside of the curve’ until with some nth ant there is no curve left.