It wasn't until I sat down with a friend of mine and actually watched a NASCAR race that I understood accelerating through the curve.
I'd heard vague rumors of this move in my thirty-plus years of driving: "Slow down on the approach, accelerate as you exit."
The trick is in assessing when you are actually exiting the curve. Watching NASCAR made it graphic and understandable.
I enter a curve from as wide an angle as possible--if the near-left lane is empty I'll swing over the dotted line--and hug the outside until I spot a point to move across and follow the inside stripe, until the curve flattens out under me and I'm floating to the outside again.
"The point" is where I can draw a straight line to the end, cutting across the top of the curve instead of following it. Or something like that. I don't know exactly what the rule is, but, like the judge said, I know it when I see it.
Every curve is different. Interstate 270 south gives a wide and tipped-up curve onto I-44 east. No brakes needed if you can swing in wide under 50 mph and float left. It's good to vroom out past the Watson Road exit onto 44 while the brake-touchy are still getting going.
Another good one is northbound I-270 onto westbound US 40, a downsloping gentle curl; like a good girdle, one feels held by the banked curve, cupped in safety while rolling under the legs of the overpasses.
Then there's the curve that takes off US 40 west onto North Outer 40 and then under the highway to South Outer 40--essentially a 180-degree turn in a hairpin-plus-J curve. A sharp curve to the right down an exit ramp that immediately swings a tight left and doesn't let up until you're near the Yield sign, lurking under the skirt of US 40, watching for the cars shooting past on the protected green at 141 South.
If I make onto South Outer 40 without using the brakes more than twice (once is ideal) . . . then I win.